THE COLORIMETRIC AND POTBNTIOMETRIC DETERMINATION ...

T H E COLORIMETRIC AND POTBNTIOMETRIC

DETERMINATION OF pH.

ELECTRO TITRATIONS

WORKS OF

DR. I. M. KOLTHOFF

AND

N. HOWELL FURMAN, PH.D.

POTEHTTOUBTBIC TiTKATIONS. A Theoretical and Practical Treatise. Second Edition, extensively revised. 482 pages. 74 figures. 8 tables. Cloth. 6 by 9.

BY D R . I. M. KOLTHOFF AND H. A. LAITINEN, P H . D .

pH AND E L E C T K O T I T B A T I O N S .

The Colorimetric and Potentiometric Determination of pH. Potentiometry, Conductometry, and Voltammetry (Polarography). Outline of Eleo-trometrio Titrations. Second edition. 190 pages. 43 figures. Tables. Cloth. 6 by 9.

PUBLISHED BY

JOHN WILEY & SONS, INCJ

pH AND ELECTRO TITRATIONS T H E COLOBIMETBIC AND POTENTIOMETBIO DETERMINATION OF pH.

POTENTIOMETBY, CONDUCTOMETBY, AND VOLTAMMETBY (POLAE-

OGEAPHY). OUTLINE OF ELECTEOMETEIC TITRATIONS

BY

I. M. KOLTHOFF, P H . D . Professor and Head of Division of Analytical Chemistry

in the University of Minnesota

AND

H. A. LAITINEN, P H . D . Assistant Professor of Chemistry, University of lUiruns

SECOND EDITION

Fourth Printing

<b^ NEW YORK

J O H N W I L E Y & S O N S , I N C . LONDON: CHAPMAN & HALL, LiBaxBD

COPTBIGHT, 1 9 3 1 , BT

ISAAC M . KOLTHOFF

COPYRIGHT, 1941, BY

ISAAC M . KOLTHOFF AND HERBERT A. LAITINEN

All Rights Reserved

Thit book or any part thereof must not be reproduced in any form without the wrilten permiaaion of the publither.

SECOND EDITION

Fourth Printing, June, 1947

P R I N T E D IN U . S . A .

PREFACE TO THE SECOND EDITION

The first edition of this book was published in 1931 under the title The Colorimetric and Potentiometric Determination of pH. Outline of Electrometric Titrations. I t consisted of the following parts:

1. Acid-Base Indicators and the Colorimetric Determination of pH.

2. The Potentiometric Determination of pH. Potentiometric Titrations.

3. Conductometric Titrations.

In the present edition these parts have been revised thoroughly and brought up to date. Moreover, a fourth part has been added, entitled:

4. Voltammetry (Polarography) and Amperometric Titrations.

These subjects are considered of such importance in pure and applied chemistry that they are offered every year in the University of Minnesota in three consecutive quarters as three credit courses to seniors in chemistry and graduate students.

Difficulties have been encountered in the recommendation of suitable textbooks for these courses. A great number of books, covering parts of the above subjects, is available. However, all these are too highly specialized to be used in introductory courses. Instead of requiring the students to purchase many of these fairly expensive reference books we have collected the theoretical and practical fundamentals of the above topics in the present monograph, which is used as a textbook in all three courses.

In the present textbook the theory has been given in a condensed form, and the student is repeatedly referred to general textbooks of physical chemistry and monographs on specific subjects which may be found in any library. The description of experimental technique is concise but adequate. Use is made of equipment which is found in most chemical laboratories.

At the end of the text an outline for a comprehensive practical course covering the fundamentals of the subjects has been added. I t has been our experience that simple procedures, such as the preparation of indicator and buffer solutions, should be included, for we have frequently

vi PREFACE TO THE SECOND EDITION

noticed an astonishing display of ignorance by students in such elementary work.

The problems included in this text are not too simple, and their solution requires a thorough understanding of the fundamentals of electrochemistry.

Students who wish to study the various topics in more detail can do so in advanced courses. I t is there that they are given an opportunity to work with the many types of ready-built instruments which are commercially available. However, we do not encourage students to use this type of equipment and to follow the supplied directions slavishly until they thoroughly understand the principles and are able to build their own apparatus with simple equipment.

With two lectures and four laboratory hours a week it is easily possible to cover the subjects dealt with in this monograph during three quarters.

I . M . KOLTHOFF

H. A. LAITINEN MiNNEi^pous, M I N N . UBBANA, I I I .

CONTENTS

PART I

THE COLORIMETRIC DETERMINATION OF pH ACID-BASE EQUILIBRIA

CHAPTER I

ACIDS AND BASES; THE REACTION OF AQUEOUS SOLUTIONS PAGES

1. Electrolytes. 2. Ion Concentration and Ion Activity. 3. Acids and Bases. 4. The Dissociation of Water, the Expression of the Reaction ; the Hydrogen-Ion Exponent. 5. The Reaction of Solutions of Weak Acids and Weak Bases. 6. Hydrolysis of Salts. 7. Thermodynamic (Activity and Concentration Constants. 8. The Reaction in a Mixture of a Weak Acid and Its Salt, or a Weak Base and Its- Salt; Buffer Solutions. Problems 1-22

CHAPTER II

ACID-BASE INDICATORS

1. Color Change of Acid-Base Indicators and pH Range of Color Change. 2. Preparation of Indicator Solutions. 3. Influence of the Concentration of the Indicator, the Temperature, and the Medium upon the Color of an Indicator 23-31

CHAPTER n i

THE COLORIMETRIC MEASUREMENT OF pH

1. Principle of the Method. Selected Sets of Buffer Mixtures. 2. The Colorimetric Measurement with Buffer Solutions. 3. The Colori-metric Measurement without Buffer Solutions. 4. Colored Solutions; Compensation for Own Color. 5. Sources of Error in the Colorimetric Method. Problems on Indicators 32-54

PART II

THE POTENTIOMETRIC MEASUREMENT OF pH POTENTIOMETRIC TITRATIONS

CHAPTER IV

ELECTRODE POTENTIALS

1. The Potential of a Metal Electrode. 2. Amalgam Electrodes. 3. The Hydrogen Electrode. 4. The Calomel Electrode. 5. Oxidation Potentials. 6. The Electromotive Force (E.M.F.) of Galvanic Cells. 7. Liquid-Junction Potential. 8. The Use of Reference Electrodes (Standard Half Cells) 55-75

vii

viii CONTENTS

CHAPTER V

THE TECHNIQUE OF POTENTIOMETRIC MEASUREMENTS PAGES

1. Principle of the Compensation Method for the Determination of the Electromotive Force of a Cell. 2. General Equipment for Poten-tiometric Measurements. 3. The Potentiometer System. 4. The Electron-Tube Method. 5. Reference Electrodes 76-86

CHAPTER VI

THE POTENTIOMETRIC MEASUREMENT OF HYDROGEN-ION ACTIVITY

1. The Hydrogen Electrode. 2. The Quinhydrone Electrodes. 3. The Oxygen and Air Electrodes. 4. Metal-Metallic Oxide Electrodes. 5. The Glass Electrode 87-103

CHAPTER VII

POTENTIOMETRIC TITRATIONS

1. The Theoiy of Potentiometric Titrations; the Equivalence Potential. 2. Titration Curves. 3. The Detection of the Equivalence Point in Potentiometric Titrations. 4. Special Determinations. Problems in Potcntiometry 104-117

PART III

CONDVCTOMETRIC TITRATIONS

CHAPTER VIII

CONDUCTOMETRIC TITRATIONS

1. The Principles of Conductometric Titrations. 2. The Performance of Conductometric Titrations. 3. Application of Conductometric Titrations to Acid-Base Reactions. 4. Application of Conductometric Titrations to Precipitation and Complex Formation Analysis. Problems 118-135

PART IV

VOLTAMMETRY (POLAROGRAPHY) AND AMPEROMETRIC TITRATIONS

CHAPTER IX

THE FUNDAMENTAL PRINCIPLES OF VOLTAMMETRY

1. General Characteristics of Current-Voltage Curves. 2. The Residual Current. 3. The Factors Which Determine the Diffusion Current. The Ukovic Equation. 4. Limiting Currents in the Absence of Indifferent Electrolytes. 5. Substances Which can be Determined Polar-ographically. 6. Maxima on Current-Voltage Curves. 7. The Analysis of Polarographic Waves. The Half-Wave Potential 13&-156

CONTENTS ix

CHAPTER X

EQUIPMENT AND TECHNIQUE USED IN VOLTAMMETRY

PAGES

1. Electrical Equipment. 2. Fabrication of Capillaries and the Dropping Electrode. 3. Platinum Microelectrode. 4. Electrolysis Cells. 5. General Technique of Voltammetric Determinations 157-164

CHAPTER XI

AMPEROMETRIC TITRATIONS

1. The Principles of Amperometric Titrations. 2 Ad%'antages and Limitations of Amperometric Titrations. 3. Performance of Amperometric Titrations. Problems on Voltammetry 165-172

PRACTICAL COURSE

I. INDICATORS 173

I I . POTBNTIOMETEY 173

I I I . CONDUCTOMBTBIC TITRATIONS 174

I V . VOLTAMMBTEY AND A M P E B O M E T R I C TITRATIONS 174

LOOABITHMS AND A N T I L O O A E I T H M S 178

INDBX OF AUTHORS 183

INDEX OF SUBJECTS 185

PART I

THE COLORIMETRIC DETERMINATION OF pH.

ACID-BASE EQUILIBRIA

CHAPTER I

ACIDS AND BASES; THE pn OF AQUEOUS SOLUTIONS

1. Electrolytes. Electrolytes dissolved in water are more or less dissociated into ions (theory of Sv. Arrhenius), and the fraction of one gram molecule dissociated is called the degree of electrolytic dissociation. A distinction may be made between strong and weak electrolytes. According to the modern views on electrolytic dissociation, strong electrolytes are completely ionized in aqueous solutions, whereas undisso-ciated molecules are present in solutions of weak electrolytes. The distinction between the two groups is not very sharp, and many intermediate cases occur. Hydrochloric acid, e.g., is considered a strong electrolyte, though in 1 iV solution undissociated molecules occur. However, the concentration of these molecules in comparison to that of the ions is so small that the acid can virtually be considered as completely ionized. Salts of alkali and alkaline-earth metals, the alkali hydroxides, various inorganic acids such as perchloric acid, the halide acids, and nitric acid belong to the strong electrolytes. The organic acids and bases are weak electrolytes, though their degree of dissociation under comparable conditions varies considerably. {Cf. Chapter I, paragraph 5.)

2. Ion Concentration and Ion Activity. The ion concentration of a solution of a strong electrolyte is equal to its analytical concentration, as the electrolyte is completely ionized. Therefore in 0.1 M solution of hydrochloric acid, [H"^] is equal to [Cl~] = 0.1 (the symbols between brackets represent ion concentrations); in 0.1 M barium chloride [Ba"'"*'] = 0.1, [Cl~] = 0.2 If a is the fraction of a gram molecule of a weak uni-univalent electrolyte dissociated into the ions, and c its analytical concentration in moles per Uter, then exc is the concentration

1

2 ACIDS AND BASES; THE pH OF AQUEOUS SOLUTIONS

of the ions in the solution, and (1 — a)c that of the undissociated molecules.

In the exact discussion of chemical equilibria it must be realized that the equilibrium conditions are not determined by the molar concentrations of the reacting components but by the corresponding active concentrations or activities.*

In dilute solutions of non-electrolytes the activity may be considered proportional to the concentration. As the proportionality factor is not known, the activity is conventionally assumed to be equal to the concentration of the non-electrolyte. I t should be reaUzed, however, that changing the composition of the solvent will cause a change in the true activity of the dissolved component.

Neutral salts as a rule decrease the solubility of non-electrolytes in water, and, therefore, the activity coefficient of the solute increases correspondingly. On the other hand, addition of alcohol to a solution of an organic acid as a rule increases the solubility, and the activity coefficient of the solute decreases correspondingly. In the general and simple derivations in this text it will be assumed that in dilute aqueous solutions of non-electrolytes the concentration and activity are identical.

In infinitely dilute solutions of electrolytes the activity of the ions is taken equal to the corresponding concentration. This does not hold any longer at finite concentrations, as on account of their high electric charge the ions exert enormous forces (interionic forces) upon each other; consequently, in the neighborhood of a cation more anions will be present than ions of the same sign, whereas more cations than anions will be present in the neighborhood of an anion. On account of the interionic effect in dilute solutions, the activity coefficient of the ions decreases with increasing ion concentration.

The following relation exists between the concentration Cj and the activity o of an ion:

ai = c,/,

where / represents the so-called activity coefficient. Theoretically it was derived by Debye and Hiickel (1923) that in

very dilute solutions the activity coefficient of an ion can be calculated by means of the equation:

- l o g / = Azî\/u,

' A thermodynamical treatment of activity in genera! is given, e.g., in G. N. Lewis and M. Randall, Thermodynamics and the Free Energy of Chemical Substances, McGraw-Hill Book Company, New York, 1923; an extensive discussion is found in F. H. MacDougall, Thermodynamics and Chemistry, Third Edition, John Wiley & Sons, New York, 1939.

ION CONCENTRATION AND ION ACTIVITY 3

where A is a constant, which is a function of the dielectric constant of the solution. In aqueous medium at room temperature it is approximately equal to 0.5 (at 15°, 0.495; at 18°, 0.498; at 25°, 0.501), Zi is the valence of the ion, and as this factor occurs in the square in the equation, it is evident that the activity of a divalent ion, for example, decreases much more with the ionic strength than that of a univalent ion. u denotes the so-called ionic strength, an expression introduced by G. N. Lewis. Its value depends upon the concentration and the valence of the ions. If c represents the ion concentration, then:

Cizf + C22I + • • • CnZn 1 ^ 2 u = ^ = - 2c,3, .

0.01 ilf KCl:

0.01MBaCl2:

0.01 MAICI3:

O.Olz^ + O.OU i u = = 0.01;

0 .024 + OOlzIa OHQ. M = = 0.03;

0.032 ci + O-OlzJi ^ QQg

At an ionic strength of 0.01 we calculate an activity coefficient of a univalent ion of 0.89, of a divalent ion of 0.63, and of a trivalent ion of 0.36.

If we are dealing with uni-univalent electrolytes the ionic strength is equal to the analytical concentration, and the Umiting Debye-Hiickel equation can be written:

- l o g / = 0.5\/c.

This equation holds only for relatively small ionic strengths (for uni-univalent electrolytes up to about 0.01); in more concentrated solutions the expression is more complicated and can be written quite generally:

- l o g / = O.SZi —,ô , ,- - Bu, ^•' ' 1 + 0.329 • 10^-bVu

where b is more or less a constant, giving an approximate value of the ionic size (expressed in centimeters), and B is another constant, accounting for the salting-out effect of the electrolyte. Even this equation holds over only a limited range of ionic strengths. The effect of B is such that the activity coefficient decreases to a minimum with increasing ionic strength. With further increase of the ionic strength the activity coefficient increases again.


The very important problem of the activity coefficient of ions cannot be dealt with in this elementary treatise in the exhaustive way, so the student is referred to reviews which have been written on the subject.^

In the general discussion of the reaction of acids, bases, salts, and properties of indicators, concentrations will be written instead of activities. I t should be emphasized, however, that in any exact study of a chemical equilibrium this approximation is not allowed. In various cases discussed later in this text the activity is introduced again in the interpretation of various phenomena, and for that reason this incomplete and concise chapter on activities has been inserted.

3. Acids and Bases. According to the classical definition, an acid is a substance which dissociates in aqueous solution into hydrogen ions and anions, whereas a base is spUt into hydroxyl ions and cations:

HA?::±H+ + A - (1)

B O H < = t B + + 0 H - . (2)

NOTE: 1. According to the above definition, a solution of an acid contains free hydrogen ions, hydrogen nuclei, or protons. However, these elementary positive charges cannot exist as such in a solution, but will combine with the solvent, i.e., water:

H+ + H2O ?± H3O+. (3)

Therefore, by combination of equations 1 and 3 it is found that the dissociation of an acid in water has to be represented by:

HA + H2O ^ H3O+ + A-. (4)

Similarly for dissociation in pure alcohol we can write:

HA + C2H6OH ?± C2H6OHH+ + A-.

As long as we are interested only in aqueous solutions it is immaterial whether the dissociation of an acid is represented by equation 1 or 4 if we only realize that all hydrogen ions are present in the hydrated form as hydroxonium ions (HsO"*"). If the acidity of various substances is compared in different solvents, the ability of the solvent to combine with protons should be taken into account.

2. Bronsted ' has pointed out that the classical terminology of acids and bases is not rational and that any substance having a tendency to split off protons should be called an acid, whereas one which has the property of combining with protons to form an acid should be called a base. Therefore, an acid always forms a conjugated system with a base:

A ^ B + H+. acid base

'P. Debye and E. Hiickel, Physik. Z., 24, 186 (1923); E. Huckel, Physik. Z., 26, 93 (1925); especially Ergeh. exakt. Naturw., 3, 199 (1924); V. K. LaMer, Trans. Am. Electrochem. Soc., 61, 507 (1927); W. M. Clark, The Determination of Hydrogen Ions, p. 489; F. H. MacDougall, Thermodynamics and Chemistry, Third Edition, John Wiley & Sons, New York, 1939.

' J. N. Bronsted, cf. esp. review in Chem. Rev., 6, 231 (1928).

ACIDS AND BASES 5

It has been mentioned that free protons do not exist in solution. Therefore, a measurable dissociation of an acid in a solvent is found only when the solvent can combine with protons, in other words, when the solvent has basic properties. For example, in water an acid is dissociated by virtue of the basic properties of HjO.

H2O 4- H+ ?:i H3O+ base acid

The so-called dissociation of an acid in water (or in several other polar solvents), therefore, is not a simple ionization, but the result of the interaction of the acid A with the base water (or solvent S):

A + H2O ?i H3O+ + B, or quite generally:

A + S <=i SH+ + B aoid base acid base

If the solvent has no basic properties (benzene and hydrocarbons are aprotonic solvents), a dissolved acid will be present completely in the undissociated form. In these aprotonic solvents a "dissociation" will occur upon addition of a base, for example, a trace of water.

3. According to Bronsted's definition acids and bases can be of varying charge type. The base corresponding to a certain acid always has a charge which is one unit more negative than the acid. Examples:

NH4+ (charge type of acid is 1 + ) NH3 (charge type of conjugate base is 0) CH3COOH (charge type of CHsCOO" (charge type of conjugate

acid is 0) base is —1) H2P04~ (charge type of acid is — 1) HPO4"" (charge type of conjugate base is — 2) HPOi" (charge type of acid is —2) PO4"' (charge type of conjugate base is —3)

4. A base "dissociates" when the solvent has acid properties. For example:

NHs + HjO ^ NH4+ + OH-

CH3COO- + H2O <=± CH3COOH + OH-base acid acid base

If the solvent has no acid properties, no dissociation of dissolved bases can occur. 5. AlkaU and alkaline-earth hydroxides are considered salts. For example, KOH

is the potassium salt of HOH. Therefore, KOH is not a base, but OH"" is the base (compare with potassium acetate).

6. Prom the above it is evident that water has both acid and basic properties; in other words it is amphoteric:

H2O + H+ ?± H3O+ base

H2O ?i H+ -t- OH-acid

By summation of these two equations we find that the "dissociation" of water is given by the equation:

H2O + H2O f i H3O+ -f- OH-aoid base

Alcohols and many other polar solvents also have amphoteric properties.


4. The Dissociation of Water, the Expression of the Reaction, the Hydrogen-Ion Exponent. The most important reaction between acids and bases in aqueous solution is that between hydrogen and hydroxy! ions:

H+ + O H - -^ H2O + 13,900 cal.

([H"*"] will be quite generally written instead of [HsO"^].) This reaction is reversible, i.e., pure water dissociates, though very

slightly, into hydroxonium and hydroxyl ions. The system being m equilibrium, the mass-law expression states:

[H+][OH-] _ [H,0] - ^ - (^)

In dilute aqueous solution the concentration (or better the activity) of the water can be considered constant; therefore, instead of equation 5 the following relation can be written:

[H+JIOH-] = K^. (6)

Kw is the ionization product of water, which is a constant at a definite temperature. On account of the high heat of reaction between hydroxonium and hydroxyl ions it may be expected that the constant will increase very much with the temperature. Actually, the product of the activity of hydrogen and hydroxyl ions, aH + -aoH-) is equal to 10-1* j^| . 24° c . and to about IQ-^^ at 100° C. If we represent the negative logarithm of an+'aoH- by pK^,, the latter can be calculated between 0° and 40° C. with the aid of the equation *

pK^„ = 14.926 - 0.0420i + O.OOOIS .

At 25°, Kw is approximately equal to 10"^*. This means that in pure water (c/. equation 6):

[H+]2 = [0H-]2 = 10-1" and

[H+] = [0H-] = 10-^. (7)

A solution in which [H"^] is equal to [OH"] is defined as being neutral. If [H+] is greater than IQ-^ (at 25°), and hence [0H-] < IQ-'', the reaction is acid; if [H+] is smaller than 10-^ (and [OH"] > lO-'^), the reaction is alkaline. In all cases the reaction can be quantitatively expressed by the magnitude of the hydroxonium-ion concentration, as

• N. Bjerrum and A. Unmack, Kgl. Dansk. Videnskab. Selskab, 9, 1 (1929).

ACIDS AND BASES; THE pH OF AQUEOUS SOLUTIONS

According to the law of mass action:

[H+][A-] [HA]

= Ka, (9)

Ka denoting the dissociation or ionization constant of the acid, and [HA] the concentration of the undissociated acid. In a pure aqueous solution of an acid

[H+] = [A-].

In such a solution, therefore:

[R+f [k-f c ~ [H+] c - [A-]

= Ka, (10)

where c represents the total (analytical) concentration of the acid. Solving equation (10) for [H+]:

[H+]==-f + V^" + XaC. (11)

If the degree of ionization of the acid is small (less than about 5 per cent), [H"*"] will be very small with regard to c. Under such conditions equation 10 can be written in the approximated form:

[H+12

c ^ ^ ^ ' "

[H+] = V ^ ,

pH = \pKa - 1 log c = = ^pKa + ^Pc,

(12)

(13)

pKa representing — log Ka or the acid exponent, and Pc = — log c. If equation 12 is used, one has to make sure that the approximation is permissible, which can be done by showing that \^KaC is virtually identical with y/Ka{.c ~ [H+]).

For a dibasic acid there are two ionization constants:

H2A?^H+ + HA- . (14)

H A - ?ii H+ + A=. (15)

[H+]tHA-] - III2AJ

[H+][A^

^' - I H A T ' ^ ^

KEACTION OF SOLUTIONS OF WEAK ACIDS AND BASES 9

For the calculation of [H^] in the solution of a free dibasic acid one can usually use equation 14 and neglect the second step of dissociation. The problem is then reduced to thiit of a monobasic acid (equations 11, 12, and 13). The approximation can usually bo made when Ki and K2 are considerably different, and the solution of the acid is not too dilute.

If these conditions are not fulfilled, the calculation becomes more involved. In addition to equations 14 to 17 we can write

[H2AI - c ~ [HA-] - [A"]. (18)

From the electroneutrality rule it follows that

[H+] - [HA-] + 2[A-]. (19)

All these equations finally yield the cubic equation

[H+]^ + [H+fifi ~ [H+](A'ic ~ KxK^) ~ 2KiK,c - 0. (20)

This equation is not readily solved. The correct answer is more easily found by a series of successive approximations. As a first approximation we write, instead of equation 19, in the solution of the dibasic acid:

[H+lapp,, - [HA-],pp,. (21)

From equation 17 it follows that [A^^ppr. = X3. Using equation 21 we neglect the second ionization of the acid. From the approximate answer we see immediately whether this approximation was permissible. Suppose, for example, that we calculate [H"*"]appr. = 10"^ and that K2 = 10-^. Then, [A^,pp,. = 10~^ and

lH+]app.. « 10-^ = [HA-] + 2 X 10-6 - jH^~j

On the other hand, if [H''"]appr. ~ 10~* and K2 — 10"**, the first approximation does not yield the correct answer. In this case, [A^^ppr. == 10""®, and we see from equation 19 that the newly approximated value of [H+] is 10~* + 10-^ - 1.1 X 10~*, and that of [HA"] - 10"* - 10~« = 0.9 X 10~*. (The difference between [H"''] and [HA""] is equal to 2 [A^, according to equation 19.)

Using these corrected values of [H"^] = 1.1 X 10~* and [HA'~] = 0.9 X 10~* in equation 17, we find that the approximate value of [A°°]appr. == 10"^ is not correct. With the above values we find that [A"iappr. - 0.8 X 10"^. Then the new approximate value of [H'^] = 1.08 X 10~* and that of [HA~] = 0.92 X 10~*. These values are almost identical with those found from the first approximation and can be considered correct. If there is any doubt, the value of [AT corre-

[H+] = 9-5 X 10-3.

[AT = 3 X 10-^

The second dissociation step may be neglected.

c = 0.001: From equation 11:

[H+]appr. = 6.2 X 10-^, whereas

[A=],pp,. = 3 X 1 0 - ^

[H+]oorr. = 6.2 X lO--* + 0.3 X 10-* = 6.5 X lO"*.

The considerations which have been advanced for acids hold equally well for bases, except that for bases [OH"] is calculated. The corresponding [H+] can be calculated from the ionization product of water (equation 6).

The great difference between the acidity found by titraticm, and the actual or true acidity corresponding to the hydrogen-ion concentration of the solution, must be emphasized. For example, 0.1 iV hydrochloric and 0.1 iV acetic acid have the same titration acidity, although in the former [H+] = 10~^ in the latter 1.35 X 10-^.

6. Hydrolysis of Salts. In any aqueous solution the amphoteric property of the water, quantitatively expressed by its ionization product, has to be considered. By virtue of its amphoteric properties water can act as a weak acid or a weak base; this hybrid character comes to the foreground in the consideration of the reaction of a salt solution. A salt of a strong acid and a strong base, like sodium chloride or potassium nitrate, does not change the reaction of the solvent, as neither the anion of the acid has a tendency to combine with hydrogen ions, nor the cation to combine with hydroxyl ions.

However, the salt of a strong base and a weak acid as a rule behaves as a strong electrolyte and is completely ionized. The anion A - on account of its basic character (c/. definition of Bronsted, paragraph 3) may interact with the water:

A - + H g O ^ H A -H O H - (22) base acid acid base

By this reaction hydroxyl ions are formed and the reaction of the water is shifted to the alkaline side. The cation B"^ (like NH4+) in a salt of a


sponding to [H+] = 1.08 X 10~* and [HA"] = 0.92 X 10~* can be

calculated again (equation 17).

EXAMPLE: Tartaric acid. Ki = approximately 10~'; Ki = approximately

3 X 10-^• c = 0.1.

THERMOPYNAMIC IONIZATION CONSTANT AND pK OF SOME ACIDS AND BASES AT ROOM TEMPBRATUKE

Name

Acetic acid Benzoic acid Boric acid Carbonic acid.. . .

Second s t e p . . . . Citric acid

Second step Third step

Formic acid Hydrocyanic acid Lactic acid Oxalic acid

Second step Phenol Phosphoric ac id . .

Second s t e p . . . . Third step

Phthalic acid Second s t e p . . . .

Salicylic acid Succinic acid

Second step Tartaric acid

Second step

Ammonia Aniline Brucine Ethylamine Diethylamine. . . . Tr ie thylamine . . . . M e t h y l a m i n e . . . . Hydrazine Hydroxylamine. . Pyridine

Constant Acid

.73X10"* 66X10-* 5 XlO-i" 5 X 1 0 - ' 5 X 1 0 - "

7 X10-* 8 X10-* 9 XIO-^ 7 X10-*

x io - i " x i o - " x io-2 X10-* x io- i " X10-' X W X 1 0 - "

3 X 1 0 - ' 9 X10-« 0 6 X 1 0 " ' 5 X10-* 7 X I Q - ' 6 XIO"^ 8 X10-*

.5

Constant Base

9

1.75X10-* 4 X 1 0 - "

X 1 0 - ' 5.6 X10-* 1.3 X 1 0 - ' 6.4 XlO-^ 4 .4 XlO-^ 3 X10-* 1 X10-* 1.4 X10-*

pK

4.76 4.18 9.19 6.46

10.35 3.06

74 41 77

9.14 3.82

19 29 89 16 13

12.30 2.88 6.41 2.97 4.18 5.57 3.01 4.55

4.76 9.40 6.04 3.25 2.90 3.19 3.36 5.52 8.00 8.85

HYDROLYSIS OF SALTS 13

In a similar manner it can be shown that, in a salt of a weak acid and a strong base:

[HA][OH-] [OB.-f ^ K

and [A-] c """'• Ka

[OH

= •'' hydr. = -^r (27)

W ^ or

[H+] = yj^^- (28«)

pH = 7 + yK, - ipo. (286)

Hydrolysis of a Salt of a Weak Acid and a Weak Base. In this case the water will react with the cation as well as with the anion:

B+ + H2O ^ BOH + H+

A- + H2O <^ HA + OH-

in, the following expressions hold:

[BOH][H+] Ku, IB+] Kb '

[HA][OH-] K„ [A-] Ka

(29)

(30)

(25)

(27)

In a solution of a salt of a weak acid and a weak base, [BOH] is not equal to [H+], as the hydrogen ions formed by hydrolysis react with the anions A~ to form HA. If the reaction of the solution is nearly neutral (pH between 6 and 8), [H"*"] and [0H~] are both extremely small, and the amounts of BOH and HA formed by hydrolysis are approximately equal.

By muItipUcation of (25) and (27), it is found that

[BOH] [HA] ^ ^ ^

[B+][A-] KaKb ^ '

If the salt is a strong electrolyte, and has a concentration c,*

[B+] = [A-] = c

• Actually, [B+] = [A~] = c - [BOH] = c - [HA], which is taken equal to c.

weak base and a svi ^xg, acid, on ., with the base water:

B+ + H20<=±B0H + H+. (. o, acid base base acid

Therefore, salts of weak bases and strong acids show an acid reaction in aqueous medium.

From equation 22 it is evident that quantitatively the degree of hydrolysis of a salt of a weak acid and a strong base will be determined by the magnitude of the ionization constant of the acid and the ionization product of water. Similarly, the hydrolysis of a salt of a weak base and a strong acid is determined by the ionization constant of the base and the ionization product of water, and it is a simple matter to calculate the hydrogen-ion concentration in such hydrolyzed salt solutions. By application of the law of mass action to equation 23 we find:

[BOH][H+] p^: j = Kuydr. (24)

•K hydr. IS usually denoted as the hydrolysis constant. We know that

^ [B+KOH-]

* = iBoir' Then we find (equation 24):

[BOH][H+][QH-] _ K^ _

[B+][OH-] ~ K,~ ""''• ^^^

By the hydrolysis the amount of [BOH] and [H+] formed (equation 23) will be equal; and therefore, in a solution of the pure salt in water, [BOH] can be put equal to [H"^]. If the salt behaves as a strong electrolyte, and has a concentration c in water, [B+] = c} Therefore we find, in a solution of a salt of a weak base and a strong acid in water, that:

[BQH][H+] ^ [R^ ^ _K^ [B+] c '> '*'- Kb

and

[H+] = V P - (26a)

pH = 7 - ^vKi + Ivc (25°) (266)

' Actually, [B+] = c — [H+1 = c — [BOH], which is approximately equal to c.

14 ACIDS AND BASES; THE pR OF AQUEOUS SOLUTIONS

and [BOH]^ _ [HA]'' ^ K^ •

or

[BOH] = [HA] = c V # F - (32)

From [HA] we now may calculate [H"*"]:

[H+][A-] = Ao [HA]

4^ [HA] ^ "KgKi [K^Ka

[A 1 c ^ At [H+] = if„ ^ = KaC - ^ ^ = J ^ ^ . (33)

pR = 1 + IpKa - IpKt, (25°). (34)

Equation 33 shows that in a solution of a salt of a weak acid and a weak base the hydrogen-ion concentration is independent of the salt concentration.

Reaction of Acid Salts. An acid salt of the type MHA, which again behaves as a strong electrolyte, is completely ionized into the ions M"'~ and HA~.

The HA ion acts as an acid:

H A - ?:4 H+ -I- A=. (35)

However, since the HA~ is the anion of the weak acid H2A, part of the ions will react with the hydrogen ions:

H A - -h H+ ^ H2A. (36)

For this reason [H"^] is not equal to [AT (equation 35), but will be smaller as part is transformed into H2A (equation 36).

I t is easily seen that:

[A=] = [H+] + [H2A]. (37)

The reaction represented in equation 35 is quantitatively governed by the second ionization constant of the acid H2A, whereas that in equation 36 is governed by the first ionization constant of H2A.

[H2A] = ffin ^1

THERMODYNAMIC AND CONCENTRATION CONSTANTS 15

From these two equations and (37) it is found that

if c is the concentration of the salt MHA in the solution. Equation 38 shows that the salt concentration is of minor influence upon the hydrogen-ion concentration of the solution. This is especially true when Ki is small in comparison with c. In such a case we can write c instead of K\ -\- c, and equation 38 assumes the following simple form:

[H+] = VK1K2. (39)

A few words may be said of the influence of the temperature upon the degree of hydrolysis. For solutions of salts of weak acids and strong bases, weak bases and strong acids, and weak acids and weak bases, it has been shown that the hydrogen-ion concentration is proportional to the square root of the ionization product of water (equations 26, 28, 33). I t has also been pointed out (page 6) that K^, increases rapidly with the temperature, and therefore it may be expected that the hydrolysis of such salts will increase appreciably with the temperature. This conclusion is justified by the fact that the ionization constants of most common weak acids and bases change only very slightly with the temperature. Considering a salt like ammonium chloride, it will be found that the ratio of the hydrogen-ion concentrations at a temperature ti to that at tz is

4 in which Kw(ti) is the ionization product of water at a temperature <i, Kw{t2) that at the temperature t2.

7. Thermodynamic (Activity) and Concentration Constants. In the table on page 10 we have given the values of ionization constants of several acids and bases. The last column gives the values of the negative logarithm pK of these constants. The constants themselves are true, so-called thermodynamic constants, relating the activities of reactants and reaction products and not their concentrations. Thus considering the ionization constant of an uncharged acid HA we have:

2 5 i ^ ^ = K., (9a)


This equation can also be written in the following form:

[ H + ] [ A - ] / H . / A -

[HA] /HA = Ka.

fH"'"l[A~~l Calling — = Kc the concentration constant, we find that it is

[HAJ not constant, but with increasing ionic strength:

A c = Ka-—T—• JH+ZA-

Similarly, we find for an anion acid (second ionization constant of a dibasic acid):

O H +aA-K2a =

or

K2C = K-

fflHA-

/ H A -

[ H + ] [ A = ] / H . / A - „ /H^ /A-= A2c-[HA-] / HA- / ] HA-

2o / H * / A -

As the activity coefficient of ions decreases going from an ionic strength of zero, say, to an ionic strength of 0.1 it is evident that Kc increases. The change of the activity coefficient with the ionic strength is greatly dependent upon the valence of the ion (see Debye-Hiickel expression, page 2). For all practical calculations we can make use of the following approximate values of the activity coefficient of ions of various charges up to an ionic strength of 0.1:

Ionic Strength

Divalent ion Trivalent ion Tetravalent ion

0

1 1 1 1

0,006

0.95 0.80 0.62 0.43

0.01

0.93 0.74 0.52 0.32

0.05

0.85 0.56 0.28 0.11

0.1

0.80 0.46 0.20 0.06

Thus we find for the concentration ionization constant of an uncharged acid or the first concentration ionization constant of an uncharged multivalent acid at an ionic strength of 0.1:

Kc = Ka 0.80'

= 1.66K„.

Similarly we find for

Kic = K2a 0.80

0.80 X 0.46 2.17 Kia.

REACTION IN MIXTURE OF WEAK ACID WITH ITS SALTS 17

ExAMPLK. What are [H+], pH, as*, and poH in 0.1 M potassium bi-phthalate?

Answer. The ionic strength in 0.1 M potassium biphthalate is 0.1.

[H+] = VKuKic = VKiaKâ X 1.56 X 2.17

As shown in the table on page 10, Kia = 1.3 X 10-^(pKia = 2.89) and Kâ = 3.9 X lQ~\vKia = 5-41). Therefore at an ionic strength of 0.1:

[H+] = 1.32 X 10-*.

pcH = 3.88.

If the pH were calculated from the activity constants without correcting for the effect of ionic strength we would have found a value of 4.15 instead of 3.88. Measurements with the hydrogen electrode yield the value of paH and not of pcH. (See Part II of this book.) In the above calculation, CH* was found to be 1.32 X 10~*. Using the approximate value of /H+ = 0.80 (a value of 0.86 is better), we would find a-a* = CH+-/H+ = i-32 X 10"^ X 0.80 = 1.06 X 10-*, and a paH of 3.97 (or better OH+ = 1.32 X 10"* X 0.86 = 1.14 X 10-* and poH = 3.95). Actually a paH of 3.96 is found.

This example shows that the approximate values of the activity coefficients given in the table are useful in the calculation of a^.* and [H"*"] at values of the ionic strength up to 0.1. At greater ionic strengths the differences between the individual ions becomes too great to allow the use of an average approximate activity coefficient.

8. The Reaction in a Mixture of a Weak Acid with Its Salts, or a Weak Base and Its Salt. Buffer Solutions. The dissociation of a weak acid into its ions is governed by the magnitude of the ionization constant:

[H+][A-] _

or

[H+] = PJZ„. (40)

If the analytical concentration of the acid is Ca, and that of the salt is c„ then the concentration of the undissociated part of the acid [HA] is Co — [H"*"], and that of the anions [A~] is c, + [H+]. Therefore, instead of equation 40, can be written:

From this quadratic equation [H"*"] can be easily found. As a rule, equation 41 can be applied in a simpler, though approximated, form. In


a mixture of the weak acid and its salt the dissociation of the acid is repressed by the common-ion effect, and therefore in most practical cases it is found that [H"^] is negligibly small with regard to Ca and c^. If this is so, equation 41 is transformed into:

[H+] = ^K<.. (42)

EXAMPLE. The ionization constant of acetic acid is 1.8 X 10~ . What is the hydrogen-ion concentration in a mixture of 0.05 A' acetic acid and 0.05 A' sodium acetate?

Ca = C, = 0.05.

I H + ] = ^ K . = 1.8X10-^ 0.05

The answer indicates that the application of the approximate equation is permissible, as Ca — [H]"^ and c, + [H]+ are virtually identical with Ca and c,. Only in extreme cases, in which the acid contains only a few per cent of its salt, the quadratic equation has to be applied. On the other hand, the hydrolysis of the salt of the weak acid must be taken into account in the computation of [H"'"] in a solution of a salt of the weak acid, containing only a trace of the free acid.

A - -f- H2O ?ri HA -h 0 H - .

Again, if the analytical concentration of the salt is c,, and that of the acid Co, it is found that

[A~] = Cs — [0H~] = Cs (approximately).

[HA] = Ca + [OH-].

From the hydrolysis equation we know that:

[HA][OH-] {ca + [OH-]}[OH-] _ ^ K^ ^^„ [A-] = c, - ' -'' - = w: ( )

As [0H~] is the only unknown in this equation it can be calculated, and from its value [H"^] can be computed.

Mixtures of weak acids and their salts have a tremendous practical significance. They furnish us simple means of preparing stable solutions of definite pH. Suppose that it is necessary to prepare a solution with a hydrogen-ion concentration of 1.8 X 10^^. As hydrochloric acid is a strong acid, the problem could be solved by diluting standard acid to a normality of 0.000018. Anyone familiar with chemical work knows that it is very hard to rely upon such a solution. The carbon dioxide content of the water, a trace of alkali which the glass vessel may yield.

KEACTION IN MIXTURE OF WEAK ACID WITH ITS SALTS 19

or impurities in the air may affect the pH of such a dilute solution of a strong acid very much, so that even the order of its magnitude may be different from the calculated one. Even if prepared with great care such a solution is not stable.

The above problem of preparing a stable solution with a [H]"^ of 1.8 X 10~^ can be easily solved if we take a mixture containing equivalent amounts of acetic acid and sodium acetate. If the concentration of acid and salt is of the order of 0.1 N, shght amounts of acidic or basic impurities hardly affect its pH, and the solution can be kept in glass bottles without change. Such solutions which resist changes in their reaction are called buffer solutions or buffer mixtures. In a similar way it can be shown that a solution of a weak base and its salt exerts a corresponding buffer action.

[BOH] ^ Cb [B-

and

[OH ] = , +. Kb = — Kb

|H- ] = f ^ r (43)

Buffer solutions are of the utmost importance in the colorimetric measurement of the hydrogen-ion concentration (c/. page 32), and therefore their properties are discussed in a more general way. From the above it is evident that solutions of mixtures of weak acids and their salts or weak bases and their salts exert a buffer action. In the preceding paragraph it has been mentioned that the ionization constant of most acids and bases changes only very slightly with the temperature. Therefore, considering equation 42, it may be expected that the pH of mixtures of weak acids and their salts will be more or less independent of the temperature. Actually it has been showoi that the hydrogen-ion concentrations of most buffer mixtures of the type under consideration change very slightly with the temperature. On the other hand, equation 43 informs us that the pH of a mixture of a weak base with its salt will decrease rapidly with the temperature, as Ky, is very sensitive to a change in temperature. For this reason the buffer solutions used for practical purposes are as a rule mixtures of a weak acid with its salt.

Another question of practical importance is: What is the suitable range in pH which can be covered by one acid and its salt? Let us suppose that the ionization constant of the acid is 10~^. Then according to equation 42 a mixture of an acid and its salt in a concentration ratio of 100 :1 has a [H+] of

[H+] = -Ka = lOOZo = 10-3J oj. p j j ^ 3_


In a mixture of 1 acid and 100 salt:

[H+] = T k ^ a = 10-^; or pH = 7.

Therefore, it might be inferred that, with this acid-salt system, buffer solutions with a pH between 3 and 7 could be prepared. This conclusion, however, is not wholly justified. The characteristic property of a buffer solution is that it resists a change in its reaction, so that the presence of a slight amount of impurities will not affect the pH. Let us now consider the following three buffer solutions {Ka = 10~^):

I. 0.01 N acid, 0.0001 N salt; [H+] = 10"^; pH = 3;

II. 0.01 N acid, 0.01 N salt; [H+] = 10"^; pH = 5;

III. 0.0001 iV acid, 0.01 iV salt; [H+] = 10"^; pH = 7;

and assume that on keeping 100 ml. of these mixtures in glass bottles an amount of alkali corresponding to 0.5 ml. 0.01 N goes into the solution. By this impurity the pH of the buffer solutions will change;

I. [H+] = - - ^ Z a =6 .6X10-* ; pH = 3.18; 1.5

II- 13"*" = S i ^ ^« = 0-99 X 10"'; PH = 5.00 100.5

III. [H+] = ^ if« = 5 X 10-«; pH = 7.30.

With the same amount of impurity, the pH of buffer I changes by 0.18; that of II is not affected; that of III changes by 0.3. Therefore, the intensity of buffer action of the three solutions, which may be expressed as the buffer ca-pacity or buffer action,'' is quite different. A maximum buffer action is observed in the mixture with equal concentration of acid and salt, and it decreases with increasing or decreasing ratio of acid to salt. The buffer intensity also depends upon the total concentration as well as upon the ratio of acid to salt; with increasing amount of acid and salt the buffer intensity increases. In practice, buffer solutions are generally used with a total concentration of acid and salt of the order of 0.05 to 0.1 N. These mixtures are stable approximately within the range 10 acid : 1 salt, and 1 acid : 10 salt, or within a pH range:

pH = pKc, ± 1.

'Compare D. D. van Slyke, / . Biol. Chem., 52, 525 (1922); I. M. Kolthoff, Acid-Base Indicators, translated by Ch. llosenblum, Macmillan Company, New York, 1937, page 24.

PROBLEMS 21

These limits, of course, are not exact, but show only the approximate range of pH of stable buffer solutions which can be obtained from an acid of known pKa- If the solutions are used immediately after their preparation, it is quite possible to prepare them in a range

pH = pKa zh 2.

For the preparation of stable buffer solutions with a pH of 3 to 5, an acid with an ionization constant of 10~* can be used; for pH of 5-7, an an acid with a Ka of about 10~^, etc.

From equation 42 it might be inferred that the hydrogen-ion concentration in a buffer solution depends only upon the ratio of the concentration of acid to salt (and Ka) and not upon the total concentration; in other words, the pH should not change on diluting such a buffer mixture with water. This is approximately, though not entirely, true. The equations have been written in an approximate and not in an exact form.

In section 7 of this chapter we have seen that

au* = Ka = -Kaj—, (44)

in which Ka is the thermodynamic constant of an uncharged acid or the first constant of a dibasic acid. In a buffer mixture of an anion acid and the divalent anion we have:

AHA- J^ Ca ^, / H A - ,... oj j , = K2 = - K2 -r—- (45)

O A - C. / A -

The activity coefficient /HA of a neutral acid molecule up to an ionic strength of 0.1 can be considered to be equal to one. The activity coefficient of an ion ( /A- in equation 44) increases with decreasing ionic strength. Therefore, if we dilute a buffer solution of a neutral acid molecule and its salt, a^* will decrease. The same is true for a mixture of an anion acid and a divalent anion, since the activity coefficient / A - of the divalent ion (equation 45) increases r " with dilution than that of the univalent anion /HA-- The changes v. on dilution, though small, have to be considered in exact work.

If a neutral salt such as potassium chloride were added to a buffer solution of buffers of the above types it is easily shown that OH+ would increase.

PROBLEMS 1. What ions are present in a solution of perchloric acid in water, glacial acetic

acid, ethyl alcohol, respectively? 2. What is the [H+] and what is the pH in a 0.005 JV HCl and in a 0.005 N NaOH

solution at 25° and at 100° C ? X^ at 25° = 10""; at 100° = lO-^l


3. What are the values of [H+], [0H~], pH, and pOH, respectively, in water at 25° and at 100° C.7

4. A 0.1 Af solution of a monobasic acid has a pH of 2.500. Compute its ionization constant.

6. What is the pH in a 1 M and 0.01 M solution of an acid with an ionization constant of 10~'? Compute the same for Ka ~ 10~^

6. What is the pH in 0.1 M solution of a chloride of a weak base at 25° C. and at 100° C. if Kb = 10-5?

7. What is the pH of a 0.1 M solution of the sodium salt of a weak acid (Ka = 10-^) at 25° and at 100° C ?

8. What is the pH of pure water in equilibrium with the air, if the air contains 0.03 volume per cent CO2, and the distribution coefficient of CO2 between water and air is 1. First ionization constant of carbonic acid is 3.0 X 10~'.

9. What is the pH of a solution of ammonium acetate, ammonium formate (hst of ionization constants, cf. page 10).

10. A solution of a salt of a weak acid and a weak base has a pH of 6.5. Calculate Zft if Ka = 5 X 10-*.

11. How does the pH of an acetate-acetic acid buffer solution change between 25° and 100° C , if Ka remains unchanged? How does the pH of an ammonia-ammonium chloride buffer change between 25° and 100° C , if Kt remains unchanged?

12. What will be the approximate value of the ionization constant of an acid for the preparation of buffer solutions with a pH of 11 to 13?

13. A mixture containing 0.04 mole of a monobasic acid and 0.06 mole of its sodium salt per liter has a poH of 5.05. Calculate the ionization constant of the acid, assuming that:

o. The activity coefficient of the acid is 1; of the anion, 1. 6. The activity coefficient of the acid is 1; of the anion, 0.8.

14. What is the paH of the above mixture in the presence of 0.5 mole KCl per liter, assuming that under these conditions the activity coefficient of the acid is 1.2 and that of its anions 0.6?

15. The poH of a buffer system of the type HA + A~ is 4.80 at an ionic strength of 0.05. Calculate paH after a tenfold dilution of the buffer, applying the limiting Debye-Hiickel expression.

, 16. Calculate the pH of a mixture which is 0.1 M in sodium phenolate and 0.001 M in phenol. Can you use the approximate equation here? Ka = 1 X lO"'". K„ = 10-".

CHAPTER II

ACm-BASE INDICATORS

1. Color Change of Acid-Base Indicators apd ^H Range of Color Change: Indicators behave like weak acids or weak bases the dissociated and undissociated forms of which have different color and constitution. Therefore, an indicator is comparable to an ordinary weak acid or weak base and it is possible to interpret the behavior of indicators quantitatively on the basis of the above definition. If the undissociated form of the indicator has acid properties, and is denoted by HI, its dissociation is represented by the same equation as that of all weak acids:

HI*=±H+ + I - . acid form basic form

has has acid color alkaline color

Quantitatively the equilibrium is governed by:

[H+][I

[HI] = ^ i , (1)

where Ki is the ionization constant of the indicator. Its negative logarithm is often called the indicator constant. The color of the indicator in a solution is determined by the ratio [I^] to [HI]:

[I"] Ki [HI] [H+] '' '

Therefore, both forms of the indicator are present in the solution at any hydrogen-ion concentration. I t is incorrect to speak of the transition •point of an indicator, since it does not change suddenly at a definite [H"*"] from one form to the other. The color change takes place gradually, as may be inferred from equation 2; if [H"*"] has the same numerical value as Ki the indicator is transformed 50 per cent into the alkaUne form; if [H"*"] is ten times as large as Kj, about 90 per cent of the indicator is present in the acid form, and 10 per cent in the alkaline form. With increasing [H"^] the concentration of the alkaline form decreases still more. The eye has a limited sensitivity for the observation of colors; only a certain amount of one form can be detected in the presence of the

23

24 ACID-BASE INDICATORS

other; so the visible color change of the indicator falls within certain limits of the hydrogen-ion concentration. If the two limits of the perceptible change are expressed in pH, the region between the two limiting values in the interval of change is usually designated as color-change interval. The distinct change from the acid to the alkaline color takes place between the two limiting values, which can be determined experimentally. I t should be realized that figures on the color-change interval reported in the literature have only an approximate character; from the above it is evident that the two limiting values depend more or less upon the subjective judgment of the obsei-ver. One author, for example, may report the color-change interval of methylorangc between pH 2.9 and 4.2, whereas another may put the limits between 3.1 and 4.4 Though at a pH of 3.1 most of the indicator is present in the acid form, one may perceive a difference in the color of the indicator between pH values of 2.9 and 3.1. By spectrophotometric measurements, however, it can be shown that even at a pH of 2.9 about S per cent of the indicator is present in the alkaline form. The magnitude of the interval is not the same for all indicators because the sensitivity with which the eye can perceive a small portion of the acid form in the presence of the alkaline form or a small fraction of the alkaline form in the presence of an excess of the acid form will be different for various indicators. For indicators which change from a colorless to a colored form (one-color indicators) the color-change interval is greatly dependent upon the concentration of the indicator.

Assuming that in a given case 9 per cent of the alkaline form can just be detected in the presence of the acid form, we have:

O = i = Jî [HI] id [H+]"

The indicator begins to change its color to the alkaUne side at :

[H+] = IQKi, or at

pH = pKi - 1,

where pKi denotes the negative logarithm of Kj and is called the indicator exponent or constant. Assuming further that the indicator is practically completely converted into the alkaline form, when about 91 per cent is present in this form, we have:

f^ ' l 10 = ''^ [HI] ' " [H+]

pH = pKi + 1.

alkaline form acid form has has

alkaline color acid color

(3)

PREPARATION OF INDICATOR SOLUTIONS 25

Therefore, the color-change interval of such an indicator lies at:

7>H = piTi ± 1.

Actually, it is found that for most indicators the pH range is of the order of 2.

For indicator bases the following relation holds:

lOH ?:± 1+ + O H -alki

alk;

[I+][OH-] ^ [lOH] " -^'«"

[lOH] ^ [ O i n ^ K^ J L _ ^ _Zi_ [1+] " XioH iîoH • [H+] " [H+]

where KIQ-Q^ is the ionization constant of the weak indicator base. In expressing the color change as a function of the hydrogen-ion concentration, the ionization product of water iv„ is introduced. The ratio /<"„ to •K iOH at a definite temperature is a constant K\. By comparing expressions 2 and 3, it is found that they are completely identical, if we read for

[I—] cone, alkaline form

[HI] cone, acid form and

[lOH] cone, alkaline form [I"^] cone, acid form

Problem, (a) Plot the change of the ratio of the concentration of the alkaline form to that of the acid form at a pH of 3.3, 3.6, 4.0, 4,5, 6.0, 5.5, 6.0, 6.4 and 6.7, if fKi = 5.

(b) The same problem, but plot the logarithm of the above ratio against the indicated pH values.

2. Preparation of Indicator Solutions. Color-Change Interval of Useful Indicators, and Some of Their Properties. An enormous number of compounds with indicator properties are found in nature and among products of the laboratory.^ In this book only a few will be selected, with which most of the colorimetric work can be done and which belong more or less to the ordinary indicators in any laboratory. However, for special research work one should consult the more extensive lists referred to, as for some reason or other indicators not mentioned in the table below may be advantageous in definite instances. Some one-color indi-

' Cf. the lists in \V. M. Clark, The Determinalion of Hydrogen Ions, Third Edition, page 76; also I. M. KolthoS, Acid-Base Indicators, The Macmillan Company, New York, 1937.


cators which can be used in the determination of pH without buffer solutions will be discussed in the next chapter.

A useful concentration of the indicator in the stock solution is of the order of 0.05 to 0.1 per cent. Ordinarily an addition of 0.1 to 0.2 ml. of such an indicator solution to 10 ml. of the liquid to be investigated will give satisfactory results. Five of the indicators mentioned in the list behave like weak bases (tropeoline 00, methyl yellow, methyl orange, methyl red, and neutral red); the rest, hke weak acids. The sulfon-phthaleins originally introduced by Clark and Lubs (1917),later extended by others (especially Bamett Cohen), are all indicators with very sharp color change from yellow to intense red, blue, or purple. Bromphenol blue in its transition interval shows a so-called "dichromatism"; the color of the indicator depends upon its concentration and "the depth of the layer observed. I t appears blue in a thin layer of the solution, and purple when seen through a greater depth. In the colorimetric determination of pH this dichromatism of the indicator interferes very much. Often the solution to be examined contains substances which affect the light absorption of the indicator (alcohol, alkaloids; in alcoholic medium the color change is from yellow to blue). Further, the indicator cannot be used in turbid solutions. When a deep layer of the liquid is viewed, only a .small amount of light from the bottom of the cell reaches the eye. Most of the Ught which enters the side is reflected by the particles and has thus traversed a thin layer of Uquid, and a blue color is perceived. A comparison of the color with that of the indicator in a clear buffer solution is scarcely possible, for a thin layer of fluid would have to be taken. For the reasons mentioned it is fortunate that Harden and Drake^ found a good substitute for bromphenol blue in tetrabrom-phenol tetrabromsulfonphthaleinr This indicator changes from yellow to blue and has the same color-change interval as bromphenol blue without showing the dichromatism.

The color change of the sulfonphthaleins may be represented by the following classical structure changes (phenol red):

C6H4—C^ I ^ C 6 H 4 = 0 S020H

quinoid form, yellow

/C6H4OH .'^-yCeHdO" -^ C6H4—C< -I- H+ -> C6H4r^CC + H+

I ^ C 6 H 4 = 0 1 ^C6H4==0 SO2O- SO2O-

yellow deeply red (quinone-phenolate)

' W.C. Harden and N. L. Drake, / . Am. Chem. Soc, 51, 562 (1929).

PREPARATION OF INDICATOR SOLUTIONS 27

In the table two representatives of the phthaleins have been mentioned: phenolphthalein and thymolphthalein. The second is only slightly soluble in water, which is an objection to its use in pH determinations. If 0.1 ml. of a 0.1 per cent indicator solution is added to a buffer solution with a pH of 10, a nice blue color appears. On standing this color fades fairly rapidly because part of the undissociated indicator settles out and thereby disturbs the equihbrium. The color change of the phthaleins can be represented by the following scheme (phenolphthalein):

cocr

deeply red, giiiBOBe phenolate

IV

The monovalent ion of phenolphthalein (III) is colorless; the divalent quinone-phenolate ion is deeply red. The alkaline form of the phthaleins is not stable; in alkaline medium it changes slowly to a colorless trivalent ion derived from the carbinol form:

+0H-

quinone phenolate, deeply red

carbinol form, colorless

Therefore, alkaline solutions of phenolphthalein and other phthaleins fade on long standing. • ' j

In the following tablcithe.color change and the pH range of the most important indicators are tabulated^. As a rule, water can be used as a solvent, but methyl yellow and the phthaleins have to be dissolved in 90 per cent alcohol. The various sulfonphthaleins and methyl red have to be neutralized with sodium hydroxide before they are soluble in water. The former behave as dibasic acids, the indicator properties being determined by the magnitude of the second ionization constant. For most purposes it is sufficient to neutralize the strong sulfonic acid group, but


when the'pH of practically unbuffered solutions is to be measured more attention should be paid to the proper preparation of the indicator solution. (See page 46.) One hundred milUgrams of the indicator are rubbed in an agate mortar with the amount of 0.05 N sodium hydroxide specified in the table. After the indicator is dissolved, the solution is diluted with water to 100 ml. (0.1 per cent) or 200 ml. (0.05 per cent).

Indicator MUliliters

O.OS N NaOH for 100 mg.

Thymol blue Tetrabromphenpl blue Bromphenol blue Bromcresol green..... Methyl red...' Chlorphenol red Bromphenol red Bromthymol blue Phenol red Cresol purple.. . . . . . .

5.7 5.3

3. Influence of the Concentration of the Indicator, the Temperature, and the Medium upon the Color-Change Interval. Concentration of the Indicator. We have seen before that the equilibrium of an indicator-acid is represented by:

[ n . Ki [HI] [HJ

(2)

If the indicator acid is colorless; and the ionis colored, then the color of the solution at a fixed pH (buffer solution) is determined by:

[I-] ^ [HI] = Kj[m]. [H

The amount of the colored form is proportional to that of the undissoci-ated indicator. Therefore, the color of a suitable buffer solution will become more intense upon addition of more one-color indicator.

Experiment. Add to 10 ml. 0.05 M'borax solution successive amounts of 0.1 per cent phenolphthalein.

The increase of the intensity cannot go on indefinitely, since most indicators are only slightly soluble and [HI] soon approaches its saturation value. If this saturation value corresponds to a concentration s.

__ INFLUENCE OF THE CONCENTRATION OF THE INDICATOR 29

the maximum color intensity of a (one-color) indicator at a special pH is given by:

[I-] = K[s.

COLOR CHANGE AND pH INTERVAL OP THE MOST IMPORTANT INDICATORS

Scientific Name

Sodium salt of diphen-ylaminoazo-p-ben-zene-sulfonic acid

Thjrmolsulfonphthalein

Dimethylaminoazoben-zene

Sodium saltofdimethyl-aminoazobenzene-sulfonic acid

Tetrabromophenol-tetrabromosulfon-phthalein

Tetrabromophenol-sulfonphthalein

Tetrabromo-m-cresol-sulfonphthalein

Dimethylaminoazoben-zene-o-carbonic acid

Dichlorophenolsulfon-phthalein

Dibromothymolsulfon-phthalein

Phenolsulfonphthalein

Dimethyldiaminophen-asinchloride

m-CresolsuIfonphtha-lein

Thymolsulfonphthalein

Phenolphthalein

Thymolphthalein

Sodium salt of jj-nitr3n-iline-azosalicylic acid

Trade Name

Tropeoline 00

Thymol blue

Methyl yellow

Methyl orange

Tetrabrom-phenol blue

Bromphenol • blue Bromcresol

green Methyl red

Chlorphenol red

Bromthymol blue

Phenol red

Neutral red

Cresol purple

Thymol blue

-

Alizarine ' yellow

Solvent

Water

Water ( + NaOH) 90 per cent

alcohol Water

Water (+NaOH)

Water ( + NaOH)

Water ( + NaOH)

Water ( + NaOH)

Water ( + NaOH)

Water ( + NaOH)

Water ( + NaOH) 90 per cent

alcohol 1 Water

( + NaOH) Water '

( + NaOH) 90 per cent

alcohol 90-per cent

alcohol Water

Acid Color

Red

Red

Red

Red

Yellow

Yellow

Yellow

Red

Yellow

Yellow

Yellow

Red

Yellow

Yellow

Colorless

Colorless

Yellow

Basic Color

Yellow

Yellow

Yellow

Orange-yellow

Blue

Blue-violet

Blue

Yellow

Red

Blue

Red

Yellow-orange

Purple

Blue

Red-violet

Blue

Violet

pH Interval

1.3- 3.0

1.2- 2.8

2.9- 4.0

3 .1 - 4.4

3.0- 4.6

3.0- 4.6

3.8- 6.4

4.2- 6.3

4 .8- 6.4

6.0- 7.6

6.4r- 8.0

6.8- 8.0

7.4- 9.0

8.0- 9.6

8.0- 9.8

9.3-10.5

10.1-12.0

From the above it is evident that the color-change interval of a one-color


indicator depends relatively much upon the concentration of the indicator in the solution.

Influence of Temperature. In Chapter I it was mentioned that the ionization constant of most ordinary acids and bases changes but sUghtly with a variation of the temperature. If the same statement holds for indicators the following conclusions can be drawn:

rj—1 77

Indicator acids: — = ~r^- (2)

As Ki does not change materially with the temperature, the equilibrium does not change at higher temperatures if [H+] is kept constant. Therefore the color-change interval of indicator acids is more or less independent of the temperature. ;

_ . .. [lOH] K^ 1 Kr ' ^ ^ Indicator bases: - ^ = ^ ^ . ^ = ^ j . (3)

Kw increases considerably with increasing temperature, whereas if IOH changes only slightly. Therefore KW/KIQB. for indicator bases increases rapidly with the temperature, the indicator base will be less sensitive to hydrogen ions at higher temperature, and its color-change interval will be shifted to lower pH values. Experimentally this has been shown to be true. Methyl orange (indicator base) and bromphenol blue (indicator acid) have the same color-change interval at room temperature. (Cf. preceding table, page 29.) Whereas the pH range of bromphenol blue is virtually the same at 100° as at 25°, the range of methyl orange is shifted from 3.1 to 4.4 at room temperature to 2.5-3.7 at 100°.

Influence of the Medium. The figures reported in the table on page 29 hold for water as. a .solvent. If organic .Uquids such as ethyl alcohol, methyl alcohol, and acetone, with a lower dielectric constant than water, are added to the aqueous solution, ^the equilibrium conditions are changed. Addition of alcohol to an aqueous solution decreases the ionization constant of weak acids and bases. Consequently indicator acids will become more sensitive to hydrogen ions in the presence of organic solvents and their color-change interval will be shifted to higher pH values. {Cf. equation 2.) -

On the other hand, in mixtures of water-^with an organic solvent, indicator bases will be less sensitive to hydrogen ions than in purely aqueous medium, as the ionization constant of the base decreases more than 2?„ does. Therefore the color-change interval of indicator bases is shifted to lower pH values in mixtures of water and alcohol.

INFLUENCE OF THE CONCENTRATION OF THE INDICATOR 31

I t should be realized that the equihbrium in a buffer mixture is also changed by the addition of alcohol. If, for example, alcohol is added to a mixture of acetic acid and sodium acetate, the hydrogen-ion concentration decreases, as the ionization constant of acetic acid is diminished. If this change of the constant is the same as that of an indicator acid, the indicator will not change its color in the buffer solution upon addition of alcohol. On the other hand, the color of an indicator base will be changed to the alkaline side. This can be easily shown by taking a buffer mixture containing approximately 0.1 iV acetic acid and 0.01 N sodium acetate. Tetrabromphenoltetrabromsulfonphthalein assumes an intermediate color, in such a solution, which does not change upon the addition of 40 to 50 per cent alcohol. (Bromphenol blue is less suitable for this experiment, as the shade observed changes by the addition of alcohol on account of the change of the light absorption. Cf. dichromatism, page 26.) If methyl orange is added to the above buffer solution it also

-assumes an intermediate color, which changes to yeUow upon the addition of alcohol.

Results of colorimetric pH determinations in mixtures of water and alcohol which were found by comparing the color of an indicator in the mixture with that of the same indicator in aqueous buffer solutions have often been reported in the literature, but data derived in such a way, without considering the effect of the medium, cannot be correct.

CHAPTER IIT

THE COLORIMETRIC MEASUREMENT OF ^H

1. Principle of the Method. Selected Sets of Buffer Mixtures. If an indicator added to different solutions assumes the same intermediate color, the solutions are considered to have the same pH. (C/., however, paragraph 6, page 45.) The same color means the same ratio of acid to basic form ([HI] : [I~]):

The colorimetric' determination of pH is based on the above principle. To the solution the pH of which is to be determined a measured volume of a suitable indicator is added and the color is compared with that of the same indicator in solutions of known pH. The method therefore is a comparison procedure whose accuracy depends primarily upon the correctness of the standard reference solutions. The pH or better the paH of the reference solution is determined by means of the hydrogen electrode. The standardization according to the potentiometric method is therefore the primary procedure upon which the whole colorimetric procedure rests. The standard reference solutions are buffer mixtures, the general theory of which has been discussed in Chapter I (page 17). Originally S. P. L. Sorensen introduced a''comDlete set of buffer solutions the pH of which he determined very accirrately at 18°. In later years various authors pubUshed mixtures of other composition, of which those of Clark and Lubs seem to be most popular.

In this book only a few setsôf buffer solutions will be selected. A more complete list will be found in W. M. Clark, The Determination of Hydrogen Ions, and in I. M. Kolthoff, Acid-Base Indicators.

_ • • ^ '

BUFFER SOLUTIONS ACCORDING TO CL'XRS''AND LUBS

The mixtures are very simple to prepare. The original materials may easily be obtained in pure form, and the equal differences in pH value— intervals- of 0.2ôffer practical advantages.

32'

PRINCIPLE OF THE METHOD. SETS OF BUFFER MIXTURES 33

STANDABD SOLUTIONS pH RANGE

0.2 N HCl and 0.2 N KCI 1.0-2.4 0.1 N HCl and 0.1 N potassium biphthalate 2 .2 -4 .0 0.1 iVNaOH and 0.1 iV potassium biphthalate.. 4 . 0 - 6 . 2 0.1 iV NaOH and 0.1 iV monopotassium phosphate 6 .2 -8 .0 0.1 N NaOH, 0.1 M H3BO3 and 0.1 AT KCI 8.0-10.0

The biphthalate mixtures are not suitable for measurements with methyl orange as an indicator. The components in the mixture seem to exert a specific effect upon this indicator, which assumes too acid a color in these buffer solutions. Therefore the pH found in this way is about 0.2 too high.

For this reason mixtures of monopotassium citrate with HCl and NaOH respectively may be valuable under certain conditions,^ and their composition will be described.

Finally, the mixtures of 0.05 M borax with 0.1 iV HCl and 0.1 iV NaOH respectively will be tabulated. Originally the pH of these mixtures was measured by S. P. L. Sorensen (1909) at 18°. Walbum has shown later that the pHof these buffer solutions changes relatively much with the temperature. The same is true for the borate buffers of Clark and Lubs.

Purity of Materials to Be Used in the Preparation of the Buffer Solutions. 0.1 N hydrochloric acid and 0.1 A'' sodium hydroxide (carbonate free) prepared and standardized according to the usual volumetric procedures.

Potassium Biphthalate. M = 204.2. The C. P. product commercially available is of sufficient purity. I t can be recrystallized from water and dried at 110-120°. Its purity has to be checked by a titration with standardized sodium hydroxide, using phenolphthalein or thymol blue as an indicator. A 0.1 M solution of the salt is prepared for making the buffer mixtures.

Monopotassium Phosphate. M = 136i2. The commercial salt (C. P.) is recrystallized twice from water ancl dried at 110-120°. Standard solution for the preparation of the buffers is 0.1 molar.

Boric Acid. M = 62.0. A C. P. product is recrystaUized from water and dried in the air. Standard solution: 0.1 M boric acid in 0.1 M KCI.

Potassium Chloride. ^ M = 74.6. A C,; P. product, twice recrystallized from water and dried at 1202. ;

Monopotassium Citrate. C8H7O7K; M = 230.

Preparation of the salt: To 420 g. crystallized citric acid (containing

n.M. Kolthoff and J. J. Vleeschhouwer, Biochem. Z., 179, 410 (1922); 183, 444 (1922).

34 THE COLORIMETRIC MEASUREMENT OF pH

1 mole of water of crystallization) dissolved in 150 ml. warm water, 138.2 g. water-free potassium carbonate (freshly ignited) is added in small portions. After the evolution of carbon dioxide has ceased the solution is boiled and filtered. The filtrate is stirred and cooled to about 15°. ' The small crystals are collected by suction, washed with ice-cold water, and recrystallized in an amount of water corresponding to about half the weight of the crystals. The crystals are dried at 80° and obtained in the anhydrous state. They can be kept in the water-free state if precautions against deliquescence are taken. The purity is tested by a titration with sodium hydroxide, using phenolphthalein or thymol blue as an indicator.

Borax^ NaaBÔy-lOHaO^JIi'= 381.2. A C. P. product is recrystallized twice from water ana dried in a desiccator over a mixture of deliquescent sodium chloride and cane sugar until constant weight has been reached. Standard solution is 0.05 M. '

BUFFER MIXTURBS OF CLARK AND LUES *

0.2 N HCl and 0.2 N KCl at 20° Composition pH

47.5 ml. HCl + 25 ml. KCl dil. to 100 ml 1.0 32.25 ml. HCl + 25 ml. KCl dil. to 100 ml..."".: 1.2 20.75 ml. HCl + 25 ml. KCl dil. to 100 ml 1.4 13.15 ml. HCl -I- 25 ml. KCl dil. to 100 ml 1.6 8.3 ml. HCl + 25 ml. KCl dil. to 100 ml 1.8 5.3 ml. HCl + 25 ml. KCl dil. to 100 ml 2.0 3.36 ml. H Q + 25 ml. KCl dil. to 100 ml 2.2

0.1 Af potassium biphthalate -|- 0.1 iV.HCl at 20°

46.70 ml. 0.1 iVHCl -f- 50 ml. biphthalate to 100 ml.. . . . . . f 2.2 39.60 ml. Q.IN HCl + 50 ml. biphthalateto 100 ml 2.4 32.95 ml. 0.1 AT HCl -t- 50 ml. biphthalate to 100 ml 2.6 26.42 ml. 0.1 N HCl -|- 50 ml. biphthalate to'lOO ml 2.8 20.32 ml. 0.1-2V HCl -|- 50 ml. biphthalate to 100 ml. 3.0 14.70 ml. 0.1 N HCl + 50 ml. biphthalate toJOO ml 3.2 9.90 ml. 0.1 N HCl + 50 ml. biphthalate toÔO ml 3.4 5.97 ml. 0.1 iV HCl -(- 50 ml. biphthalate to 100 ml f'.... 3.6 2.63 ml. Q.\N HCl + 50 ml. biphtlialate to 100 ml '.. 3.8

0.1 M potassium biphthalate + 0.1 AT NaOH at 20°'

0.40 ml. 0.1 JV NaOH -1- 50 ml. biphthalate to 100 ml '. 4.0 3.70 ml. 0.1 N NaOH + 50 ml. biphthalate to 100 ml;.;_^^^_^^.,... ...-.•.''.... 4.2 7.50 ml. 0.1 iV NaOH + 50 ml. biphthalate to 100 m l : . . . . . 777.'. 4.4

12.15 ml. O.IN NaOH + 50 ml. biphthalate to 100 ml ; 4.6 17.70 ml. 0.1 N NaOH + 50 ml. biphthalate to 100 ml .^.: 4.8

* The pH values reported in these tables have been calculated from the potential measurements using Sorensen's standard equations (1909). The corresponding âH values are 0.04 unit higher than the tabulated values. (See page 88.)

PRINCIPLE OF THE METHOD. SETS.OF BUFFER MIXTURES 35

BuFFBB MrxTUBES OF CLAEK AND LuBS—Continued

0.1 M potassium biphthalate + 0.1 N NaOH at 20° Composition pH

23.85 ml. 0.1 AT NaOH + 60 ml. biphthalate to 100 ml 5.0 29.95 ml. 0.1 N NaOH + 50 ml. biphthalate to 100 ml 5.2 35.45 ml. 0.1 N NaOH + 50 ml. biphthalate to 100 ml 5.4 39.85 ml. 0.1 N NaOH + 50 ml. biphthalate to 100 ml 6.6 43.00 ml. 0.1 AT NaOH + 50 ml. biphthalate to 100 ml 6.8 45.45 ml. 0.1 AT NaOH + 50 ml. biphthalate to 100 ml 6.0

0.1 Af monopotassium phosphate + 0.1 iV NaOH at 20°

5.70 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 6.0 8.60 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 6.2

12.60 ml. 0.1 N NaOH + 50 ml. phosphate to 100 ml 6.4 17.80 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 6.6 23.45 ml. 0.1 N NaOH + 50 ml. phosphate to 100 ml 6.8 29.63 ml. 0.1 AT NaOH + 60 ml. phosphate to 100 ml 7.0 35.00 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 7.2

"39.50 ml. ,0.1 -A' NaOH + 50 ml. phosphate to 100 ml 7.4 42.80 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 7.6 45.20 ml. 0.1 AT NaOH + 50 ml. phosphate to 100 ml 7.8 46.80 ml. 0.1 N NaOH + 50 ml. phosphate to 100 ml 8.0

0.1 M H3BO3 in 0.1 M KCl + 0.1 AT NaOH at 20°

2.61 ml. 0.1 AT NaOH + 50 ml. boric acid to 100 ml 7.8 3.97 ml. 0.1 N NaOH + 60 ml. boric acid to 100 ml 8.0 6.90 ml. 0.1 A NaOH + 60 ml. boric acid to 100 ml 8.2 8.50 ml. 0.1 A NaOH + 50 ml. boric acid to 100 ml 8.4

12.00 ml. 0.1 AT NaOH + 50 ml. boric acid to 100 ml 8.6 16.30 ml. 0.1 AT NaOH + 50 ml. boric acid to 100 ml 8.8 21.30 ml. 0.1 AT NaOH + 60 ml. boric acid to 100 ml 9.0 26.70 ml. 0.1 N NaOH + 60 ml. boric acid to 100 ml 9.2 32.00 ml. 0.1 AT NaOH + 50 ml. boric.acid to 100 ml 9.4 36.85 ml. 0.1 N NaOH + 60 ml. boric acid to 100 ml 9.6 40.80 ml. 0.1 A NaOH + 60 ml. boric acid to 100 ml.. 9.8 43.90 ml. 0.1 A? NaOH + 60 ml. boric acid to 100 ml . . . . . 1 0 . 0

CITRATE BUFFERS OF KOLTHOFF AND VLEESCHHOUWEB

0.1 M monopotassium citrate and 0.1 iV HCl at 18° (Add tiny crystal of thymol or a few milligrams of mercuric iodide to prevent growth

of molds) /

Composition pH 49.7 ml. 0.1 AT HCl + 50 ml. citrate to 100 ml.../ 2,2 43.4 ml. d. 1 AT HCl + 50 ml. citrate tS lOO ml..:' 2.4 36.8 ml. 0.1 AT HCl + 50 ml. citrate to 100 ml.-f 2.6 30.2 ml. 0.1 AT HCl + 50 ml. citrate to 100 ml 2.8 23.6 ml. 0.1 AT HCl + 50 ml. citrate to 100 ml 3.0 17.2 ml. 0.1 N HCl + 50 ml. citrate to 100 ml 3.2 10.7 ml. 0.1 AT HCl + 60 ml. citrate to 100 ml 3.4 4,2 ml. 0.1 iV HCl + 50 ml. citrate to 100 ml 3.6


CiTBATB BUFFERS OF KOLTHOFF AND VMiESCHHOuwBK—Continued

O.i M monopotassium citrate and 0.1 A'' NaOH at 18*

(Add tiny crystal of thymol or a few milligrams of mercm-ic iodide to prevent growth of molds)

Composition pH 2.0 ml. 0.1 N NaOH + 50 ml. citrate to 100 ml 3.8 9.0 ml. 0.1 AT NaOH + 50 ml. citrate to 100 ml 4.0

16.3 ml. 0.1 N NaOH + 60 ml. citrate to 100 ml 4.2 23.7 ml. 0.1 N NaOH + 50 ml. citrate to 100 ml 4.4 31.5 ml. 0.1 A'' NaOH + 50 ml. citrate to 100 ml .- 4.6 39.2 tol. 0.1 AT NaOH + 50 ml. citrate to 100 ml 4.8 46.7 m]. 0.1 A NaOH + 50 ml. citrate to 100 ml 5.0 64.2 ml. Q.IN NaOH + 60 ml. citrate 6.2 61.0 ml. 0.1 N NaOH + 50 ml. citrate 5.4 68.0 ml. 0.1 N NaOH + 50 ml. citrate 5.6 74.4 ml. 0.1 A' NaOH + 60 ml. citrate 5.8 81.2 ml. 0.1 iV NaOH + 50 ml. citrate ' 6 . 0

BORATE MrxTURBs OF SOEENSEN

0.05 M borax + 0.1 A HCl

Composition

ml. Borax

5.25 5.5 5.75 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.5

10.0

ml. HCl

4.75 4.5 4.25 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

Sorensen, 18°

7.62 7.94 8.14 8.29 8.51 8.68 8.80 8.91. 9.01 9.09 9.17 9.24

Walbum, pH at .

10°

7.64 7.96 8.17 8.32 8.54

- 8.72 8.84 8.96 9.06 9.14

^^.22 9.30

40°

7.55 7.86 8.06 8.19 8.40 8.66 8.67 8.77 8.86 8.94 9.01 9.08

70°

7.47 7.76 7.95 8.08 8.26 8.40 8.50 8.58 8:67 8.74 8.80

• 8.86

0.05 M borax + 0.1 A NaOH

10.0 9.0 8.0 7.0

- 6.0 '

0.0 1.0 2.0 3.0 4.0

9.24 9.36 9.50 9.68 9.97

9.30 ' J 9.42 X 9.57 9.76

10.06

— ~ 9 T 0 8 — 9.18 9.30 9.44 9.67

8.86 8.94 9.02 9.12 9.28

COLORIMETRIC MEASUREMENT WITH BUFFER SOLUTIONS 37

A change of temperature affects the pH of buffer solutions only slightly, and for practical purposes it can be assumed that the data

'reported hold for temperatures between 15° and 30°. The only exception is furnished by mixtures of boric acid and sodium hydroxide, the pH of which decreases markedly with increase in temperature. (C/. last two tables.) This change is caused by a shift of the equilibrium between boric acid and its polymolecular complexes.

In the general discussion of buffer solutions (page 21), it was mentioned that one of their characteristics is that they are very insensitive to dilution with water. For this reason it is not at all necessary to prepare the buffer mixtures in a volumetric flask; the important thing is the correct ratio of the acid and basic component. Therefore in the monopotassium phosphate-sodium hydroxide mixtures, for example, both solutions have to be measured out exactly. The phosphate is pipetted into the flask, in which the mixture is kept, the sodium hydrox-

lide-is addedJrom a buret, and the volume is made up to 100 ml. by adduig the required volume of water from a graduate. How slightly the pH of a phosphate mixture is affected by dilution with water is shown by the following figures:^ Clark and Lubs' buffer pH = 7.00; diluted twice pH = 7.05; diluted 5 times pH = 7.13; diluted 10 times pH = 7.17; diluted 20 times pH = 7.18.

2. The Colorimetric Measurement with Buffer Solutions, In the determination of the pH of an unknown, a suitable indicator has to be found in the first place. Only indicators which show an intermediate color between the extreme acid and alkaUne one can be used. Beginners often overlook this elementary rule and thereby make the most serious mistakes. If the approximate value of the pH of the solution to be examined is not known, the order of its magnitude has to be approximated, in order to select the correct indicator. A few simple tests as a rule will supply the required information. To a small fraction of the solution a drop of pheriolphthalein is added. If the indicator is colorless it means that the pH of the solution is smaller than 8.0. (Cf. pH interval of indicators, page 29.) Another test is made with methyl orange or bromphenol blue. If one of these indicators assumes the alkaline color, it means that the pH is larger than 4.5. Therefore the pH of the unknown lies^ between 4.5 and 8.0. A few more tests with methyl red (pH interval 4.4-6.0), b"romthymol blue (6.0-7.6), and phenol red (6.8-8.0) will show the approximate value of pH and indicate which indicator(s) should be used in the determination. Instead of testing small amounts of the liquid with indicator solutions, indicator

' I. M. Kolthoff, Biochem. Z., 195, 239 (1928), where a more general discussion is given.


papers (phenolphthalein or thymol blue paper, litmus, congo red, etc.) as a rule can be used by application of the spot method. Also, a universal indicator is a great convenience in finding the approximate pH.

When the approximate value of the pH is known, 3 or 5 or 10 ml. (depending upon the amount of liquid available) are measured out by means of a graduate and transferred into a test tube of Pyrex glass or any other resistant glass (diameter about 1.5 cm., length about 15 cm.). Soft glass should not be used as it may give off alkali. A measured amount of the indicator solution is added carefully from a pipet of 1 ml., which is graduated in 0.01 ml. As a rule 0.1 to 0.2 ml. of 0.05 per cent indicator solution to 10 ml. liquid will be a proper amount. Then some buffer solutions (4 to 6) the pH of which overlaps that of the unknown are treated in exactly the same way. Especially if one-color indicators are used, it is extremely important to add to the unknown and the buffer solutions exactly the same amount of indicator, and to have test tubes of the same inside diameter.

The best way of judging the color is to observe, against a white background, the light transmitted through the whole length of the tube. A suitable colorimeter can be used as well, though it is not necessary at all in routine work. Enough reference solutions must be taken so that the color of the unknown falls between two of the series and not beyond. If buffer solutions with pH differences of 0.2, respectively, are taken, the pH of the unknown can be approximated within 0.1 very easily, and with some practice to 0.05. With buffer solutions that differ by 0.1 pH unit or less, the experimental error can be reduced to 0.01 to 0.02 in pH. If possible, indicators should be selected the indicator exponents (—log Ki) of which are of the same order of magnitude as the pH of the unknown. At this range, the color of the indicator is most sensitive for a small change in pH. If the pH lies,nearer the end of the transition interval of the indicator, the color changes in a less sensitive way with a small variation in pH.

3. The Colorimetric Measurement without Buffer Solutions. In Chapter II it was found that the relation between the color jof an indicator acid and the hydrogen-ion concentration of a solution is given by the expression:

[H+] = ^îKt (1)

or

pH = log ^ - I : pZ i (2)

Ki is a constant for each indicator. -If the ratio of the'concentration of

( y B C

M E

COLORIMETRIC MEASUREMENT WITHOUT BUFFER SOLUTIONS 39

the acid to the alkaline form of the indicator in the unknown can be determined in an experimental way, the pH can be computed according

"to equation 2. Therefore on this basis it is possible to derive pH without the use of buffer solutions. From the experimental point of view it is desirable to distinguish between the use of one- and two-color indicators,

(a) Two-Color Indicators. Gillespie' proposed the following simple technique. He sets up in a comparator (c/. Fig. 3, page 45) two tubes, one of which contains some drops (let us say a drops) of a given indicator fully transformed into the acid form, and the other of which contains (10 — a) drops of the indicator fully transformed into the alkaline form. By changing a from 1 to 9, pairs of tubes are obtained containing [HI] and [I~] in a ratio changing from 1/9 to 9/1 . If the two comparison solutions and the tested solution, to which 10 drops of the same indicator are added, are kept at the same volume and the view is through equal depths of each, a simple comparison of the

-unknown with various pairs oi acid and basic solutions of the indicator will show the ratio of acid and basic form of the indicator in the tested solution. Instead of working with drops it is preferable to measure.the various amounts of -pm. 1. Gillespie's bi-indicator (0.01-0.02 per cent) by means of a pipet colorimeter, of 1 ml. graduated in 0.01 ml. In order to increase the accuracy a bicolorimeter can be used instead of the pairs of test tubes. The principle of the bicolorimeter is shown in Fig. 1.

A and C are fixed; B moves along a graduated scale which is read by a pointer on B. The pointer may move over 100 scale divisions. The acidified indicator solution of suitable strength may be placed in 5 ; the alkahne solution of equal strength in C. The solution to be examined is placed in E, and enough indicator is added to make the concentration the same as in B and C. B is then moved until the colors are matched; the scale reading gives the ratio of the acid to the alkaline color. "The solution to be examined, if colored or turbid, is received in the small tube A. In this case an amount of water equal to that of the solution is placed in D (compare measurement of pH in colored solutions, page 44). Another principle which has proved to be useful in-the construction of a bicolorimeter is that of two wedges of equal size, cemented or fused together. One wedge is filled with the completely acid solution of the indicator, the other with the alkaline solution of the same indicator concentration. The pair of wedges is placed in such a position that it can move up and down, so that various ratios of the acid and alkaline form can be observed through an eyepiece, which makes it possible to

' L. J. GiUespie, J. Am. Chem. Soc, 42, 742 (1920); Soil Sci., 9,115 (1920).

40 THE COLORIMETRIC MEASUREMENT OF pR

view small sharply defined segments of the liquid at a time. On one side of the simple apparatus is placed a scale on which the ratio of acid to basic form in any position can be read. The liquid to be tested is put into a cylinder with plane walls, or iiito a cell, and treated with enough indicator to give a depth of color equal to that in the double-wedge apparatus. The colors are matched against a white background. Other methods, more or less useful in routine -work, where the transition colors of various indicators are imitated by suitable mixtures of stable inorganic colored salt solutions or colored glass disks, have been proposed in the literature. For details the reader is referred to special textbooks on pH determinations. (See Clark; Kolthoff; Britton.) Finally, it should be mentioned that the ratio of the acid to basic form can be determined very accurately by spectrophotometric measurements. This method, though very valuable for special research, has not been developed in such a simple form as to justify its use in ordinary practical work. Besides, it should always be remembered that, even if the colorimetri.c method could be developed to a great perfection, it would still be less satisfactory than the potentiometric method, on account of uncertainties inherent in the principle of the procedure itself. {Cf. page 45.)

For the preparation of the indicator in the completely acid form, solutions of bromcresol green, chlorphenol red, methyl red, bromthymol blue, phenol red, or cresol red of the proper strength in water can be acidified with acetic acid so that the concentration of the acid is about 0.1 N. They are completely present in the alkaline form, if so much sodium carbonate is added to the aqueous solution that the concentration of the salt is about 0.01 to 0.02 N. Methyl orange and bromphenol blue in about 0.01 N hydrochloric acid are completely transformed into the acid form, whereas in 0.01 N sodium carbonate or bicarbonate they are present in the alkaline form. Thymol blue has two color-change intervals, one at the acid range from red to yellow between pH 1.2 and 2.8, and one at the-alkaline range between 8.0 andO.G from yellow to blue.' For measurements of pH in the neighborhood of 2 the acid form of the indicator is obtained by acidifying the solution with so much hydrochloric acid that the concentration of, the acid is about 0.25 N. This solution has to be freshly prepared before the experiment. The indicator is completely present in the yellow form in a solution of about 1. per cent monopotassium phosphate. In making measurements at a pH around 9.0 the indicator in the monopotassium phosphate-solution is taken as the completely acid solution, whereas the-" indicator is present in the completely alkaline form (blue color) in about 0.05 JV sodium carbonate solution.

In the beginning of this paragraph it was mentioned that, if the ratio

COLOKIMETEIC MEASUEEMENT WITHOUT BUFFER SOLUTIONS 41

o! the acid and the alkaline form of the indicator in the unknown has been determined, the pH can be calculated if pKi is known:

PH = log — - + pKi.

In the following table the most reliable values of pKi are tabulated.* The constants given hold for a temperature of 20°; where necessary, the influence of the temperature upon the magnitude of the constant is indicated. It will be shown later (page 47) that the indicator constants are also a function of the electrolyte content of the solution. Values of ,pK are also given at various ionic strengths of potassium and sodium salts. If the salt content and the kind of salt in the solution tested are approximately known, the proper indicator exponent pKi can be selected from the table.

•~pKi VAI/TJES'OP TWO-COLOE INDICATOKS AT 20° AT VABIOUS IONIC STRENGTHS

Indicator

Thymol blue (acid range)

Methyl orange Bromphenol blue Bromcresol green

Methyl red

Bromcresol purple

Bromthymol blue

Phenol red

Thymol blue

pKi at Ionic Strength Zero;

at Various Temperatures

1.65 (15-30°)

3.46-0.014^-20°) 4.10 (15-20°) 4.90 (15-30°)

5.00-0.006(<-20°) 6.25-0.005((-20°)

6.40-0.005(«-20°)

7.30 (15-30°)

8.00-0.007(i-20°)

9.20 (15-30°)

pKi at Ionic Strength of

0.01

3.46 4.06 4.80

5.00 6.15

6.28

7.19 1

7.92

9.01

0.06

1.65

3.46 4.00 4.70

5.00 6.05

6.21

7.13

7.84

8.95

0.1

1.65

3.46 3.85 4.66

5.00 6.00

6.12

7.10

7.81

8.90

0.6

1.65

3.46 3.75(KC1) 4.50(KC1) 4.42(NaCl) 5.00 5.9 (KCl) 5.85(NaCl) 5.9 (KCl) .5,8 (NaCl) 6.9 (KCl) 6.8 (NaCl) 7.6 (KCl) 7.5 (NaCl)

Methyl orange, methyl red, and thymol blue (acid range) distingtiish themselves favorably by the fact that their constant is not affected by the presence of electrolytes up to an ionio strength of 0.5. . ^

(6) One-Color Indicators. The experimental procedure may be simplified by the use of one-color indicators, one form of which is color-

* Cf. I. M. Kolthoff, / . Phys. Chem., 34, 1466 (1930).


less and the other one is colored. I t was developed by Michaelis and co-workers (1920), and has since been extended by other workers. If,

' for example, 11 ml. of a tested solution containing 1 ml. of indicator matches the color of 11 ml. of an alkaline solution containing 0.5 ml. of the same solution of the indicator in the alkaline form, it is easily seen that in the tested solution 50 per cent of the indicator is transformed into the alkaline form, and 50 per cent is present in the acid form; hence:

pH =, log — + pKi = pKi.

Quite generally, if we determine the concentration c of the alkaline form, and the total concentration of the indicator in the tested solution is a, then:

c pH = log + pKi.

a — c ' The determinations can be made with any ordinary colorimeter or even with test tubes of equal bore. To one test tube containing a proper volume of the solution to be tested (e.g., 10 ml.) a measured volume (preferably 1 ml.) of the proper indicator solution is added from a pipet. To a second test tube containing approximately 9 ml. 0.1 N sodium carbonate, such a volume of indicator solution (accurately measured from a pipet of 1 ml. or a microburet divided in 0.01 ml.) is added that the color developed approximately matches that of the first tube. The volume in thei second tube is now made up to the volume in the first tube. Other trials with more or less indicator are made until a complete color match is obtained. This amount of indicator then corresponds to the fraction of the 1 ml. added to the solution tested, which has been transformed into the alkaline form. If only a small fraction (5 to 10 per cent) is transformed into the alkaline form, the accuracy of the procedure can be somewhat increased by making the color match with an indicator-solution ten times more dilute than the standard solution.

In the following table the pKi values of suitable one-color indicators are tabulated. Again the influence of the ionic strength and the temperature has been indicated. The dinitrophenols and p-nitrophenol can be prepared in a strength of 0.04 per cent in water; m-nitrophenol is less colored in alkaline medium and is better used as 0.1 per cent solution. The nitrophenols are colorless in acid medium, and-yellow"in the alkaline form. The methoxytriphenylcarbinols can/be used in 0.02 per cent solution in 60 per cent alcohol; they are weak bases, the cation of which is red, and the alkaline foriii colorless. Quinaldin red has proved to be

COLORIMETRIC MEASUREMENT WITHOUT BUFFER SOLUTIONS 43

useful in physiological work; a 0.03 per cent solution in 50 per cent alcohol can be kept for a long time. In acid medium the indicator is

"Colorless, in alkaline medium red. Pinachrom (M) (Tables of Schulz No. 611) is p-ethoxyquinaldin-p-ethoxyquinolin ethylcyanine; it behaves like a base, which is colorless in acid medium and red in alkaline medium. I t is very slightly soluble in water, but is soluble in hydrochloric acid, forming a colorless solution. The stock solution can be prepared by neutralizing the basic group with hydrochloric acid (molecular weight = 518): 100 mg. indicator is dissolved in 40 ml. of alcohol, 1.9 ml.

pKi VALUES OF ONE-COLOR INDICATOBS AT 20° AND VAHiotrs loisric STRENGTHS

Indicator

2,4,2',4'; 2"-Pentameth-oxytriphenylcarbinbl *

Quinaldin red 2,4,2',4',2",4",-Hexa-

methoxytriphenylcar-binol

(3-Dinitrophenol (1-oxy-2,6-dinitrobenzene). . .

a-Dinitrophenol (1-oxy-2,3-dmitrobenzene). . .

7-Dinitrophenol (1-oxy-2,5-dinitrobenzene)...

2,4,6,2',4',2",4"-Hepta-methoxytriphenylcar-

m-Nitrophenol

pKi at Ionic Strength Zero;

at 20°

1.86+0.008(<-20°) 2.63-0.007(t-20°)

3.32+0.007(<-20°)

3.70-0.006(«-20'^)

4.10-0.006(i-20°)

5.20-0.0045(<-20°)

7.34-0.013(f-20°) 7.00-0.01 l(e-20°) 8.35-0.01(<-20°)

pKi at Ionic Strength of

0.01

2.80

7.34

i 1

0.05

1.86

3.32

3.95

3.95

5.12

5.90

8.30

0.1

1.86 2.90

3.32

3.90

3.90

5.10

5.90 7.47

8.25

, 0 .5

3.10

(KCl)

3.80(KC1)

3.80(KCl)

5.00(NaCl)

7.64(KCI)

8.15(NaCl)

* Properties of the methoxytriphenylcarbinols, c/. H, Lund, / . Am. Chem. Soc, 49, 1346 (1927); I. M. Kolthoff, J. Am. Chem. Soc., 49, 1218 (1927).

1

of 0.1 iV hydrochloric acid is added, and the solution is made up to a volume of 100 ml. with water. The solution has a weak violet color and is kept in a Pyrex bottle. The pinachrom does not change its color instantaneously; after addition of the indicator to the solution to be tested one has to wait at least two minutes before the comparison is made. The alkaline solutions of the indicator (for comparison) cannot be kept a long time, as they are unstable. The free red base is very slightly soluble in water and precipitates after standing for a short time.


The alkaline solutions for comparison are made up in about 0.01 iV sodium carbonate solution by carefully mixing a known amount of the indicator with the carbonate; shaking of the tube should be avoided. ' The solutions for comparison can be kept for one hour but not longer.

For the measurements, 1 ml. of 0.01 per cent indicator solution (see , above) is added to 10 ml. of the solution to be tested. The color is compared with that of standards containing known amounts of 0.002 per cent indicator in 0 01 N sodium carbonate.^

Phenolphthalein is also a one-color indicator, the monovalent anion and the undissociated form of which are colorless, whereas the divalent ion is intense red-violet. The simple computation of pH from the ratio of the concentration of the colored to the' uncolored form cannot be applied here, on account of the fact that the first and second step of the dissociation of the phenolphthalein overlap each other. Therefore, Michaelis and Gyemant * give an empirical table for this indicator. '

4. Colored Solutions: Compensation for Own Color. If-the color* of the solution to be tested is very intense the colorimetric method no longer will yield satisfactory results, and even if the solution is only slightly colored, the direct method of matching its color by the addition

of indicator to a clear standard buffer solution will no longer be applicable. • However, the interference can be overcome in a simple way. Suppose that the buffer solution and the colored solution have the same pH. Upon the addition of a suitable indicator they will not show the same color, as the unknown already contains some colored component. If the color effects are additive the interference caused by the color of the unknown can be elimuiated by making use of the simple principle of the Walpole ''comparator and the so-called block comparator.

Walpole Comparator (Fig. 2). The interior is painted black. The various liquids are placed in the four plane-bottom cells to the same depth in each. Light is made to

pass up through these solutions either by means of a reflectmg surface or by some suitable direct illumination placediîindemeath the appara-

/' " C/. I. M. Kolthoff, J. Am. Chem. Soc, 60, 1604 (1928). 6 L. Michaelis and A. Gyemant, Biochem. Z., 109,165 (1920). Cf. I. M. Kolthoff,

Acid-Base Indicators, page 313. ' Walpole, Biochem. J., 24, 40 (1910).

nd

ion 3la Lc ixa,

B lifer f Cf toil

I s s t Sol It

o i l '

Liglit

FiQ. 2. Walpole comparator.

SOURCES OF ERROR IN THE COLORIMETRIC METHOD 45

tus. The cell containing the buffer solution and indicator is replaced by others until a perfect match is obtained.

^'~^'Block Comparator (Hurwitz, Meyer, and Ostenberg).^ This simple instrument should be available to anyone experimenting in the pH field. Six deep holes just large enough to hold the test tubes are bored parallel to one another in pairs in a block of wood. Perpendicular to these holes and running through each pair are bored smaller holes through which the test tubes may be viewed. All the holes are painted a non-reflecting black. The center pair of test tubes holds, first, the solution to be tested plus the indicator and, second, a water blank. At either side are placed the buffer solutions plus indicator, each backed by a sample of the colored solution under test.

If the Gillespie method (c/. page 39) is applied tocolored solutions it • is"desirable to have three groups of three holes (one after the other) in order to compensate for the color.

-•••• The comparator device can also be used for slightly turbid solutions, although relatively thin layers of Uquid should be observed.

/ooo^ '000

Ught

Control Q ® O '^™*'°'

Standard Q ( x ) Q Standard Eye

FiQ. 3. Comparator.

5. Sources of Error in the Colorimetric Method, (a) Slightly Buffered Solutions. Acid-base indicators behave, as we have seen, like substances with a weak acidic or basic character, and therefore they have a tendency to change the p R when added to a sUghtly buffered or unbuffered solution. As the molecular concentration of indicators in colorimetric work is of the order of 10~^ to 10~®, the acid or base error of the indicator will be noticeable only in solutions with extremely slight buffer action. In practical work one often deals with these solutions; for

8 Proc. See. Expil. Biol Med., 13, 24 (1915).


example, in the measurement of the pH of pure water or of solutions of neutral salts in pure water, of extremely weak acids and bases in water, etc. Suppose one adds to 10 ml. of pure water (pH = 7.0 at 24°) 0.1 ml. of a 0.04 per cent solution of methyl red. This dye has an indicator constant of 10~^, and it is a simple matter to calculate that the addition of the above trace of methyl red will change the pH of water from 7.0 to about 5.0. Actually this can be shown to be so; the authors observed a color corresponding to a pH of 5.1 in a buffer mixture.

I t will be easily understood that in the measurement of pH in slightly buffered solutions reliable results will be obtained only if the indicator solution added has the same pH as the unknown. Fawcett and Acree ' call these indicator solutions adjusted or isohydric.

The problem now arises: if the pH of the solution tested is unknown, how then is it possible, to select an isohydric indicator solution? The question fortunately can be answered in an empirical way. Theoretically it has been shown '* and practically verified that the pH measured in an unbuffered solution is independent of the amount of indicator added, if the indicator solution is isohydric. If the indicator solution added has a more acid reaction than the solution tested, decreasing pH values will be found with increasing amount of indicator. On the other haiid, if the indicator solution is more alkaline, the pH found will increase with increasing amount of indicator. An intelligent application of this simple rule enables us to solve the problem of measuring the pH of unbuffered solutions. Let us consider the hardest problem, which is the measurement of pH of pure, carbon dioxide-free water. (Naturally, the experiments have to be carried out under such conditions that no carbon dioxide from the air can enter during the measurements.) By preliminary experiments it is found that the pH of pure water :is in the vicinity of 7 (6.5 to 7.5); therefore an indicator Jike brom-thymol blue with a color-change interval in this neighborhood has to be used. For ordinary work the solution of this indicator is prepared by neutralizing the strong sulfonic group with sodium hydroxide (c/. page 28); the sulfonphthalein, however, exerts its indicator properties in neutraUzing the monovalent anion H I " , which is yellow, to the divalent anion 1° (blue). A solution of the monovalent salt has a pH smaller than 7.00, and therefore, if increasing amo;unts of this solution are added to pure water, a decreasing pH will be observed. This could be confirmed in an experimental way. A solution of bromthymol blue was êpaTe'dpcoiitaining 0.1 per cent of indicator, and the mono- and divalent anion in a ratio of

"E. H. Fawcett and S. F. Acree, / . Bad., 17, 163 (1929); 7nd. Eng. Chem., Anal. Ed., 2, 78 (1930).

'" Cf. I. M. KolthofE and T. Kameda, J. Am. Chem. Soc, 53, 825 (1931).


96 :4. Upon addition of 0.1 ml. of this indicator solution to 15 ml. of pure water a pH of 6.37 was measured; with 0.3 ml., a pH of 6.25; with 0.5 ml., of 5.95. On the other hand, if an indicator solution of the same strength was prepared, containing the mono- and divalent anion in a ratio of 4 :96, a pH of 7.68 was measured upon addition of 0.1 ml. of indicator to 15 ml. of water; of 7.80 with 0.3 ml. of indicator; of 8.00 with 0.5 ml. Empirically, it was found that an indicator solution containing the mono- and divalent anion in a ratio of 65 : 35 was isohydric with pure water. With 0.1, 0.3, and 0.5 ml. of this indicator solution, respectively, a pH between 6.78 and 6.76 was measured. (On account of the difference in electrolyte content between the water and the buffer solution used for comparison, the experimental value had to be corrected for the salt influence, and yielded then a pH of 7.03 to 7.01; see (6) —(below).)

Quite generally the problem of measuring the pH of unbuffered, or slightly buffered, solutions can be solved in a similar way. First of all the approximate pH of the solution to be tested is determined, so that the proper indicator or indicators can be selected. Two solutions of the indicator are prepared, one containing it in the acid form (for sulfon-phthaleins the univalent anion) and the other containing the indicator in the alkaline form. A mixture containing both forms in equal portions is prepared, and measurements are made with successive amounts of indicator. If the pH increases with increasing amounts of indicator, the mixture has too alkaline a reaction, and another is prepared containing the acid and basic form, e.g., in a ratio of 75 :25. If the indicator mixture 1: 1 was too acid, the two forms have to be mixed in a ratio of 25:75 and the measurements repeated. Only the isohydric mixture yields results which do not change with the amount of indicator added.

It should be remembered that these indicator mixtures are not stable , upon standing; they should be freshly prepared before the experiments.

(6) The Salt Effect. In the beginning of this chapter it was stated that the colorimetric measurement of pH is based upon the fact that if an indicator in two solutions assumes the same color the pH of both liquids is the same. Strictly speaking, this statement is not quite correct on account of the fact that in all our quantitative expressions of the equilibrium we have written concentrations instead of activities of the components. In Chapter I, paragraph 2, it was mentioned that an equilibrium constant is determined by the activity of the reacting components and not by their concentrations. Therefore, if we express the ionization constant of an acid like an indicator acid, Ki in the expression:

Ki = ^ s i : ^ (3)

48 THE COLORIMETEIC MEASUREMENT OF pH

is a true constant (a denotes the activity of the various components); its ^ value is independent of the presence of salts.

On the other hand, Ki in the expression:

is not constant at different electrolyte contents of the solution, as the activity coefficient of the various components changes with the ionic strength.

The potentiometric measurements with the hydrogen and quinhy-drbne electrodes give us the value of the activity of the hydrogen ions an*, and in colorimetric work it is desirable to find the same expression. The pH values of the various buffer solutions (see page 34) are measured with the hydrogen electrode and, therefore, actually are pdH. values. At a certain activity of the hydrogen ions the equilibrium in a solution of an indicator of the t jê HI, is determined by the expression (cf. equation 3):

ai- Ki

If /o represents the activity coefficient of the undissociated indicator acid, and/ i the same for the ions, equation 4 can be written in the following form:

/o [HI] a n .

/ i , [I-] Ki (5)

The color of the indicator is determined by the ratio of the concentrations and not of the activities of [HI] to [I~]: ^

[HI] a^. h ~

In Chapter I, paragraph 2, we saw that the activity coefficient of an ion decreases with increasing ionic strength of the solution, whereas that of undissociated molecules increases, as a rule. The latter effect, however, will be neglected for the present.

Let us consider that to equal volumes of t^6~soluT}ibiis which have the same paH but which are of different ionic strength equal amounts of an indicator acid HI are added. In general, then, the colors of the indicator in both solutions will not be the same. If the ratio of [HI] : [I~] in solution 1 with an ionic strength wi is called Ri, and the ratio in


solution 2 with an ionic strength wg is called R2, we find from expression 6 that:

'R' {7) '[7) ^ approx. — - (7) •^2 Vo / l \/0/2 (/l)2

In expression 7, (/i)i refers to the activity coefficient of I~ in solution 1 and (/i)2 to that in solution 2. If solution 1 has an ionic strength smaller than solution 2 the ratio (/i)i/(/i)2 and, therefore, also R1/R2 will be greater than 1. This means that the indicator has a more acid color in solution 1 than in solution 2, although both solutions have the same paR. With an indicator base instead of an indicator acid the reverse effect would be observed.

I t is evident, then, that the statement that two solutions which impart the same color to an indicator acid have the same pdH. is not correct. Let us consider again our two solutions with ionic strengths of til and W2- If the indicator acid has the same color in both, it follows from equation 5 that

(aH^l ^ (fo\ . (fo\ _ (/l)2 {as.)2 V/i/ i" V/1/2 (/i)i

If solution 1 again has the smaller ionic strength, ia^+)i will be smaller than (aH+)2 when the indicator acid has the same color in both solutions, or the paH of solution 1 will be greater than that of solution 2. Expressed differently, the experimental value of paHj is too small.

In the colorimetric measurement of pH, as a rule, buffer solutions are used with an ionic strength of 0.05 to 0.1. If the indicator in the solution to be tested has the same color as in some buffer mixture, their paR is the same only if both solutions have the same ionic strength. If an indicator acid is used and the solution to be tested has an ionic strength smaller than the buffer mixture, the paH found by colorimetric measure-nient is too small, and a correction has to be applied (added) for 'the" difference between the ionic strength of the buffer mixture and the solution to be tested. This correction, called the salt correction, depends primarily upon the ionic strength of the buffer solution taken for comparison. Since the ionic strength of the ordinary buffer solutions is of tlie order of 0.1, we will relate the salt corrections listed below to this ionic strength. However, the salt correction does not depend solely upon the difference in ionic strength between the buffer mixture and the solution tested, but also upon the kind of ions present and the individual characteristics of the indicator." Theoretically, the salt correction will

" A review of the complicated relations is given in / . Phys. Chem., 32, 1820 (1928).

50 THE COLORIMETRIC MEASUREMENT OF pH.

be larger for an indicator the acid form of which is a monovalent anion and the alkaline form a divalent anion (sulfonphthaleins, phenolphthal-ein) than for an indicator the acid form of which is an uncharged molecule and the alkaline form a monovalent anion (mononitrophenols). For methyl orange and methyl red the salt error is negligibly small on account of the hybrid nature of the dimethylaminoazobenzene sulfonic acid and dimethylaminoazobenzene carbonic acid. Therefore, these indicators have distinct advantages in the colorimetric pH measurement. In the following table the salt corrections for various indicators are reported in solutions of different ionic strength. I t is assumed that comparisons are made with buffer solutions with an ionic strength of 0.1.

A positive correction ( + ) means that the figure has to be added to the experimental value; a negative sign {—) means it has to be subtracted, if comparisons are made with a buffer with an ionic strength of 0.1.

SALT COBBECTION roa INDICATORS AT VARIOUS IONIC STRENGTHS

(Ionic Strength of Buffer Solution Used for Comparison Is 0.1)

Ionic Strength

0.0025 0.005 0.01 0,02 0.05 0.1 0.5 (KCl) 0.5 (NaCl)

T. B. in its acid ran

Ionic Strength

0.0025 . 0.005 O.Oi 0.02. 0.05 0.1 0.5 (KCl) 0.5 (NaCl)

T. B.*

0.00 0.00 0.00 0.00 0.00 0.00

ge (pH 1.3 -

B . T . B .

+0.14 +0.12 +0.11 +0.07 +0.04

0.00 - 0 . 2 0 . -0 .28

M. 0.

- 0 .04 -0 .04 - 0 . 0 2

0.00 0.00 0.00 0.00 0.00

2.8).

P.K.

+0.14. +0.12 +0.11 +0.07 +0.04

0.00 -0.20 -0 .29

B. P. B.

+0.15 +0.14 +0.14 +0.13 +0.10

0.00 -0 .10 -0 .18

^^

T.B. \

+0.16 +0.12 +0.09 +0.05

0.00 -0 .12 -0 .19

B. C. G.

+0.21 +0.18 +0.16 +0.14 +0.05

0.00 -0 .12 -0 .16

— '

Ppht.

+0.18 +0.12 +0.10 +0.05 " OrOO -T-ii. 16 -0 .21

M. R.

0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00

Tpht.

+0.11 +0.09 +0.05

- 0.00 - 0 . 1 9

C. P. K.

+0.15 +0.13 +0.12 +0.05

0.00 -0 .16 -0 .19

T. B. = Thymol blue B. C. G. = Bromcresol green B. T. B. = Bromthymol blue Ppht. = Phenolpbthalein

M. O. = Methyl orange B. P. B. = Biomphenol blue M. E. = Methyl red C. P. R. = CMorphenoI red P. R. = Phenol.red Tpht. = Thymolphthalein


EXAMPLE. Colorimetrically, it is found that an acetic acid-sodium acetate buffer with an acetate concentration of 0.005 N has a pH of 4.8, using bromcresol green as an indicator and an ordinary buffer solution for comparison. Then the corrected pH is 4.8 + 0.18 = 4.98. To another dilute acetic acid-acetate buffer, 0.5 N sodium chloride is added (which decreases its pH). Using the same indicator, a pH. of 4.80 is found. Then pH corrected = 4.8 — 0.16 = 4.64. It should be emphasized that at higher ionic strengths (above 0.1) the type of ions present has a relatively great influence upon the correction, and therefore the result of the colorimetric measurement is more or less uncertain.

Finally, a few words may be said of the pKi values of indicators tabulated on pages 41 and 43. I t has been indicated there that pKi is a function of the ionic strength. According to equation 6:

TT—r = aH+—— (monobasic indicator acid), (6) U 1 Jo-Ki

whereas in the computation of pH from colorimetric measurements we have assumed th&t

However, Kj in equation 8 is not constant, because fi/fo (equation 6) changes with the ionic strength; and it is easily seen that for indicator acids K'I (equation 8) increases with the electrolyte content of the solution or pK'i decreases. (See also section 7, Chapter I.)

(c) The Protein Effect. I t was Sorensen who showed that proteins may render the colorimetric determination of pH difficult or impossible. The effect is more or less specific and depends upon the kind of protein present and the indicator used. As a rule the positively charged protein (acid side of the isoelectric point) exerts a larger influence than the negatively charged protein (alkaline side of the isoelectric point). Especially the diazo indicators are. affected by the positively charged protein hydrates. On the other hand, in casein and egg albumin solutions of pH around 6.0 (near the isoelectric point), methyl red gives rehable results.^^

Quite generally, therefore, in the presence of proteins, it is not safe to rely upon the data obtained by the colorimetric method unless they have been controlled by the potentiometric method (hydrogen electrode).

(d) Other Factors. In colloidal solutions (c/. also above under "Protein Effect") the indicator equihbrium may be changed on account

" Several examples of the deviation shown by indicators of diSerent type in various kinds of protein solutions are given in W. M. Clark, The Determination of Hydrogen Ions, Third Edition, pages 184 and 185; and I. M. Kolthoff, Acid-Base Indicators.


of a specific adsorption of either the acid or alkaline form of the indicator. Under such conditions an entirely wrong value of the pH of the solution is obtained. Thus, for example, if neutral red is added to a soap solution with a pH of about. 11 (strongly alkaline to phenolphthalein) it assumes a reddish color, owing to an adsorption of the acid form of the indicator by the colloidal fatty acid particles.

Also in the presence of finely divided particles the indicator may assume a color not corresponding to the pH of the solution, on account of a surface reaction. A striking example is provided by an experiment with lanthanum hydroxide: A saturated solution of that substance in water has a pH of about 9.0. If some of the hydroxide is shaken in water and thymolphthalein is added, the suspension assumes a dark blue color, indicating that the pH is larger than 10.5. However, what happens is that the indicator, reacting with the hydroxyl ions on the surface of the hydroxide, is transformed into the alkaline form, and remains adsorbed as such (blue form) on the surface. If the suspension is allowed to settle, the supernatant liquid is colorless.

There is also a possibility that the ionization constant of the indicator will be changed at the interface between two substances. This can be shown to be true even for the interface water-air by the following experiment: Thymolblue in a solution with a pH of about 2.6 has a yellowish orange color. On violent shaking with air the mixture turns nicely red and forms a red froth; on standing it assumes its original color. The indicator has a larger ionization constant at the interface air-water than in aqueous solution. By shaking with air the concentration of the indicator at the interface increases considerably, and the effect is demonstrated by the color change and the formation of a red foam.

Quite generally in the presence of finely divided substances and in colloidal solutions one has to be careful with the results of the color-imetric method. A verification with the hydrogen electrode is highly desirable. Moreover, it may be recommended that "the colorimetric determination be repeated with an indicator of different type from the one used before. If, for example, an indicator acid has been used, it is advantageous to repeat the readings with an indicator base.

Finally, it should be emphasized that the data on the indicator constants hold only for water as a medium. If organic solvents, like alcohol or acetone, are added to water, all equiUbrium constants change. If the color of an indicator in an alcohol-water mixture is compared with that of the same indicator in an aqueous buffer solution, the same color does not mean the same pH (c/. page 30) .Jf

"Correction for the influence of alcohol, see e.g., I. M. Kolthoff, Acid-Base Indicators.

PROBLEMS ON INDICATORS 53

PROBLEMS ON INDICATORS

1. An indicator has an indicator constant of 5.00 (= — log Ki). What is its color-change interval, if 5 per cent of the acid form can be perceived by the naked eye in the presence of 95 per cent of the alkaline form, and 10 per cent of the alkaline form in the presence of 90 per cent of the acid form?

2. Bromphenol blue (indicator acid) and methyl orange (indicator base) both have a transition color in 10~* N hydrochloric acid. In what direction does the color of the indicator change on heating, assuming that the ionization constants of the indicators do not change? Compute how much the ratio of the acid to the basic form of the indicators changes on heating from 25° to 100° (Ky, = 10~^* at 25° and 10-12 g t jQQO) assuming that the ratio at 25° is 1 : 1?

3. In a mixture of water and alcohol the ionization constant of bromphenol blue is 10 times smaller than in water; that of methyl orange, 10 times larger. Calculate the sensitivity of both indicators for hydrogen ions, if the acid form of both of them in pure water is just perceptible at [H+] = 10"*.

4. On the addition of 0.1 ml. of a 0.1 per cent solution of phenolphthalein to 10 ml. of a borate bxiffer mixture, it is found that 60 per cent of the indicator is transformed "into the alkaline form. What is the concentration of the alkaline form, if 0.2 and 0.5 ml. indicator solution, respectively, are added to 10 ml. of the buffer mixtures?

5. Calculate the ratio of acid to basic form of an indicator acid with an ionization constant of 10"^ in buffer mixtures with a pH of 4.0; 4.5; 5.0; 6.3; and 6.0. Between what range in pR would you use the indicator for colorimetric work?

6. The pH of a solution is measured with bromcresol green (pKi = 4.70) as an indicator without the use of a buffer solution. It is found that the ratio of the yellow to the blue form is 40 : 60. What is the.pH of the solution?

7. An indicator base, red in acid, colorless in alkaline medium, with an ionization constant Kb equal to 10"' (not Ki\), is used for the colorimetric determination of pH without buffer solutions, at 26° (Kw = 10~'^). Ten milliliters of the solution to be tested is added to 1 ml. of 0.01 per cent indicator solution. By comparing with solutions of the indicator in 0.01 N hydrochloric acid it is found that 0.4 ml. of the 1 ml. indicator added is transformed into the acid form. What is the pH of the solution?

8. Calculate the change of pH in the neutralization of the following acids (after addition of 0 per cent, 10 per cent, 60 per cent, 90 per, cent, 99 per cent, 100 per cent, 101 per cent of the equivalent amount of sodium hydroxide), assuming that the volume does not change during the neutralization: 0.1 iV HCl; 0.01 JV HCl; 0.1 N acetic acid {Ka = 1.8 X 10"'); 0.1 M boric acid {Kd = 10^'). Corhbine the results in a graph, plotting the pH figures on the ordinate, and the percentage of acid neutralized on the abscissa. Draw arrows on the graph, indicating the range of distinct color change of methyl orange (or bromphenol blue); methyl red (or bromcresol green), phenol red, and phenolphthalein~(or thjTnol blue). Show which indicators can be used for the detection of the quantitative neutralization of the above acids.

9. Calculate the ratio of the acid to the basic form of the indicator in the colorimetric measurement of the pH of distilled water in equilibrium with the atmosphere. Use methyl red and bromcresol green as indicators; pK of methyl red is 5.00; of bromcresol green, 4.90. Normal air contains 0.03 volume per cent carbon dioxide;


distribution coefficient of carbon dioxide between water and air is 1, and the first ionization constant of carbon dioxide 3 X lO"^.

10. Bromthymol blue is added to two phosphate buffer mixtures of the same pH (or pdH), one having an ionic strength of 0.01, the other of 0.25. Does the indicator have the same color in both solutions? If not, which of the two will show a more alkaline color? What would be the effect, if an indicator base lOH were used instead of bromthymol blue?

PART II

THE POTENTIOMETRIC MEASUREMENT OF pH


CHAPTER IV

ELECTRODE POTENTIALS

1.jrhe Potential ofli Metal Electrode. According to modern views, a metal is considered to consist mainly of metal ions and free electrons of higii mobility. "When a metal is placed in -water, there is a tendency for metal ions to leave the metal and enter the liquid phase, in which they are freely soluble. However, when a metal ion leaves the solid phase, the solid is left negatively charged and the solution becomes positively charged. As a result of the large electrostatic force set up, the further transfer of metal ions is hindered and a state of equilibrium is reached in which a layer of positive ions is present in the solution near the metal surface, constituting an electrical double layer with the excess electrons left in the metal. If the metal is placed in a solution already containing some of the particular metal ions, these ions will oppose the tendency for metal ions from the metal to enter the solution. Quite generally we may say that the *metal ions are soluble in both the metal and: the liquid phase and hence that they tend to distribute themselves between the two phases. This leads in general to the establishment of an electrical double layer. Suppose, for example, that silver is placed in pure, air-free water. Some silver ions leave the metal and enter the metal-solution interface, leaving the metal negatively charged. If the solution contains a silver salt, say silver nitrate, silver ions from the solution enter the metal. In order to maintain electroneutrality of the solution, an equivalent amount of nitrate ions is dragged to the interface, forming the negative side of the double layer, while the metal becomes positively charged. The tendency of a metal to send its ions into solution is often called its electrolytic solution tension, a term introduced by Nernst.

65

56 ELECTRODE POTENTIALS

The fact that there is an electrical double layer at the interface between a metal and a solution means that there is a difference in potential between the two phases. The phase containing the excess of positive electricity is at a more positive potential than the phase with the excess of negative electricity. Thus, in our example of silver in a silver nitrate solution, the potential of the silver is positive with respect to the solution. It is in the relative change of this potential difference between a metal and a solution as a function of the metal-ion activity that we are mainly interested.

The thermodynamic relation between the potential of a metal electrode and the activity of the metal ions in solution can be derived by considering the distribution of metal ions between the metal and the solution. The distribution of uncharged molecules between two phases A and B may be treated by considering the partial molar free energies or chemical potentials HA amd IIB of the unionized solute in the two phases. For such a system not in equilibrium, the difference in chemical potential of the solute in the two phases, IIA — PB, represents the free energy per mole of solute necessary to transfer solute from phase B to phase A. When the system is at equilibrium, HA = PB-

In considering the distribution of charged particles, such as metal ions, between two phases it is necessary to consider also the electrical work necessary to transfer the charged particles from one phase to another at a different electrical potential. For metal ions of valence n, the electrical work necessary per mole in transferring metal ions from phase B to phase A is nF{\f/A — ^B), where \f/A and ^s are the electrical potentials of the two phases, and F is the faraday (96,500 coulombs) of electricity. At equilibrium,

HA + nF^/A = PB + nF^B. (1)

That is, the electrochemical potential ^ of" the solute becomes equal in the two phasesr If w£ represent byphase A- thenietal,-and by-phase-B-the solution, the difference in potential between the metal and the solution becomes

Â-H= ^p • (2)

The activity (aM"+) of the metal ion M"+ in solution is defined (G. N. Lewis) by the relation

PB = kB + RT In iau«+)B, (3)

^ For a complete discussion of chemical potential and electrochemical potential the reader is referred to F. H. MacDougall, Thermodynamics and Chemistry, Third Edition, John Wiley & Sons, New York, 1939.

THE POTENTIAL OF A METAL ELECTRODE 57

where ks is a constant at a constant temperature. In terms of the metal ion concentration [M"" ] we have

MB = A;B + Erin/[M"+]. (4)

For the activity of the metal ions in the metals a similar expression holds:

MA = fc^ + BT ln(aM«+)4. (5)

From equations 2, 3, and 5,

, , -kA + ks RT (aM»+)B ,„. l x - WB = ^ j ; In 7 r— (6)

nF nF (aM"+)A In a pure metal, the activity of metal ions (aM''+)A is a constant at a

given temperature, and r>/TT

' IAA — fe = constant -{ = In (aM"+)B- (7) nt

Equation 7 shows how the phase-boundary potential difference 4'A — fe between the metal and the solution varies with the activity of the metal ions in solution. Such a potential difference at a single phase boundary can never be measured and remains thermodynamically undefined because the values of h^ andfcs are unknown. In practice, however, one is not concerned with the absolute value of the phase-boundary potential, but only in changes in the potential difference caused, for example, by changes in the composition of the solution. The difference in potential between two electrodes can be accurately determined by measuring the e.m.f. of a cell composed of the two electrodes used as half cells. By means of a reference electrode having a constant potential, changes in the potential of another electrode can be measured. The.difference in

" potential between the two electrodes will be, called the potential of the electrode under investigation with respect ito the constant reference electrode. /

By international agreement, the normal hydrogen electrode {cf. page 59) is arbitrarily assigned a potential equal to zero at all temperatures. In practice, other electrodes of constant potential are more convenient as working reference electrodes. The potential of a given working electrode, once it has been measured with reference to the normal hydrogen electrode, can be used as a reference in measuring electrode potentials (see page 73).

With reference to the normal hydrogen electrode, the potential of a given electrode will be designated by IIH, or sometimes simply by IT. It


is evident that equation 7 may be written

n = constant' -\ = In aM^+j (8) nF

where aj^»+ is the activity of metal ions in solution. For a unit activity of metal ions, the potential of the electrode has a definite value 11°, which is called the standard or normal potential of the metal-metal ion electrode. In terms of the standard electrode potential,

NT

n = n° + —hiaMn+j (9) or in terms of metal ion concentration,

NT n = n' ' + ^ i n / [ M » + ] . (10)

nr I

Introducing the known values of the constants; R = 8.315 volt-coulombs or joules,

F = 96,500 coulombs,

and converting from natural to ordinary logarithms,

n 8.315 X 2.3026 T ,

" ' = " + .96,500 ^^»g^»"M>.^ (11) or

T 0 = 0° + 1.984 X 10-* - logio 0^"+. (12)

n

and 0 = 0" + — , logio aM"+. (13)

At a tenaperature of 25° C , T

I n = n , 0.05913 n

At a temperature of 30° C , T

I n = 0 , 0.06006

= 298

logio 0]^"+.

= 303

logid.OM''+-and n = n" 4 logid.aM'»+- (13a) n

2. Amalgam Electrodes. Iri the above discussion, the activity of the metal ions in the pure metal was set equal to a constant at a given temperature. Let us consider, however, an amalgam of a, metal less noble than mercury, such as zinc. The activity of zinc in the mercury can be varied by changing the concentration of zinc^ and equation 6 can be written in terms of the normal hydrogen electrode to give

n = n"' + g | i ( M»|)soK ^ n«" + ^ h i ^ ^ ^ ^ (14) nF (aM^+Jamalg. "•^ (aM)amalg.

THE HYDROGEN ELECTRODE 59

where n"" is the normal potential of the zinc amalgam electrode, whose value is determined by the convention adopted as to the unit activity-state of zinc in the amalgam. If the concentration of zinc is expressed in terms of its mole fraction in the amalgam, the activity of zinc becomes

where Xzn is the mole fraction of zinc, and 7jr is its activity coefficient in terms of the mole fraction.

3. The Hydrogen Electrode. Since hydrogen gas is not an electronic conductor, it.cannot be used directly as a metallic electrode. However, a suitable noble-metal electrode of large area, such as platinum coated with a layer of finely divided platinum (platinum black), acts as a metallic hydrogen electrode when immersed in a solution saturated with hydrogen gas. The expression for the potential of a hydrogen electrode may be derived by considering the following equilibria, and their equilibrium-constant expressions:

H2 (gas) ^ H2 (dissolved in liquid phase) ^ H2 (dissolved in metal).

H2 (dissolved in metal) ^ 2H.

Gaseous hydrogen is known to dissolve in certain metals such as palladium, and a small fraction of the dissolved hydrogen is dissociated into atomic hydrogen. If even an immeasurably small concentration of atomic hydrogen exists in the metal, it is perfectly valid thermodynam-ically to write the overall equiUbrium constant expression for the above three reactions:

K = — ^ ^ . (15) <^H2 (gas)

The activity of hydrogen gas may be set equal to its partial pressure in the gas phase since hydrogen behaves very nearly as an ideal gas. We then have

K = ^. I (16) PH2

The dissolved atomic hydrogen in the metal behaves like a metal in a dilute amalgam. A consideration of the distribution equilibrium between hydrogen ions (protons) in the metal and hydroxonium icais in the solution leads to the equation --

n = (n«)' + f ^ t n ^ . (17) From equations 16 and 17

n = n" + ^ In - ^ ^ . (18)

60 E L E C T R O D E POTENTIALS

But by convention n" = 0, since, for a unit hydrogen-ion activity and unit partial pressure of hydrogen, the electrode becomes a normal

»hydrogen electrode whose potential is set equal to zero at all temperatures. Therefore equation 18 becomes simply

n (19)

In practical work with the hydrogen electrode, the partial pressure of hydrogen in general will not be exactly 760 mm. of mercury. If B is the barometric pressure and p„ is the vapor pressure of water in millimeters of mercury at the working temperature, the partial pressure of hydrogen is B — p„. According to equation 19, the potential of the hydrogen electrode under the working conditions is

''' • ^ ^ ' '(20) Pv

+ -y In am-

The first term on the right-hand side of equation 20 is the correction term which must be subtracted (algebraically) from the measured hydrogen electrode potential in order to relate it to a hydrogen pressure of one atmosphere. The correction term is given for various temperature and barometric pressures in the following table.

CORRECTION IN MILLIVOLTS FOB BAHOMETBIC PBESSTJRB B (MILLIMETEBS MERCURY)

AND WATER-VAPOR PBESSUEE AT VABIOUS TEMPERATURES

Temperature, <°c.

20

25

30

-

•

B

760 760 740 730

760 750 740 730

760 750 740 730

Water Vapor Pressure, mm.

17.4

N.

\

23.5

31.5

Corrections, millivolts

0.29 0.46 0.64 0.81

0.40 0.58 0.76 0.94

0.55 0.73 0.92 1.10

OXIDATION POTENTIALS 61

With decreasing hydrogen pressure the potential of the hydrogen electrode becomes less negative (or more positive), since at reduced pressure the tendency for hydrogen ions to be sent into the solution is decreased. Therefore, if the hydrogen electrode is the negative electrode of the cell used in the measurement, and the partial pressure of hydrogen is less than 760 mm., the correction must be added (arithmetically) to the figure measured in order to relate it to the normal pressure.

EXAMPLE. The potential of the hydrogen electrode as measured against some calomel reference electrode at 25° and a barometric pressure of 740 mm. is —0.5434 volt. Then the corrected value is —0.5442 volt.

4. The Calomel Electrode. A calomel electrode consists of a layer of mercury covered with solid mercurous chloride in a solution containing chloride ions. The calomel electrode is essentially a mercury--mercurous ion electrode at which the mercurous ion activity is determined by the solubility of calomel in the chloride solution. From equation 9 the potential of the mercury-mercurous ion electrode is

n -Br , H s g . Hg2++ = n a g , Hg2++ + ^ ^^ ^Hg2++

The activity of mercurous ions is given by the activity product, Sa.p., expression for mercurous chloride,

< Hg2++*0ci~ = Sa.p,

Combining the above equations,^

nng, Hg2++ = nag. Hg2++ + 1 ^ In -2— •

or

rrO , ^ ^ 1 C ^ ^ 1 nag;Hgj++ = nag, agj+t + -r^ aioa.p. jr "^ «cr-j .

The first two terms on the right-hand side'may be combined to give Hiig, Hg2Ci2) the normal potential of the calomel electrode, which is evidently the potential of the calomel electrode containing a unit activity of chloride ions. ^We have then ,

0 'PT Hag, HgjCU - nag,"ag2Ci2 "J'y '^^ < ci---

6. Oxidation Potentials. The transfer of electrons from,one substance to another is a process of oxidation-reduction, the substance losing electrons being oxidized and the substance gaining electrons being reduced. Thus when a metal goes into solution with the formation of

62 ELECTRODE POTENTIALS i

metal ions it gives off electrons and is oxidized. On the other hand, in\ the electrodeposition of a metal the metal ions combine with electrons and are reduced:

M t^ M"+ + ne, (21)

where e represents a mole of electrons. In a more general way the process can be expressed by the reaction

Ox + net^ Red. (22)

Ox represents a substance in the oxidized form, which is called the oxidant; Red denotes the substance in the reduced form, which is called the redudant. The oxidant and reductant together comprise an oxidation-reduction system. If an oxidant exerts its oxidizing power it is transformed into the corresponding reductant, and conversely;' for example, if a metal such as silver reduces some oxidant such as ferric ions it is transformed into its oxidized form, or metal ions. In all oxidation-reduction reactions we are dealing with two oxidation-reduction systems; the electrons furnished by the reductant of one system react with the oxidant of the other system. /

Let us consider the oxidation-reduction reaction

Ag + Fe+-^+ <^ Ag+ + Fe++ (23)

If metallic silver is placed in a solution containing a mixture of ferric and ferrous salts in solution, the system will reach a condition of chemical equilibrium. The equilibrium-constant expression for the reaction is

fa^gâ^\ ^ ^ (24) \ aFe+++ /equU.

If the system has been allowed to reach equilibrium, the addition of some unattackable metal such as platiniim to the solution will not affect the state of equilibrium. I t is of interest, however, to calculate what will be the potential of a piece of noble metal in such a solution. Suppose that the silver and the platinum are connected externally by a piece of copper wire. If a difference of potential existed between the silver and platinum, a current would flow in the copper wire. If electrons flowed from the silver to the platinum, the following reactions would occur at the metal-solution interfaces. At the silver electrode, silver would be oxidized to silver ions, ^ —

Ag -^ Ag+ + e;

and at the platinum electrode, ferric ions would be reduced to ferrous

ions, Fe+++ -f- e -> Fe++


The net reaction in the solution would be

Ag + Fe+++ -^ Ag+ + Fe++ ' (23)

which is the original oxidation-reduction reaction which was allowed to reach equilibrium. Since a flow of electricity in either direction in the copper wire would cause the system to leave its state of chemical equilibrium it follows that no current could flow under such conditions, and therefore the silver and platinum electrodes are at the same potential.

The potential of the silver electrode is given by equation 9, which becomes

T>rp

HAg = n« -f — In (aAgOequii. (25)

in the equilibrium mixture. Combining equations 24 and 25, the potential of the platinum electrode (ferric-ferrous electrode) in the equilibrium mixture-is "

n . e . . p e - - = n i „ ^ , . +^lnK + ^ In (^^ (26) r t \aFe++ /equil.

The first two terms on the right-hand side are constants at a given temperature and may be combined to give a single constant n|-e++, Ke+++-Equation 26 then becomes

nFe++ Fe+++ = nê++ Fe+++ + - ^ 1 ^ 1 " ^ ^ ) (27) t \aFe++ /equU.

Equation 27 may be applied to a series of equilibrium states with different ratios of activities of ferric and ferrous ions. I t is evident that in general the potential of an unattackable metal electrode in a solution containing a mixture of ferric and ferrous ions is given by

n i j r , aFe+++ ,„„, nFe++, Fe+++ = nFe++, Fe+++ + I ^ T l^ . (28)

J t OFe++

where nFe++, Fe+++ is the normal potential of the ferrous-ferric electrode, that is, the potential of the electrode in a solution containing ferric and ferrous ions at equal activities.

More generally, the expression for the potential of an electrode at which the reversible reaction J-

Ox -t- ne ?:4 Red occurs becomes

n = n < ' 4 - ^ h i ^ ^ . (29)


From equation 29 it is apparent that the oxidation potential is deter mined by the ratio of the activities of oxidant and reductant and not by the total activity of each. Approximately, then,

nF [Red]

assuming that the activity coefficients of the oxidant and reductant are equal. I t follows that the intensity of the oxidizing or reducing action of an oxidation-reduction system is determined in the first place by n ° and also by the ratio of the concentrations of the oxidized and reduced forms. On the other hand, the capacity to exert an oxidizing or reducing action is determined by the total concentration of both, just as the buffer capacity of a buffer solution depends upon the concentration of ithe acid and its salt. Considering the electrode reactions

Sn++++ + 2e?±Sn++ and

C e + + + + + e ^ C e + + +

the expressions for the electrode potentials are, respectively,

V

and

„ n , R1' 1 «Sn++++ nsn++ Sn++++ = n^n++ Sn + + + + + " ^ !»

•*^ asn++

TTO , ^ ^ 1 «Ce++++ nce+++ Ce++++ = nce+++, Ce++++ + " ^ 1"

In many oxidation-reduction systems, hydrogen ions take part in the electrode reaction. In general, if we consider the reversible electrode reaction

Ox -1- mH+ +ne:^ Re'd + p H2O, (30)

the expression for the electrode potential becomes

n = n ° -f- —; In ^ ^ (31) X nF flRed

The normal potential n ° is the potential of the electrode when the oxidant and reductant are at equal activities and the hydrogen ions are at unit activity. Examples of reversible oxidation-reduction systems of this type are the uranyl-uranous and the quinone-hyHroquinone systems:

UO2++ + 2H+ + 2e^ U0++ + H2O and

C6H4O2 + 2H+ -f- 2e <=± C6H4O2H2.


The expressions for the oxidation potentials of these systems arw/ respectively,

TT TTO RT auo,++ a|+ nuo++ U02++ = nuo++ U02++ + i ; i ; In

2i' auo++ and

TT nO I ^^ i„ Qquinone < H+ ^^QHj, Q - ilQHj, Q + " ^ ^'^ I

^r ' hydroquinone

In many oxidation-reduction systems hydrogen ions participate in the reaction and influence the oxidation potential of the system even though the electrode reactions are not strictly reversible. For example, the oxidizing action of insoluble higher oxides may be represented by

MO2 + 4H+ + 2e ;^ 'M++ + 2H2O.

If the electrode reaction were reversible, the oxidation potential would be given by _

' TT TTO I -^ -^ 1 ' ^ H ^ nM++ MOo = nM++ MO2 + TT^ Jn

^f 0,1,1++

since the activity of the slightly soluble oxide MO2 is constant. Actually this equation does not hold rigorously because of the irreversible nature of the electrode reaction, but the oxidation potential changes rapidly with changing pH of the solution, approximately in accordance with the above equation.

In the reduction of most oxidizing anions containing oxygen, hydrogen ions participate in the reaction:

M n 0 4 - + 8H+ + 5e <^ Mn++ + fflgO.

CrzOy^ + 14H+ + 6e <=i 2Cr+++ + THgO.

The expressions for the oxidation potentials, assuming, reversible electrode reactions, are respectively 1

TT TTO , I ^ - ^ 1 ' H+ OUnOr

16^ aMn++

and

nCr+++.Cr207-"= ncr+++, CrjO,- + - ^ 1 1 RT 1„ <*H+ aCrjO

„2 QF aci+++

. . ^ J These equations likewise are not exactly followed, owing to the

irreversible nature of the electrode reactions. Unstable intermediate compounds are formed between the oxidized and reduced forms, and their activities should determine the potential instead of that of the completely reduced form. In a dichromate solution, for example, the


trivalent chromium ions apparently have no influence upon the potential. On the other hand, hydrogen ions have an enormous effect on the oxidation potential, as indicated by the equations. It is a well-known fact that the oxidizing power of a permanganate solution increases greatly with the acidity. In extremely weakly acid medium (pH about 5-6) it oxidizes iodide to iodine but it does not affect bromide or chloride. At a pH of about 3 (acetic acid medium) it oxidizes bromide but leaves chloride unattacked. CUoride is oxidized by permanganate only at much higher hydrogen-ion concentrations.

In the following table, the normal potentials of some metal-metal ion electrodes and those" of various other oxidation-reduction, systems are ^ven with reference to the normal hydrogen electrode.^

It should be reahzed that we are often dealing with oxidation-reduction systems in which both oxidant and reductant are ions of a high-valence type. The ionic strength of the solution then has a marked effect upon the oxidation potential. Let us consider the following two systems:

Ce++++ + e^Ce+++ and

Fe(CN)6^ + e ^ Fe(CN)6^.

The oxidation potential of the cerium system is given by:

nce4+,.ci+ = n?;e4+, Ce3+ + " ^ hi ,Q^3+J 3

in which f^ and /s denote the activity coefficients of the quadrivalent and the trivalent cerium ions. The.activity cotefB.cient oi the quadrivalent ones decreases much more with increasing ionic strength than that of the trivalent, and, therefore, the oxidation potential of the ceric-cerous system decreases with increasing ionic strength. It is easily shown that the reverse is true for the oxidation potential of the ferri-ferrocyanide system. It is evident, then; that the n° values are of limited practical significance, since the oxidation potential of a system in which the ratio of oxidant to reductant is constant may vary considerably with the ionic strength. Oxidations or reductions are usually carried out in solutions of relatively large ionic strengths, in which the activity coefficients cannot be calculated with^^rearsonable degree of accuracy. In such cases it is better to have Available values of oxidation potentials in media of various electrolytes of differing ionic strength.

' For a mbre complete list see W. M. Latimer, The Oxidation States of the Elements and Their Potentials in Aqueous Soluiions, Prentice-Hall, New York, 1938.

/ X!


SELECTED LIST OF OXIDATION POTENTIALS (AGAINST N HYDROGEN ELECTRODE)

OF SYSTEMS WHICH ARE OF ANALYTICAL INTEREST

Reaction

Zn ?± Zn++ + 2e S= + Hg ; i HgS + 2e Or ^ Cr++ + 2e 2CN- + Au ?± Au(CN)2- +e Fe ^ Fe++ + 2e Eu++ <z± EU+++ + e Cr++ f± Cr+++ + e Cd ^ Cd++ + 2e Cb™ f± Cb^ + 2e H2Se ?=± Se + 2H+ + 2e 2Cu + 2 0 H - 5=i CujO + H2O + 2e Tl ?± T1+ + e Ag + 2CN- ^ Ag(CN)2- + e Co ?sCo++ + 2e Ni «:± Ni++ + 2e V++ ^ V+++ + e Cu + I - ?=i Cul + e Ag + I - :Fi Agl + e Sn ?i Sn++ + 2e Pb ?:i Pb++ + 2e H2 ?:* 2H+ + 2e Ti+++ + H2O ?=± TiO++ + 2H+ + e 28203= ?± S406= + 2e Sn-<-+- f± Sn++++ + 2e Re + 4H2O ->• Re04" + 8H+ + 7e Cu+ ^ Cu++ + e 2Hg + 2C1- :p± Hg2Cl2 + 2e V+++ + H2O <^ V0++ + 2H+ + 2e 2Ag + 2 0 H - ?i Ag20 + H2O + 2e Fe(CN)6" ?=* Fe(CN)6" + e 4 0 H - ?± O2 + 2H2O + ie U0++ + H2O ^ UO2++ + 2H+ + 2e { Cu ?± Cu+ + e I 2 1 - 5:± I2 + 2e Mn04= ^ MnOr + e ; 2SbO+ + 3H2O ^ Sb206 + 6H+ + 4e H2O2 ?± O2 + 2H+ 4- 2e 1 Mo(CN)6- ^ Mo(CN)s" +.e ' ,' Se + 3H2O ?± H2Se03 + 4H+ + 4e ^ Fe++ <^ Fe+++ + e 2Hg <^ Hg2++ + 2e Ag ?=> Ag+ + e

I IH in Volts

- 0 . 7 6 - 0 . 7 0 - 0 . 6 - 0 . 6 0 - 0 . 4 3 - 0 . 4 3 - 0 . 4 1 - 0 . 4 0

-0.37 {3M H2SO4) - 0 . 3 6 - 0 . 3 5 - 0 . 3 4 - 0 . 2 9 - 0 . 2 8 - 0 . 2 5 - 0 . 2 - 0 . 1 9 - 0 . 1 5 - 0 . 1 4 - 0 . 1 3

0.00 +0.10 +0 .1 +0.15 +0.15 +0 .17 . +0.27 +0.31 +0.35 +0.36 +0.41

Ca+0.42 +0.52 +0.53 +0.54 +0.64 +0.68 +0.73 +0.74 +0.77 +0.80 +0.80

68 E L E C T R O D E POTENTIALS

SELECTED LIBT OF OXIDATION POTENTIALS (AGAINST N HYDROGEN ELECTRODE'

OF SYSTEMS W H I C H A R E OF ANALYTICAL INTEREST (Continued)

Reaction

Os + 4H2O ?=> Os04(s) + 8H+ -+• 8e Hg 5=±''Hg++ + 2e 3 0 H - ^ HO2- + H2O + 2e Hg2++ ^ 2Hg++ + 2e NO + 2H2O ^ NO3- + 4H+ + 3e V0++ + 3H2O ?:* V(0H)4+ + 2H+ + e TeOaCs) + 4H2O f± HeTeOe + 2H+ + 2e 2Br- ?± Br2 + 2e JI2 + 3H2O ?± IO3- + 6H+ + be Pt ^ Pt++ + 2e 2H2O ?± O2 + 4H+ + 4e Mn++ + 2H2O ?± Mn02 + 4H+ + 2e T1+ ?± TI+-H- + 2e AU+ <^ AU+++ + 2e PdCU= + 2CI- ?± PdCl6= + 2e 2Cr+++ + 7H2O ^ CrzOv" + 14H+ + 6e 2CI- ^ CI2 + 2e Gl- + SHaO f± CIO3- + 6H+ + 6e Pb++ + 2H2O ?i PbOa + 4H+ + 2e Mn++ ^ Mn+++ + e IO3- + HjO ^ IO4- + 2H+ + 2e Mn++ + 4H2O <=i Mn04- + 8H+ + 5e iBn + 3H2O <=± BrOs- + 6H+ + 5e Mn02 + 2H2O ?± Mn04- + 4H+ + 3e Ce+++ <=i Ce++++ + e Pb++ ?± Pb++++ + 2e . Co++ ?± Co+++ + e Ag+ T± Ag++ + e

I I H in Volts

+0.85 +0.85 +0.87 +0.91 +0.99 +1.00 +1.02 +1.09 +1.20 ^l.-i +1.23 +1.24 +1.25 +1.29 +1.29 +1.36

- + 1 . 3 6 +1.44 +1.46 +1.51 +1.51 +1.52 +1.52 +1.59 +1.60 +1.69 +1.84 +1.98

For a given medium, say 1IV sulfuric acid, the expression for the oxidation potential then becomes: ''x

[Ox] - n = n'

0/ + —1 "^ nF "" [Bed]'

where 11°' is the formal oxidation potential which is equal to the oxidation potential of the system in the particular medium when the concentration of the oxidant is equal to that of the reductant.'~These foraial oxidation potentials are of more practical impdrtance than the normal potentials w jich refer to activities.

From the expression of the formal oxidation potential it is evident that the oxidation potential of a system can be varied greatly when a

THE ELECTROMOTIVE FORCE (E.M.F.) OF GALVANIC CELLS 69

substance is added which forms a complex with the oxidant or the reductant, or which forms complexes of different stabilities with both the oxidant and reductant. Fluoride, for example, forms a stable complex with ferric ions and thus decreases the oxidation potential of the ferric-ferrous system considerably.

6. The Electromotive Force (E,M.F.) of Galvanic Cells. In the above discussion we have restricted ourselves to the consideration of the potentials of single electrodes. Sometimes it is desirable to calculate thermodynamically the e.m.f. of galvanic cells containing several metal-solution interfaces or cells with liquid junctions (interfaces of two solutions in contact). For such cells a more general thermodynamic treatment is necessary.

Let us consider, for example, a cell made up of a normal silver elec^ trode and a normal ferric-ferrous electrode which will be written

Ag I Ag+ (a = 1) II Fe+++ (ai), Fe++ (ai) [ Pt

A single vertical hne indicates a phase boundary at which a potential difference occurs; a double vertical Une indicates either that a liquid-junction potential between two solutions has been eliminated (see page 71) or that the value given for the e.m.f. of the cell does not include the liquid-junction potential. The e.m.f. of the cell is given by the difference between the electrode potentials, namely,

E = n?.e++ Fe++ - nig.

If the values of the electrode potentials are known, the magnitude of the cell e.m.f. can be calculated, and it is unnecessary to give a sign to the e.m.f. since we know that the electrode having the more positive potential with respect to the normal hydrogen electrode is the positive electrode of the cell. Thermodynamically, howevei', it is convenient to adopt a convention regarding the sign of the cell e.m.f. in order to enable the free energy change of the cell reaction to be related to the e.m.f. of the cell.

In general, suppose that the passage of n faradays of electricity through a cell causes the following reversible reaction to occur:

aA + hB + ••• :f±pP 4-gQ+ •••. (32)

The cell, by convention, is written in such a way that reaction 32 proceeds from left to right when n faradays of positive electricity flow through the cell from left to right. The change in free energy, A^


associated with the cell reaction in the direction written is

A^= - RTlaK + RTlri "^ " ^ ' ' ' , (33) OA O B • • •

where K is the equiUbrium constant of the reaction. When the reaction takes place reversibly in a galvanic cell, the

decrease in free energy is equal to the electrical work done by the cell, that is,

A^= — .nFE, (34)

where nF is the number of coulombs of electricity involved in the reaction of a.moles of A, etc., as given in equation 32, and E is the e.m.f. of the cell. If the cell reaction takes place spontaneously from left to right, the free energy of the system decreases and A ^ h a s a negative sign. From equation 34, the e.m.f. of the cell is taken to have a positive sign if the cell reaction occurs spontaneously from left to right when the cell is short circuited. By the convention adopted for the direction in which the cell is written, E is taken as positive if positive electricity flows inside the cell as written from left to right when the cell is short circuited.

From the point of view of an observer outside the cell, positive electricity flows from the positive to the negative electrode outside the short-circuited cell, and hence the e.m.f. of a cell is given a positive sign if the electrode having the more positive potential is the right-hand electrode in the cell as written.

In order to adopt the same convention for the e.m.f. of a cell as calculated from the potentials of the two electrodes, it is necessary to subtract the potential of the left-hand electrode from that of the right-hand electrode of the cell as written. Thus

E = Hr - Hi. (35)

Combining equations 33 and 34, we have

RT RT a^p 4 -—- In A — In ——;— nF nF al 4 -

^ = — In Z - — In : f - ^ - , (36)

which is the general expression for the e.m.f. of a reversible cell. The e.m.f. of a cell in which all substances entering in the cell reaction are present at unit activity is represented by E°, and'is called the standard or normal e.m.f. of the cell. From equation 36 it is evident that

B'^ = ~;lnK, (37)

LIQUID-JUNCTION POTENTIAL 71

and therefore equation 36 may be written

RT tP n1 ,

^ = °-5rln^f^- (38)

Let us consider the application of equation 38 to a cell composed of a normal hydrogen electrode and a reversible metal-metal ion electrode,

H2 (1 atm.) I H+ (o = 1) II M"+ (a = aM»+) | M.

The cell reaction correspondiag to the passage of n faradays of positive electricity from left to right inside the cell is

^ H2 (1 atm.) + M"+ (a = aM"+) -^ TiH+(a = 1) + M.

The e.m.f. of the cell, from equation 38, is

since the hydrogen gas, the hydrogen ions, and the metal are at unit activity. From equation 35,

E° = nSi.M"+ - n&,.H+-

But, by convention, IIHJ, H+ = 0. Hence '

E = uli,M'^ ^ In - — nF aM"+

or RT

-B = HM. M"+ + ^ 7 In OM-H-. (39) Tlr

Comparing equations 9 and 39 it is evident that the potential of a metal-metal ion electrode, and, quite generally, the potential of any reversible electrode, is equal to the e.m.f. of the cell composed of the normal hydrogen electrode written as the left-hand electrode and the particular electrode as the right-hand electrode.

7. Liquid-Junction Potential. So far we have assumed that the e.m.f. of a cell built up trom two half cells is determined only by the difference in potential at both electrodes. This is true only in an approximate way, as a potential difference develops at the junction whenever two solutions of different composition are brought together. The principal cause of the potential difference was attributed by Nernst to unequal rates of diffusion of ions across the junction. The velocity with which ions move under a potential gradient of 1 volt per centi-

72 ELECTRODE POTENTIALS f

meter is expressed by the so-called ion mobility. Hydrogen and hydroxyl ions distinguish themselves by a very high mobility as compared with other ions. (See table, page 119). Suppose that we brings a solution of hydrochloric acid of concentration ci in contact with a similar solution of concentration C2, Ci being larger than C2. Then on account of their high mobility the hydrogen ions have a tendency to diffuse more rapidly from ci to C2. The dilute solution becomes charged positively with respect to the concentrated solution, with the result that the rate of diffusion of chloride ions is increased and the rate of diffusion of hydrogen ions is decreased until the two rates of diffusion become equal. A stationary state is soon reached at which hydrogen and chloride ions move at equal rates toward the dilute solution, in the form of an electrical double layer of hydrogen and chloride ions. The potential difference between the two solutions at the stationary state is called the liquid junction or diffusion potential.

In simple systems the liquid-junction potential may be calculated thermodynamically. Consider the liquid junction

HCl (ci) I HCl (C2)

which was discussed above. The passage of 1 faraday of positive electricity from left to right across the liquid junction results in the transfer of t^+ moles of hydrogen ions from left to right and the transfer of <cr moles of chloride ions from right to left. The equation for the process at the jimction is

<H+ H+(ci) + tci- C I - fe) -^ «H+ H+(C2) + tci- CI-(ci).

The equilibrium constant of the reaction is evidently unity. Therefore E° = 0, and the e.m.f. at the liquid junction is

F L(aH+)iJ L(acr)2J

or s P RT\. . (aH+)i ^ , , («ci-)i1 -

F L (aH+)2 (aci-)2J

If it is assumed that in each solution the hydrogen ions and the chloride ions have equal activity coefficients

(aH+)i = («ci-)i = / i e i ,

(aH+)2 = («cr)2 = /2C2,

^^^'^ ,RT^ hex B . = ( « H - - « c r ) y - l n ^ -

THE USE OF REFERENCE ELECTRODES ' 73

The liquid junction e.m.f. has a positive sign here if Ci is greater than C2. By the sign conventions given above, this means that the right-hand solution (C2) is positively charged with respect to the left-hand solution.

The above equation is valid for any two different solutions of the same uni-univalent electrolyte in contact. It is evident that, if the trapsference numbers of the cation and anion were equal (equal ion mobilities), the liquid-junction potential would be zero. Such a condition is closely approximated by potassium chloride, since the mobilities of the two ions are nearly the same. In order to eliminate liquid-junction potentials a saturated solution of potassium chloride is often used to make electrolytic contact between the hquids in two half cells. The presence of a very high concentration of potassium chloride at the two ends of the salt bridge tends to diminish the junction potential at each

"end of the bridge, since the potassium and chloride ions dominate the conducting of the current. Moreover, the salt bridge introduces two

-opposing liquid junctions which counteract each other and make the total liquid-junction potential small. As long as we do not work in strongly acid or alkaline solutions (pH between about 3 and 11), the liquid-junction potential will be extremely small, if partially eliminated by the saturated-salt bridge. However, it should be remembered that the liquid-junction potential is not completely eliminated by the saturated-salt bridge, and in measurements of high precision it is preferable to have liquid junctions of a simple nature which can be included in the calculation of the e.m.f. of the cell.

8. The Use of Reference Electrodes (Standard Half Cells). In the discussion of the hydrogen electrode (paragraph 3, page 59) it was mentioned that the potential of a hydrogen electrode is given by

n = HH = 0.0591 log aH+ (25°),

where a^+- is the activity of hydrogen ions in the solution to be tested; Therefore [

However, the normal hycirogen electrode is'impracticable as a working electrode. Its acidity is so high that the, hquid-junction potential at the boundary between the strongly acid solution and the liquid with a larger pH is certainly not eliminated by the saturated-salt bridge. Therefore, instead of the normal hydrogen electrode, some other standard half cell is used as a working reference electrode; as a rule, some kind of calomel electrode (discussion, see page 61) is taken. To avoid confusion


with regard to the sign it is convenient to use a diagram as given in Pig. 4. In this figure the normal hydrogen electrode has a potential of zero or

is negative by an amount equal to Ilo.with'v respect to the calomel electrode. Experimentally, the potential of the unknown He against the calomel electrode is measured and is negative.

. It is readily seen that HH is equal to the nu-Do- merical difference between Uc and ITo, that

is, I IIH I = I lie I — I HO j . Since IIH is negative when aH+ is smaller thanl, we can write, instead of equation 40,

+ 0 - T

nK<

>'

•N HjE paH. = n d - I no 0.0591

(41)

The value of IIo has been determined for various standard half cells at different temperatures. The influence of the temperature, of course, is

FIG. 4. determined not only by the temperature coefficient of the standard half cell but also by that

of the normal hydrogen electrode. The data are given on page 88.

PROBLEMS ON ELECTROMOTIVE FORCE

1. Define the normal hydrogen electrode; the normal silver electrode, normal ferric-ferrous iron electrode.

2. What is the e.m.f. of the cell:

Cu 1 CuS04 (1 M) II CdS04 (1 M) | Cd,

assuming that the activities of the ions are the same as their concentrations?

3. Derive the thermodynamic expressions for the e.m.f. of the cells:

Hu (i atm.), Pt I HCI (ci), Hg2Cl2 (s) | Hg | HgaCla (s), HCl fe) | Pt, Ha (1 atm.)

Na, Hg (xi) I NaBr (ci), AgBr (s) i Ag | AgB>(s), NaBr (ca) | Na, Hg (xa).

4. Calculate the potential diSerence at the liquid junctions at 25° C

HCl (0.1 N) I HCl (0.01 N)_

KCl((3.1N)\KCliOMN) The transference numbers of the cations are respertively-O.'SSâmi 0.49 in HCI and KCl. ^ X

5. Calculate the e.m.f.'s of the cells at 25°:

Ha (1 atm.), Pt | HCl (0.1 N) \\ HCl (0.01 N) \ Pt, Hj (1 atm.)

H2 (1 atm., Pt) I HCl (0.1 N) \ HCl (0.01 N) \ Pt, Hj (1 atm.)

PROBLEMS ON ELECTROMOTIVE FORCE 75

The activity coefficients of both ions are 0.80 and 0.90 in 0.1 AT HCl and 0.01 N HCl, respectively. tH""" = 0.83 in both solutions.

6. What is the equiUbrium constant K of the reaction:

Cd + Cu++ ?± Cu + Cd++

[Cd++] [Cu++]

K

if both metallic copper and cadmium are present in the solid state? The normal potential of copper is +0.3448 volt; of cadmium, —0.40 volt.

7. Calculate the equilibriimi constant of the reaction:

Q + 2H+ + 2Ag ^ QH + 2Ag+

The normal potential of the quinhydrone electrode is 0.6990 volt; of silver, 0.7995 volt.

8. The equilibrium constant of the reaction

Fe++ + Ag+ ^ Fe+++ + Ag

is 7.03,. Calciilate the e.m.f. of the cell

Pt I Fe+++ (o = 1), Fe++ (a = 1) j( Ag+ (a = 1) | Ag.

9. A mixture of potassium terrocyanide and potassium ferricyanide is diluted 100 times. How does the oxidation potential change: (a) if the ratio of the activity coefficients of the ferro- and ferricyanide ions remains unchanged; (b) if this ratio increases 30 times?

10. Give a quantitative expression of the oxidation potential of the following systems, and show what the influence of the hydrogen-ion concentration is:

KMn04 -> Mn++; Ce"" ^ Ce™; Fe™ -> Fe^^; PbOa -» Pb++;

Quinone -> Hydroquinone; Fe(CN)6^ -^ Fe(CN)6^.

11. Hydrogen fluoride forms a stable complex with ferric ions. What is the effect of HF upon the oxidation potential of a mixture of ferrous-ferric iron?

12. The free energy change of the reaction

2H2 (1 atm.) + O2 (1-atm.) ^ 2H2O (Uq.) is —113,000 calories. |

Calculate the e.m.f.'s of the following cells, assuming that both the hydrogen and oxygen electrodes are reversible:

H2 (1 atm.), Pt 1 0.1 N HCl ] O2 (1 atm.) Pt

H2 (0.1 atm.), Pt I 0.1 N HCl | O2 (0.1 atm.) Pt

What would be the effect of replacing the 0.1 N HCl by 0.1 iV NaOH?

CHAPTER V

THE TECHNIQUE OF POTENTIOMETRIC MEASUREMENTS

1. Principle of the Compensation Method for the Determination of the Electromotive Force of a Cell. As there are no reliable or simple means for measuring the potential of a single electrode, it is always measured against some other standard electrode (standard half cell). By connecting the two electrodes, a cell or an element is built up the e.m.f. of which can be measured. If the terminals of the cells were connected with a sensitive voltmeter, no exact results could be expected,

FIG. 5. Principle of the potentiometer. S, storage battery.

AB, slide wire. C, sliding contact.

G, galvanometer. Ex, cell of unknown e.m.f.

as the cell, would send a current through the system. - This current would cause chemical reactions to occur at both electrodes, and on account of this polarization the e.m.f. of the cell would changeûring the measurement. Therefore, the procedure usually employed is the Pog-gendorf-Du Bois-Reymond method, by which the e.m.f. to be measured is balanced by an opposed but known electromotive force. When the unknown is balanced, no current can flow through the ce l l^h ich can be indicated by a " null-point " instrument like-a-galvaffometer.

The principle may be illustrated by an arrangement shown in Fig. 5. JS is a battery having an e.m.f. greater than that of the unknown cell X the e.m.f. of which is to be determined. AB is a sUde wire of strictly uniform cross section throughout its length, connected to the terminals *- 76''

EQUIPMENT FOR POTENTIOMBTEIC MEASUREMENTS 77

of the battery by thick copper wires SA and SB of negligible resistance. Hence there is a uniform fall of potential from A to B. The contact C, which slides along the wire AB, is so connected to the unknown element X that the positive pole of the battery corresponds to the positive pole of X. The negative pole of X is connected to B, the negative pole of the battery. In the circuit CXGB there are two different electromotive forces, Ec-B between C and B, and that of X, which furnish current in opposite directions. C is moved along AB until the null-point instrument G indicates that no current is flowing through CXGB. As the sum of the electromotive forces is then zero, the e.m.f. of X is equal to Ecs- Since SA and SB have a negligibly small resistance, Eji-B is equal to the electromotive force of the battery i Batt.- Then

F - ^ ^ F ^C-B — - J D • •'^Batt.

CB/AB represents the ratio between the resistances of BC and AB. When we are working with a slide wire of uniform cross section such as is used in conductivity work, this ratio is equal to that of the lengths of CB and AB. If the total length of AB is equal to 1000 mm. (or other units of length), then Ex, representing the e.m.f. of X, is:

^x — T ^ ^Batt . j (1)

where CB represents a length expressed in the same units. 2. General Eqtiipment for Potentiometric Measurements. Storage '

Batteries. The storage battery or accumulator is a convenient and reliable source of current for the potentiometer. When it has been I discharged to an e.m.f, below 1.9 volts it must be recharged. It should be remembered that a freshly charged accumulator changes its e.m.f.

"a little during the first minutes of its discharge. Therefore it is fecom-^ mended that the accumulator be allowed to discharge for a period of about 10 minutes through a resistance of 1000-5000 ohms before it is used with the potentiometer system. As the battery furnishes some current during the measurements, it is advisable to determine ^Batt. a* the beginning and the ehd of a set of readings. The e.m.f. should not have changed more than 0.1 millivolt. The same holds if dry cells are used instead of an accumulator.

Standard Cells. For the calculation of Ex (equation 1, paragraph 1) it is necessary to know JE'Batt.- This is determined by switching X outôf the circuit and putting in its place a standard cell of known e.m.f. The Weston cell is commonly employed as a standard. The construction of

78 THE TECHNIQUE OF POTENTIOMETRIC MEASUREMENTS \

this cell is illustrated in Fig. 6. The "normal" Weston cell contains an\ excess of cadmium sulfate crystals so that it is saturated at all temperatures jit which the cell is used. In the "unsaturated" cell which is often used, the concentration of cadmium sulfate in solution is that of a saturated solution at 4° C. The positive pole of the cell is of pure mercury (purified by nitric acid and redistilled in a vacuum), and is covered with a layer of a paste of mercurous sulfate intimately mixed with mercury. This mixture can be prepared electrolytically. The negative pole is composed of an amalgam containing 12.5 per cent of cadmium by

FIG. 6. Weston standard cell.

weight. The amalgam is formed by heating pure mercury over a steam bath and stirring in the pure cadmium. It can also be prepared elec-trolytically.i

The temperature coefficient of the "saturated" Weston cell is extremely small.

E.m.f. = 1.01830 + 0.00004 (20 - t")

between .15° and 25° C. Null-Point Instruments. As a rule a galvanometer is used as a nuU-

ôint" instrument; it is a current-indicating instrument which usually consists of a coil of îre in the magnetic field of a strong permanent magnet. This coil is introduced into the circuit in which the presence or absence of current is to be detected. A current flowing through the turns of the suspended coil produces a-magnetic field which by its interaction with the field of the permanent magnet tends to turn the coil so that it will embrace the maximum number of jines of force. Depending upon the kind of work, galvanometers of varipusTîstances are used. The sensitivity is usually expressed in terms'of the resistance through which a unit voltage will cause a given deflection. ,This is a megohm

' Cf. Ostwald-Luther, Physiko-chemische Messungen, Fifth Edition, 1930; and W. M. Clark, The Determination oj Hydrogen Ions, Third Edition, page 342. •

THE POTENTIOMETER SYSTEM 79

sensitivity and is defined as the number of megohms (million ohms) of resistance which must be placed in the galvanometer circuit in order that from an impressed e.m.f. of 1 volt there shall result a deflection of 1 mm. For most potentiometric titrations carried out according to the classical method the small portable galvanometer furnished by the Leeds and Northrup Company will serve the purpose (Fig. 7). Its sensitivity is of the order of 1 megohm. For more accurate work the authors prefer the so-called portable lamp and scale galvanometer of Leeds and Northrup

FIG. 7. FIG. 8.

(Fig. 8), which is about 20 to 50 times more sensitive than the type in Fig. 7, and is highly recommended for accurate measurements of ordinary cells. Other galvanometers which serve various purposes are described in the Leeds and Northrup Company catalogs.

The capillary electrometer,^ which is a volt-indicating instrument, is not so easy to manipulate as the galvanometers, and at present it is relatively seldom used for the kind of work imder discussion.

If the resista;nce of the ceil to be measured is extremely high (as it is with the glass electrode, see page 100), the ordinary type of galvanometer is not sensitive enough to serve as a null-point instrument. Resort must then be made to the binant or quadrant electrometer.

3. The Potentiometer System. In the discussion of the principle of the potentiometric method (paragraph 1, page 76), Afi represents a slide" wire as used in conductivity work. I t renders good service in potentio-metric-titration work, and it is highly recommended to beginners for getting better acquainted with the principleSjOf the method. By placing a variable resistance- (rheostat) between one of the ends of the bridge and the battery and swit'ching in the standiard cell, it is easy to adjust Ejie^n. at 2 volts. ^ ^

Then according to equation 1, paragraph 1, we have:

E. = CB

1000 • E Batt.

CB

1000 2 volts,

' CJ. Kolthoff and Furman, Poterdiometric Titrations, 1931.

80 THE TECHNIQUE OF POTENTIOMETRIC MEASUREMENTS

FIG. 9. Principle of the potentiometer.

where CB is the length read on the slide wire. Instead of using the stretched wire it is more convenient to have it wound on a drum of hard rubber or other insulating material. These wound slide wires are marketed in various forms.

At present the so-called potentiometers are mainly used in potentio-metric work. From the pedagogical point of view they have the disadvantage of indicating e.m.f. values without forcing the student to understand the principle. On the other hand, the convenience of these

Battery iustrumcnts is so great that i|i|i 1 1 _ they are generally appUed. The

so-called s tudent ' s potentiometer, as suppUed by the Leeds and Nor thrup Company, is of sufficient accuracy for most work. There are more accurate instruments, bu t , on account of the uncertainty caused by the liquid-junction potential , readings more accurate than 0.1

milhvolt often have no actual significance. The principle of the potentiometer is illustrated in Fig. 9.

AB is a set of 22 coils each of 100 ohms resistance, in series with which is an extended sUde wire BC of 100 ohms resistance. One contact point D is so arranged t ha t i t can make contact between any two of the 100-ohm coils, and a second point E can be brought into contact with any point on the wire. The scale of the extended wire is divided into 1000 equal pa r t s . The terminals of the total resistance -of 2300 ohms are brought out to a pair of binding posts. A second pair of binding posts leads to the sUding contact. If by changing D and E the e.m.f. of X{Ex) is exactly balanced, we have :

_ BE

DE represents the resistance of DE, and AC that of AC. In our figure AC is equal to 2300 ohms; D ^ is read directly on the instrument. If the e.m.f. of the battery is so regulated by some kind of a resistance that it is equal to 2.3000 volts, we ha,ve: ^

DE _ DE ^ E^ - J^ iiBatt. - 2300 2.300 =' 'DS millivolts.

Under these conditions, therefore, the potentiometer indicates directly the e.m.f. of the unknown after the system has been balanced. In order

THE POTENTIOMETER SYSTEM 81

to regulate E^M. exactly to 2.3000 volts the normal element is switched in by means of a double-throw switch in place of the cell X. At 20° the e.m.f. of the saturated normal cell is 1.0183 volts. The potentiometer switches are set to correspond to the voltage of the standard cell {DE= 1018.3), and the regulating resistance Kheo is adjuste'd until the galvanometer indicates that the circuit is currentless. Then:

1.0183 = ^ £ ? B a t t 2300

^Batt. = 2.3000 volts. A sketch of the student's potentiometer is given in Fig. 10. The

variable resistance Rheo is the resistance box. For it two rough rheostats may be substituted, one „ 3„, xi...„ '

•' .. ) Ba.+Eheo. +E.M.P.-

having a resistance of 1000-2000 | Q A ,i^c f, ohms, the other of 10 to 20 ohms. (Fig. 1-1.)

To'make a reading, set the potentiometer switches to correspond to the voltage of the standard cell, and adjust first the rheostat of high resistance roughly and make the finer adjustment with the rheostat of small resistance. When the system is balanced, the e.m.f. between A and C (Fig. 10) is 2.3000 volts. To make a reading of the unknown proceed as follows: Reverse the double-throw switch so that the e.m.f. to be measured is brought into the circuit. Now manipulate

FIG. 10. Leeds and Northrup student's potentiometer.

Hh 1000 Jl • — ' 10 a — •

1

1 I to PotenKometer

FIG. 11. J-

the two dials of the potentiometer until no current flows through the galvanometer. The unknown e.m.f. (Ex) is then read off directly. In accurate work it is advisable to adjust ^Batt. after each reading. Two dry cells or two accumulators may serve for a battery.


Battery

<^^-0-6

In work where the highest accuracy is not required, as in potentio-metric titrations, the e.m.f. of the unknown can be read directly on a, millivolt meter by means of the following device (Fig. 12): AB is an ordinary rough rheostat of about 1000-2000 ohms; CD is a similar one

of about 10-20 ohms. Adjustment is made by changing E and F until no current flows through the galvanometer. Then X is switched out, and by means of a double-throw switch the millivolt meter V is switched in. The e.m.f. of X is then read directly on V without any standard cell at all. ,

Various other slight modifications of the potentiometer system have been proposed, without, how- , ever, introducing distinct advan-above. It has been mentioned in the first

Switch

1 X

FIG. 12.

tages over the methods discussed 4. The Electron-Tube Method.

paragraph of this chapter that in making e.m.f. measurements of a cell every precaution must be taken not to draw any more current from the experiniental cell than is absolutely unavoidable, on account of polarization phenomena. In observing the deflection of the galvanometer it therefore is essential just to tap the key for the. shortest period in which the observation can be made. By means of the electron tube it is possible to make observations without extracting any appreciable amount of current from the cell, though the cell is left continuously in the circuit; therefore, the vacuum tube is of advantage in continuous-reading potentiometric devices, especially in potentiometric titrations. Moreover, it has another distinct advantage where the resistance of a cell is so large that galvanometers of the ordinary type are riOt sensitive enough. ^^

Goode' first apphed vacuum-tube circuits to potentiometric titrations.^ ^ a n y improvements have since been made as vacuum-tube technique has advanced. Garman and Droz * and Willard and Hager designed direct-reading vacuum-tube voltmeters operated from 110-volt power lines. In these circuits the e.m.f. is read directly on a-calibrated microammeter or galvanometer in the circuitr~~Snuth and Sullivan

3 K. H. Goode, / . Am. Chem. Soc, 44, 26 (1922);i7, 2483 (1925). * R. L. Garman and M. E. Droz, Ind. Eng. Chem., Anal, Ed., 7, 341 (1935). 5 H. H. Willard and O. B. Hager, Ind. Eng. Chem., Anal. Ed., 8, 144 (1936). ' G. F. Smith and V. R. Sullivan, Electron Beam Sectometer, G. Frederick Smith

Chemical Company, 1936. ^

THE ELECTRON-TUBE METHOD 83

eliminated the necessity for a microammeter or galvanometer by introducing an electron-ray tuning indicator such as is common in modern radio receiving sets. By noting the change of the shadow angle of the indicator, the change in the e.m.f. of a cell during a potentiometric titration is determined visually. A somewhat simplified circuit based on the same principle has recently been designed by Serfass.'

Although the power-Une-operated circuits are convenient in n o t | requiring batteries, the circuits are somewhat complicated by t h e ' necessity of compensating for line voltage fluctuations. A simple , battery-operated direct-reading vacuum-tiube"voltmeter of low current*

^ _ ^ ^ Socket <yy-\A/ Connections

Pin Bi B2

FIG. 13. Electron-tube Circuit of Garman and Droz.

Bl lOOO-ohm uniform volume control. ^2 2000-ohni, 0.5-watt resistor. Bj 2500-ohm, 0.5-watt or SOOO-ohm semi-

' variable resistor. .B4 _50,000Tohm_ volume .control with switch

cover plate for S2.

Si S.P.D.T. switch. M 0-50 microamperes. Bl l.o-volt dry cell. Bz 45-volt battery. 1,2 unknown e.m.f..

consumption has been designed by Garman and Droz * and commercially introduced by the Leitz Company as the "Electro-titrator."

The circuit diagram is shown in Fig. 13. I t consists of a pentagrid converter tube 1A7G in a Wheatstone-bridge circuit. The arms of the bridge are (1) the effective cathode-to-plate resistance, (2) the plate-load resistance R3, (3) the effective cathode-to-grid-2 resistance, and (4) the load resistance R^. The microammeter M reads the condition of balance of the bridge. Bi controls the sensitivity of the meter and hence

' E. J. Serfass, Ind. Eng. Chem., Anal. Ed., 12, 536 (1940). s R. L. Garman and M. E. Droz. Ind. Eng. Chem., Anal. Ed., 11, 398 (1939).


that of the voltmeter as a whole. Grid 4 controls the electron stream by apportioning the current between grid 2 and the plate. A negative potential on grid 4 causes an increase in the plate current and a simultaneous reduction of current in grid 2. The degree of unbalance of the bridge is thus almost doubled. In using the instrument as a voltmeter, switch Si is thrown to the right (Fig. 13) and Ri is adjusted until the meter reads zero for zero external'e.m.f. Si is then thrown to the left to read the e.m.f. of the imknown cell connected with the negative terminal going to grid 4. The meter readings are directly proportional to the unknown e.m.f. and may be calibrated with a suitable cell of known e.m.f. By varying resistor R4, the sensitivity of the meter can be varied over wide limits. "

The instrument may also be used as a titrimeter for potentiometric titrations. For this purpose, the electrode which increases in negative potential (with respect to the other electrode of the titration cell) is connected to post 1. The meter is adjusted to read zero at the beginning of the titration by throwing switch Si to the left and adjusting Ri. The sensitivity is adjusted so that the meter just deflects over the full range during the complete titration.

5. Reference Electrodes. Calomel electrodes are generally used as reference electrodes. A calomel electrode is one in which mercury and calomel are covered with a potassium chloride solution of definite concentration. A layer of pure mercury is placed on the bottom of the electrode cell, and upon this is put a layer of mercury and calomel paste and the potassium chloride solution. The mercury and calomel are intimately mixed by rubbing them together in a mortar so that the mercury is in a very finely divided state, and the mixture has a black or grayish black appearance. The mixture is washed several times with the potassium chloride solution with which the cell is filled. The intimate mixture of mercury and mercurous chloride can be prepared electrolytically-according to Lipscomb and H u l e t t ' o r Erving.^" The potassium chloride solution with whiqh the electrode vessel is filled must be saturated with calomel by shaking the chloride solution with calomel or the mercury-calomel paste for some time.

Various forms of calomel electrodes are described in the literature; some are shown in Fig. 14. '

Model III is a wide-mouthed bottle which is well adapted for potentiometric titrations. Through one of the two holes of-the"Stopper passes the siphon which makes electrolytic contact with the solution to be

9 G. T. Lipscomb and G. A. Hulett, J. Am. Chem. Soc, 38,'22 (1916). " W. Wi Erving, J. Am. Chem. Soc, 47, 301 (1925).

REFERENCE ELECTRODES 86

titrated. I t is a narrow U-shaped tube filled with a gel of saturated potassium chloride in agar. This gel is prepared by heating 30 g. potassium chloride, 3 g. of agar, and 100 ml. of water gently, until all has gone into solution and the solution is clear. After all the air bubbles have gone, the siphons can be filled by sucking up the salt-agar solution.

FIG. 14 (I). Calomel electrode.

FIG. 14 (11).

im n/r%

^ ^

1^

Mt

FIG. 14 (III). Calomel electrode.

-KClsol'n

.'Sintered glass

FIG. 14 (IV).

On cooling, the solution stiffens to a gel. The siphons can be kepi for a long time if their terminals are placed, when not in use, in a saturated solution of potassium chloride. If the siphons are kept in the air, the gel dries out, and small air bubbles enter, which cause a high resistance. Such siphons have to be rejected. When the calomel electrode (bottle-type) is not in use, the hole through which the siphon passes is closed by a small rubber stopper in order to prevent evaporation of the solution.

' 86 THE TECHNIQUE OF POTENTIOMETRIC MEASUREMENTS ,

Figure 14 (IV) is a salt bridge with sintered-glass terminals as describe'd by Laitinen." This type of salt bridge is particularly advantageous for carrying out potentiometric titrations at elevated temperatures.

Various calomel electrodes are used; they are generally defined by the strength of the potassium chloride solution with which they are filled. When we talk of a 0.1 JV calomel electrode we mean that the vessel is filled with 0.1 N potassium chloride. One of the four following calomel electrodes is used: the 0.1 iV, the 1 N, the 3.5 N, and the saturated calomel electrode. The potential of these electrodes changes with the temperature; the absolute temperature coefficient (not with respect to the normal hydrogen electrode) is -0.00079 for the 0.1 N; -0.00061 for the 1N, -0.00046 for the 3.5 N, and -0.00020 for the saturated calomel electrode. ,

In extremely accurate work it should be remembered that when a calomel electrode is brought from a higher to a lower temperature it is very slow in assuming its constant value. Therefore for highly accurate work it is recommended that the calomel electrodes be kept in a thermostat, and not exposed to changes in temperature. This is one of the reasons why the authors prefer, the quinhydrone electrode in accurate work as a standard half-cell. According to the recommendation of Stig Veibel,'^ such an electrode can be easily prepared as follows: Fill a Pyrex tube with a mixture of 0.01 N hydrochloric acid and 0.09 N potassium chloride in water (standard acid mixture), and shake this solution for one minute with 50 to 100 mg. quinhydrone. The tube is closed by a two-hole stopper, one holding the siphon for the salt bridge and the other a glass tube through which the platinum gauze or wire electrode has been sealed. The platinum is ignited to dull redness before being placed in the solution. As the potential of such an electrode is constant for only one or two days it is recommended that the quinhydrone-acid mixture be replaced and the platinum' reignited every day.

Iii niea'surements of silver, mercury, and halide-iori concentrations the saturated salt bridge cannot be used, as chloride would diffuse in the solution to be measured. A special arrangement can be made>to prevent this diffusion of the salt into the bulk of the solution. In potentiometric

V titrations with the silver or mercury electrode, where the liquid-junction '; potential is more or less immaterial, a salt bridge of potassium nitrate, 1 potassium sulfate, or ammonium nitrate (as a gel in 3 per cent-agar) can , be used. y~~~~

" H . A. Laitinen, Ind. Eng. Chem., Anal. Ed.,,13, 393 (1941). " S. Veibel, / . Chem. Soc, 123, 2203 (1923).

CHAPTER VI

THE POTENTIOMETRIC MEASUREMENT OF HYDROGEN-ION ACTIVITY

1. The Hydrogen Electrode. When a noble metal, coated with an adherent layer of a noble metal to increase its surface, is saturated with hydrogen gas it behaves like an electrode of metallic hydrogen., Various forms of hydrogen electrode vessels have been described in the literature.

Salt bridge H a - ^ = ;

FIG. 15 (I). Hydrogen electrode in streaming

hydrogen.

FIG. 15 (II). Dip electrode according to Hilde-

brand.

FIG. 15 (III). H2 electrode for potentiometric

titrations.

The form shown in Fig. 15 (I) is very well adapted to measurements in streaming hydrogen; as a rule a constant potential is established within two to three minutes. Number II in Fig. 15 is a slight modification of the Hildebrand type of electrode and is generally used for potentiometric titrations. The authors prefer the type shown as III, for the solution can be protected from oxygen of the air during the titration. (See below.)

1 Cj. W. M. Clark, The Determination of Hydrogen Ions, Third Edition, 1928, page 281.

87

88 THE POTENTIOMETRIC MEASUREMENT OF pK

STANDARD EQUATIONS FOR THE CALCULATION OP paH FROM MEASUREMENTS WITH

THE HYDROGEN ELECTRODE

„ , , , ^ ^ „ IIo.i iv - 0.3365 + 0.00006(( - 25) 0.1 A C.E. paB. =

1 N C.E. i>aH =

Sat. C.E. pan =

0.0591 + 0.0002(i - 25)

Hi AT - 0.2828 + 0.00024(i - 25) 0.0591 + 0.0002(i - 25)

nsat. - 0.2438 + 0.00065(< - 25) 0.0591 + 0.0002(4 - 25)

r. • , , , TT ^ô HQH -0.6992+0.00074(< - 2 5 ) Quinh. electrode poH = 2.08 + -^^^ ^

(m0.01iVHCl+ 0.0591+0.0002(i-25) 0.09 N KCl)

In the measurement of paH(=— log aH+) the potential of the hydrogen electrode, after it has attained its constant value, is determined against some reference electrode. Such measurements do not yield the exact value of the potential as they always involve a liquid-junction potential (see page 71). I t is possible to devise cells without liquid junction for the measurements of paH, but, from the practical point of view, these are not convenient.^ On the other hand, only approximate values of paH can be obtained in the measurement of potentials in cells involving a Uquid-junction potential. The error involved depends upon the pH of the unknown, its composition, and the kind of reference electrode and salt bridge used. In general, the error is small when dealing with buffer solutions with a pH of about 3 to 11 and when a saturated potassium chloride solution is used as a salt bridge. For an exact discussion of this involved subject the student is referred to an excellent review by Hamer.' The standard values tabulated above refer to measurements with buffer solutions with a pH of 3 to 11. When the paK of the standard acid mixture (a solution which is 0.01 A'' in hydrochloric acid and 0.09 N in potassium chloride) is measured it is better to use the following values of the standard potentials of the reference electrodes: 0.3386 for 0.1 N C.E. (instead of 0.3365); 0.2848 for 1 N C.E. (instead of 0.2828), and 0.2457 for saturated C.E. (instead of 0.2438).

In the above table, UQAN denotes the potential measured against the 0.1 N calomel electrode (0.1 N C. E.) and corrected to a hydrogen pressure of 760 mm. (cf. page 60), etc. The exact value of the paH of the

2 Compare, e.g., W. J. Hamer and S. F. Acrce, / . Research Natl. Bur. Standards, 23, 647 (1939).

3 W. J. Hamer, Trans. Eledrochem. Soc, 72, 45 (1937). See also D. A. Maclnnes, D. Belcher and T. Shedlovsky, / . Am. Chem. Soc, 60, 1094 (1938), who give 0.3358 volt as the standard potential of the 0.1 iV calomel electrode.

THE HYDROGEN ELECTRODE 89

standard acid mixture (0.01 A'' in HCl and 0.1 N in KCl) is not known; its most probable value is 2.08 ± 0.01.^

Deposition of Coat on the Electrode. One of the essentials of a hydrogen electrode is that it shall have a good coat of "black" on the metal. As a rule, platinum electrodes are used, though other noble metals like iridium, palladium, or gold can be taken. The electrode is well cleaned in a cleaning mixture (10 per cent potassium dichromate in sulfuric acid), and thoroughly washed with water. Then it is electroplated with a cover of the same noble metal; this can be done by electrolyzing in a solution of 1 to 3 per cent chloroplatinic acid, with a platinum foil or a platinum cylinder as an anode.^ It is the experience of the authors that a thin coat of platinum, barely sufficient to obscure the luster of the polished metal beneath, is preferable to a thick coating. With a thin layer of black, equilibrium is attained much more quickly than with a heavy layer of platinum. This is rather important if measurements are to be made in the presence of organic substances like benzoates or phthalates. An electrode covered with a thick layer of platinum black is then very slow in reaching its constant potential. In the measurement of slightly buffered or unbuffered solutions an extremely thin layer of black is necessary, as platinized platinum in a hydrogen atmosphere adsorbs cations from a solution, leaving the solution more acid.^ The electrode is washed thoroughly with water after the electrolysis and polarized cathodically in about 0.5 N sulfuric acid. The hydrogen formed at the electrode reduces chlorine, which is adsorbed from the platinizing liquid. After a vigorous evolution of gas for about ten minutes, the current is discontinued, and the electrode is washed repeatedly, first with cold and later with tepid water. When not in use, the electrode is kept under water. After having been used for some time, it becomes rather sluggish in attaining its constant potential. Then it has to be cleaned and replated.

Hydrogen Generators. Electrolytic generators of hydrogen have been employed very frequently, and are especially satisfactory when a moder-

* Compare I. M. Kolthoff, Rec. trav. chim., 49, 401 (1930); see also D. I. Hitchcock and A. C. Taylor, / . Am. Chem. Soc, 69, 1812 (1937), who report the same value. When the proper corrections for the liquid-junction potential has been apphed, the most probable value of the paH of the standard mixture at 25° C. is 2.10, according to E. A. Guggenheim and T. D. Schindler, J. Phys. Chem., 38, 533 (1939).

' Detailed directions for electroplating of hydrogen electrodes to be used in different kinds of solutions are given by A. E. Lorch, Ind. Eng. Chein., Anal. Ed., 6, 164 (1934).

«C/. I. M. KolthoS and T. Kameda, J. Am. Chem. Soc, 51, 2888 (1929); also A. Unmack, Den. Kongelige Yelerinaer og Landboh^jskole Kopenkavn, Aarsskrift, 1933, pages 19-44.

90 THE POTENTIOMETRIC MEASUREMENT OF pH

ate supply of hydrogen of the highest purity is required at frequent intervals. A convenient supply of hydrogen is also on the market as compressed gas in tanks. The gas should be purified by washing it through various solutions before it enters the electrode vessel. As a rule, the following arrangement gives satisfactory results. The gas is passed through a wash bottle with 0.2 N potassium permanganate, through alkaline pyrogallol (1-2 g. pyrogallol in about 35 ml. 4 N sodium hydroxide), a wash bottle with very dilute sulfuric acid (about 0.1 A'' acid, to neutralize alkali which might splash over), two wash bottles of water, then in the thermostat through the solution the pdH. of which is to be determined, and finally through the solution in the hydrogen electrode cell used. The oxygen is not quite completely removed by this arrangement, but the above washing gives excellent results in most measurements when the pH is smaller than 11.^ If strongly alkahne solutions or liquids with an extremely small buffer action have to be measured it is necessary to remove all traces of oxygen. This can be done by omitting the wash liquid with alkaline pyrogallol (which gives off a trace of carbon monoxide) and passing the gas over platinized asbestos at 500° C. or copper or nickel wire or gauzes at 500°. The gas is then washed through dilute alkali to remove traces of carbon dioxide which might be present in the gas.

Standard Solutions for Checking the Apparatus. In the routine measurement of hydrogen-ion concentrations it is desirable to check the system frequently. The following solutions are recommended: * A solution which is 0.01 N in hydrochloric acid and 0.09 A in potassium chloride (standard acid mixture), pdH. = 2.08 (25° C ) ; 0.1 M monopotas-sium citrate, paH = 3.72 (25° C.); 0.05 M monopotassium phthalate, paB. = 4.01 (25° C ) ; 0.05 M borax, paH. = 9.18 (25° C ; at 18° C. paH = 9.23).

Interfering Factors in the Use of the Hydrogen Electrode. Oxygen has a tendency to give the electrode a positive charge, and under some conditions even traces may be very harmful. If the hydrogen gas is prepared practically free from oxygen by the procedure described above, the traces of oxygen left do not interfere with the measurement of well-buffered or acid solutions. The platinum black acts as a catalyst for the combination of hydrogen and oxygen. In the measurement of unbuffered or strongly alkaline solutions care should be taken to remove the oxygen as completely as possible.

' A chromous sulfate solution in dilute sulfuric acid is about 50 times more efficient in removing oxygen than an alkaline pyrogallol solution, according to H. W. Stone, / . Am. Chem. Soc, 58, 2591 (1936).

8 Cf. D. I. Hitchcock and A. C. Taylor, J. Am. Chem. Soc, 59, 1812 (1937).

THE QUINHYDRONE ELECTRODE 91

Various substances may poison the hydrogen electrode; traces of ar-senious trioxide, or arsine and hydrogen sulfide, are notorious examples.

The paH of protein solutions can be measured accurately with the hydrogen electrode. The pJatinized electrode may soon become covered with a film of the protein, thus making the electrode sluggish. If this happens, cleaning and replating are necessary. For measurement of the paH of protein solutions Schulz ' recommends the use of a blasted iridium electrode, covered electrolytically with a noble metal. After electroplating and cathodic polarization the electrode is immersed in a solution of collodion in glacial acetic acid and then in water. After washing with water, dilute sodium hydroxide and with distilled water the collodion-coated electrode is ready for use. The equilibrium potential is attained within three hours.

Organic substances may interfere as they may be hydrogenated at the platinized electrode. This is especially true of aromatic compounds; with most alkaloids and dyestuffs, e.g., the authors could not get reUable results. Even in the presence of benzoic acid or benzoates it takes a long time before the electrode attains equilibrium. A very thin coat of black is recommended under these conditions. Ahphatic compounds without double or triple bonds do not interfere, as a rule, unless they have a specific oxidizing (per-acids) or reducing action.

Oxidizing substances quite generally are reduced by the hydrogen electrode (ferric iron, dichromate, permanganate, and under certain conditions nitrate ions); therefore reliable measurements are impossible in the presence of these substances. The same holds for salts of metals which are below or just above hydrogen in the electromotive tension series; salts of copper, silver, bismuth, mercury, etc., are reduced by the hydrogen electrode, which will behave as an electrode of the corresponding metal.

Finally, the electrode cannot be used in the presence of strongly reducing substances, like stannous chloride, chromous chloride, or sulfites, as the electrode would indicate the reduction potential of the reducing system present.

From this review we see that the application of the hydrogen electrode is relatively limited, and it is fortunate that for various determinations we have other electrodes available for the potentiometric measurement of pH.

2. The Quinhydrone Electrode. The quinhydrone electrode introduced for practical work by Biilmann and Lund'" is very simple and convenient for the measurement of pH in neutral or acid solutions.

» G. Schulz, Thesis, Marburg, Germany, 1931. " E . Biilmann, Ann. chim., (9) 15, 109 (1921); Biilmann and H. Lund, Ann.

chim., 16, 321 (1921); 19, 137 (1923).

92 T H E P O T E N T I O M E T R I C M E A S U R E M E N T OF p H

The quinhydrone electrode is an oxidation-reduction electrode. Quinhydrone is an equimolecular compound of hydroquinone and ben-zoquinone. On page 65 we saw that the oxidation potential of such a system is given by the expression:

n = Constant + ^ ^ log "^"'""""^ - 0.0591 paU (25° C ) . oqumone

When the salt content of the solution is small, the activity coefficient of the quinone can be taken equal to that of the hydroquinone. Since the quinhydrone yields equimolecular amounts of quinone and hydroquinone in the solution, aguinone is equal to fflHydroquinone? and the above expression becomes:

n = n° - 0.0591 paE. (25° C ) .

Thus, the potential of the quinhydrone electrode changes with the paK of the solution exactly as the hydrogen electrode does. Therefore, the e.m.f. of a cell composed of a hydrogen electrode and a quinhydrone electrode in the same solution is a constant and independent of the paH. of the solution. This constant is equal to 11°. At an ionic strength of zero, n° is equal to 0.6994 volt at 25° C. In the standard acid mixture (0.01 N in HCl and 0.09 N in KGl) the n° value is 0.6992 volt. At small ionic strengths 11° varies in the following way with the temperature:

n ° = 0.6992 + 0.00074 (25° - t°) (between 0° and 38° C ) .

Depending upon the kind of reference electrode used, the paH is calculated with the aid of one of the following equations.

STANDARD EQTTATIONS FOB THE CALCULATION OF pH FBOM MBASTJBEMBNTS WITH

THE QulNHYDEONE ELECTRODE (BtTFFER SOLUTIONS)

O . l i V C E . ^ „ H ^ 0.3625 - 0 . 0 0 0 6 8 ( . - 2 5 ) - n o . i .

1 N C.E. paH =

Sat. C.E. paH =

0.0591 + 0.0002(i - 25)

0.4162 - 0.00050(< - 25) -Tli^

0.0591 + 0.0002 (< - 25)

0.4552 - 0.00009(f - 25) - Hsat.

0.0591 + 0.0002 (« - 25)

nQ,H. Quinhydrone electrode poH = 2.08 H

(in 0.01 iV HCl 4-0.09 AT ^ 0 . 0 5 9 1 + 0 . 0 0 0 2 0 - 2 5 ) KCl)

It may be mentioned that the cell hydrogen electrode-saturated calomel electrode has a temperature coefficient larger than any of the


other calomel electrodes. The reverse is true for the cell quinhydrone electrode-calomel electrode. With the saturated calomel electrode the temperature coefficient is almost negligibly small. As a matter of fact, if the quinhydrone electrode (in the standard acid mixture) is used as a reference electrode in measurements with the quinhydrone electrode there is no temperature modulus at all.

Pre'paration of Quinhydrone (Biilmann). Quinhydrone may be suitably prepared as follows: 100 g. ferric ammonium sulfate is dissolved in 300 ml. water at 65° C , and this solution is poured into a solution of 25 g. hydroquinone in 300 ml. water. The quinhydrone precipitates in fine needles; after cooling in ice it may be collected by suction. Yield, 15 g. I t may be recrystalHzed from 50 per cent acetic acid in water, whereupon it is washed acid free, but the product prepared according to the method of Biilmann is useful for most purposes without any further purification. I t has been our experience, however, that slight traces of acid may be formed at its surface after being kept for some time. These traces of acid are immaterial in the measurement of buffei'ed systems, but if the solution has an extremely small buffer action large errors may arise. Our recommendation then is to wash the quinhydrone first with water and finally, just before it is used, with the solution to be measured. Or a pure product of quinhydrone which is quite stable can be prepared by mixing solutions of pure hydroquinone and quinone in equimolecular ratio.

Electrodes and Electrode Vessels. The quinhydrone electrode is extremely simple to manipulate. As an electrode a bright piece of pure freshly ignited platinum wire, foil, or gauze is commonly used, but gold electrodes also seem to be suitable. The electrode is ignited in a flame before being placed into the solution. According to Morgan, Lammert, and Campbell " the greatest source of error in the quinhydrone electrode lies in the sealing of the electrode in the soft glass. Large deviations of the order of 100 millivolts may be found when the glass of the electrode is cracked. For this reason it may be better not to ignite the electrode in a flame, but to clean it in cleaning solution, and wash it later with water. The danger is also avoided when the connection of the electrode to the circuit is made without mercury but by sealing it to a thin platinum wire. The solution is first saturated with quinhydrone, by shaking it for about one minute with 50-100 mg. (for 20 ml. of liquid) of the compound, and allowing the excess to settle to the bottom of the vessel. Some suitable forms of electrode vessels are shown in Fig. 16.

In potentiometric titrations some quinhydrone is added to the acid 1' J. L. R. Morgan, O. M. Lammert, and M. A. Campbell, / . Am. Chem. Soc,

53, 454 (1931).


solution; the bright platinum electrode is placed in it; the liquid is stirred, and the titration can be started. The quinhydrone electrode may often be applied where the hydrogen electrode does not yield good results, as in the presence of metals which lie below hydrogen in the electromotive scries or of many aromatic compounds (alkaloids). Under these conditions, however, one should be careful about accepting the results. Both quinone and hydroquinone are substances which react readily Avith many other compounds. In this way the equilibrium in the electrode may be disturbed. The authors, for example, are not con-

- Salt bridBe with agar

FIG. 16. Quinhydrone electrode.

vinced that the quinhydrone electrode yields completely reliable results in the presence of substances like aniUne, toluidine, phenols, and amino acids. A comparison with the hydrogen electrode is desirable if possible.

As the quinhydrone electrode is so convenient, it has been used for various practical purposes, e.g., for the determination of the acidity of soils, of dairy products, of foodstuffs (like cheese, lemonades, fruit juices, and sugar solutions).^^

Limitations and Sources of Error. The quinhydrone electrode can be used only up to a certain pH, since hydroquinone is a very weak acid, and in alkaline solution it combines with hydroxyl ions. In general, therefore, good results can be expected only when the pH is smaller than about 8.0, although it is impossible to give an exact upper hmit for its usefulness. If measurements are made immediately after the saturation with quinhydrone good results may be obtained up to a pH of 9 in well-buffered solutions. However, in alkaline solutions another factor must be considered which is especially essential in potentiometric titrations. In alkaline medium, hydroquinone is readily oxidized by oxygen from the air to brown products, some of which have a distinct acidity and may neutralize part of the base. This oxidation can be avoided by working in an inert atmosphere of nitrogen or hydrogen—this, however, at

12 For literature references, see W. M. Clark, The Determination of Hydrogen Ions, Third Edition, page 416; Kolthoff and Furman, Potentiometric Titrations, Second Edition, 1931.


the cost of the simplicity of the method. In potentiometric titrations, therefore, it is advisable to start always with acid solutions, and to add the base to the stirred liquid. Under such conditions an oxidation of the hydroquinone at the place where the base drops in is avoided.

Another source of difficulty with the quinhydrone electrode is the so-called salt error. I t has already been stated (page 92) that, since we use quinhydrone, the concentration of quinone is equal to that of hydroquinone in the solution. Actually we should have said that the activity of the two compounds in the solution is the same. This is true as long as we work in pure water as a solvent. Salts, however, change the solubilities of both compounds and, correspondingly, their activities. Therefore the ratio of the two activities in a salt solution may not be the same as in pure water. This change of the activity ratio causes the so-called salt error of the quinhydrone electrode.

S. P. L. Sorensen and K. Linderstrom-Lang (1921-1924) suggested the use of quinhydrone electrodes without salt error. Quinhydrone in solution is partly dissociated into its components:

Q.H. ^ H.Q. + Q. quinhydrone hydroquinone quinone

Thermodynamically the following relation holds:

Q H . Q . - « Q . ^ j^

< Q.H.

In solutions saturated with quinhydrone, aQ.n. is constant. If the system is saturated with respect not only to Q.H. but also to either H.Q. or to Q. the activity of the third component will remain constant. Such an electrode will not show a salt error. Naturally the normal potential will become different, if we are working with systems saturated to H.Q. or to Q. Whereas the normal potential of the ordinary Q.H. electrode at 18° is equal to 0.6990 volt, it. amounts to 0.7546 with the quinone-quinhydrone electrode (saturated with Q. and H.Q.) and to 0.6191 with the hydroquinone-quinhydrone electrode (saturated with H.Q. and Q.H.). This latter electrode has another advantage as it can be used at a slightly higher pH than the ordinary Q.H. electrode. Since the solution is saturated to H.Q., a slight ionization of the hydroquinone does not affect the ratio H.Q. to Q. The salt error of the ordinary quinhydrone electrode is easily determined by measuring the e.m.f. of the following cell: quinhydrone electrode: salt-containing solution: hydrogen electrode. The e.m.f. of such a cell at an ionic strength of zero is 0.6994: volt at 25° C. In the presence of salts the difference in e.m.f. between this value and that measured yields the value of the salt error.


Numerical data of salt errors in various solutions have been given by various authors." Kolthoff and W. Bosch found a relatively large "salt error" in sodium benzoate solutions.

When other oxidation-reduction systems are present which have oxidation potentials different from that of the solution to be examined they will interfere with exact measurements. So, for example, ferrous-iron solutions will reduce part of the quinone. Reliable measurements cannot be made in presence of dichromate, permanganate, stannous tin, sulfite, thiosulfate, etc. If the oxidizing or reducing agent acts so slowly that the ratio of hydroquinone to quinone is not appreciably changed within the time of attainment of equilibrium in the system, it does not interfere. This is true, for instance, of measurements in the presence of nitric or perchloric acid.

I t should be noted that the quinhydrone electrode may give rise to errors in heterogeneous systems. Thus it was shown by Unmack '* that the quinhydrone electrode gives distinct deviations in fat emulsions owing to the fact that the distribution coefficient of the quinone between water and the fat layer is different from that of hydroquinone. As a result of this unequal distribution the concentration (activity) of the hydroquinone in the aqueous layer becomes greater than that of quinone, and high values of pH are found.

Even in suspensions of solids (e.g., of soil) there is a possibility of finding deviating results with the quinhydrone electrode, if either the hydroquinone or the quinone is adsorbed or if both are adsorbed but not in equimolecular amounts.

Finally, it may be mentioned that boric acid has the property of forming complexes of relatively strong acidity with dihydroxybenzenes, like hydroquinone. Therefore, reliable results cannot be expected in the presence of boric acid or borates.

3. The Oxygen and Air Electrode. When oxygen is supplied to an electrode like platinum, it has a tendency to send oxygen ions into the solution just as the hydrogen electrode tends to form hydrogen ions:

i 0 2 + 2e^ [0=].

But oxygen ions take up protons in their electron shell, according to:

[0=] 4- H+ ^ [OH-].

" See, e.g., F. Hovorka and W. C. Dearing, / . Am. Chem. Soc, 57, 446 (1935), A. von Kiss and A. Urmanczy, Z. physik. Chem., A169, 31 (1934).

'* A. Unmack, Royal Veteriruiry and Agricultural College, Copenhagen, Yearbook, 1934, page 175.

THE OXYGEN AND AIR ELECTRODE 97

Then,

and since

[0H-] =

we have

[0=] =

[H+]

KJi'

The potential of the oxygen electrode is given by:

n = ( n V + — I n ^ ^ (c/. page 64).

„, 0.0591 , 1 0, , 0.0591 , [H+f

n = n « + - ^ l o g ^ = no+-^logL-±,

n = n° + 0.0591 log [H+].

Theoretically, therefore, the oxygen electrode changes its potential with the pH of the solution in exactly the same way as the hydrogen electrode. Unfortunately, however, theoretical results are never obtained with such a system on account of the fact that the oxygen electrode is not completely reversible; probably a thin film of the noble metal oxide is formed at the surface.

The phenomena occurring at the oxygen electrode are not known exactly.^^ From a practical viewpoint it may be stated that the oxygen electrode cannot he used in the exact determination of the pall. Where the hydrogen or quinhydrone electrode cannot be used the glass electrode (page 100) should be applied.

The oxygen electrode can be used for approximate measurements of pH if it is calibrated in solutions of similar compositions as the unknown under the same conditions. The oxygen electrode shows a definite drift in potential with time and does not assume a constant value. For this reason the oxygen electrode is not even very suitable in potentiometric titrations in general, although it may be useful under certain conditions. For practical purposes it is most convenient to work with the air electrode. This is simply a bright platinum electrode placed in a solution saturated with air. It is very useful in the determination of the acidity of solutions containing strongly oxidizing agents, such as permanganate or dichromate. The potential of these oxidizing agents themselves

15 See especially T. P. Hoar, Proc. Royal Soc, A142, 628 (1933); W. T. Richards, J. Phys. Chem., 32, 990 (1928).


depends upon the pH, and the role of oxygen as potential-determining constituent is of subordinate significance.

Higher Oxide Electrodes. The general theory of these electrodes has been discussed on page 65. The electrode reactions are not completely reversible, and, therefore, higher oxide electrodes are not suitable for the exact determination of pH.

4. Metal-Metaliic Oxide Electrodes. In Chapter IV (page 58, equation 10) we saw that the potential of a metal electrode is given by the equation:

n = n° + ^:^log[M"+]. n

Suppose that the metal forms a slightly soluble oxide or hydrous oxide the solubiUty of which, in the solution to be examined, is negligibly small.

M(0H)2 <=i M++ + 2 0 H - .

If the solution is saturated to the hydroxide

[M++][0H-]2 = ,SM[OH],

'S'M[0H]2 _ ^

[OBrf ~ Ki

Introducing this expression in the above equation we find:

(M++1 = ™ 5 - T S ^ * IH+f - KIH+P.

= n°' + 0.0591 log [H+].

Therefore the metal-metallic oxide electrode changes its potential with the pH in exactly the same way as the hydrogen electrode. The practical application of the metal-metallic oxide electrodes is limited, because the solubility of the hydroxide must be negligibly small and the hydroxide must not react with the components of the solution (mercuric oxide forms complexes with various anions; antimony oxide forms complexes with tartrates and other organic hydroxy acids).

The mercury-mercuric oxide electrode can be used for the measurement of paH in strongly alkaline solutions (pH > 9.0). However, its application is rather limited on account of the fact that it reacts with halides and many other anions with formation of complexes.

HgO + 4 1 - + H2O ?=> Hgl4= + 2 0 H - .

The silver-silver oxide electrode can also be used for the measurement

METAL-METALLIC OXIDE ELECTRODES 99

of paH in strongly alkaline solutions, but again its application is very limited.

More promising is the antimony-antimonious oxide electrode, and much work has been done to develop this electrode as a substitute for the hydrogen electrode. ** The best study of this electrode has been made by Roberts and Fenwick." They use antimony powder obtained by electrolysis of antimony fluoride and dip a platinum wire into it covered with a thin coat of antimony. Of special significance is the fact that the stable modification of antimonious oxide (cubical form) has to be used. This is obtained by heating precipitated antimony oxide (orthorhombic) in an evacuated Pyrex tube for 24 hours at a temperature of 470° C. If no air is present and the equilibrium is reached from the alkaline side, the antimony-antimonious oxide electrode actually behaves like a hydrogen electrode:

n = n° + 0.0591 log [H+] (25°),

where n" is 0.1445 volt with regard to the normal hydrogen electrode. However, for practical purposes the method described by Roberts

and Fenwick has some disadvantages; the procedure is rather a tedious one, and it takes a long time for the electrode to attain its constant potential. Therefore, various authors have tried simpler arrangements. They used an antimony electrode—either a bright rod of antimony obtained from a melt or a piece or wire of platinum electroplated with antimony. We were not able to get highly satisfactory results with either of the two electrodes. The potential did not change in an exactly linear way with the pH of the solution. Probably the difficulty is explained by the fact that in none of the attempts the form of antimony which is stable at room temperature had been used. This point should be examined further; such a study seems rather promising with regard to the application of the simple antimony electrode as a substitute for the hydrogen electrode.'^

For potentiometric titrations a satisfactory electrode is obtained if spectroscopically pure antimony is melted in a vacuum and poured into a cylindrical mold. The melt is cooled very slowly in a vacuum. The rod so obtained is joined to a copper wire, which is connected to the

" Review, c/. Kolthoff and Furman, Potentiometric Titrations, Second Edition, 1931.

1' E. J. Roberts and F. Fenwick, J. Am. Chem. Soc, 60, 2143 (1928). 1* Extensive studies on the antimony electrode and the best conditions undei

which reproducible results are obtained have been made by G. A. Parley, ITVI. Eng. Chem., Anal. Ed., 11, 316, 319 (1939). With molded, hard-rubber, flat-surface types of electrodes be obtained a reproducibility of 0.15 pH.


circuit. The rod is placed in the solution and some antimonious oxide (stable modification) is added to it. The solution is stirred and the titration can be started. If more accurate data of pH arc desired, the electrode can be standardized in buffer solutions of known pH. The actual measurements have to be made later under the same conditions, as various factors—absence or presence of air, stirring of the solution or of the electrode—affect the potential more or less.

In the presence of strongly oxidizing substances, like permanganate and dichromate, the trivalent antimony is oxidized to the pentavalent state, and the potential changes very much.

Organic compounds which form complexes with antimonious oxide interfere with measurements with the antimony electrode.

5. The Glass Electrode. Haber and Klemensiewicz '" showed that the e.m.f. of a cell such as the following

Ag 1 AgCl, 0.1 N HCl I glass I solution X \\ KCl, sat., HggCla ] Hg, (A)

in which a thin glass wall separates a solution X of unknown pl i from a 0.1 A'' hydrochloric acid solution, varies with the hydrogen-ion activity of solution X in the same way as the e.m.f. of a similar cell in which the glass wall has been replaced by a system of two hydrogen electrodes, namely,

Ag I AgCl, 0.1 A HCl I Pt, Ha, Ft I solution X\\ KCl, sat., HggCla | Hg. (B)

Many investigations have been carried out to determine the behavior of the glass electrode as a pH electrode.2"' Between pH values of 0 and 9, the glass electrode follows the theoretical hydrogen electrode relation very closely, but it gives deviating results in very acid or alkaline medium. The range of exact applicability depends upon the composition of the glass.

Although the exact mechanism of the glass electrode is somewhat in doubt, its function as a pH electrode may be briefly explained as follows. Cells A and B, above, are thermodynamically identical if hydrogen ions are transferred reversibly from one solution to the other, since the same net transfer of hydrogen ions occurs in the two cells between two solutions having different hydrogen-ion activities. The essential difference between cells A and B is that, in B, hydrogen ions are first reduced to gaseous hydrogen and then oxidized to hydrogen ions at a different

" F. Haber and Z. Klemensiewicz, Z. physik. Chem., 67, 385 (1909). "° Cf. M. Dole, Principles of Experimental and Theoretical Electrochemistry,

McGraw-Hill Book Company, New York, 1935, page 427; W. M. Clark, The Determination of Hydrogen Ions, Third Edition, page 420; H. T. S. Britton, Hydrogen Ions, page 88; Kolthoff and Furman, Potentiometric Titrations, Second Edition, 1931.

THE GLASS ELECTRODE 101

activity, whereas in A no oxidation or reduction occurs at the glass-solution interfaces, but simply a reversible transfer of hydrogen ions takes place. It is therefore quite reasonable to expect that the presence of strong oxidizing or reducing agents would not affect pH measurements with the glass electrode. The hydrogen electrode can, of course, also act as an oxidation-reduction electrode owing to the metallic nature of the electrode.

The deviating results obtained in strongly acid solutions (pH < 0) have been explained by Dole " by assuming that hydroxonium ions, HsO"^, are actually transferred through the glass. Since in strongly acid solutions the water is in a lower activity state than in neutral or weakly acid solutions, the transfer of water is accompanied by a free energy change which appears in the measured e.m.f. This effect is present, of course, at all pH values but is immeasurably small except in very acid medium.

No exact mathematical theory has yet been formulated to explain the error obtained in strongly alkaline medium. Quahtatively, however the deviating results are caused by the migration of other cations through the glass in solutions in which the concentration of hydrogen ions is very low in comparison with that of other cations. Anions in general are unable to migrate through glass; thus the "alkah error" is primarily a cation effect and is greatest with small cations such as sodium and lithium while larger ions such as potassium and calcium have a much smaller effect. The composition of the glass has a marked effect on the magnitude of the alkali error. I t has been shown ^ that there is a definite correlation between the'rate of solution of a particular type of glass in an alkaline solution and the alkaU error. The Beckman Company has recently developed a glass electrode which with proper care can be used to measure pH values as high as 13.5 with only very small corrections.^' The alkali error increases rapidly, in general, with increasing temperature.

Another source of error is the "asymmetry potential" of the glass wall. If the two surfaces of the glass electrode acted alike, the e.m.f. of a cell such as

Ag I AgCl, 0.1 N HCl I glass \ 0.1 N HCl, AgCl | Ag (C)

would be zero. Ordinarily such a cell has a very low e.m.f., of the order

" M. Dole, / . Am. Chem. Soc, 54, 2120, 3095 (1932). " D. Hubbard, E. H. Hamilton, arid A. N. Finn, / . Research Natl. Bur. Standards

22, 339 (1939). 23 National Technical Laboratories, Pamphlet 34, Pasadena, CaUf., 1940.


of 1 or 2 millivolts. Usually the asymmetry potential is compensated by calibrating the glass electrode in a solution of exactly known paH before each measurement.

Maclnnes and Dole * use a glass electrode of the form shown in Fig. 17. A thin glass diaphragm, D, is fused onto the end of an ordinary glass

tube B. This tube is then partly filled with an electrolyte (0.1 A hydrochloric acid). In this electrolyte is placed a silver-silver chloride electrode C. ^ The upper part of the tube is coated inside and outside with a thin layer of paraffin. The thin diaphragm D determines the electrode function of the glass electrode. I t is about 0.001 mm. thick and shows colors, owing to interference of light. The diaphragm can be fused on the end of the glass tube in the following way. A bulb is blown on the end of a tube of suitable glass until portions of the film show interfering colors. The end of the supporting tube B is then heated to a low red heat, the correct temperature being found by experience. The heated tube is then placed against the thin bulb. If the conditions are right the film of glass will fuse onto the tube. The potential of the glass electrode can be measured against any standard half cell.

Several types of commercial pH meters using a vacuum-tube voltmeter circuit with a glass electrode are on the market. The meter scale is graduated directly in pH units and is calibrated by means of a solution of known paH, such as 0.05 M potassium biphthalate.

The advantages of the glass electrode are: (1) the observed e.m.f. is unaffected by the presence of oxidizing or reducing agents or of capillary-active substances such as proteins; (2) it is not necessary to add hydrogen gas or quinhydrone to the unknown solution; (3) the glass electrode can be used in

colored, turbid, or colloidal solutions; (4) correct results are obtained in unbuffered solutions because the current passing through the cell is extremely small; (5) very rapid equilibrium is obtained; (6) pH measurements can be made on very small amounts of liquid.

FIG. 17. Glass Electrode of Maclnnes.

" D. A. Maclnnes and M. Dole, / . Am. Chem. Soc, 52, 29 (1930). « Cf. Maclnnes and Beattie, / . Am. Chem. Soc, 42, 1117 (1920).

THE GLASS ELECTRODE 103

Disadvantages of the glass electrode are its fragility and its high resistance, necessitating special vacuum-tube amplifying circuits, or a quadrant electrometer to replace the galvanometer of the usual potentiometer circuit. Its limitations in extremely acid or alkaline medium must also be borne in mind.

CHAPTER VII


1. The Theory of Potentiometric Titrations. The Equivalence Potential, It has been stated in the preceding chapters that the potential of a metal electrode is a linear function of the metallic-ion exponent in the solution. Therefore the change in potential during a titration is an indication of the change of the metallic-ion exponent. At the theoretical end point of a titration there is, as a rule, a sudden change of the ion exponent which is indicated by a corresponding jump of the potential of the electrode. Therefore the electrode can be considered more or less as a specific indicator for the corresponding metallic ions in the solution, and it is called an indicator electrode.

Similarly, in an oxidation-reduction reaction the potential of a piece of bright platinum is an indicator for the ratio of the oxidant and the reduetant in the solution.

It is of interest to consider what the potential of an electrode will be at the equivalence point, this being the theoretical end point of the titration.

Neutralization Reactions. In acid-base reactions the pH. at the equivalence point is determined by the kind of salt which is formed. If a strong acid is titrated with a strong base, the reaction at the end point is determined by the ionization product of water. At room temperature (24°) the pH of the solution will be 7; and

n = n'' + 0.0591 log [H+] = n° - 0.0591 x 7.

In the titration of a weak base with a strong acid,

pH = 7 — |p6 + |p<, (equation 266, page 12)

at the equivalence point. If the base is strong and the acid weak,

pH = 7 + ^pa — IPC (equation 286, page 13).

The various combinations were discussed in Chapter I and do not need further consideration here.

Precipitation Reactions. The ion concentration at the equivalence point is determined by the solubility product S of the slightly soluble

104

THE THEORY OF POTENTIOMETRIC TITRATIONS 105

substance formed during the titration. If the salt has the composition BA,

[B+][A-] = ,S,

then at the equivalence point

[B+] = [A-] = V ^ .

Simple relations hold for any composition of the precipitate.

n = n° + 0.0591 log [B+] = n° + 0.0591 log \ ^ .

„ 0.0591, „ , , = n H — log(S (at the equivalence pomt).

z

Oxidation-Reduction Reactions. An oxidant Oxi is titrated with a reducing agent Red2; the reaction can be represented by the equation:

Oxi + Red2 ^ Redi + 0x2, (1)

Fe+++ + Cu+ <=± Fe++ + Cu++

which is governed by the partial reactions

Oxi + e <= Redi,

0x2 + e ?= Red2.

If both systems are present in the solution and the electrode is in equi-Ubrium with the solution:

n = n? + 0.0591 log - ^ = n^ + 0.0591 log - ^ , (2) [RediJ [Red2]

in which H? denotes the normal potential of system 1, n2 that of system 2. The equihbrium constant of equation 1 is given by:

[Oxi] [Reda] ^ = A. [Redi] [OX2]

From equations 1 and 2 it is seen that

, [Oxi] [Red2] , ^ n» - 11;

Hence, there is a simple relation between the normal potential of the two systems and their equilibrium constant. At the equivalence point the amount of Reda added is equivalent to the original amount of Oxi, and from equation 1 it is easily seen that the concentration of Oxj left in the solution is equal to that of Red2, which has not entered into the

106 POTENTIOMETRIC TITRATIONS

reaction. Similarly the concentration of the reaction products Red and 0x2 at the equivalence point are identical; therefore

[Oxi] = [Red2],

[Redi] = [Ox,].

From this relation and equation 3 it follows that at the equivalence point

[Oxi] [Red2]

[Redi] [0x2]

According to equation 2:

= VK. (4)

n = n; + 0 .059 i iog -^ [RediJ

n = n^ - 0.0591 log [Red [0X2

2J

2n = n? + n U 0.0591 log J ^ - ^ = n? + n° ,Redi] [Red2j

(at equivalence point) or

^ n?+n^ nE.P. - ^

In more complicated systems, where more than one electron enters the reaction, the relations at the equivalence point can be found in a similar way.

2. Titration Curves. Neutralization Reactions. The change of the pH of the solution and the variation in the potential of the electrode during the titration can be represented by the same graph, if 1 unit in pH on the axis corresponds to a change of 59.1 milUvolts (at 25°). The curve obtained in plotting the change in potential (or pH) against miUiliters of reagent added is called the titration curve.

From what has been said in Chapter I and in this chapter it is a simple matter to construct the titration curve for various systems. For the sake of simplicity, we will assume that the volume does not change during the titration. Under these conditions the pH and the potential have been calculated in the titration of 0.01 TV hydrochloric acid with a strong base. The first column in the following table gives the equivalent amount of base expressed in percentages added; the second column, the hydrogen-ion concentration, the third, pH; the fourth, the potential

T I T R A T I O N CURVES 107

of the electrode; and the fifth, All/AC. This quotient represents the increment of the potential for a given addition of reagent. As is seen

TITRATION OF 0.01 A'' HCl WITH SODIUM HYDROXIDE. KU 10"

Per Cent Neutralized

0

90

99

99.9

E.P. 100

100.1

101

110

[H+j

10-2

10-3

10-^

10-5

10-7

10-5

10-10

10-11

pB

2

3

4

5

7

9

10

11

H H J

nO - 2 X 0.059

n " - 3 X 0.059 -..,

n " - 4 X 0.059 <

n " - 5 X 0.059 <

n ^ - 7 X 0.059 <

n" - 9 X 0.059 <

n ' - l O X 0.059 ••••

n ^ - l l X 0.059

AH

Ac

6.5

65

1180

1180

65

P»

_n

T

K \

\ ~ .

u -i-

69 n

59 n

59 ir

EH ' " 2

,. V.

. V.

. V. '

•

,

40 50 60 70 80 90 100 110 % Neutralize^

FIG. 18. I. 0.01 A HCl + NaOH. II . 0.1 N acetic acid + NaOH.


from the table, ATI/AC reaches a maximum at the equivalence point, which means that the second derivative at this point is equal to zero.

The titration curve is shown in Fig. 18. The following table gives the data of the titration curve of 0.1 AT

acetic acid with sodium hydroxide. (Cf. Fig. 18.)

TiTBATION OF 0.1 N AcETIC ACID WITH SODIUM HYDROXIDE. Ka = 1.8 X 10~^.

Per Cent Neutralized

0

9

60

90

99

99.8

99.9

E.P. 100

100.1

100.2

101

[H+]

1.36 X 10-5

1.6 X 10'"''

1.8 X 10-^

2.0 X 10-'

1.8 X 10-'

3.6 X 10-*

1.8 X 10-*

1.36 X 10-^

10-10

5 X 10-"

10-"

pH

2.87

3.80

4.75

6.70

6.75

7.45

7.75

8.87

10

10.3

11

n " -

n " -

n " -

n " -

i i » -

uP-

n " -

n » -

n » -

n » -

n " -

HHa

2.87 X 0.069 = n " - 0.170

3.80 X 0.059 = n" - 0.224

4.75 X 0.059 = n » - 0 . 2 8 0

5.70X0.059 =nO-0.336

AH

Ac

6.75 X 0.059 = n0-0.398-... "> 52

7.45 X 0.059 =0"-0.440.;:; '•> 170

7.75 X 0.059 =n ' ' - 0 .457< '>660

8.87X0.059 = n' '-0.623< '•>670

10X0.059 =n<'-0.590< '•;>2oo

10.3 X 0.059 =n' '-0.610<( > 49

11 X 0.069 ^n"- 0.649-'"

Precipitation Reactions. From the composition of the solution and the solubility product of the slightly soluble compound formed it is an easy matter to calculate the data for the construction of the titration curve. As has been shown on page 105, at the equivalence point

[B+1 = [A-] = Vs .

With a known excess a of one of the two ions near the equivalence point, the solubility of BA cannot be neglected. Suppose that it is equal to x; then we have

(a + x)x = S,

from which x can be calculated.

THE DETECTION OF THE EQUIVALENCE POINT 109

A simple example is given in the following table, where the data for the construction of the titration curve in the determination of 0.01 N silver nitrate with chloride are reported. The solubility product of silver chloride is approximated to 10^^°.

TITRATION or 0.01 A'' SILVER NITRATE WITH CHLORIDE. Âgci = 10"'".

Per Cent Reagent

0

90

99

99.9

E.P.lOO

100.1

101

110

[Ag+]

10-2

1 0 - '

10-^

1.6 X 10-5

10-5

6.4 X 10-"

io-«

1 0 - '

PAg

2.0

3.0

4.0

4.80

5.00

5.20

6.0

7.0

H A S

n ' ' A g - 2 X 0.059

n ' - S X 0.059-..,

n ' ' - 4 X 0.059 <'

n O - ^ S O X 0.059 <'

n^-S.OO X 0.059 <'

II<'-5.20 X 0.059 <

^ - 6 . 0 X 0.059 <'

n " - 7.0 X 0.059 ••'"

A H

Ac

7

52

118

118

52

7

Oxidation-Reduction Reactions. In the following table the data for the construction of the titration curve of

Oxi + Red2 *^ Redi + 0x2

with the partial reactions:

Oxi + e^ Redi

0x2 + e <=i Red2

have been collected. The first column again gives the percentage of reagent added; the second the ratio of [Oxi]/[Redi] until the equivalence point has been reached, and thereafter the ratio [Ox2]/[Red2]; the third column gives the potential during the titration.

3. The Detection of the Equivalence Point in Potentiometric Titrations. If the potential of the "indicator electrode" is measured against some standard reference electrode, the change in e.m.f. of the cell is equal to the variation of the potential of the indicator electrode during the titration. The maximum change in potential occurs at the equivalence point, or, if the titration curve is not symmetrical at both sides


TITRATION OF AN OXIDANT Oxi WITH A RBDUCTANT RED2

Per Cent Reagent (Redj) Added

9 50 91 99 99.8 99.9

E.P. 100

100.1 100.2 101

[Oxi]

[Redi]

10 1 0.1 0.01 0.002 0.001

n§-n?

VTO "•"'"'

Ratio [Rcd2]

1000 500 100

n" + 1 X 0.059

n" H " - 1 X 0.059 n ' ' - 2 X 0.059 n ' ' - 2 . 7 X 0.059 n" - 3 X 0.059

2

n5 + 3 X 0.059 nl + 2.7 X 0.059 n^ + 2 X 0.059

of this point, very close to it. This means that the equivalence point is located at the point where All/AC reaches a maximum, or its second derivative is equal to zero. I t is not necessary to plot all the readings in a graph, as the maximum may be read directly from the tabulated data. In the vicinity of the equivalence point the reagent is added drop by drop, and the readings are noted after the potential is constant after each addition. Then the change of AH/AC for each drop of reagent added can be calculated, and its maximum or the minimum of the second derivative can be found. The method yields highly accurate results within a fraction of a drop. The volume of the drop, of course, must be known or be determined. When, for example, we find the following values for All/AC:

D R O P S

A D D E D

0-..

•>0.5

K >1.5

2'C' •>2.5

3<' •>3.5

4'n'

;;>4.5

5-'"

A n

AC

2oa...

400<

goo-:;

800<.

600-'

DROPS

ADDED

:> 1

:• 2

;• 3

> 4

SECOND

DERIVATIVE

- 2 0 0

- 5 0 0

+ 100

+ 200


the maximum is found between 2.5 and 3.5 drops and the second derivative is equal to zero after the addition of 2J^ drops.

Various modifications of the classical procedure of potentiometric titrations have been described in the literature. An extensive discussion of these methods is given by Kolthoff and Furman; ^ some of them are briefly discussed below.

Titration to the Equivalence Potential. If the potential of the indicator electrode is measured against a reference electrode the potential of which is equal to that of the indicator electrode at the equivalence point, the e.m.f. of the cell will be zero at this point. Pinkhof ^ originally introduced this method, and it has been modified somewhat by Treadwell.' When this method is used a sudden reversal of polarity

FIG. 19. The Pinkhof system. S, solution to be tested. E, indicator electrode. /?, reference electrode. G, galvanometer. K, key.

marks the end point (Fig. 19). No potentiometer is necessary, and a galvanometer or capillary electrometer serves as indicating instrument. The deflection of the galvanometer decreases during the titration, is zero at the equivalence point, and reverses after this point has been passed. According to the authors' experience, the method has special advantages in titrations with the quinhydrone electrode. The latter is also used as a reference electrode, and is placed in a buffer solution of the same pH as that of the solution at the equivalence point. A general disadvantage in the application of the Pinkhof system is that it is neces-

' I. M. Kolthoff and N. H. Furman, Potentiometric Titrations, Second Edition, 1931.

' J. Pinkhof, Dissertation, Amsterdam, 1919. = W. D. Treadwell and L. Weiss, Helv. Chim. Acta, 2, 680 (1919).


sary to prepare a different electrode for each type of titration. Therefore Erich Miiller * has modified the method. He uses the calomel electrode as a reference electrode, but switches into the circuit an e.m.f. which is just equal to that of the indicator electrode-reference electrode at the equivalence point. The reagent is added until the null-point instrument shows no deflection or just changes the direction of its deflection. The value of the equivalence potential is found empirically; the potential where All/AC reaches a maximum corresponds to that at the end point.

The Pinkhof method and its modifications have this advantage in common: the titration may be performed very quickly, and a result can be obtained in some minutes—this, however, very often at the cost of the accuracy of the titration. Usually we will find that especially near the equivalence point the potential does not become constant immediately after addition of the reagent. If the readings are made immediately after the addition of the reagent, there is no assurance that the equivalence point has been reached when the null-point instrument does not show a deflection. There are also certain other disadvantages. The Pinkhof (and Miiller) system is balanced only at the equivalence point; therefore polarization may occur when readings are made during the titration. Finally, the equivalence potential is dependent upon conditions of the solution; the temperature and especially electrolytes influence its magnitude. The influence of electrolytes is especially marked in oxidation-reduction reactions, where hydrogen ions often greatly affect the normal potential of the system. For these reasons the Pinkhof method and its modifications cannot be recommended for highly accurate work, although they may have some advantages in certain practical cases and routine analyses.

Bimetallic Systems. Noble metals like platinum or gold act as indicators for the electron activity of the oxidation-reduction system in the solution. If now we could find an electrode material which would not respond to a change of an electron activity in the solution, it would be an ideal electrode for potentiometric titrations. If the indicator electrode and the " inert" electrode are placed in the same solution, then the change of the e.m.f. of such an element would be exactly the same as the variation in potential of the indicator electrode during the titration. Such a system, which eliminates the use of a standard half cell, is called a bimetallic electrode system.

Kamienski ^ claimed that a silicon carbide electrode ("Carborundum") actually behaves like such an inert electrode. Experiments in

* Erich Miiller, Die elektrometrische Massanalyse, Dresden, Third Edition. 5 Kamienski, Z. physik. Chem., 146, 48 (1929).


our laboratory, however, showed that the silicon carbide electrode behaves like an oxidation-reduction electrode.

Most electrodes so far studied do not behave in the ideal way as described above. Some metals such as a tungsten-platinum alloy when placed in a " well-buffered " mixture of an oxidant and a reductant attain the same potential as a platinum or gold electrode. However, when placed in a pure solution of the oxidant or reductant they show a marked difference in potential against platinum; this difference depends very much upon the previous treatment of the metal. If a pair of electrodes such as platinum and palladium are placed in a ferrous iron solution, they will show a certain potential difference. Upon titration with an oxidizing agent this difference falls rapidly to zero, and remains there until just before the equivalence point. A larger change in the potential difference gives warning that the abrupt and characteristic break in potential at the end point will soon be reached. After the end point has been passed, the potential difference will soon drop to zero again. The difference in behavior between the two electrodes is explained by the fact that one (platinum) approaches equilibrium very quickly in solutions of pure reductant or oxidant, whereas the other is very slow in the extreme cases where the oxidation-reduction system is not buffered. After a long time of waiting, however, both electrodes will reach the same state of equilibrium, and the potential difference between the two will be zero. A bimetallic system may be obtained artificially by using two similar electrodes (such as platinum) which are slightly polarized. Originally Hostetter and Roberts * observed that a palladium wire shows almost no change in potential during a ferrous iron titration with dichromate. Later the bimetallic system was studied systematically by Willard and Fenwick,'^ who made important applications.* An elegant application of polarized electrodes has been made by Foulk and Bawden ^ in their so-called dead-stop end point.

Differential Titrations. The principle is the following: Suppose that two similar indicator electrodes are placed in the solution to be titrated, one of which can be protected from the bulk of the solution by placing a cap over it, which can be moved up and down. If both electrodes are in the solution, they will attain the same potential and the e.m.f. is equal to zero. Some reagent is added, during which one electrode is protected

6 Hostetter and Roberts, / . Am. Chem. Soc, 41, 1337 (1919). ' H . H. Willard and F. Fenwick, J. Am. Chem. Soc., 44, 2504, 2516 (1922); 45,

84, 623, 645, 715, 928, 933 (1923); van Name and Fenwick, 47, 9, 19 (1925). s For the characteristics of various combinations, cf. also Furman and Wilson,

J. Am. Chem. Soc, 50, 277 (1928). « Foulk and Bawden, J. Am. Chem. Soc, 48, 2045 (1926).


by the cap. Then the two electrodes are in contact with solutions of different composition and there will be an e.m.f. between them. This, however, will be very small until the equivalence point is approached. Here an abrupt change in potential occurs at the unprotected electrode. Actually the differential titration can be carried out according to the above principle. After each addition of reagent the e.m.f. is read, the cap is lifted, and the solution is made homogeneous by stirring. The e.m.f. will drop to zero. Then the cap is placed over one of the electrodes, reagent is added again, etc. A maximum difference in e.m.f. is observed at the equivalence point. The method was originally suggested by Cox '" in a less practical form. It has been developed by Maclnnes and co-workers" according to the above principle. An

- -Electrode

FiQ. 20. Maclnnes and Jones' apparatus.

Fia. 21. Mailer's apparatus.

illustration of the Maclnnes electrode with cap is given in Fig. 20. Maclnnes and his collaborators showed that the differential method is capable of high precision (of the order of 0.002 per cent!).

A convenient form of differential system has been given by Erich Miiller (Fig. 21). A trace of the solution is withdrawn into a capillary tube, in which one electrode is mounted.

4. Special Determinations. Any reaction which can be made the basis of an ordinary titration can be useful for potentiometric purposes, if a suitable indicator electrode is available. Therefore a great number of potentiometric titrations have been described in the literature, a review

10 D. C. Cox, J. Am. Chem. Soc, 47, 2138 (1926). " Maclnnes and Jones, / . Am. Chem. Soc, 48, 2831 (1926); Maclnnes, Z. physik.

Chem., 130, 217 (1927); Maclnnes and Dole, J. Am. Chem. Soc, 51, 1119 (1929). Maclnnes and I. A. Cowperthwaite, / . Am. Chem. Soc, 53, 555 (1931).

SPECIAL DETERMINATIONS 115

of which Is given by Kolthoff and Furman. ' The electrodes suitable for pH measurements can be used in all kinds of acidity and basicity determinations {cf. page 87). With regard to the determination and titration of metallic ions, we are limited in our choice. Metals in the electromotive series above hydrogen are easily oxidized and polarized, and they are useless in potentiometric titrations. They can be used for the measurements of metallic-ion concentrations, if special precautions against oxidation and polarization are taken. In general only noble metals such as silver and mercury are suitable for potentiometric titrations. They also serve as anion indicators, if the anion forms a slightly soluble or stable complex compound with the metal.

[Ag+][C1-] = 8,

and [Ag^ [cn = .. ,,,

[Ag+]= ^ [C1-]

The potential of the silver electrode is given by:

n = n° -t- 0.0591 log [Ag+].

In a suspension of silver chloride with an excess of alkali chloride

n = n° + 0.0591 log [Ag+] = n» + 0.0591 log • [C1-]

= n°' - 0.0591 log [c r ] .

Under these conditions, therefore, the silver electrode behaves like a chloride-ion electrode.

In oxidation-reduction reactions a bright platinum gauze or wire will serve as an indicator electrode, as a rule. Very often the electrode is slow to attain its constant potential, especially near the equivalence point. Under these conditions it is often desirable to perform the titration at a higher temperature. The potentiometric method is of especial advantage where two or more oxidizing substances are present in the solution. If one system has an oxidation-reduction potential of a different order of magnitude from the second, the system with the higher

" KolthofE and Furman, Potentiometric Titrations, Second Edition, 1931.


normal potential will be reduced first. After complete reduction a jump in potential occurs, and a second break occurs after reduction of the second system.

Another general advantage of potentiometric titrations is that no visual error can be made in the detection of the end point, and a high degree of precision can be reached. Especially in the titrations of colored systems, or of those for which we have no suitable visual indicator, the potentiometric methods have great importance.

PROBLEMS IN POTENTIOMETRY

1. At 25° a hydrogen electrode against some standard half cell has an e.m.f. of —0.6000 volt. The normal hydrogen electrode against the half cell has an e.m.f. of — 0.3000 at the same temperature. What is the pH of the solution if the barometric pressure during the measurement is 740 mm. and the vapor tension of the solution 24 mm. of mercury?

2. At 25° the potential difference between the hydrogen electrode (hydrogen pressure 1 atmosphere) and the quinhydrone electrode both placed in the same solution is 0.6990 volt. If the quinhydrone electrode is considered a hydrogen electrode of low hydrogen pressure (show how), what will be its pressure?

3. Show that the potential difference between an antimony-antimonious oxide electrode is a simple function of the pH of the solution.

4. The potential of the normal calomel electrode (against the normal hydrogen electrode) is 0.2847 volt; that of the 0.1 A' calomel electrode, 0.3376 volt. What is the e.m.f. of a cell N calomel—0.1 N calomel electrode? What would you expect if the activity of the chloride ions in both electrodes were the same as the corresponding potassium chloride concentrations?

5. The pR of the following solutions is to be measured: 0.1 Af boric acid; 0.1 M acetic acid; 0.1 Af copper sulfate, 0.01 M lead chloride; 0.1 M ferric chloride; 0.1 M morphine chloride; 0.1 Af sodium sulfide; 0.1 JVf ferrous sulfate, O.llf zinc sulfate, 0.1 Af iodine in potassium iodide. Specify which of the following electrodes can be used: hydrogen electrode, quinhydrone electrode, antimony electrode, glass electrode; and give a reasonable justification of your choice.

6. Calcxilate the change of the potential of the hydrogen electrode in the titration of 0.1 Af lactic acid with sodium hydroxide, assuming that the volume does not change during the titration. Compute the data after addition of 0 per cent, 9 per cent, 50 per cent, 91 per cent, 99 per cent, 99.8 per cent, 99.9 per cent, 100 per cent, 100.1 per cent, 100.2 per cent, 101 per cent, of the equivalent amount of sodium hydroxide. What is AE/AC near and at the equivalence point? Ka — 1.5 X 10~ . K^ = 10-". « = 25°C.

7. Solve the same problem for the titration of 0.1 M and 0.001 M hydrochloric acid.

8. After the addition of 90 ml. 0.1 N sodium chloride to 100 ml. 0.1 N silver nitrate, the potential of the silver electrode against some standard half cell is 0.4000 volt. (Ag electrode is positive.) After the addition of 110 ml. it is 0.0814 volt (25°). Calculate the solubility product of silver chloride, assuming that activities and concentrations of the ions are identical.

PROBLEMS IN POTENTIOMETRY 117

9. One-tenth normal silver nitrate is titrated with potassium bromide. Assume that the volume does not change during the titration. How much is the potential of the silver electrode after 0 per cent, 90 per cent, 99 per cent, 99.8 per cent, 99.9 per cent, 100.1 per cent, 100.2 per cent, 101 per cent addition of the equivalent amount of bromide? The solubility product of silver bromide is 5 X 10~^'.

10. A solution of eerie cerium is titrated with a ferrous sulfate solution. What is the oxidation potential after the addition of 9 per cent, 50 per cent, 91 per cent, 99 per cent, 99.8 per cent, 99.9 per cent, 100 per cent, 100.1 per cent, 100.2 per cent, 101 per cent, and 110 per cent of the equivalent amount of ferrous iron solution?

^Ce". Ce"' = +1-6 volt. n V " , Fe" = '^^•'^Q Volt.

PART III


CHAPTER VIII


1. The Principles of Conductometric Titrations. Electrometric titrations can be divided into three groups: the potentiometric, the conductometric and the amperometric. The last are discussed in Part IV of this monograph. The theory underlying these three groups is entirely different. The theory of potentiometric titrations is very similar to that of ordinary titrations, so far as the change of the potential of a suitable electrode is a linear function of the change of the logarithm of the ion concentration or the logarithm of the ratio of concentration of oxidant to reductant in the system to be titrated. A large jump in potential at the equivalence point means a sharp color change of a suitable indicator; and the titration to a definite potential is comparable to an ordinary titration in which the reagent is added until the indicator has assumed a definite color. Therefore, the electrode in a potentiometric titration can be compared to a specific indicator for the ion or oxidation-reduction system to be titrated.

In conductometric work, on the other hand, all ions present contribute to the electrical conductivity of the solution. If an electrolyte is added to a solution of another electrolyte without changing the volume to any appreciable extent, the conductivity increases in so far as the electrolytes do not react with each other. If an ion of one electrolyte unites with an ion of the other to form a slightly dissociated or slightly soluble substance or if it changes the total ion concentration by an oxidation or reduction process, then the conductivity of the solution may change in three diiferent ways, before the equivalence point has been reached: (1) the conductance decreases; (2) the conductance remains unchanged; (3) the conductance increases.

The conductance of various ions for the electric current is different. I t is usually expressed by the mobility X of the ion. The equivalent conductivity A of an electrolyte BA is equal to the sum of the mobiUties of both ions: , , , ,

ABA = AB+ -r AA-. 118

THE PRINCIPLES OF CONDUCTOMETRIC TITRATIONS 119

The equivalent conductance A is the conductance in reciprocal ohms of a solution containing one gram equivalent of solute when placed between electrodes which are 1 cm. apart; hence it is equal to the specific conductance divided by the concentration, the concentration being expressed in equivalents per milliliter.

A = ;^ 1000.

K denotes the specific conductance of the solution; C the concentration expressed in equivalents per liter. The equivalent conductance, in other words, is the specific conductance the solution would have if the electrolyte were present in a concentration of one equivalent per milh-liter. On account of the interionic effect the equivalent conductance or the mobihty of^the ions decreases with increasing electrolyte content of the solution. The values reach a maximum at infinite dilution. In dilute solutions the following relation holds between the equivalent conductance Ac at a concentration C and A^:

Ac = Aoo — A\/C.

A is a constant which is different for various electrolytes. The mobility of the ions increases very much with the temperature, as their migration velocity increases. The increase of the mobility of most ions is 2 to 2.5 per cent for 1°C. increase in temperature; for hydrogen ions the change is only 1.5 per cent; for hydroxyl ions, 1.8 per cent.

In the following table the mobilities of some ions at 25° and at infinite dilution are reported. The data are taken from reliable studies reported in the literature.'

MOBILITY OF SOME IONS AT 25° AT INFINITE DILUTION

Li+ 39 OH" 196 Na+ 60.5 CI- 76 Ag+ 62 NO3- 72 K+ 74 HCO3- 47 NH4+ 74 IO3- 41 H+ 350 CH3COO- 40 |Ba++ 64 |C03= 83 |Ca++ 60 40204= 70 iMg++ 53 |S04= 81 |Pb++ 73 |Fe(CN)62 97 T1+ 75 jFe(CN)8= 101 4Ni++ 52 |Fe++ 54 |Fe+++ 68.4

* Mainly from Landolt-Bornstein-Roth, Physikalisch-Chemische Tabellen, Fifth Edition, J. Springer, Berlin.

120 CONDUCTOMETRIC TITRATIONS

Let us now consider how the conductance of a solution of a strong electrolyte BA will change upon the addition of a reagent CD, assuming that the cation B"*" reacts with the anion D~ of the reagent. If the product of reaction is slightly dissociated or insoluble, the reaction may be expressed by the equation:

B+ + A - + C+ + D - - » BD + A - + C+ ion to be reagent insoluble or

determined slightly dissociated

Therefore, by the reaction between B"*" and D ~ ions, the B ions during the titration are replaced by C ions.

Case 1. The mobility of the B ions (XB) is greater than that of C; the conductance of the BA solution decreases upon the addition of the reagent CD. This case generally occurs in the titration of strong acids with strong bases or in the reverse titration. The hydrogen and hydroxyl ions distinguish themselves from the other ions by a much greater mobility. (See table of mobility of ions.)

Case 2. XB and Xc are equal. The conductance remains unchanged by the addition of CD until the equivalence point has been reached. This case is encountered in most precipitation reactions. In the titration of silver nitrate with barium chloride, the barium ion takes the place of the silver ion, and, as both ions have about the same mobility, the conductivity does not change during the reaction. If, instead of barium chloride, sodium chloride is used as a reagent, the conductivity decreases slightly, as XAS is greater than XNa- On the other hand, with potassium chloride as a reagent, the conductivity increases slightly because XAg is smaller than XK.

Case 3. The conductivity increases from the beginning of the titration if a shghtly dissociated substance is titrated and the reaction product is a strong electrolyte. This case in general occurs in the neutralization of a weak acid with a strong base or a weak base with a strong acid. The conductivity then increases after the equivalence point has been reached, at least if the reagent is a strong electrolyte.

In a conductometric titration the conductance is measured after the addition of successive amounts of reagent. The points thus obtained are plotted to give a graph which as a rule consists of two straight lines intersecting at the equivalence point. Therefore, this point is found graphically. In contrast to ordinary and potentiometric titration methods, measurements near the equivalence point have no special significance. As a matter of fact, the values found near the equivalence point are often worthless in the construction of the two straight lines, on account of the fact that the reaction product by its dissociation or solu-

THE PERFORMANCE OF CONDUCTOMETRIC TITRATIONS 121

bility contributes to the conductivity of the solution, whereas \vc must use the data in which the conductivity contributed by the reaction product itself is negligibly small. Even if the conductivity of the reaction product at the equivalence point is appreciable, the reaction often may be made the basis of a eonductometric titration, if the conductance of the reaction^product AB is practically completely suppressed in the presence of a reasonable excess of A or of B. Near the equivalence point the points often do not lie on one of the two straight lines, but the conductivity found is higher than the corresponding ones on the straight Unes (titration of very weak acids and bases: hydrolysis; precipitation reactions). (C/. Figs. 31 and 32.)

The point mentioned, that a marked hydrolysis, solubiUty, or dissociation of the reaction product does not affect the accuracy of the method very much, makes the application of conductometric titrations possible ivhere ordinary or potentiometric titration methods fail to give results. This will be shown by several examples in the following review.

On the other hand, it is emphasized here that the conductometric method can be much less generally applied than the ordinary or potentiometric or amperometric ones, on account of the fact that large amounts of foreign electrolytes, which do not take part in the reaction, affect the accuracy greatly. The relative change of the conductivity during the reaction and upon the addition of an excess of reagent mainly determines the accuracy, and this change is decreased by the presence of foreign electrolytes. Of course one must not infer from this that the conductometric method is rendered impossible by the presence of foreign electrolytes; if precision methods are used in the measurement of the conductivity and the titration is carried out in a thermostat, the method can be applied in the presence of relatively large amounts of indifferent electrolytes—at the cost, however, of the simpUcity of the method.

2. The Performance of Conductometric Titrations. For details about the measurement of electrical conductance and the significance of the cell constant the reader is referred to textbooks on electrochemistry.

An ordinary conductometric titration can be carried out in a relatively short time (ten minutes or longer).

A titration cell as shown in Figs. 22 or 23 can be used. Figure 22 shows the more or less classical model of Dutoit. The two platinized platinum electrodes are in a vertical position in order to prevent the deposit of a precipitate in precipitation reactions. The electrodes are welded to a platinum wire which is sealed in the glass and makes electrolytic contact outside the vessel in a mercury pocket. The cell is placed in a block of wood or paraffin. Successive portions of the reagent are added from a microburet which can be connected in some way to a


reservoir containing a supply of the standard solution. A reagent which is at least ten to twenty times more concentrated than the solution to be titrated is recommended. The cell in Fig. 22 also contains a thermometer divided into 0.1 degree. A change in temperature during the titration will affect the result very much, as the conductivity increases

7

Electrode • I

FIG. 22. Titration vessel. FiQ. 23. Titration vessel with handle.

greatly with increasing temperature (for most salts about 2 to 2.5 per cent for 1°). If the heat of reaction is fairly high, irregularities in the conductivity curve may occur on account of the temperature effect. As a rule, however, the heat effect during a titration is very small. After the addition of reagent the cell is shaken to secure homogeneous mixing; in this manipulation one has to be careful not to warm the solution by taking the whole cell in his hand. A glass handle attached to the cell, as in Fig. 23, is convenient for the shaking. If work is done with solutions of quite different conductance, one should have a few titration cells available with different cell constants adapted to the

THE PERFORMANCE OF CONDUCTOMETRIC TITRATIONS 123

special purpose. The accuracy in the location of the end point in con-ductometric titrations as a rule is not greater than 0.5 to 1 per cent. For precise work the titration should be performed in a thermostat.

I t is not necessary to know the absolute values of the specific conductivity of the solution during the titration; the reciprocal value of the resistance can be plotted, as it is proportional to the conductance. More accurate results are obtained if the dilution effect is taken into account. The values of the reciprocal of the resistance are multiplied W (.V ~\- v)/V, in which V is the original volume and v the volume of reagent added.

The conductance can be measured according to the classical method of the Wheatstone bridge, using a telephone for the detection of the minimum. Though this method is quite satisfactory, it has a practical disadvantage, namely, that one needs a quiet room, undisturbed by noises. This requirement might prevent a more general application of conductometric titrations. Fortunately, at the present time the telephone can be replaced by other instruments or arrangements so that the minimum can be detected visually.

In the first place, the Leeds and Northrup or any other make of alternating-current galvanometer may be mentioned. The equipment provides means for utilizing current from a 60-cycle 110-volt a-c. circuit, and the galvanometer is especially recommended for conductometric titration work. I t is not suitable for highly precise measurements, and even in titrations some difficulties may arise by polarization of the electrodes and the heating of the solution in the cell. If these difficulties are overcome, it seems that the a-c. galvanometer will be the simplest apparatus for detection of the point of balance on the Wheatstone bridge.

Of the various types of direct-reading conductance meters described in the literature, the following may be mentioned. Jander and Schor-stein ^ use an a-c. galvanometer with a Wheatstone bridge. Sand and Griffin' use a dry rectifier with a d-c. galvanometer on a bridge circuit. Treadwell * and Callan and Horrobin ^ use a vacuum-tube circuit for applying the alternating current to the cell and for reading the relative resistance of the cell. A disadvantage of these vacuum-tube circuits is the necessity of using calibration curves for the determination of the cell resistance.

Garman * has designed a vacuum-tube circuit with a self-contained

2 G. Jander and H. Schorstein, Z. angew. Chem., 45, 701 (1932). ^ H. T. S. Britton, Condtictometric Analysis, London, Chapman & Hall, 1934. «W. D. Treadwell, Helv. Chim. Acta, 8, 89 (1925). 5 T. Callan and S. Horrobin, / . Soc. Chem. Ind., 47, 329 (1928). 8 R. L. Garman, Ind. Eng. Chem., Anal. Ed., 8, 146 (1936).


bridge, oscillator, and detector which indicates the resistance of the cell on a d-c. current microammeter. The circuit diagram is shown in Fig. 24.

An alternating voltage is obtained from the upper section of the triode 6A6 vacuum tube (Fig. 24) used as an oscillator, and applied to

AA4 -o o-

llOv-Ac-Bc

10 R»

FIG. 24. Vacuum-tube circuit for conductivity determination according to Garman.

ffs. Ri. Rb-Re K? Rs

Bio.

5 to 7 megohms, 1 watt. l-megohm volume control. 50,000-ohm volume control. Voltage divider, 1000 ohms, 25 watts. Voltage divider, 20,000 ohms, 25 watts. Volnme control, 15,000 ohms. General radio potentiometer, 1000 ohma. General radio potentiometer, 100 ohms. IS ohms, 100 watts. 140 ohms, 100 watts.

Ci. Condenser, 0.01 mfd., mica. CitCîd. Condensers, paper, 0.5 mfd., 200 volts. C^. Electrolytic condenser, 8 mfd. Cg. Electrolytic condenser, 4 mfd. T\. Low ratio audio transformer. Tg. Single-button carbon microphone trans

former. Ll. Choke, 30 H. Li. Choke, 30 H. 200 ohma. tia.. 0-500 microammeter.

the bridge through the condensers C3 and C4. The circuit is designed to eliminate the necessity for calibration curves in conductometric titrations by making the meter reading a linear function of the resistance of the conductance cell. The output voltage of a conductance bridge is a parabolic function of the resistance of one of its arms (the conductance cell). The output voltage of the bridge is applied to the primary of the

GONDUCTOMETRIC TITRATIONS AND ACID-BASE REACTIONS 125

step-up transformer T'2- The stepped-up voltage is applied to the grid of the lower section of the triode 6A6 vacuum tube. The circuit is so arranged that the plate current of the tube is a parabolic function of the grid potential so that the plate current becomes a linear function of the resistance of the conductance cell. The linearity between plate current and resistance holds only over a certain range, from 100 to 500 microamperes of plate current. Therefore, in practice the bridge is always in a state of slight unbalance to bring the plate current into the correct range. A rectifier and filter system is included to permit operation on both 110-volt a-c. and d-c. lines.

3. Application of Conductometric Titrations to Acid-Base Reactions. In this section a condensed review of the application of conductometric titrations to acid-base reactions is given. For details the reader is referred to monographs on the subject.'

Strong Acids with Strong Bases. In the following graphs the ordinate represents the conductivity and the abscissa the volume of reagent added. In the titration of a strong acid with a strong base (or vice versa) a sharp break in the conductivity occurs at the equivalence point (Fig. 25). Theoretically the minimum should not occur exactly at the equivalence point where pH is 7, but slightly at the alkaline side, as the mobility of the hydrogen ions is much greater than that of the hydroxyl ions. From a simple differential equation it can be computed that the minimum occurs at a hydroxyl-ion concentration of 1.4 X 10~^. The difference between this and the neutral point is so small that it cannot be determined experimentally.

I t is of interest to note that the shape of the conductivity line is practically independent of the dilution. Extremely dilute solutions of strong acids or strong bases, of the order of 0.0001 N, can be titrated with the same accuracy as more concentrated solutions, if care is taken to exclude carbon dioxide.

On the whole, the application of the conductometric titration has practical significance only when the solution has a dark color so that the indicator method fails to give results.

Intermediate Weak Acids and Bases. The shape of the neutrahza-tion curve depends upon the concentration and the ionization constant of the acid or base. As a result of neutraUzation of the dissociated part of the acid, the conductivity will drop, and on account of the formation of its salt, which behaves as a strong electrolyte, the conductance

' I. M. Kolthoff, Konduklometrische Tiirationen, Dresden, 1923, VerlagSteinkopff; H. T. S. Britton, Conductometric Analysis, D. Van Nostrand Company, New York, 1934; G. Jander and O. Pfundt, Die visxielle Leitfahigkeitstitration, Second Edition, F. Enke, Stuttgart, 1934.


increases. The practical neutralization curve is obtained by adding the figures of the " acid-depression curve " to those of the " salt line." The more strongly the acid is ionized, the more its neutralization curve approaches that of a strong acid, and the less it is ionized the more it behaves like an extremely weak acid; the latter case will be discussed later.

In Fig. 26 the neutralization curves are given for the neutralization of 0.1 N, 0.001 N, and 0.0001 N acetic acid, respectively. From the above it is evident that frequently a flat minimum will occur in the neutralization curve. Its location can be calculated from the ionization constant, the concentration, and the mobilities of the ions present in the

FIG. 25. Strong acid and strong FIG. 26. Acetic acid with sodium hydroxide.

system. The minimum itself has no analytical significance, though it may give us an indication of the magnitude of the ionization constant of an acid, which may be of importance in dealing with a solution of an unknown acid. If the acid is relatively highly ionized, the neutralization, line mil give a curve up to the equivalence point, and it is hard to find with any degree of accuracy the point of intersection of the neutralization curve with the sodium hydroxide line, which is the straight line found after addition of an excess of base.

This occurs, for example, in the neutralization of 0.01 N salicyUc acid as is shown in Fig. 27. An analysis of the curve shows that the equivalence point is found at the point of intersection of the salt line and sodium hydroxide line. The equivalence point can be determined experimentally. Suppose that 100 ml. 0.01 N salicyUc acid is titrated with 0.5 N sodium hydroxide so that the sodium hydroxide line can be drawn. In order to find the shape of the salt line a second determination

COMDUCTOMETRIC TITRATIONS AND ACID-BASE REACTIONS 127

is made in which 100 ml. of water instead of dilute acid is taken and successive amounts of 0.5 N sodium salicylate of exactly the same strength as the sodium hydroxide are added. From these data, the salt line can be constructed and the equivalence point can be found with an accuracy of at least 1 per cent.

From a practical viewpoint this method is of hardly any significance. Righellato and Davies ^ recommend the addition of a known amount of ammonium salt to the solution of the acid. The first end point after the neutralization of the acid is not found with any accuracy, but the second one indicating the end point in the replacement titration (see page 130) of ammonium salt can be found accurately. Since the amountof ammonium salt added is known the amount of strong base required for the neutralization of the acid is easily found. It is far simpler, however, to decrease the dissociation of the acid by the addition of a sufficient amount of ethanol. The ethanol decreases the ionization of the acid, and the part of the neutralization curve before the end point may become a straight line in the presence of enough alcohol. This method is recommended by the authors if the neutralization curve in water remains a curve to the end point. In general the neutralization curve in water will be a straight line before the end point if the ionization constant is smaller than 5 X 10~^ in the titration of 0.1 N solutions, smaller than 5 X 10""^ in the titration of 0.01 A solutions, and smaller than 5 X 10"*^ in the titration of 0.001 A'' solutions. If these conditions are not fulfilled the addition of alcohol is recommended.

Very Weak Adds and Bases. The initial conductivity is very small, and during the neutralization the conductivity increases according to the salt line. On account of the hydrolysis of the salt formed, the experimental data near the equivalence point are higher than the corresponding points on the salt and sodium hydroxide hne; therefore, in . the construction of the two lines, points should be taken at such a dis-

5 E. C. Righellato and C. W. Davies, Trans. Faraday Soc, 29, 429 (1933).

Fia. 27. Neutralization of 0.01 A'' salicylic acid with sodium hydroxide.

ABE, neutralization curve. EDt sodium hydroxide line. OEC, salt line. AF, acid depression curve.


tance from the equivalence point that the hydrolysis is negligibly small and the points can then be combined to give straight lines. If the acid is extremely weak (e.g., hydrogen peroxide) the hydrolysis is so large that the titration does not yield useful results. For the titration of 0.1 A'' solutions, the ionization constant should be larger than about 10~^°, for 0.01 N solutions larger than 10~^, for 0.001 A'' solutions larger than 10~^. These figures have no exact significance; they indicate only the order of magnitude of the ionization constant at which useful results can still be obtained.

From the above we see that the conductometric titration can be applied where the potentiometric or ordinary methods do not give satisfactory results.

In Fig. 28 neutralization curves of 0.1 N and 0.01 N boric acid with sodium hydroxide are shown. Several apphcations can be made.

Hydroxybenzenes, like phenol and resorcinol, can be titrated very nicely. A systematic study has shown that resorcinol and hydroquinol behave like dibasic acids; pyrocatechol, on the other hand, as a monobasic acid. The trivalent phenols, pyro-gallol and phloroglucinol, behave like dibasic acids. The method has been applied to the titration of nitro-phenols, pheno lph tha le in , and other weak acids whose salts are colored. Phenol

phthalein in 50 per cent alcohol behaves like a dibasic acid, a break occurring after the neutralization of the carboxyl and phenol groups. The conductometric method should be very useful to organic chemists in cases where they want to know quantitatively the acid or basic character of a colored substance. It also can be recommended for the determination of the equivalent weight of amino acids ' and polypeptides, and the acid- or base-combining power of proteins. A practical application of the method can be made in the determination of vanillin in vanillin sugar. The aromatic substance is extracted with alcohol and titrated as a strong base.

FIG. 28. Neutralization of boric acid with sodium hydroxide.

» See E. M. P. Widmark and E. L. Larsson, Biochem. Z., 140, 284 (1923).

CONDUCTOMETRIC TITRATIONS AND ACID-BASE REACTIONS 129

What has been said for very weak acids holds also for very weak bases. Aniline, hexamethylenetetramine, and pyridine can be titrated accurately with hydrochloric acid.

Neutralization of Weak Acids with Weak Bases. Though in analytical work one always uses a strong acid or a strong base as a reagent, the neutraUzation of a weak acid with a weak base has practical significance, e.g., when a pure ammonium salt of a weak acid has to be prepared or when a weak acid must be titrated in the presence of an ammonium salt or the salt of another weak base.

Figure 29 shows the titration lines of 0.01 A'' acetic acid with ammonia. The neutraUzation curve up to the equivalence point is about the same as found with sodium hydroxide, since both sodium and ammonium acetate are strong electrolytes. After the equivalence point has been reached, an excess of ammonia leaves the conductivity p rac t i ca l ly unchanged, as the dissociation of the weak base is depressed by the presence of the ammonium salt. On account of the hydrolysis, the values near the equivalence point are somewhat lower than the corresponding points on the straight lines. If the acid or base to be titrated is extremely weak (e.g., boric acid with ammonia), no straight lines are found on account of the strong hydrolysis.

Mixtures of a Strong and Weak Acid. Here again the conductometric method can be advantageously apphed, whereas the ordinary or poten-tiometric method does not yield satisfactory results. The above case is a combination of two which have been discussed before. First, the strong acid is neutralized and the conductivity drops, following a straight line. Near the first equivalence point, the weaker acid will be neutralized and the conductivity will soon increase according to the salt line of the weak acid. In Fig. 30, the change in conductivity during the neutralization of a mixture of 10 ml. 0.01 N hydrochloric acid, 10 ml. 0.01 N acetic acid, and 10 ml. of water with 1 N sodium hydroxide is shown. The case has practical significance, e.g., for the determination of traces of mineral acids in vinegar. If the suppression of the dissociation of the second acid is not practically complete, say at a distance of 50

. C.C. N Ha

FIG. 29. Neutralization of 0.01 N acetic acid with ammonia.


per cent or less from the first equivalence point, the authors recommend that the titration be carried out in the presence of an adequate amount of ethanol. The conductometric titration can be used in the determination of the purity of sulfonphthaleins. The sulfonic agroup behaves as a strong acid and is first neutralized; after the first break, the conductivity increases, and after neutralization of the phenolic group a second break occurs. Periodic acid behaves as a dibasic acid. The first ioni

zation constant is very great, and a break in the conductivity line occurs at the first equivalence point. The second ionization constant is small, and, therefore, a second break occurs at the second equivalence point.'"

The application of the conductometric method to the titration of a mixture of two weak acids with quite different ionization constants (like acetic and boric acid) has little practical significance, for a sharp break never occurs after the neutralization of the stronger acid. The difference in mobility of the anions of the two acids determines the acuteness of the break, and as this difference always is very small, the angle between the two

salt lines will be very obtuse. Therefore, as a rule, the first equivalence point cannot be found with a high degree of accuracy.

Replacement Titrations. When a salt of a weak acid is titrated with a strong acid, the anion of the weak acid is replaced by that of the stronger one and the weak acid itself is liberated in the undissociated form. Similarly, the addition of a strong base replaces the weak base in a salt of the weak base.

Many important applications of these replacement reactions can be made to conductometric titrations, especially where successful results are not obtained with the indicator or potentiometric method.

If, for example, hydrochloric acid is added to a solution of sodium acetate, the acetate ion is replaced by the chloride ion. The conductivity increases slightly on account of the fact that XQI is a little greater than Xacetate- After all the acetic acid has been liberated, continued addition of hydrochloric acid gives rise to a strong increase in con-

- C.C. Na OH

FiQ. 30. Mixture of 0.01 N hydrochloric and 0.01 N acetic acid.

I N. Rae, J. Chem. Soc, 1931, 876.

CONDUCTOMETRIC TITRATIONS AND PRECIPITATION 131

ductance. Figure 31 shows the conductance lines in the titration of 0.01 N sodium acetate with N hydrochloric acid. On account of the dissociation of the acetic acid, the experimental figures near the equivalence point are somewhat higher than the corresponding ones on the straight lines. If the ionization constant of the liberated acid is smaller than about 5 X 10~^, 0.01 N solutions of its salt can be titrated accurately. For 0.1 A solutions, the constant may even be as large as 5X10-*. Ethyl alcohol decreases the ionization of weak acids, and in the presence of enough alcohol even salts of stronger acids than those i n d i c a t e d above can be titrated.

The method furnishes a simple means for the evaluation of salts of weak acids, such as acetates, benzoates, and succinates. Similarly, it can be applied to the determination of ammonia in ammonium salts by titration with sodium hydroxide. The ammonium content of fertilizers can be determined rapidly in this way.

In this review, a condensed summary has been given of the application of conductometric titrations to acid-base reactions. For details concerning the combination of different systems and specific substances (carbon dioxide, phosphoric acid, alkaloids, phenols, salts of heavy metals, etc.) the reader is referred to the monographs on the subject (page 125).

From all that has been said, it may be inferred that the significance of conductometric titrations should be more generally recognized. They often furnish us information which could otherwise be obtained only by elaborate work.

4. Application of Conductometric Titrations to Precipitation and Complex Formation Analysis. A reaction usually can be made the basis of a conductometric titration if the reaction product is a slightly soluble substance or a stable complex. The usefulness and accuracy are mainly dependent upon the following factors:

FIG. 31. Titration of 0.01 A' sodium acetate with hydroohloric acid.

(a) Errors in the determination of the conductance data. (b) Solubility of the precipitate or stability of the complex.


(c) Speed of formation of the precipitate. (d) Constant composition (purity) of the precipitate.

(a) The same error in the determination may affect the accuracy of the titration in different ways. This depends upon the acuteness of the angle between the precipitation line (Hne combining the conductance data during the precipitation) and the reagent line (line giving the conductance data with excess of reagent). The more acute the angle is, the more accurate the result. If the angle is very obtuse, a small error in the conductance data can cause a large deviation. Therefore, one should always endeavor to choose such experimental conditions that the angle is as acute as possible. The following rules should be borne in mind:

(1) The smaller the mobility of the ion which replaces the reacting ion, the more accurate will be the result. If a silver salt is titrated with lithium chloride, the conductivity decreases during the precipitation and increases after the equivalence point. If hydrochloric acid were used as a reagent, the conductivity would increase from the beginning of the titration, and the angle between the precipitation and reagent line would be very obtuse. Therefore, generally it is recommended that cations be titrated with lithium salts and anions with acetates.

(2) The larger the mobility of the anion of the reagent which reacts with the cations to be determined (or vice versa), the more acute is the angle. For example, it is more advantageous to titrate silver salts with sodium chloride than with sodium nitroprusside, as the mobility of the chloride ion is larger than that of the nitroprusside.

(3) The titration of a slightly ionized salt does not give good results, since the conductivity increases relatively much from the start of the determination.

(4) As was mentioned at the beginning of this chapter, the accuracy of a conductometric titration always suffers from the presence of electrolytes that do not take part in the reaction.

(b) On account of the solubility of the precipitate, the experimental figures near the equivalence point deviate from the straight line, as is shown in Fig. 32. AEDFC is the experimental curve. If the solubility of the precipitate were negligibly small, the conductivity at the equivalence point would be equal to BG instead of DG. By an excess of the ion which is precipitated or an excess of reagent, the solubility is depressed, and if the solubility is not too large, it usually is possible to construct the precipitation and reagent line by joining points on AE and FC.

It can be shown that 0.1 iV solutions can still be titrated if the solu-

CONDUCTOMETRIC TITRATIONS AND PRECIPITATION 133

bility of the precipitate formed is less than about 0.005 A''; (uni-univalent electrolyte); for 0.01 A' solutions the solubility should be smaller than about 0.0005 A .

(c) The formation of a microcrystalline precipitate is usually a time reaction. After the addition of a small amount of reagent, the conductance does not immediately become constant; one must wait for some time. Seeding the solution with the precipitate itself has a favorable effect, though in the titration of very dilute solutions even this does

FIG. 32. Precipitation Line.

not overcome the difficulty. Quite generally it is much better to add enough alcohol to make its concentration about 30—40 per cent. The speed of formation of the precipitate then becomes much larger, and, furthermore, another advantage is gained, the solubihty of most shghtly soluble substances is materially reduced by alcohol. Of course, one should realize that on the addition of alcohol to a solution the temperature rises; therefore, before the titration is started, the mixture should be cooled to room temperature.

(d) If the precipitate has strong adsorptive properties, the method does not yield successful results. So, for example, the titration of heavy metals with sodium sulfide or ferrocyanide cannot be recommended on account of the inconstant composition of the precipitate. If a micro-crystalline precipitate like barium sulfate or calcium oxalate is formed, occlusion phenomena may play a part. Finally, it may be mentioned that under certain conditions the surface conductance of the sohd precipitate may affect the results.

Since no complete summary of precipitation or complex reactions which have been made the basis of a conductometric titration has been given in the literature we conclude this chapter with such an up-to-date


list. For the sake of brevity the various t i trations which can be made with a certain reagent are tabulated below.

Silver nitrate as reagent: Chloride/'- ' bromide,'-'^ iodide/^ cyanide/^ thio-cyanate,'"- ohromate/'^ selenite/^ cyanate/*' '^ selenooyanide," molybdate," tuiigstate.-^'

Mercuric perchlorate as reagent: Chloride,'^ bromide,'^ iodide/^ cyanide/ ' thio-cyanate/* selenocyanide/^ formate/ ' ace ta te ' ' and its homologs.^'

Lead nitrate as reagent: Iodide/" ferrocyanide/' ferricyanide/" sulfate/"' ^ sulfite/" thiosulfate/" pyrophosphate/" molybdate/^' ^' tungstate/^ sele-nite/* selanate/^ oxalate/" tartrate/" succinate/" benzoate.^"

Barium acetate {or barium chloride) as reagent: Sulfate/'^' ^'' ^' chromate/^ carbonate/^ pyrophosphate/^ oxalate/* tartrate/* citrate/'' selenate.^*

Thallous sulfate as reagent: Iodide.^" Uranyl acetate (or nitrate) as reagent: Phosphate/"' "' ' ' ' ' - ' ^ arsenate.^' Lithium sulfate as reagent: Barium/*' '* strontium/' ' * calcium/'' *

lead.2"' 31 Lithium oxalate as reagent: Calcium/' ' ^ ^ ' '• ^ barium/^ strontium/^ silver/^

lead/^ copper/^ cadmium/^ nickel/^ cobalt/^ manganese/^ ferrous iron/^ magnesium.^^

111. M. Kolthoff, Z. anal. Chem., 64, 229 (1923). 12 For microtitration of chloride see G. Jander and H. Immig, Z. Elektrochem.,

43, 207 (1937). 13 R. Ripan and R. R. Tilioi, Z. anal. Chem., 117, 47 (1939); at pH = 9. " O. Pfundt, Angew. Chem., 46, 218 (1933). i=R. R. Tilici, Z. anal. Chem., 99, 110 (1934); 100, 405 (1935). 18 R. R. Tilici, Z. anal. Chem., 99, 415 (1934). I 'C. Candia and I. G. Murguloscu, Bull. soc. chiin. Romania, Chem. Abs., 30,

7062 (1936). 181. M. Kolthoff, Z. anal. Chem., 64, 332 (1923). 1' R. R. Tilici, Z. anal. Chem., 107, 111 (193G). » I. M. Kolthoff, Z. anal. Chem., 64, 369 (1923). 21E. Miillcr and H. Kogert, Z. anorg. allgem. Chem., 188, 60 (1930). 22 E. Rother and G. Jander, Angew. Chem., 43, 930 (1930). 22 J. Bye, Bull. soc. chim., 6, 174 (1939). 21 R. R. Tilici, Z. anal. Chem., 114, 409 (19,38). 25 R. R. Tilici, Z. anal. Chem., 102, 28 (1935). 261. M. Kolthoff, Z. anal. Chem., 61, 433 (1922). 2' P. Dutoit, Bull. soc. chim., 7, 1 (1910); / . chim. phys., 8, 2 (1910). 281. M. Kolthoff and T. Kameda, Ind. Eng. Chem.., Anal. Ed., 3, 129 (1931). 29 P. B. Mojoiu, Thesis, Lausanne, 1909. 2" L. Deshusses and J. Deshusses, Helv. Chim. Acta, 7, 681 (1924). 81 A. Chretien and J. Kraft, Bull. soc. chim. (5), 5, 1399 (1938). 32 F. H. H. Van Suchtelen and A. Itano, / . Am. Chem. Soc, 36, 1793 (1914). «3 G. A. Freak, J. Chem. Soc, 115, 55 (1919). " I. M. Kolthoff, Z. anal. Chem., 62, 1 (1922). " I. M. Kolthoff, Z. anal. Chem., 62, 161 (1922).

PROBLEMS 135

Sodium (or lithium) chromate as reagent: Barium,^^- '* strontium,^^- * lead,^^- *' silver,'* thallous thallium.^^

Sodium sulfide as reagent: Zinc,'' copper,^' bismuth,' ' silver,'' cadmium," ferrous iron."

Hydrogen sulfide as reagent: Lead,'^ cadmium,^^ copper/' silver,'^ and bismuth.'*

Potassium ferrocyanide as reagent: Zinc," lead." Calcium ferrocyanide as reagent: Potassium *" (in 36 per cent alcohol; K2CaFe

(CN)6 precipitates). Potassium ferricyanide as reagent: Cobalt,'* nickel," cadmium,'* copper." Lithium halides as reagent: Silver.^'' '^' '* Bismuth oxyperchlorate as reagent: Phosphate.^"-Sodium perchlorate as reagent: Potassium *^ (at 0° C , not accurate).

PROBLEMS 1. One thousandth normal hydrochloric acid is titrated with sodium hydroxide.

Calculate the conductance of the solution after the addition of 0 per cent, 20 per cent, 40 per cent, 60 per cent, 80 per cent, 100 per cent, 120 per cent, 140 per cent, 180 per cent, of the equivalent amount of base, assuming that the volume does not change during the titration. XH = 350; XQH = 196; Xjia = 51; Xoi = 76. Plot the results in a graph,

2. Tenth normal acetic acid is titrated with sodium hydroxide. Calculate the data of the neutraHzation curve (see problem 1), and plot the results in a graph. Ionization constant acetic acid is 1.8 X 10"^; XH = 350; XOH = 196; XNa = 51; Xacetate = 40.

3. The same problem as 2, but instead of 0.1 N acetic acid 0.0001 N acetic acid is taken.

4. A 0.01 A solution of ammonium chloride is titrated with sodium hydroxide. Calculate the conductance of the solution after the addition of 0 per cent, 20 per cent, 40 per cent, 60 per cent, 80 per cent, 100 per cent, 120 per cent, 140 per cent, 160 per cent, 180 per cent, of the equivalent amount of base, assuming that the volume does not change during the titration. Plot the results in a graph. Ionization constant of ammonia is 1.8 X 10~^; XNH4 = 74; Xci = 76; XNa = 51; XOH = 196.

6. A 0.1 Af solution of silver nitrate is titrated with lithium chloride. Calculate the conductance of the solution after the addition of 0 per cent, 20 per cent, 40 per cent, 60 per cent, 80 per cent, 100 per cent, 120 per cent, 140 per cent, 160 per cent, 180 per cent, of the equivalent amount of chloride, assuming that the volume does not change during the titration. Plot the results in a graph. Solubility product of silver chloride is 10-i»; XAS = 62; XNOS = 72; Xn = 39; Xci = 76.

6. The same problem as 5, but calculate for 0.001 A silver nitrate solution. (Solubility of silver chloride.)

'»I. M. Kolthoff, Z. anal. Chem., 62, 97 (1922). ^'G. Hengeveld, Thesis, Lausanne, 1911. " H. Immig and G. Jander, Z. EleUrochem., 43, 207, 214 (1937). '«I. M. Kolthoff, Z. anal. Chem., 62, 209 (1922). •o J. H. Boulad, / . Soc. Chem. Ind., 52, 270T (1922). «i J. Harms and G. Jander, Angew. Chem., 49, 106 (1936). " G. Jander and O. Pfundt, Z. anal. Chem., 71, 417 (1927).

PART IV

VOLTAMMETRY (POLAROGRAPHY) AND


CHAPTER IX

THE FUNDAMENTAL PRINCIPLES OF VOLTAMMETRY»

1. General Characteristics of Current-Voltage Curves. Voltam-metry is defined as that part of electrochemistry which deals with the determination and interpretation of current voltage (c-v.) curves obtained in electrolysis experiments.^ The c-v. curves are useful for the detection and quantitative determination of many inorganic and organic compounds which can be reduced or oxidized at suitable electrodes. To make the principles clear we will start with a simple electrolysis experiment.

Suppose that we construct an electrolysis cell consisting of two half cells, one of which is a silver-silver chloride electrode of large area in a solution of potassium chloride, and the other a small platinum-wire electrode in a solution containing potassium chloride' and thallous

' (o) As a general reference book, see I. M. Kolthoff and J. J. Lingane, Polar-ography. Polarographie Analysis and Voltammetry. AmperoTnetric Titrations. The Interscience Company, New York, 1941.

Other review papers and monographs on the subject are: (6) J. Heyrovsk^, Polarographie, in W. Bottger, "Physikalische Methoden der

analytischen Chemie," Bd. 2 and 3, Akad. Verlagsgesellschaft, Leipzig, 1936, 1939. (c) H. Hohn, Chemische Analysen mil dem Polarographen, Julius Springer,

Berlin, 1937. (d) I. M. Kolthoff and J. J. Lingane, Chem. Rev., 24, 1, (1939). (e) For a complete bibUography from 1922 to 1938, see J. HejTovsk^ and J.

Klumpar, Collection Czechoslov. Chem. Commun., 10, Nos. 2 and 3, 1938. ' For nomenclature see L M. Kolthoff and H. A. Laitinen, Science, 92, 152 (1940). ' Quite generally in electrolysis experiments discussed in this chapter an indif

ferent salt is added in a concentration which is large in comparison with the concentration of the electro-reduced or oxidized substance. By indifferent electrolyte we mean an electrolyte which is not reduced or oxidized in the potential region studied. The purpose of the addition of indifferent electrolyte is explained on page 147.

136

GENERAL CHARACTERISTICS OF CURRENT-VOLTAGE CURVES 137

chloride with the dissolved oxygen removed. We may represent the cell:

Ag I AgCl (s), KCl II KCl, TlCl I Pt.

The potential of the silver-silver chloride electrode is considerably more positive than the potential of a metallic thallium electrode would be in the thallous chloride solution. The potential of the platinum electrode in the oxygen-free thallous chloride solution is indeterminate and variable, but it is more negative than that of the silver electrode. If the above cell were short-circuited, practically no current would flow, since in order for a current to flow metallic thallium would have to enter solution, or some other oxidation process would have to occur at the platinum electrode. No such process can occur at the unattackable electrode in this cell. Actually in the short-circuited cell the platinum electrode simply would assume the potential of the silver-silver chloride electrode without the passage of any appreciable current. The platinvim electrode is said to be polarized since its potential can be altered arbitrarily (over a certain range) without the passage of a current. Actually a small residual current would flow, but this will be neglected in the present discussion and will be considered later.

We will consider now what will happen if an e.m.f. is applied to the cell in such a direction that the platinum electrode is made negative with respect to the silver-silver chloride electrode. Suppose that the thallous chloride solution is kept well stirred. By vigorous stirring the concentration of the solution is kept uniform throughout and a change in concentration at the electrode surface (concentration polarization) is prevented; moreover we assume that no other types of polarization effects are encountered. The c-v. curve obtained in this somewhat ideaUzed case is shown by ABC in Fig. 33. From A to 5 , practically no current flows. The potential of the silver-silver chloride electrode in the potassium chloride solution is fixed, and remains constant even when small currents pass through. I t is a depolarised electrode. Upon increasing the applied e.m.f. from A to B (Fig. 33) the platinum electrode, being perfectly polarized, adopts the correspondingly increasing negative

FIG.

D G J Applied ejoS.

33. Current-voltage curves in electrolysis without polarization.

138 THE FUNDAMENTAL PRINCIPLES OF VOLTAMMETRY

potential. At point B the potential of the platinum electrode has been made equal to the potential of a metalUc thallium electrode in the thallous chloride solution. At this point an increase in the applied e.m.f. causes a current to flow due to the deposition of thallous ions on the platinum surface. The small electrode is said to have become depolarized by the deposition of thallous ions. With an increasing applied e.m.f. the current increases linearly in accordance with Ohm's law, the slope of the line being inversely proportional to the resistance of the electrolysis cell. If the applied e.m.f. is again decreased, the current will follow the line CB until point B is reached, which is the usual null potential of the thallium-plated electrode in the particular thallous ion solution against our silver-silver chloride electrode. A further decrease in the applied e.m.f. results in a current flowing in the opposite direction (BD) owing to the dissolution of thallium from the electrode.

Now suppose that the experiment is repeated using a solution containing a tenfold smaller concentration of thallous chloride. The null potential of a thaUium electrode has been shifted a distance of 59 millivolts (BF) in the negative direction (Chapter IV). Otherwise the c-v. curve is exactly similar (we suppose that a sufficiently high concentration of potassium chloride is used so that the resistance of the cell remains the same). Another

tenfold decrease in thallous chloride concentration shifts the null potential to point H, 59 millivolts more negative than F.

Now suppose that the above experiment is repeated with a given concentration of thallous chloride but that the solution is not well stirred or is not stirred at all. If an e.m.f. is suddenly applied corresponding to the current C in the previous discussion, this current will flow for the first instant, but, owing to the fact that the solution is not vigorously stirred, the concentration of thallous chloride near the electrode surface begins to decrease (concentration polarization). Suppose that the concentration of thallous chloride near the electrode decreases to one-tenth that in the bulk of the solution. The current decreases from point C to point K where the thallium plated electrode is in equilibrium with the concentration of thallous ions at the electrode surface. The current now

FIG.

Api>lied e.m,f.

34. Current-voltage curves in electrolysis with concentration polarization.

GENERAL CHARACTERISTICS OF CURRENT-VOLTAGE CUR^ ES 139

reaches a steady value which is determined by the rate of diffusion of thallous ions from the bulk of the solution to the electrode surface; in other words, the number of thallium ions diffusing from the bulk of the solution to the electrode is equal to the number which is deposited when the steady state is reached. Similarly, point L corresponds to a concentration of thallous ions at the electrode surface which is 0.01 of that in the bulk of the solution. As the potential of the small electrode is made more and more negative, the concentration of thallous ions at the electrode surface is continually decreased, until at point M the concentration at the electrode surface is negligibly small in comparison with that in the bulk of the solution. A further increase in the apphed e.m.f. from M to iV can no longer appreciably decrease the thallous-ion concentration at the electrode surface. The microelectrode is said to be in a state of virtually complete concentration polarization. The current can no longer increase, because it is determined by the rate of diffusion of thallous ions from the bulk of the solution to a region of practically zero concentration.

The region MN is therefore called a diffusion current region. Since the rate of diffusion is proportional to the difference in concentration in the two regions between which the diffusion occurs, the diffusion current is proportional to the concentration of thallous chloride in the bulk of the solution. This proportionality forms a basis for making quantitative determinations from c-v. curves.

Although the stationary platinum wire electrode is simple in principle it has certain disadvantages in practical work which has led to the development of other types of microelectrodes in voltammetry. In the first place, it has already been mentioned that the current does not immediately become constant after applying a given potential to the microelectrode. I t is necessary to wait for several minutes until a steady current state is reached at each applied e.m.f. Also the overvoltage of hydrogen on platinum and most metals which can be plated on platinum is small, so that the evolution of hydrogen interferes with many reduction processes which otherwise might be carried out. A platinum electrode which is rotated at a constant speed eliminates the disadvantage of waiting for a steady current, but undesirable polarization phenomena often are encountered with rotating electrodes due to the tremendously increased current densities.*

Platinum electrodes have an advantage which should not be overlooked, namely, that their only limitation in the direction of positive potentials is the evolution of oxygen, at least, if other electro-oxidizable substances such as iodide, bromide, or ferrocyanide are absent, whereas,

• H. A. Laitinen and I. M. Kolthoff, / . Am. Chem. Soc, 61, 3344 (1939).


with less noble metals, anodic dissolution of the electrode metal occurs at less positive potentials than does the evolution of oxygen.

The use of a mercury electrode is advantageous because of the very high hydrogen overvoltage on this metal. It is possible to deposit even very base metals, such as sodium and potassium, in the form of dilute amalgams without hydrogen evolution. However a stationary drop of mercury cannot serve as a microelectrode in practice because diffusion to such an electrode is easily disturbed and the results therefore are not reproducible.

Well-defined diffusion conditions and reproducible currents can be obtained by employing a dropping-mercury electrode, which was introduced by J. Heyrovsky in Prague in 1922,^ and which has been developed largely in his laboratory. Originally, Heyrovsky worked with a manual apparatus, and he introduced the term polarometry (polarized electrodes) for voltammetry carried out with the dropping electrode. Later, when Heyrovsky and Shikata (1925) constructed the seh'-register-ing apparatus for the determination of c-v. curves, the word polarog-raphy was introduced. The apparatus was called the polarograph, and a c-v. curve obtained with it a polarogram. The steep part of the c-v. curve is called a wave by Heyrovsky. In deference to the pioneer work of Heyrovsky we will often use these terms when dealing with voltammetry with the dropping-mercury electrode as the indicator electrode. By indicator electrode we mean that the characteristics of the c-v. curve are determined solely by the phenomena during electrolysis at that electrode.

The dropping-mercury electrode consists of a glass capillary from which mercury is allowed to fall in small, slowly forming drops (see page 159). At this electrode the current is never steady but fluctuates regularly with the growth of each drop. The average current over the life of the drop is measured. When the potential of the dropping-mercury electrode is changed, the same type of concentration changes occur near the electrode as in the platinum microelectrode described above. When the concentration of reducible material has reached a negligibly small value at the surface of the drops, a region of diffusion current is reached on the c-v. curve. The diffusion current again is proportional to the concentration of the diffusing substance.

In Fig. 35, a c-v. curve with two polarographic waves is shown. If two or more reducible substances are present in solution which are reduced at potentials differing sufficiently from each other, a rising step or "polarographic wave" is obtained for each substance. It will be seen

s J. Heyrovskî', Chem. Listy, 16, 256 (1922); Phil. Mag., 46, 303 (1923).

THE RESIDUAL CUKRENT 141

below that the "half-wave potential" serves as a means of identifying each substance and the height of each wave is a measure of the concentration of material responsible for it. Thus under favorable conditions a qualitative and quantitative analysis of a solution containing several substances may be made in a single determination. In the following, c-v. curves obtained with the dropping electrode will be considered in more detail.

rnH)i Potential of Droppingt Electrode

FIG. 35. Current-voltage curve of two reducible substances.

2. The Residual Current. If a c-v. curve is determined for a solution containing no substances which are reducible or oxidizable at the electrode it is observed in general that a small current flows over the whole range of potentials which it is possible to investigate. With the dropping-mercury electrode this residual current is also known as the charging or condenser current. It arises from the fact that, as each electrically charged mercury drop grows, it is necessary to build up a charge on the mercury corresponding to the applied potential. As the area of a drop increases, electrons must flow into, or away from, the mercury reservoir in the external circuit, depending upon whether the mercury surface is the negative or positive side of the double layer. At a certain potential, known as the electrocapillary zero, the mercury is uncharged, and therefore the charging current is zero. At this potential, — 0.52 volt vs. S.C.E. (S.C.E. = saturated calomel electrode), also called the isoelectric point of mercury, the surface tension of the mercury-solution interface has its maximum value. If the mercury has an excess of either positive or negative charges, the amount of work necessary to increase the area of the interface decreases owing to the electrostatic repulsion between the charges at the mercury surface, and consequently the surface tension is decreased. If the mercury is kept flowing through the capillary at a constant pressure the drop-time t (the time required for the formation


of a single mercury drop), to a fair approximation, is directly proportional to the surface tension at the drop surface. A graph showing the variation of the surface tension with the potential is known as the electro-capillary curve of mercury; the maximum point is known as the electro-capillary maximum.

Such a curve is shown plotted in Fig. 36, in which the drop time, t, is plotted as a function of the potential of a dropping-mercury electrode. Electrocapillary ions and uncharged substances decrease the surface tension of mercury and may shift the location of the maximum to more positive or negative potentials. On the above graph is also plotted the

0.0 -0.2 -0.4 -0.6 -0.8 -1.0 -1.2 -1.4 -1.6 -1.8 Potential of Droppingr Electrode (rs. S.C.E.)

-2.0

F I G . 36. Electrocapillary curve of mercury (top curve) and residual current.

residual current observed using an air-free solution of 0.1 A potassium chloride.

Suppose that we make a cell consisting of a large saturated calomel electrode connected by a salt bridge to a dilute, air-free, potassium chloride solution with a dropping-mercury electrode inserted in it. If the cell is short-circuited, the mercury in the dropping-electrode reservoir is brought to the potential of the saturated calomel electrode, which is positively charged with respect to the electrocapillary zero. As each mercury drop forms it carries away positive charges from the reservoir, and therefore it is necessary for electrons to flow from the reservoir to the saturated calomel electrode. A current in this same direction would be observed if an oxidation (anodic) process were occurring at the dropping electrode. By convention, a current in this direction is given a negative

THE FACTORS WHICH DETERMINE DIFFUSION CURRENT 143

sign while a current corresponding to a reduction (cathodic) process at the dropping electrode is given a positive sign. As mentioned above, the charging current should pass through zero at the electrocapillary maximum and change sign as the potential becomes more negative. Actually, the observed current as a rule becomes zero at a potential more positive than —0.52 volt because of a trace of reducible material (oxygen) remaining in the solution.

With stationary (or rotating) microelectrodes, the charging current is zero because the electrode area is constant with time. Actually a much smaller residual current is obtained with these electrodes than with the dropping electrode, but a small residual current due to traces of reducible or oxidizable material is observed.

In all measurements of diffusion currents, it is necessary to subtract the residual current from the apparent diffusion current in order to find the true diffusion current.

3. The Factors Which Determine the Diffusion Current. The Ilkovic Equation. It has been mentioned above that the diffusion current is determined by the rate of diffusion of the substance undergoing electrode reaction from the bulk of the solution to a region near the microelectrode where the concentration is vanishingly small. On the basis of diffusion theory, Ilkovic ^ derived the following equation for the diffusion current at the dropping-mercury electrode:

id = 0.63 nFCD^m^t^, (1)

in which the numerical factor 0.63 arises theoretically from the geometric characteristics of the dropping electrode, nF is the number of coulombs involved per mole of electrode reaction, C is the molar concentration and D is the diffusion coefficient of the diffusing material, m is the mass of mercury flowing through the capillary per second, and t is the drop time. In the equation, id is expressed in amperes, C in moles per milliliter, D in square centimeters per second, m in grams per second, and t m. seconds.

The measured diffusion current of various substances has been found to be in essential agreement with that calculated from the Ilkovic equation.'

The various algebraic factors in the Ilkovic equation may be divided for convenience into two parts: the quantity nFCD^ which is deter-

*D. Ilkovic, Collection Czechoslov. Chem. Commun., 6, 498 (1934); / . chim. phys., 36, 129 (1938).

' D. Ilkovic, loc. dt; J. J. Lingane and I. M. Kolthoff, / . Am. Chem. Soc, 61, 825 (1939).


mined by the properties of the solution, and the quantity m'^t^^ which is determined by the characteristics of the capillary.

The second quantity is important because it establishes a relationship by means of which diffusion currents measured with different capillaries may be compared. To make such a comparison, it is necessary only to determine the mass of mercury flowing per second through each capillary, and the drop time at the diffusion current region. Maas ^ has experimentally verified the proportionality between the factor m f''* for various capillaries and the diffusion current. The proportionality was found to hold if the drop time was greater than 4 seconds. For this reason it is advisable to choose a drop time of at least 4 seconds in measurements with the dropping electrode, although in our laboratory we found the relation satisfied with a drop time of 3 seconds.

Another important apphcation of the quantity nv'^t}''^ is in the comparison of the diffusion current obtained with the same capillary over different potential regions of the c-v. curve. I t has already been mentioned that the surface tension of mercury, and therefore the drop time of the capillary, varies according to the electrocapillary curve when the potential of the dropping electrode is changed. The mass of mercury flowing per second is practically independent of the electrode potential if a constant head of mercury is held on the dropping electrode. I t is evident, therefore, that the quantity m^t^^ must pass through a maximum near the electrocapillary maximum and decrease as the potential of the electrode is made more negative. These relationships may be seen quantitatively from the following table,^ which also gives the residual current and drop-time values plotted in Fig. 36.

RELATION BETWEEN THE POTENTIAL OF THE DBOPPiNa-MBRCtrBY ELECTRODE

AND THE RESIDUAL CURRENT, m AND t

Dropping-Meroury Electrode,

volts vs. S. C. E.

0.0 - 0 . 5 - 0 . 8 - 1 . 1 - 1 . 6 - 1 . 9

microamperes

-0 .18 -1-0.10

0.21 0.29 0.38 0.70

mg. sec. '

2.661 2.621 2.626 2.626 2.672 2.681

U seconds

2.75 3.08 2.88 2.66 2.18 1.56

TO«<^

mg.^ sec.-'^

2.27 2.29 2.28 2.24 2.18 2.08

8 J. Maas, Collection Czechoslov. Chem. Commun., 10, 42 (1938). ' Id, page 136.

THE FACTORS WHICH DETERMINE DIFFUSION CURRENT 145

From the last column of figures it is seen that the quantity m^H^^ is practically constant over a potential region from 0 to —0.8 volt (vs. S.C.E.), but is lower by 10 per cent at a potential of —1.9 volts. Therefore, the measured diffusion current (corrected for residual current) of a certain solution of copper, for example, is 10 per cent lower at a potential of —1.9 volts than at a potential of —0.5 volt. An important implication of the change in the quantity mî^ with the potential is encountered in the analysis of a mixture of two components. Suppose, for example, that we are dealing with a mixture of copper and manganese of such concentrations that equal diffusion currents would be obtained for both constituents at the same value of m^t^^ The diffusion current of copper in such a mixture would be measured at a potential near the electro-capillary maximum, say —0.5 volt (vs. S.C.E.). Manganese gives a wave at much more negative potentials, and its diffusion current would be measured at, say, —1.9 volts. If the quantity m^H^ did not change we would measure a diffusion current due to both copper and manganese a t —1.9 volts, which would be exactly twice that due to copper alone at —0.5 volt. Actually, however, if the copper gave a diffusion current of 10 microamperes at —0.5 volt, its diffusion current at —1.9 volts would be only 9 microamperes, and that of manganese also would be 9 microamperes. If the change of the quantity mî^ were not taken into account, we would reach the erroneous conclusion that the diffusion currents of manganese and copper were in the ratio of 8 to 10 instead of being equal. I t is apparent that this correction becomes more important with an increasing ratio of copper to manganese concentration.

Turning now to the factor nFCD^, which depends on the properties of the solution, we see that, for a given substance using a given capillary, equation 1 becomes

id = KC. (2)

That is, the diffusion current is proportional to the concentration. I t should be emphasized that the measured diffusion current must be corrected for the residual current in order to obtain the true diffusion current id, and a proportionality with the concentration.

In order to calculate diffusion currents by means of the Ilkovic equation, the diffusion coefficient, D, of the substance undergoing electrode reaction must be known. For simple ions in dilute solutions in a 0.1 iV indifferent electrolyte solution, the diffusion coefficient may be calculated from the equation'"

D- = ^ ^ (3)

»» J. J. Lingane and I. M. Kolthoff, / . Am. Chem. Soc, 61, 825 (1939).


in which Xf is the equivalent ionic conductance of the diffusion ion at infinite dilution and Zt is the valence of the ion. At 25°, equation 3 becomes

X? Bi = 2,67 X 10-' ' i- cm.2 sec."^ (3a)

In the following table, the diffusion coefficients of various ions at 25° as calculated from equation 3a are given. The values are for the simple (aquo) ions. I t should be emphasized that if a given aquo ion is transformed into a complex ion its diffusion coefficient in general will be

DIFFUSION COEFFICIENTS OF SEVERAL. IONS

Ion

H+ Na+ K+ T1+ Pb++ Cd++ Zn++ Cu++ Ni++ OH-ci-IO3-BrOs-Fe(CN)6

—1 equiv.

350 50.5 74 75 73 54 54 54 62

196 76 41 54

100

2 —1 cm. sec.

9.34 X 10"^ 1.35 1.98 2.00 0.98 0.72 0.72 0.72 0.69 5.23 2.03 1.09 1.44 0.89

changed. Thus copper in an ammoniacal medium diffuses as the ammonio ion and has a different diffusion coefficient from that in the absence of ammonia.

The influence of temperature on the diffusion current may be expected to be quite marked, because the equivalent conductances of most ions change about 2 to 2.5 per cent per degree. Moreover, an increasing temperature decreases the viscosity of mercury and consequently increases the mass of mercury flowing through the capillary per second. Actually, the diffusion current of most metal ions increases about 2 per cent per degree rise in temperature." With a stationary platinum micro-electrode the temperature coefficient of the diffusion current is even larger, being about 4 per cent per degree. I t is evident that in order to

" V . Nejedly, Collection Czechoslov. Chem. Commun., 1, 319 (1929).

LIMITING CURRENTS 147

measure diffusion currents with an accuracy of ± 1 per cent the temperature should be controlled to at least ±0.5° with the dropping-mercury electrode, and to ±0.25° with stationary microelectrodes.

4. Limiting Currents in the Absence of Indifferent Electrol3rte. In the above sections the discussion was restricted to the electrolysis of solutions containing a relatively large concentration of an indifferent elec-troljiê, that is, a salt whose ions are not reducible except at much more negative potentials than the particular substance yielding a diffusion current.

Suppose that we consider the electrolysis of a 0.001 M thallous chloride solution in 0.1 A' potassium chloride. Owing to the large excess of potassium chloride present, the current is carried through the solution practically entirely by a diffusive force, and the supply of thallous ions is limited by their rate of diffusion. Hence the horizontal current region is called a diffusion current region. If, however, a 0.001 M thallous chloride solution is electrolyzed in the absence of any added salt, the current is carried entirely by the thallous and chloride ions, and, since the transference number of both ions is 0.5, one-half of the current is carried by each type of ion. The thallous ions are attracted to the cathode by an electrical force as well as by a diffusive force. Hence the limiting current is determined by the rate of supply of thallous ions by migration as well as by diffusion, that is,

ii = id + im, (4)

where ii is the limiting current in the absence of added electrolyte, id is the diffusion current, and im is the migration current. The migration current is given by the product of the transference number of the reducible ions and the total limiting current, namely

im = tiii. (5)

Combining equations 4 and 5 we have.

ii 1 id I — ti

(6)

Thus the limiting current of thallous chloride in the absence of added salt is twice the diffusion current obtained with the same concentration of thallous chloride in an excess of indifferent electrolyte. The theoretical relationship between the limiting current and the diffusion current becomes much more involved if salts of higher charge types or salts with ions of differing mobilities are considered. I t should be noted that, in the reduction of anions such as iodate ions, the diffusion current is larger than the limiting current because the electrical migration of the reduc-


ible ions occurs in tlie direction away from the cathode where the reduction occurs.

Limiting currents in the absence of added salt are of little practical importance, but it should be constantly borne in mind that, in order to obtain a true diffusion current of an ionic substance, a large (about 100 fold) excess of indifferent electrolyte must be present in the solution.

5. Substances Which Can Be Determined Polarographically. A large number of substances, both inorganic and organic, which are reducible at the dropping-mercury electrode and a smaller number which are oxidizable give characteristic polarographic waves. Only a brief mention of typical substances which may be determined polarographically is made here. For details, the reader is referred to the monograph by Kolthoff and Lingane.

A. Cathodic Waves. 1. Inorganic cations. A large number of metal ions, either in the form of simple (aquo) ions or in the form of complex ions, are reducible at the dropping-mercury electrode to form dilute amalgams. Even the alkali-earth metals and the alkali metals give cathodic waves at very negative potentials. In order to obtain true diffusion currents of these metals it is necessary to use as an indifferent electrolyte salts such as tetra-substituted alkyl ammonium halides or hydroxides which are not reducible before the evolution of hydrogen from water. Often the formation of metal-ion complexes can be made use of to determine two metals in a mixture when the simple metal ions give waves occurring at the same potential.

For example, a mixture of thallous and lead ions in potassium chloride gives only a single wave since the half-wave potentials of the simple lead and thallous ions are nearly identical. In the presence of potassium cyanide or hydroxide, which form a complex with lead but not with thallous ions, the half-wave potential of lead is shifted to more negative values while that of thallous ions remains unchanged. The c-v. curve in cyanide or hydroxide medium has two waves which C&n easily be resolved.

2. Inorganic anions. Certain oxygen-containing anions, such as iodate, bromate and nitrite, tellurite, and selenite, are reducible at the dropping-mercury electrode. The positions of the waves are greatly influenced by the pH of the medium because hydrogen ions are involved in the electrode reactions. These reductions are irreversible in nature, but in well-buffered solutions the diffusion currents are reproducible and proportional to the concentration of reducible anion. The exact location of these waves often depends upon the concentration and valence of indifferent ions which are present in the solution. Nitrate ions are reducible in the presence of lanthanum ions, owing to the formation of

SUBSTANCES DETERMINED POLAROGRAPHICALLY 149

positively charged ions of the type La(N03)++ or La(N03)2"^ which enable the nitrate ions to be reduced at the negatively charged electrode. The presence of sulfate interferes in the reduction of nitrate.

3. Uncharged substances. The reduction of oxygen is important as a method of determining oxygen, for example, in technical gases or in natural water sources or in biological respiration studies, and also because oxygen from the air interferes with many polarographic determinations and must therefore be removed from the electrolysis solution. The c-v. curve of an air-saturated solution of 0.1 A? potassium chloride

16

14

12

% OIO § E

B ° a

-•J

s S 6 u

a 4

2

0

1 1

-0.4 -0 .8 -1.2 -1.6 Potential (vs. S.C.E.)

-2.0 -2 .4

Fia. 37; Current-voltage curves of oxygen in 0.1 A'' KCl with trace of methyl red to suppress maximum.

containing a trace of methyl red to suppress the maximum in the curve (paragraph 6, page 151) is shown in Fig. 37. The curve has two waves: the first corresponding to the reduction of oxygen to hydrogen peroxide, the second to the reduction of oxygen to hydroxyl ions.

Other uncharged substances which are reducible are sulfur dioxide, nitric oxide, cyanogen, and hydrogen peroxide. The last gives a reduction wave which is the same as the second reduction wave of oxygen.

4. Organic compounds. A large number of organic compounds are reducible at the dropping-mercury electrode and give well-defined


waves. Among these are aldehydes and ketones, quinones, nitro com pounds, azo and diazo compounds, and unsaturated compounds with conjugated double bonds.

B. Anodic Waves. Two general types of anodic waves are obtained with the dropping-mercury electrode. First, a true oxidation of a solute may occur. Thus hydroquinone can be oxidized to quinone in exact analogy to the reduction of quinone to hydroquinone. A definite diffusion current region is obtained as the potential is made sufficiently positive.

I t has been mentioned already that the useful range of application of the dropping-mercury electrode is limited in the direction of positive potentials by the potential at which anodic dissolution of mercury occurs. In a solution of potassium nitrate, the anodic dissolution occurs at a potential of about +0.35 volt (vs. S.C.E.) For this reason the platinum microelectrode is advantageous as an indifferent anode since its useful range extends to the potential at which oxygen evolution begins, namely, about +1.0 volt. Thus anodic waves due to the oxidation of ferrous ions or ferrocyanide ions can be obtained with a platinum microelectrode.

The second general type of anodic wave obtained with the dropping-mercury electrode is caused by the depolarization of the dropping electrode by the formation of insoluble or complex mercury salts. In these oxidations, the dropping electrode is acting primarily as a mercury-mercurous ion electrode, where the concentration of mercurous ions at the electrode surface is determined by the potential applied to the electrode in accordance with the Nernst equation

n = n°H,,H..- + f f hi c°Hg, . (7)

In the absence of any depolarizing substances, the mercurous ions formed by anodic dissolution diffuse into the bulk of the solution, and sufficient current flows to maintain the concentration of mercurous ions at the electrode surface at the value given by equation 7. Suppose, however, that the solution contains a small concentration, say 0.001 M, of chloride ions. When a sufficiently high concentration of mercurous ions is reached at the electrode surface to exceed the solubility product of mercurous chloride, a precipitation of calomel occurs at the electrode surface, and a larger current must flow at the same potential in order to maintain the mercurous-ion concentration at the value demanded by equation 7. The concentration of chloride ions at the electrode surface is decreased, owing to the formation of calomel, to the value required to satisfy the solubility product of the precipitate. As the potential of the

MAXIMA ON CURRENT-VOLTAGE CURVES 151

dropping electrode is made more positive the concentration of chloride at the electrode surface approaches zero, and the current is determined by the rate of diffusion of chloride ions from the bulk of the solution. Thus a region of practically constant diffusion current is obtained until a potential is reached at which an appreciable current flows as the result of the dissolution of mercury in a medium containing no chloride ions.

The same phenomena occur with any substance forming a stable mercury complex or insoluble mercuric salt. The wave, of course, is obtained at more negative potentials with decreasing solubility, or increasing stabihty in the complex formation, of the resulting mercury salt. Use of the anodic waves is made in the quantitative determination of the halide ions, sulfite, thiosulfate, sulfide, cyanide, hydroxyl, thiocyanate, and also of organic molecules containing the sulfhydryl group, such as cysteine.

Difficulties are sometimes encountered through the formation of a film of insoluble salt on the surface of the dropping electrode. Such a film prevents the passage of mercurous ions with the result that an irregular wave is obtained which is not determined by the rate of diffusion and is not proportional to the concentration. For example, iodide in very dilute solution (10""^ M) gives a smooth anodic wave, but in higher concentrations it gives a very irregular wave.

C. Catalytic Waves of Hydrogen. Certain substances catalyze the evolution of hydrogen on the dropping-mercury electrode by lowering the hydrogen overvoltage. These substances cause the appearance of a so-called catalytic wave at more positive potentials than the normal discharge potential of hydrogen. Such catalytic waves are much larger than those which would be caused by a simple reduction of the same concentration of catalyst. Examples of substances giving catalytic waves are the platinum metals, namely, platinum, ruthenium, and palladium; perrhenate ions; and various quinoline derivatives. Certain organic compounds, such as some proteins, cysteine, and cystine, cause a catalytic wave in the presence of a small concentration of cobalt or nickel ions in ammonia-ammonium chloride buffers. Proteins and sulfhydryl compounds can be distinguished by the fact that proteins give the catalytic wave with either cobaltic or cobaltous ions, but sulfhydryl compounds give a wave only with cobaltous and not with cobaltic ions. Especially from the biological viewpoint these catalytic waves are very important.

6. Maxima on Current-Voltage Curves. Current-voltage curves obtained with the dropping-mercury electrode are frequently distorted by maxima unless measures are taken to prevent their occurrence. These maxima vary in shape from sharp peaks to rounded humps which


decrease to the normal diffusion current (Fig. 38). The height and shape of a maximum varies in general with the concentration and charge type of indifferent electrolyte present in the solution, with the concentration of reducible material, and with the drop time of the capillary. With stationary platinum microelectrodes, such maxima are never observed if a steady current state is reached at each point of the curve.

I t is apparent that on a maximum on a c-v. curve an added supply of reducible material is reaching the electrode over that supplied by

80

72

64

1-a

g | 4 0

a •S32

i W24

X6

8

0

-

1

-

_

' > -i ^

- 1 — tr- V \j a" 1 1 1 1 1 1 1 1 0 -0 .2 -0.4 -0.6 -0.8 -1.0 -1.2 -L4

PotenUal(v8.S.0j:.)

Fia. 38. Suppression of the positive lead maximum by anionic methyl red in neutral solution.

Curve I: 50 ml of 2.3 X 10~^ M lead nitrate in 0.1 A'' potassium chloride. Curve I I : 0.1 ml of 0.1 per cent methyl red added. (I. M. Kolthoff and

,J. J. Lingane, Chem. Rev., 24, 1 (1939).

diffusion alone. Frumkin (1934) and later Antweiler ^ have shown that a stirring effect in the solution near the dropping electrode accompanies the maximum. Antweiler attributes this to an electro-osmosis process occurring in the liquid film near the electrode. The top of the mercury drop is subject to a shielding effect by the glass capillary; this shielding effect causes a lower current density at the top than at the bottom of

" N. J. Antweiler, Z. Elektrochem., 43, 596 (1937); 44, 719, 888, (1938). M. V. Stackelberg, ibid., 46, 466 (1939).

THE ANALYSIS CP POLAROGRAPHIC WAVES 153

the drop, and consequently a tangential potential gradient occurs at the drop surface. A potential gradient also exists perpendicular to the drop surface (zeta potential). Under the influence of these two potential gradients the electro-osmosis occurs. If either potential gradient is zero, * the stirring and consequently the maximum is eliminated. Although this theory fails to account for a number of observations on polarographic maxima, its essential foundation, namely the stirring effect, is undoubtedly correct, and it allows many useful predictions to be made.

From the analytical point of view, maxima are usually nuisances which must be eliminated in order to measure true diffusion currents. Heyrovsky has distinguished between "positive" and "negative" maxima according to whether they occur on the positive or negative side of the maximum in the electrocapillary curve. (See Fig. 36.) He stated as a general rule that positive maxima can be eliminated by the addition of traces of capillary-active anions, and that negative maxima can be eliminated with capillary-active cations. Thus the positive maximum of lead is eliminated by a trace of methyl red in neutral medium (anion) but not in acid medium (cation). On the other hand, the negative maximum of nickel is not suppressed by methyl red in neutral medium but is ehminated in acid medium. The rule of Heyrovsky is not always valid, however. For example, positive dyes are often as effective as negative dyes in suppressing the positive oxygen maximum. From a practical point of view, the use of capillary-active non-electrolytes such as gelatin or tylose in very dilute (0.01 per cent) solution is often to be recommended, since their effectiveness is more general than that of capiUary-active electrolytes.

7. The Analysis of Polarographic Waves. The Half-Wave Potential. Frequently it is possible to obtain useful information concerning the mechanism of electrode processes by comparing the actual shapes of the rising portions of polarographic waves with those predicted theoretically. In order to illustrate the procedure we will derive the equation of a polarographic wave for the reduction process

Ox + ne^ Red. (8)

If the electrode process is reversible, the potential at any point on the wave is given approximately by

n = n°o.,Red + ^ i n ^ , (9)

where the equation is written in terms of the concentrations (rather than the activities) CQX and Cited of the oxidant and reductant at the eko-trode surface. The current at any pomt is determined by the rate of


diffusion of the oxidant to the electrode surface and is therefore proportional to the difference in concentration between the layer of solution at the electrode surface and the bulk of the solution. Thus

i = K{Co. - C°oJ, (10)

where C is the concentration of oxidant in the bulk of the solution. When the diffusion current region is reached, CQX becomes negligibly small in comparison with CQX, and

id = KCo^ (11)

From equations 10 and 11 we have

Cl. = ^ ' - (12)

If we assume that no reductant was present originally in the solution, its concentration at the electrode surface will be proportional to the current at any point, that is,

CLd = ki. (13)

From equations 9, 12, and 13 we have

n = n°o, Ked -^lnkK + ^ In ^^^^ (14)

When the current has reached one-half of its diffusion current value, t^ becomes equal to {id — i) and the last term of equation 13 has become zero. The potential at this point is called the half-wave 'potential, denoted by IIj^. I t is apparent from equation 13 that the half-wave potential in this case is independent of the concentration of oxidant in the solution. The half-wave potential, because it is frequently independent of the concentration, is the most convenient reference point on a polarographic wave for giving the potential at which a given electrode process occiu:s. I t is used for the identification of unknown substances giving a polarographic wave. In the following diagram, the half wave potentials of various inorganic substances are given. Equation 14 may be written in terms of the half-wave potential to give

n . n « + ^ , „ ! i ^ - (15)

or

U^n^ + ^-^log ^ ' (25°). (15a) n I

According to equation 15a, a graph of log (id — i)/i plotted against the potential of the dropping electrode should be a straight hne with a slope

THE ANALYSIS OP POLAROGRAPHIC WAVES 155

of 0.059/n for a reversible reaction. Such a graph constitutes a mathematical analysis of a polarographic wave, and any deviations from linearity or a difference between the actual and theoretical slope is an indication that the electrode reaction does not proceed reversibly according to equation 8. It should be observed that the iR drop through the

" POLAEOQEAPHIC SPECTBTJM " ACCORDINQ TO V. M AJEB

Values of the half-wave potentials of inorganic ions in various media.

I. Reduction and deposition potentials of cations in neutral or acidic solution. II . Reduction and deposition potentials of ions in alkaline solution. I I I . Reduction potentials of anions and molecules in neutral (solid line) or in acidic (dotted

line) solution and in ammonia buffer (dash line). NO3 and NO2 in 0.1 N lanthanum chloride. IV. Reduction potentials of complexes. Solid line, in 10 per cent sodium potassium tartrate;

dashed line, in 1 .AT potassium cyanide. V. Depolarizing potentials of anions (anodic polarization). VI. Deposition potentials of cations of the commonly used indifferent electrolytes present in

excess (1000 X) in the solution. VII. Potentials of the large mercury reference electrode in solutions containing the usual

anions in about 1 iV concentration. (The numbers 0, 1, and 2 refer to chloride concentrations of 1, 0.1, and 0.01 N.

All values are the potentials at the half diffusion current except those which are marked by a little circle signifying the contact point of a 45° tangent at a 2-cm. wave. The values of the potentials refer to the 1 N calomel electrode as zero and to room temperature.

electrolysis cell was neglected in the above derivation and strictly speaking should be taken into account. In practice it is possible to keep the iR term negligibly small because polarographic currents in general seldom exceed 50 microamperes and are usually much smaller. In exact work it is recommended, however, that the average resistance of


the solution during the formation of the drop be determined by the classical method and a correction applied for the iR drop.

Equation 15 applies to any reversible reduction process of the type given by equation 8 in which the reduction product is soluble in the liquid phase. In metal-ion reduction the reduction product is an amalgam whose concentration is proportional to the current, and hence equation 15 applies.

I t will be left as exercises for the student to derive equations of polarographic waves for the following (assume reversible behavior): (a), Ox + ne <= Red, where CQK and Cîed are the concentrations of oxidant and reductant in the bulk of the solution; (&) the reduction of metal ions to form an insoluble metal; (c) the anodic wave of chloride ions to form mercurous chloride (see problems).

CHAPTER X

EQUIPMENT AND TECHNIQUE USED IN VOLTAMMETRY

'If L-MAAAAAA-

J •AAAA/*—'

t r-VWVVV-i

Lvw-I

1. Electrical Equipment. A simple circuit suitable for student use in determining c-v. curves and for amperometric titrations is shown in Fig. 39.

The applied e.m.f. is regulated by means of the two "potentiometer"-type radio rheostats connected in series. Either of two fixed resistors Ri and R2 of known resistance of about 10,000 ohms and 1000 ohms, respectively, is connected in series with the electrolysis cell. By measuring the potential drop En across the known resistance, the current can be calculated by means of Ohm's law. The resistors may be substituted if desired by a single standard decade resistance box (1 to 9999 ohms). For most c-v. curve determinations the 10,000-ohm res i s to r is used. In amperometric titrations the currents are frequently larger, and the 1000-ohm resistor is more convenient. In measurements with the dropping-mercury electrode, the current, and therefore the potential drop across the resistor, fluctuate with the formation of the mercury drops. In order to measure the average current, the push button is held down and the potentiometer is adjusted until the galvanometer fluctuates an equal number of divisions on each side of its zero point. The most satisfactory null-point galvanometer is the enclosed lamp-and-scale type (page 79). Excessive fluctuations of the galvanometer may occur when large currents are being measured. These fluctuations can be suppressed

157

rri

Ml To Potentiometer

Fio. 39. Manual apparatus for determination of current-voltage

curves.

158 EQUIPMENT AND TECHNIQUE USED IN VOLTAMMETRY

by inserting a large resistance (50,000 to 100,000 ohms) in series with the push button. I t is convenient to use two push buttons in parallel, one with the series resistance for coarse adjustments and one without for fine adjustments. The fluctuation of the current can be decreased by inserting one or more condensers of suitable capacity without changing the sensitivity of the galvanometer. The current can also be measured directly by using a wall-type current-reading galvanometer in series with the electrolysis cell. This type of galvanometer must be provided with a sensitivity regulator (Ayrton shunt) and may be calibrated

Fia. 40. The Heyrovsky polarograph.

directly by using the standard resistor in series with it. A microam-meter may be used for current measurements with platinum microelec-trodes since no periodic fluctuation of the current occurs with such electrodes. A microammeter is particularly convenient for amperometric titrations with rotating microelectrodes (Chapter XI).

The Heyrovsky polarograph is a self-registering instrument for determining and photographically recording c-v. curves. I t consists essentially of a slide wire wound on a revolving drum connected by a set of gears to a cylinder around which a sheet of photographic paper is attached. As the potentiometric drum revolves, a continually increasing

FABEICATION OF CAPILLARIES AND DROPPING ELECTRODE 159

e.m.f. is applied to the electrolysis cell. The potential drop across the slide wire is adjusted to any desired value (usually 2 or 4 volts) by a regulating resistance (see measurement of e.m.f. with potentiometer, page 79). Each turn of the drum then corresponds to 100 or 200 millivolts of applied e.m.f. The drum with shde wire is rotated by an electric motor A. A roll of sensitive photographic paper is carried by the cylinder C enclosed in a light-tight housing, and connected by a system of gears to the bridge so that the two revolve simultaneously. The gear ratio is accurately adjusted so that one complete revolution of the drum (100 or 200 millivolts) corresponds to about 1 cm. on the photographic paper. (? is a powerful galvanometer light the beam of which is reflected onto the photographic paper by the mirror of the sensitive d'Arsonval galvanometer E. The housing of the photographic roll is provided with a narrow colhmating slit through which the hght beam of the galvanometer enters. After each complete revolution of the drum (100 to 200 millivolts) corresponding to about 1 cm. on the photographic paper an auxiliary light, automatically flashed on, illuminates the entire length of the slit and a thin line is printed on the paper. These lines mark the increments of applied e.m.f. After development, the entire c-v. curve, called a polarogram, is found on the photographic paper. The polaro-graph is ideally suitable for work with the dropping electrode; it cannot be used with the stationary electrode, with which the current does not reach a final value immediately.

2. Fabrication of Capillaries and the Dropping Electrode. A suitable capillary for use as a dropping-mercury electrode may be prepared by drawing out a piece of 0.5-mm. Pyrex capillary tubing. The tubing should be allowed to thicken somewhat by gentle pressure in the flame so that the drawn-out capillary will not be too slender and fragile. The tip should have a uniform internal diameter of about 0.03 to 0.04 mm. for at least 2 cm. of its length. Capillary tubing with an internal diameter of about 0.05 mm. is commercially available and may be used directly in lengths of 6 to 10 cm. as the electrode capillary. The finished capillary may simply be connected with rubber tubing to a leveling bulb which serves as a mercury reservoir into which the electrical contact is made. Rubber tubing used in this way should be thoroughly cleaned by boiling first in a dilute solution of sodium hydroxide and then in several portions of distilled water, after which it should be carefully dried. In order to obtain reproducible results, the capillary must be kept immaculately clean. The entrance of water or solution into the capillary must be prevented. When the dropping electrode is not in use the tip should be kept immersed in mercury, with the pressure reduced to prevent the mercury in the reservoir from draining out. Before the


>

l . lF

H

electrode is placed in the solution the pressure is increased so that the mercury starts dropping. The cleanliness of a capillary may be checked by measuring the drop time in distilled water with a constant head of mercury on the capillary. This is done by measuring with a stop watch the time required for the formation of 5 to 10 drops of mercury. The drop time should be from 3 to 6 seconds (see page 144)and should beexactly reproducible for a given capillary. If the capillary has an irregular

or variable drop time it must be cleaned. Sometimes it suffices merely to immerse the tip of the capillary in

s^;;^ K r^ aqua regia with the mercury flowing through it, and rinse ^ T"'^ r ^ with distilled water. If the capillary becomes dirty on

the inside it may be cleaned by removing the mercury and drawing aqua regia through it by means of a suction pump. A thorough rinsing by sucking distilled water through the capillary, followed by drying with filtered air, completes the cleaning process.

In order to maintain a constant mass of mercury, m, flowing through the capillary per second it is necessary to have a constant head of mercury, which may vary from 20 to 80 cm., depending upon the characteristics of the capillary. In general, a large head of mercury is to be preferred to prevent the "m value" of the capillary from varying with changes in the surface tension of the mercury-solution interface. A constant head may be obtained with the simple leveling-bulb arrangement described above, or by means of a special constant-pressure device. Such a device,' based on the principle of the Mariotte flask, is shown in Fig. 41. The capillary

may also be connected to a vertical glass tube provided with a side arm connected to a leveling bulb by means of which the head of mercury is maintained at a constant value.^

For the calculation of diffusion currents the quantities m and t must be known for the capillary used. The mass of mercury flowing per second may be determined by placing the tip of the capillary in water contained in a weighing bottle, and allowing the mercury to drop for a known length of time, collecting 10 to 20 drops. The pool of mercury is dried by decanting the water into another weighing bottle, adding and decanting several portions of acetone, and allowing the remaining acetone to evaporate. The dry mercury is then weighed and the mass of mercury flowing per second is calculated. The drop time t is determined during

1 E. F. Mueller, Ind. Eng. Ckem., Anal. Ed., 12, 171, (1940). 2 J. J. Lingane and H. A. Laitinen, 7nd. Eng. Chem., Anal. Ed., 11, 604 (1939).

F]G. 41. Dropping electrode with constant head of mercury (E. F.

Mueller).

ELECTROLYSIS CELLS 161

tKe actual measurement of the diffusion current and is measured at the same potential of the dropping electrode as that at which the diffusion current is determined. It is convenient to determine t in an indifferent salt solution at various potentials of the dropping mercury (see electro-capillary curve, page 142) and plot the results obtained. Then values of t at any potential are on record for future reference.

3. Platinum Microelectrode, The stationary platinum microelec-trode consists of a platinum wire about 4 mm. long and 0.5 mm. in diameter sealed into a piece of soft glass tubing into which mercury is introduced for electrical contact.

A rotating platinum microelectrode suitable for amperometric titrations can be made as follows. A piece of platinum wire about 2 to 3 mm. long is sealed in the side of a 10-mm. bulb on the end of a piece of 6-mm. soft glass tubing. The tubing is mounted in a cone-drive laboratory stirring motor adjusted to rotate the electrode at a speed of about 600 r.p.m. Electrical connection to the electrode is made by means of a piece of copper wire inside the glass tubing, sealed with a small piece of Wood's metal to the platinum wire and connected to the cone-drive shaft of the motor. The top of the shaft is drilled to form a small cup into which a drop of mercury is introduced. The electrical connection is made through the drop of mercury. I t is not advisable to use the binding posts provided with the motor for electrical contacts because the resistance of such contacts is usually high and variable. A synchronous motor of perfectly constant speed should be used in the determination of c-v. curves.

4. Electrolysis Cells. It has already been pointed out in Chapter IX that the second electrode in voltanmietry is a large unpolarizable one. Since the phenomena occurring at the microelectrode are determined by the potential of the latter, it is desirable to have a reference electrode of known potential (such as the S.C.E.) to relate the measured half-wave potentials. The S.C.E. may be used directly as the large electrode by designing the electrolysis cell properly. The electrolysis cell shown in Fig. i2A contains a sintered-glass plate which serves to separate the two halves of the cell. A plug of agar gel made up in saturated potassium chloride or potassium nitrate if chloride must be absent in the electrolysis cell prevents mixing of the solutions in the two halves of the cell. A saturated calomel electrode is made as usual in the left side of the cell. The right-hand side of the cell (capacity about 50 ml.), which accommodates the electrolysis solution and microelectrode, is provided with a 1-mm. capillary inlet tube for the gas used in removing the air from the electrolysis solutions. This type of cell and reference electrode is very convenient for most work if the presence of chloride ions in the electrol-


ysis solution does not interfere. The reference electrode has to be made up only infrequently when its potential has been found to change. The sintered-glass plate is most conveniently cleaned by sucking aqua regia through it by means of a suction pump.

In the investigation of anodic waves with the dropping-mercury electrode, and in some cathodic studies, chloride ions may interfere (Chapter IX) and the cell cannot be used as shown. Cell A may then be used by filling the left-hand side with 0.1 A' potassium nitrate and making up an agar

Fia. 424. Electrolysis cell FIG. 42JS. Calomel electrode

plug in the same solution. The saturated calomel electrode (Fig. 425) is inserted in the left-hand side of the cell. I t is provided with a wide agar salt bridge of low resistance and has a large area to prevent polarization by the passage of small currents.

Simpler types of polarographic cells may be used but have certain disadvantages. A simple cylindrical cell may have a pool of mercury on the bottom to serve as a large electrode. The potential of the mercury however, depends upon the composition of the electrolysis solution. If potassium chloride is taken as an indifferent electrolyte, the pool of mercury assumes in the presence of air the potential of a calomel electrode corresponding to the chloride-ion activity of the solution and is relatively constant in potential during the course of the electrolysis. In the absence of depolarizing ions such as the halides, the potential of

TECHNIQUE OF VOLTAMMETRIC DETERMINATIONS 163

the large electrode is more subject to change with changing current. A cell with such a pool of mercury must be provided with a third electrode (external S.C.E.) by means of which the potential of the microelectrode may be measured at each point of the c-v. curve. For this purpose, another switch should be provided on the apparatus described in paragraph 1.

5. General Technique of Voltammetric Determinations. It has been mentioned previously that oxygen is reducible at fairly positive potentials at the dropping-mercury electrode and also at the platinum micro-electrode. It is necessary, therefore, to remove the dissolved oxygen of the air from electrolysis solutions whenever regions of potentials are being investigated at which oxygen is reduced. This is accomplished simply by bubbling tank nitrogen or hydrogen through the electrolysis solution for 15-30 minutes before determining the c-v. curve. During the actual course of the measurements, the gas stream is shut off to prevent its stirring effect from interfering with the diffusion process near the microelectrode and with the formation of drops of mercury of normal size. It is usually unnecessary to purify the commercial tank gases since ordinarily their oxygen content is sufficiently low to prevent interference. For the determination of very dilute solutions (10""^ M or less), further purification may be necessary, it can be accomplished by passing the gas through an electrically heated tube containing copper turnings at a temperature of about 500° C.

With the dropping-mercury electrode it is usually necessary to remove oxygen. With the platinum microelectrodes c-v. curves are"often determined at potentials positive to the saturated calomel electrode,'at which potentials oxygen is not reduced and need not be removed. In neutral or alkaline medium, oxygen is quickly removed'from a solution by the addition of a small amount of solid sodium sulfite.

The effect of the temperature on the diffusion current has been discussed in Chapter IX. A thermostat regulated to ± 0.1 ° is recommended for analytical work. The electrolysis cell should be immersed m the thermostat during the period required for oxygen removal so that thermal equilibrium will be reached. No temperature control is necessary in amperometric titrations.

With the dropping-mercury electrode, the applied e.m.f. is adjusted by setting the potentiometer reading to the desired value and adjusting the electrolysis battery rheostats until the system is in balance. This is done as described in paragraph 1 by holding the push button down and adjusting until equal fluctuations occur on both sides of the galvanometer zero. The current is then measured by measuring the potential drop across the standard resistor in the same way. The intervals between


the points on the c-v. curve depend on the part of the curve being measured. On the steeply rising portions, readings should be taken at intervals of about 25 millivolts, particularly if the curve is to be subjected to logarithmic analysis. On the constant diffusion current regions, current readings should be taken at intervals of 0.1 volt. The c-v. curves are plotted with increasing negative potentials of the dropping electrode to the right, positive currents (indicating cathodic processes at the dropping electrode) being plotted upward and negative currents (indicating anodic processes at the dropping electrode) being plotted downward.

With the stationary platinum microelectrode, a somewhat different procedure must be followed, owing to the inherent differences in the nature of the microelectrode. Since the electrode surface is not being constantly renewed, the potentiometer key cannot be held down during the measurements. The usual procedure of tapping the push button is employed. Since the current does not reach its final value immediately it is necessary to wait at each value of the applied e.m.f. until a steady current state is reached. Usually a period of two to three minutes suffices. It should be realized that as the current drifts downward the appfied e.m.f. also varies because of the changing iR drop across the standard resistance. Therefore adjustments of the applied e.m.f. are also carefully made until the current (and applied e.m.f.) have reached their final constant values. A more rapid approach to a steady diffusion state is reached if the applied e.m.f. is increased very slowly between successive points. Care should be taken to avoid even a momentary discharge of gases (hydrogen or oxygen) at the microelectrode because any gas bubbles on the electrode surface will decrease the effective electrode area and therefore the diffusion current will likewise be decreased.

Strictly speaking, the measured values of the potential have to be corrected for the iR drop across the cell. Under ordinary conditions this correction is negligibly small, but it has to be considered when the currents are greater than about 10 microamperes and also when the resistance of the cell is great.

CHAPTER XI


1. The Principles of Amperometric Titrations. A third class of electrometric titrations differing in principle from those based on poten-tiometric or conductometric methods has recently been developed. They are called ampercmetric titrations ^ because they are based on the measurement of the diffusion current of the substance being titrated, or that of the reagent, or of both, during the titration. In Chapter IX, the proportionality between the diffusion current of a reducible or' oxidizable substance and its concentration has been discussed. The change in the concentration of any substance giving a diffusion current may be followed during a titration by its diffusion current. The potential of a suitable microelectrode is maintained at the proper value, and measurements of the diffusion current are made after the addition of successive amounts of reagent. Quite generally, the end point is found graphically. The currents measured during the titration and corrected for the dilution effect are usually located on one of two straight lines (reaction and reagent lines) which intersect at the end point.

We may distinguish between different types of titration graphs depending upon whether the substance being titrated or the reagent, or both, are reducible or oxidizable at the applied e.m.f. used. Consider the titration of a substance A with a reagent B which removes A from the solution by precipitation, complex formation, oxidation, or reduction. We will assume that the reaction product is not reducible or oxidizable at the potential of the microelectrode used during the titration.

Case 1. Substance A yields a diffusion current (anodic or cathodic); B does not. For example, if a reducible substance such as lead is titrated with a precipitating reagent such as oxalate which does not undergo electrode reaction in the diffusion current region of lead ions, the diffusion current decreases continuously until the equivalence point is reached. Since the solubility of lead oxalate is extremely small, the current at the equivalence point is practically equal to the residual current of the titra-

' For nomenclature and historical development, see I. M. KolthoiT and Y. D.' Pan. J. Am. Chem. Soc, 61, 3402 (1939).

165

166 AMPEROMETRIC TITRATIONS

tion medium and remains constant with further additions of oxalate. If the solubility of the precipitate is not negligibly small (e.g., titration of lead with sulfate) there will be an appreciable diffusion current at the equivalence point. As an excess of reagent is added, the solubility is decreased and the measured current approaches the residual current of the titration medium at the applied e.m.f. If the current before the end point is corrected for volume changes during the titration (see page 171), a graph of the current plotted against the volume of reagent added consists of two straight lines connected in general by a curved line owing to the solubility of the precipitate or instability of the complex.

Volume of reagent, ml.

o

Volume of reagent, ml.

b

Volume of reagent, mL Volume of xeagent, mL

C d

FIG. 43. Amperometric titration curves.

Such a graph is shown in Fig. 43a. The end point is determined by the point of intersection of the extrapolated straight-line portions. In Fig. 43a, AB is the precipitation and DE the reagent line. Examples of this type of titration are the determination of lead with oxalate or sulfate, or of silver and mercurous ions with chloride.

Case 2. Substance A is not reduced or oxidized at the microelectrode while the reagent B yields a diffusion current. An example is the titration of lead with dichromate in acid medium at a potential more positive than that at which the reduction of lead ions occurs. If the dropping-mercury electrode at a potential of 0.0 (vs. S.C.E.) is used as an indicator electrode, only a residual current is observed until an excess of dichromate has been added. After the end point a reduction of dichromate to

ADVANTAGES AND LIMITATIONS 167

chromic ions occurs at the dropping electrode, and the titration curve shown in Fig. 43& is obtained after correction for dilution. Other examples of this type of titration are those of sulfate, oxalate, and ferrocyanide with lead at potentials at which lead yields a diffusion current. The titration of cobalt with a-nitroso-jS-naphthol at potentials at which cobalt is not reduced but the reagent yields a diffusion current belongs to this class, as does also the titration of arsenic trioxide in acid medium with potassium bromate, the rotating platinum microelectrode being the indicator electrode.

Case 3. Both substances A and B give diffusion currents at the same applied e.m.f. If lead is titrated with dichromate at a potential of the dropping-mercury electrode of —1.2 volts (vs. S.C.E.), both lead and dichromate give diffusion currents. Therefore the measured current decreases as lead ions are removed as lead chromate and increases again after an excess of dichromate has been added. The titration curve is shown in Fig. 43c. The position of the minimum does not necessarily coincide with the equivalence point, and therefore points on the straight-line portions of the curve are of more importance in determining the end point than those on the curved portion. In this respect amperometric titrations are closely analogous to conductometric titrations, since in both the end point is found by extrapolation of straight lines on both sides of the end point. Other examples of this type are the titration of nickel in ammoniacal medium with dimethyl glyoxime, or that of copper with a-nitroso-^-naphthol.

Case 4. Substance A gives an anodic diffusion current at the same potential as that at which B gives a cathodic diffusion current. For example, if titanous ions are titrated with ferric ions using the dropping-mercury electrode as an indicator electrode at a potential of —0.3 volt, the current at first is negative because of the oxidation of titanous ions to titanic ions at the electrode surface. At the end point the current is equal to the residual current, and as an excess of ferric ions is added a positive current due to the reduction of ferric ions to ferrous ions is obtained. A titration curve of this type is practically a straight line, although a slight change in slope occurs in general at the equivalence point owing to the difference in the diffusion coefficients of the substance being titrated and the reagent (Fig. 43d).

2. Advantages and Limitations of Amperometric Titrations. Amperometric titrations potentially have a very wide field of applicability. Any of the numerous substances yielding diffusion currents which are proportional to the concentration could, in principle, be titrated or used as a reagent in amperometric titrations with the dropping-mercury electrode or with platinum microelectrodes. Moreover, certain other


substances which themselves do not undergo electrolytic oxidation or reduction can be determined by precipitation with a reagent which gives a diffusion current. For example, sulfate ions do not yield polarographic waves, but may under suitable conditions be titrated with lead or barium. In the previous section several examples of amper-ometric titrations have been mentioned. A promising field of application appears to be the titration of metal ions with organic reagents. Examples of this type of application which have been investigated are: nickel with dimethylglyoxime and cobalt, copper, or palladium with a-nitroso-jS-naphthol.

Since it is not necessary for either the substance being titrated or the reagent to undergo a strictly reversible electrode reaction but merely to give a well-defined diffusion current the range of apphcabihty of amper-ometric titrations is even greater than that of the potentiometric titrations. As in conductometric titrations, the points on the titration curve near the equivalence point are not of great importance in locating the end point. Therefore limitations such as a relatively high solubility or a slow reaction in the vicinity of the equivalence point have Uttle effect on the accuracy of the titration.

From the point of view of expedience, also, amperometric have an advantage over potentiometric titrations. Conductometric titrations have a great Hmitation since high concentrations of indifferent electrolytes make the results less accurate. In amperometric titrations, on the other hand, a certain concentration of indifferent electrolyte usually should be added to eliminate the migration current and obtain straight titration lines. A comparatively wide variation in the concentration of indifferent electrolyte is permissible without appreciable effect upon the accuracy. In the titrations of a non-reducible substance, say sulfate, with a reducible ion, say lead, no indifferent salt has to be added, as enough electrolyte is formed during the titration to eliminate the migration current after the end point.

Another advantage of amperometric titrations lies in the titration of extremely dilute solutions. With the dropping-mercury electrode the titration of 10~^ N solutions can usually be carried out without difficulty and in certain cases 10~* N solutions can be titrated.

The rotating platinum microelectrode, though not having nearly the range of applicability of the dropping-mercury electrode, can be used in the titration of even more dilute solutions. For example, a 10 ~^ N arsenite solution can be titrated with bromate to an accuracy of 1 per cent.

Amperometric titrations carried out with the dropping electrode have advantages over direct polarographic determinations in that the

ADVANTAGES AND LIMITATIONS 169

results of the former are more accurate, and the characteristics of the capillary (m and t, see page 143) need not be known, while the temperature need not be adjusted or known, as long as it is kept constant during the titration.

Amperometric titrations have certain limitations which must be borne in mind. In the titration of reducible substances, for example, it has already been mentioned that indifferent electrolytes do not interfere. On the other hand, the presence of any substance in large concentrations which is reducible at the same potential or at more positive potentials than the substance being titrated will interfere.

For example, a high concentration of sodium nitrate does not interfere in the titration of lead with sulfate, but a high concentration of copper which is more easily reducible than lead ions would interfere. Under such conditions it is necessary to remove the interfering substances by chemical separation. A quantitative separation is not necessary; in the above example if the concentration of copper is reduced, say to a concentration equal to that of the substance titrated, the titration curve will approach the diffusion current of copper rather than the residual current as an excess of sulfate is added. For the above reason titrations of dilute solutions are usually carried out in the absence of oxygen, unless the potential is so positive that oxygen is not reduced.

In amperometric titrations involving precipitation reactions difficulties are sometimes encountered due to the formation of supersaturated solutions. If so, it is necessary to wait after the addition of each portion of reagent until solubility equihbrium is reached. Supersaturation effects close to the end point are of little practical consequence. However, it must be emphasized that at points removed more than about 40 per cent from the end point one has to wait until the supersaturation is completely overcome. In order to increase the speed of precipitations and to decrease the solubility it is advantageous to carry out the titration in a medium of about 30 per cent ethanol when dealing with inorganic precipitates which are formed relatively slowly and have relatively large solubihties under the experimental conditions. Quite generally, the accuracy obtained in amperometric precipitation titrations may be affected by coprecipitation phenomena. These should be studied systematically whenever they occur, and the effect of the kind and amount of indifferent electrolyte and of alcohol upon the coprecipitation should be investigated.

Occasionally interference has been found to be caused by the reduction of metal ions from colloidal particles of the precipitate. This effect may be prevented by coagulation of the precipitate or by the addition of a trace of gelatin which peptizes the precipitate by a protective


colloid action. Under these conditions the colloidal particles of precipitate are covered with a coating of gelatin which prevents the interfering depolarization of the electrode by the precipitate. The addition of gelatin was found necessary, e.g., in the titration of chloride with silver or mercurous nitrates.

3. Performance of Amperometric Titrations. It is necessary to determine the shapes of the c-v. curves both of the substance to be titrated and of the reagent in the particular titration medium used, if they are not already known. In general a sufficient concentration of indifferent electrolyte must be present to eliminate the migration current and to reduce the resistance of the electrolysis cell. If the migration current is not completely eliminated, the titration lines are not straight. For example, if a solution of lead nitrate containing no other electrolyte is titrated with potassium sulfate the initial current is the sum of the diffusion current and the migration current of lead. As the titration proceeds, the concentration of lead is decreased while that of potassium nitrate is increased. Consequently the migration current is constant!}^ becoming a smaller fraction of the total current, with the result that the titration line before the end point is curved.

A measured volume of the solution to be titrated is introduced into the titration cell, which may conveniently be of the type shown in Fig. 42. If maxima occur on the c-v. curves of the substance titrated or of the reagent it is desirable to add a suitable substance which suppresses the maxima and which does not interfere with the course of the titration. Dissolved air is removed, if necessary, by bubbling nitrogen or hydrogen for about ten minutes.

The potential of the microelectrode is then adjusted so that the diffusion current of the substance to be titrated or the reagent, or both, is obtained. The diffusion current is measured in the usual way (Chapter X). A measured volume of the reagent is added from a microburet, nitrogen is passed through for one minute to remove oxygen and to mix the solutions, and the current is measured again. If necessary, the potential of the microelectrode is readjusted to its original value after each addition of reagent. A shift in the electrode potential occurs in general upon the addition of reagent, even though the applied e.m.f. is maintained at a constant value, because of the changing iR drop through the cell. In order to minimize this effect, the resistance of the cell should be kept low by having a sufficiently high concentration of indifferent electrolyte. If the current at the end point is very small (negligible solubility of precipitate) readings are taken at smaller intervals near the end point to obtain greater accuracy. On the other hand, if the

/

PROBLEMS ON VOLTAMMETRY 171

solubility is not negligible, no increase in accuracy can be obtained by taking closely spaced readings near the end point.

The values of the current are corrected for the dilution effect during the titration and plotted against the volume of reagent. If V is the original volume of solution, the corrected current after the addition of X milliliters of reagent is given by

• - Ijtl • '^cotr. y • ^ j

where i is the measured current. In order to keep the dilution correction small and also to minimize the addition of oxygen dissolved in the reagent it is preferable to choose a reagent at least ten times as concentrated as the solution to be titrated and to add it from a microburet. The end point is determined by the point of intersection of the two straight titration lines.

When a rotating platinum microelectrode is the indicator electrode it is not usually convenient to remove the dissolved oxygen because of the large currents obtained with very small concentrations of the oxygen. However, many titrations may be performed at potentials at which oxygen is not reduced (positive potentials with reference to S.C.E.). In order to obtain straight titration lines it is necessary to maintain a constant speed of rotation during a given titration. Since titrations with the rotating microelectrode may be performed very rapidly (ten minutes or less) an ordinary laboratory stirring motor is usually entirely satisfactory (see Chapter X).

Titrations with the rotating electrode in which the presence of oxygen does not interfere may be carried out very rapidly and conveniently, yielding results of high accuracy even in extremely dilute solutions. In the relatively few instances in which they may be applied these ampero-metric titrations have great advantages over potentiometric titrations.

PROBLEMS ON VOLTAMMETRY

1. At 25° C. the diffusion current of 0.001 M thallous chloride in 0.1 A'' potassium nitrate is 6.13 microamperes, that of 0.001 M lead chloride is 8.78 microamperes. Calculate the ratio of the diffusion ooefBcients of the thallous and lead ions.

2. The diffusion current of thallous chloride at a potential of —0.6 volt was found to be 10 microamperes. Calculate the diffusion current at a potential of —1.6 volt with t = 3.00 seconds at —0.6 volt and 2.03 seconds at —1.6 volt while m remains the same at both voltages.

3. The diffusion current of 0.001 N HCl in 0.1 JV KCl is greatly decreased when the solution is saturated with air. Explain. (Write electrode reactions of oxygen.)

4. Explain how to find the true diffusion current of manganese in a mixture of lead and manganese in a suitable medium.

172 AMPERO METRIC TITRATIONS

5. The anodic wave of 0.001 iV chloride starts at a potential of 0.21 volt (vs. S.C.E.). Calculate the potential at which the wave of 0.1 A' chloride starts.

6. The normal potential of the quinhydrone electrode is —0.453 volt (vs. S.C.E.). Derive the equations of the polarographic waves of quinone and hydroquinone, and give the half-wave potentials at a pH of 6 and 7.

7. A solution of A is titrated with reagent B forming a precipitate of the composition AB. The titration is carried out at a potential at which both A and B yield a diffusion current. The reduction of A which has a diffusion coefficient DA involves a electrons, and that of B with a diffusion coefficient DB involves 6 electrons per molecule. Calculate the ratio of the current at the end point to that of a 0.001 M solution of A if the solubility of AB is equal to s.

8. The half-wave potential of lead is —0.396 volt (vs. S.C.E.). Lead forms with the anion A" a complex ion PbA2". The half-wave potential of lead in a 0.1 Af solution of A" was found to be —0.700 volt. Calculate the instability constant of the complex ion.

PRACTICAL COURSE

INDICATORS

Required: Volumetric flasks; pipets, burets; also some pipets of 1 ml. divided in 0.01 ml.

1. Prepare 0.1 per cent solutions of the following indicators (e/. page 28); tropeolin 00; methyl orange; methyl red sodium; thymol blue; bromphenol blue; p-nitro-phenol; bromcresol green; chlorphenol red; bromthymol blue; phenol red; neutral red; and phenolphthalein.

2. Prepare a complete set of buffer mixtures (pH 2 — 10), according to Clark (cf. page 34); and citrate buffer mixtures (pH 2 — 6), according to Kolthoff and Vleeschhouwer (see page 36).

3. Determine color-change interval of various indicators and compare figures with those in the literature (cf. page 29).

4. Determine the pH of 0.05 M monopotassium phosphate; 0.05 M monopotassium citrate; 0.05 M monopotassium phthalate; 0.1 M ammonium chloride (sublimated product); 0.1 Af sodium bicarbonate; tap water; ordinary distilled water (cf. page 46); conductivity water (cf. page 46), and some unknowns.

6. Determine the pH of a buffer solution with pH around 6 with p-nitrophenol as indicator according to the method of Michaelis (cf. page 42).

6. Determine the pH of a colored and of a slightly turbid solution, using the comparator (see page 45).

7. Determine the neutralization curve of some acid or base (ask instructor). Submit detailed report with interpretation of your experiments.

POTENTIOMETRY

1. Platinize the hydrogen electrode (cf. page 89); prepare salt bridges (cf. page 85); prepare 15 g. quinhydrone (cf. page 93); prepare a saturated calomel electrode (cf. page 84). ^

2. Measure the potential of a hydrogen electrode in a mixture which is 0.01 N in HCl and 0.09 A in KCl against the saturated calomel electrode and against the quinhydrone electrode in an identical mixture using a KCl salt bridge. If the correct value (cf. equations, page 92) is found, determine the pH of 0.05 M monopotassium phosphate, potassium biphthalate, borax, and sodium carbonate and some unknowns with the hydrogen electrode.

3. Add to a buffer solution of Clark of pH 5.0 so much KCl that its concentration is 0.5 M. Measure the pH before and after adding the KCl with the hydrogen electrode and also colorimetrically using methyl red and bromcresol green.

4. Measure the pH of some buffer solutions and unknowns with the quinhydrone electrode.

173

174 PRACTICAL COURSE

5. Titrate 0.1 N hydrochloric acid with 0.1 N NaOH, 0.1 N h3-dn)chloric acid with 0.1 yV borax, 0.1 A acetic acid with 0.1 A" NaOH and calculate Ka-

using the hydrogen, quinhydrone, or antimony electrode (c/. pages 87, 91, 99). Plot the re.sults and the pH values in a graph, and indicate the color-change intervals of some suitable indicators.

6. A silver electrode for potentiometrio titrations is prepared by electroplating a platinum gauze electrode in a potassium-silver cyanide solution at low current density, until a bright layer of silver is deposited. The electrode is thoroughly washed. Titrate 0.1 A KCl + 0.1 iV AgNOs,

0.1 AT KI -f- 0.1 A AgNOa, and a mixture of chloride and iodide.

(Use salt bridge filled with ammonium nitrate or potassium sulfate.) 7. For oxidation-reduction titrations use a bright platinum wire or gauze electrode.

Titrate: 0.1 A' ferrous iron with 0.1 A' potassium dichromate or eerie sulfate in acid medium;

The above mixture of iodide and chloride in dilute sulfuric acid with 0,1 N potassium permanganate.


Platinize the electrodes of a conductometric titration cell and titrate: 100 ml. 0.01 N HCl with 0.5 N sodium hydroxide. 100 ml. 0.01 N acetic acid with 0.5 N sodium hydroxide. 100 ml. 0.001 N acetic acid with 0.05 A'' sodium hydroxide. 100 ml. 0.1 Af boric acid with 0.5 N sodium hydroxide. 100 ml. 0.01 N sodium acetate with 0.5 N hydrochloric acid. 100 ml. 0.01 N sodium chloride with 0.5 A' silver nitrate. 100 ml. of a mixture of 0.01 N NaCl and 0.01 N KI. The same, but inl N ammonia.

VOLTAMMETRY AND AMPEROMETRIC TITRATIONS

Work preferably carried out in thermostat; otherwise measure temperature in each experiment.

Currenl-voltage Curves: 1. Make voltammetric cell, manual apparatus, and a capillary for the dropping elec

trode (see Chapter X). 2. Determine m and t of the capillary and the c-v. curve of 0.001 M thallous chloride

or 0.001 M lead chloride in 0.1 N potassium chloride in the presence of a trace of methyl red as a maximum suppressor. Also determine the residual current of the mediutt). Compare the calculated value of the diffusion current (Ilkovic equation, page 143) with the experimental value. Analyze the polarographic wave.

3. Determine the limiting current of 0.001 M thallous chloride, and compare with the diffusion current.

VOLTAMMETRY AND AMPEROMETRIC TITRATIONS 175

4. Determine the diffusion current of lead chloride in 0.5 iV potassium nitrate as indifferent electrolyte at the following concentrations of lead: 2 X 10"^, 5 X 10~ , 10""', and 2 X 10~^ M. Is id proportional to C? Is Uyi constant? Report the

value of 1114. 5. Determine the anodic wave of 0.001 M sodium thiosulfate in 0.1 A'' potassium

nitrate, and analyze the wave according to

2 SjOs" + Hg f± Hg (8203)2= + 2e.

6. Determine the c-v. curves of air saturated solutions of 0.001 A'', 0.01 A'', and 0.1 A potassium chloride. Also determine the waves in the presence of a maximum suppressor, e.g., a trace (5 X 10~^ M) of methyl red or O.OS per cent gelatin. Interpret the double wave.

7. Analyze qualitatively and quantitatively an unknown containing, e.g., copper, cadmium and zinc, or lead chloride and zinc chloride, etc., using the dropping-mercury electrode.

8. Determine the c-v. curve of an air-saturated solution of 0.1 N potassium chloride using a platinum microelectrode (see page 164).

Amperometric Titrations: 9. Using the dropping electrode titrate 0.005 M lead nitrate in 0.1 N potassium

nitrate with 0.025 M potassium dichromate at Ila.e. = — 1.0 volt (vs. S.C.E.). 10. Titrate 0,01 M potassium sulfate in 20 per cent ethanol with 0.1 M lead nitrate

at Ha.e. = - 1.2 volts (vs. S.C.E.). 11. Using a rotating platinum wire microelectrode, titrate 0.001 N AS2O3 in 1 Af HCl,

0.05 N KBr with 0.01 N KBrOs, at n = +0.2 volt (vs. S.C.E.). (Do not remove air.) Carry out the same titration potentiometrically with the rotating electrode as indicator electrode (use a switch to disconnect the electrolysis cell but do not add special equipment for the potentiometric titration).

LOGARITHM TABLES

178

Natural Numbers.

lO II 12

13

14

IS

16 17 18 19

2 0

21

22

23

24

25 2 6

2 7

28

29

3 0

31

3 2

3 3

3 4

3 5

3 6

3 7

3 8

3 9

4 0

41 4 2

4 3

4 4

4 5 4 6

4 7

4 8

4 9

5° SI

5 2

S3

5 4

0

0 0 0 0

0 4 1 4

0792

1139 1461

1761

2041

2304

2SS3 2788

3 0 1 0

3 2 2 2

3 4 2 4

3617 3802

3979

4 1 5 0

4314

4472

4 6 2 4

4771 4 9 1 4

5051

S185

5315

5441

5563 5682

5 7 9 8

5 9 "

6021

6 1 2 8

6232

6335

6435

6532

6 6 2 8

6721

6812

6902

6 9 9 0

7076

7 1 6 0

7243

7324

1

0 0 4 3

° 4 S 3 0 8 2 8

" 7 3 1492

1 7 9 0

2068

2330

2577

2810

3 0 3 2

3 2 4 3

3 4 4 4

3 6 3 6

3 8 2 0

3 9 9 7 4166

4 3 3 0

4 4 8 7

4 6 3 9

4 7 8 6

4 9 2 8

5065

S 1 9 8

5328

S453

SS7S

5 6 9 4

5809

5922

6031

5138

6243

6345

S444

6542

6637

6 7 3 0

6821

6911

6 9 9 8

7084

7168

7251

7332

2

0 0 8 6

0 4 9 2

0 8 6 4

1206

1523

1 8 1 8

2095

2355 2601

2833

3 0 5 4

3 2 6 3

3 4 6 4

3 6 5 5

3 8 3 8

4 0 1 4

4 1 8 3

4 3 4 6

4 5 0 2

4 6 5 4

4 8 0 0

4 9 4 2

5079 5211

5 3 4 0

5 4 6 5

5 5 8 7

57°5 5821

5933

6 0 4 2

6 1 4 9

6 2 5 3

6 3 5 5

6 4 5 4

6 5 5 1 6 6 4 6

6 7 3 9 6 8 3 0

6 9 2 0

7007

7093

7177

7 2 5 9

7 3 4 °

S

0 1 2 8

0531

0 8 9 9

1239

1553

1847

2 1 2 2

2 3 8 0

2625

2856

3 0 7 5 3 2 8 4

3 4 8 3

3 6 7 4

3 8 5 6

4 0 3 1 4 2 0 0

4 3 6 2

4 5 1 8

4 6 6 9

4 8 1 4

4 9 5 5

5092

5 2 2 4

5 3 5 3

5 4 7 8

5599

5717

5 8 3 2

5 9 4 4

6053

6 1 6 0

6 2 6 3

6 3 6 5

6 4 6 4

6561

6 6 5 6

6 7 4 9

6 8 3 9

6 9 2 8

7016

7101

7185

7267

7 3 4 8

LOGARITHMS

4

0 1 7 0

0 5 6 9

° 9 3 4 1271

1 5 8 4

1875

214S

2405

2 6 4 8

2 8 7 8

3 0 9 6

3 3 0 4

3 S 0 2

3 6 9 2

3 8 7 4

4 0 4 8

4 2 1 6

4 3 7 8

4 5 3 3 4 6 8 3

4 8 2 9

4 9 6 9

S105

5 2 3 7

5 3 6 6

5 4 9 0

5611

5729

SS43

5955

6 0 6 4

6 1 7 0

6 2 7 4

6 3 7 5 6 4 7 4

5571 6 6 6 5

6 7 5 8

6 8 4 8

6 9 3 7

7 0 2 4

7 1 1 0

7193

7275

7356

5

0 2 1 2

0 6 0 7

0969

1303

1 6 1 4

1903

2175

2 4 3 0

2672

2 9 0 0

3 1 1 8

3 3 2 4

3 5 2 2

3711

3 8 9 2

4 0 6 5

4 2 3 2

4 3 9 3

4 5 4 8

4 6 9 8

4 8 4 3

4 9 8 3

S 1 1 9

5 2 5 0

5 3 7 8

S502

5623

e

0253 0645 1004 1335 1644

1931 2 2 0 1

2455 2695

2923

3139

3345

3541

3729

3909

4082

4 2 4 9 4 4 0 9

7

0 2 9 4

0 6 8 2

1038

1367

1673

1959 2227

2 4 8 0

2718

2945

3 1 6 0

3 3 6 5

3 5 6 0

3 7 4 7

3 9 2 7

4 0 9 9

4 2 6 5

4 4 2 5

4564I4579

4 7 1 3

4 8 5 7

4 7 2 8

4 8 7 1

4 9 9 7 S O U

5132

5263

5391

5514

5635

5 7 4 0 5752

5 8 5 5 5966

6 0 7 5

6 1 8 0

6 2 8 4

6 3 8 5

6 4 8 4

6 5 8 0

6 6 7 5

6 7 6 7

6 8 5 7 6 9 4 6

7033 7118

7202

7 2 8 4

7364

5866

5977

6 0 8 5

6191

6 2 9 4

6395

6493

6 5 9 0

6 6 8 4

6 7 7 6

6866

6955

7042

7126

7 2 1 0

7292

7372

S 1 4 5 5276

5403

5 5 2 7

5647

5763

5 8 7 7 •5988

6 0 9 6

6 2 0 1

6 3 0 4

6 4 0 5

6503

6599 6693 678s 6875 6964

7 0 5 0

7135 7218

7 3 0 0

7 3 8 0

8

0 3 3 4 0 7 1 9

1072

1399 1703

1987

2253

2 5 0 4

2742

2967

3181

3 3 8 3

3 5 7 9

3 7 6 6

3 9 4 S

4 1 1 6

4 2 8 1

4 4 4 0

4 5 9 4

4 7 4 2

4 8 8 6

5 0 2 4

5159

5289

5416

5539

5 6 5 8

S77S 5 8 8 8

5999

6 1 0 7

6 2 1 2

6 3 1 4

6 4 1 5

6 5 1 3

6 6 0 9

6 7 0 2

6 7 9 4

6 8 8 4

6 9 7 2

7059

9

0 3 7 4

0 7 5 5 1106

1 4 3 0

1732

2 0 1 4

2279

2529

2765

2989

3201

3 4 0 4

3 5 9 8

3 7 8 4

3 9 6 2

4 1 3 3

4 2 9 8

4 4 5 6

4 6 0 9

4 7 5 7

4 9 0 0

5 0 3 8

5 1 7 2

53°2

5 4 2 8

5SSI

5 6 7 0

5786

5 8 9 9

6 0 1 0

6117

6 2 2 2

6 3 2 5

6 4 2 5

6 5 2 2

6 6 1 8

6 7 1 2

6 8 0 3

6893 6981

7067

7143 7152

7226

7 3 0 8

7 3 8 8

7235 7 3 1 6

7396

PROPORTIONAL PARTS.

1

4

4

3

3

3

3

3

2

2

2

2

2

2

2

2

2

2

2

2

I

I

I

I

I

I

I

I

1

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

2

8

8

7

6

6

6

5

S

S

4

4

4

4

4

4

3

3

3

3

3

3

3

3

3

3

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

a 2

2

3

12

II

10

10

9

8

8

7

7

7

6

6

6

6

5

5

5

5

S

4

4

4

4

4

4

4

4

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

2

2

2

4

17

15

14

13

12

II

ir 10

9

9

8

8

8

7

7

7

7

6

6

6

6

6

S

S

5

S

S

5

S

4

4

4

4

4

4

4

4

4

4

4

3

3

3

3

3

5

21

19

17

16

15

14

13

12

12

II

II

10

10

9

9

9

8

8

8

7

7

7

7

6

6

6

6

6

6

5

S

S

S

i S

5

S 5

4

4

4

4

4

4

4

6

25

33

21

19

18

17

16

15

14

13

13

12

12

II

II

lo 10

p 9 9

9

8

8

8

8

7

7

7

7

7

6

6

6

6

6

6

6

5

5

S

S

S

S

S

5

7

29

26

24

23

21

20

IS

17

16

16

IS

14

14

13

12

12

II

II

II

10

10

10

9

9

9

9

8

8

8

8

8

7

7

7

7

7

7

6

6

6

6

6

6

0

6

8

33

30

28

26

24

22

9

37

34

31

ag 37

23

2IJS4

20 21

19121

18

17

16

15

IS

14

20

19

I8

17

17

16

14:15

I3|IS

I3|I4

12 14

12

II

II

II

10

10

10

10

9

9

9

9

8

8

8

8

8

7

7

7

7

7

7

7

6

6

13

13

12

12

12

tl

II II to to 10

to

9 9 9 9

9 8 8 3 S

8

8

7

7

7

LOGARITHMS 179

Natural Numbers,

ss 56 57 S8 59

60 61 62

63 64

65 66 67 68 69

70

71 72

73 74

75 76 77 78 79

80 81 82

83 84

8S 86 87 88 89

90

91 92

93 94

9S 96 97 98 99

0

7404 7482

7SS9 7634 7709

7782

7853 7924

7993 8062

8129

819s 8261

8325 8388

8451 8513 8573 8633 8692

8751 8808 886s 8921 8976

9031 9085 9138 9191

9243

9294

9345 9395 9445 9494

9542 9590 9638 9685

9731

9777 9823 9868 9912 9956

1

7412 7490 7566 7642 7716

7789 7860

7931 8000 8069

8136 8202 8267

8331 8395

8457 8519 8579 8639 8698

8756 8814 8871 8927 8982

9036 9090

9143 9196 9248

9299

9450 9400 94SO 9499

9S47 9595 9643 9689 9736

9782 9827 9872 9917 9961

2

7419 7497 7574 7649

7723

7796 7868 7938 8007

807s

8142 8209 8274 8338 8401

8463

8525 8585 8645 8704

8762 8820 8876 8932

8987

9042 9096 9149 9201

9253

9304 9355 9405 9455 9504

9552 9600 9647 9694

9741

9786 9832 9877 9921 9965

3

7427

7505 7582 7657 7731

7803 7875 7945 8014 8082

8149 821S 8280

8344 8407

8470

8531 8591 8651 8710

8768 882s 8882 8938 8993

9047 9101 9154 9206 9258

9309 9360 9410 9460

9509

9557 9605 9652 9699

9745

9791 9836 9881 9926 9969

4

7435 7513 7589 7664 7738

7810 7882

7952 8021 8089

8156 8222 8287

8351 8414

8476 8537 8597 8657 8716

8774 8831 8887 8943 8998

9053 9106

9159 9212 9263

9315 9365 9415 9465 9513

9562 9609

9657 9703 975°

9795 9841 9886

9930 9974

6

7443 7520 7597 7672

7745

7818 7889

7959 8028 8096

8162 8228 8293

8357 8420

8482

8543 8603 8663 8722

8779 8837 8893 8949 9004

9058 9112 9165 9217 9269

9320

9370 9420 9469 9518

9566 9614 9661 9708

9754

9800

9845 9890

9934 9978

G

7451 7528 7604 7679

7752

782s 7896 7966 8035 8102

8169

8235 8299

8363 8426

8488

8549 8609 8669 8727

8785 8842 8899

8954 9CX39

9063 9117 9170 9222

9274

9325 9375 9425 9474 9523

9571 9619 9666

9713 9759

980s 9850 9894

9939 9983

7

7459 7536 7612 7686 7760

7832 7903 7973 8041 8109

8176 8241 8306 8370

8432

8494 8555 8615 867s 8733

8791 8848 8904 8960

901S

9069 9122

917s 9227 9279

9330 9380

9430 9479 9528

9576 9624 9671 9717 9763

9809 9854 9899 9943 9987

8

7466

7543 7619 7694 7767

7839 7910 7980 8048 8116

8182 8248 8312 8376

8439

8500 8561 8621 8681

8739

8797 8854 8910 896s 9020

9074 9128 9180 9232 9284

9335 9385 9435 9484

9533

9581 9628

9675 9722 9768

9814

9859 9903 9948 999:

7474 7551 7627 7701

7774

7846 7917 7987 8055 8122

8189

8254 8319 8382

8445

8506

8567 8627 8686

8745

8802 8859 891S 8971 9025

9079

9133 9186 9238 9289

9340 9390 9440 9489 9538

9586 9633 9680

9727 9773

9818 9863 9908 9952 9996

PROPORTIONAL PARTS.

1

0

0

0

0

0

0

0

0

0

0

0

0

0

2

2

2

2

I

I

I

I

1

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

I

z I

I

I

I

I

I

I

I

I

I

I

I

I

3

3

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

I

I

I

I

I

I

I

I

I

I

I

I

I

4

3 3 3 3 3

3 3 3 3 3

3 3 3 3 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

5

4 4 4 4 4

4 4 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 2

2

2

2

2

2

2

2

2

2

2

3

2

C

5 5 5 4 4

4 4 4 4 4

4 4 4 4 4

4 4 4 4 4

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 3 3

7

s s 5 S 5

5 S S 5 5

5 S 5 4 4

4 4 4 4 4

4 4 4 4 4

4 4 4 4 4

4 4 3 3 3

3 3 3 3 3

3 3 3 3 3

8

6 6 6 6 6

6 6 6 5 S

5 5 5 5 S

S 5 5 5 5

5 S 4 4 4

4 4 4 4 4

4 4 4 4 4

4 4 4 4 4

4 4 4 4 3

0

7 7 7 7 7

6 6 5 6 6

6 6 6 6 6

6 S S

s s

s s 5 S S

S 5 S 5 S

s s 4 4 4

4 4 4 4 4

4 4 4 4 4

180 ANTILOGARITHMS

Log.

.00

.01

.02

•03 .04

•OS .06

.07

.08

.09

.10

.11

.12

•13 .14

•15 .16

• 17 .18

.19

.20

.21

.22

•23 .24

•2S .26

.27

.28

.29

•30

•31

•32

•33 •34

•35 •36 •37 •38 • 39

.40

.41

.42

•43 .44

•45 .46 •47 ,48 •49

0

1000

1023

1047

1072

1096

1122

1148

"75 1202

1230

I2S9 1288

1318

1349 1380

1413

1445

1479

1514

1549

1585 1622

1660

1698

1738

1778

1820

1862

1905

1950

199s 2042

2089

2138

2188

2239

2291

2344

2399

2455

2512

257° 2630

2692

2754

2818

2884

2951 3020 3090

1

1002

1026

1050

1074

1099

1125

1151

1178

1205

1233

1262

1291

1321

1352

1384

1416 1449

1483

1517

1552

1589 1626

1663

1702

1742

1782

1824

1866

1910

1954

2000

2046 2094

2143 2193

2244 2296

2350 2404

2460

2518

2576

2636

2698

2761

2825

2891

2958

3027

3097

2

1005

1028

1052

1076

1102

1127

IIS3 1180

1208

1236

1265

1294

1324

1355 1387

1419

1452 i486

1521

1556

1592 1629

1667

1706

1746

1786

1828

1871

1914

1959

2004

2051

2099

2148

2198

2249

2301

2355 2410

2466

2523 2582

2642

2704

2767

2831 2897

2965

3034

3105

3

1007 1030

1054 1079

1104

1130

1156

1183

1211

1239

1268

1297

1327

1358 1390

1422

1455 1489

1524 1560

1596 1633 1671

1710

1750

1791

1832

1875 1919

1963

2009

2056

2104

2153 2203

2254 2307

2360

2415 2472

2529 2588

2649

2710

2773

2838

2904

2972

3041 3112

4

1009

1033

IOS7 1081

1107

1132

1159 1186

1213

1242

1271

1300

1330 1361

1393

1426

1459 1493 1528

1563

1600

1637

1675 1714

1754

1795

1837 1879 1923

1968

2014

2061

2109

2158 2208

2259 2312

2366

2421

2477

2535

2594

2655 2716

2780

2844 2911

2979 3048

3119

5

1012

103 s

1059 1084

1109

"35 1161

1189

1216

1245

1274

1303

1334

136s 1396

1429

1462

1496

1531

1567

1603

1641

1679

1718

1758

1799

1841

1884

1928

1972

2018

2065

2113

2163

2213

2265

2317 2371

2427

2483

2541 2600

2661

2723

2786

2851 2917

2985

3055 3126

G

1014

1038

1062

1086

1112

"38 H64 1191

1219

1247

1276

1306

1337 1368

1400

1432 1466

1500

1535

1570

1607

1644

1683 1722

1762

1803

1845 1888 1932

1977

2023

2070

2118

2168

2218

2270

2323

2377 2432

2489

2547 2606

2667

2729

2793

2858

29''4 2992

3062

3133

7

1016

1040

1064

1089

1 U 4

1140

1167

"94 1222

1250

1279

1309

1340

1371

1403

1435 1469

1503 1538

1574

1611

1648

1687

1726

1766

1807

1849 1892

1936

1982

2028

2075 2123

2173

2223

2275 2328

2382

2438

2495

2553 2612

2673

2735 2799

2864

2931

2999

3069

3141

8

1019

1042

1067

1091

1117

"43 1169

"97 I22S

I2S3

1282

1312

1343 1374 1406

1439 1472

1507 1542

1578

1614

1652

1690

1730 1770

1811

1854 1897 1941

1986

2032 2080

2128

2178

2228

2280

2333 2388

2443 2500

2559 2618

2679

2742

2805

2871

2938

3006

3076

3148

9

1021

I045 1069

1094

1119

1146

1172

1199

1127

1256

1285

1315 1346

1377 1409

1442

1476

1510

1545 1581

1618

1656 1694

1734

1774

1816

1858

1901

1945 1991

2037

2084

2133 2183

2234

2286

2339

2393

2449 2506

2564

2624

2685

2748 2812

2877

2944

3013 3083

3155

P K O P O R T I O N A L PASTS.

1

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

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0

0

0

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2

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0

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2

2

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3

3

3

3

3

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2

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2

2

2

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2

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3

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2

2

2

2

2

2

2

2

2

2

2

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2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

7

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

4

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5

5

5

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1 8|9

2

2

2

2

2

2

2

2

2 1 2

2

2

2

2

2

2

2

3

3

3 2 3

2'3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

4

S

S

S

5

5

5

5

3

3

3

3

3

3

3

3

3

3

4

4

4

4

4

4

4

4

4

4

4 S

S

5 S

s s

5

S 6

6

6

6

5 6

5 6

6

6

6 6

ANTILOGARITHMS 181

Log.

•5° •SI •52 •53 •S4

•55 •56 •S7 •58 •59

.60

.61

.62 •63 .64

•65 .66 .67 .68 .69

.70

.71

.72

•73 .74

• 75 .76

.77

.78 •79

.80

.81

.82

.83

.84

.85

.86

.87

.88

.89

.90

.91

.92

•93 •94

•95 .96 •97 .98 •99

0

3162

3236

33^'^ 3388

3467

3548

363^ 3715 3802

3890

3981

4074

4169

4266

4365

4467

4571

4677 4786

4898

SOI 2

5129

5248

5370

5495

5623

5754 5888

6026

6166

6310 6457 6607

6761

6918

7079

7244

7413 7586

7762

7943 8128

1

3170

3243

3319

3396

3475

3556

3639

3724 3811

3899

3990 4083

4178 4276

4375

4477 4581 4688

4797

4909

5023

5140 5260

5383 5508

5636 5768

5902

6039

6180

6324

6471

6622

6776

6934

7096

7261

7430 7603

7780

7962

8147 8318 8337

8511 8710

8913 9120

9333

9550 9772

8531 8730

8933 9141

9354

957»

9795

2

3177

3251

3327

3404

3483

3565 3648

3733

3819 3908

3999

4093 4188

428s

4385

4487

4592 4699

4808

4920

5035 5152

5272

5395 5521

5649 5781

5916 6053

6194

6339 6486

6637

6792

6950

7112

7278

7447 7621

7798

7980

8166

8356

8551

8750

8954 9162

9376

9594

9817

3

3184

3258

3334 3412

3491

3573

3656

3741 3828

3917

4009

4102

4198

4295

4395

4498

4603

4710

4819

4932

5047 5164

5284 5408

5534

5662

5794

5929 6067

6209

6353 6501

6653 6808

6966

7129

7295 7464

7638

7816

7998 8185

837s 8570 8770

8974

9183

9397 9616

9840

4

31912

3266

3342 3420

3499

3581 3664

3750

3837 3926

4018

4111

4207

4305 4406

4508

4613 4721

4831

4943

5058

S176

5297 5420

5546

5675 5808

5943 6081

6223

6368

6516

6668

6823

6982

7145

7311 7482

7656

7834

8017

8204

8395 8590

8790

8995 9204

9419

9638

9863

5

3199

3273 3350 3428

3508

3589

3673 3758 3S46

3936

4027

4121

4217

4315 4416

4519 4624

4732 4842

4955

5070 5188

5309

5433

5559

5689 5821

5957 6095

6237

63S3 6531 6683 6839 6998

7161 7328

7499 7674

7852

8035 8222 8414 8610 8810

9016 9226 9441 9661 9886

G

3206 3281

3357 3436 3516

3597 3681

3767 385s 3945

4036

4130 4227

4325 4426

4529 4634 4742 4853 4966

5082 5200 5321 5445 5572

5702 5834 5970 6109 6252

6397 6546 6699

6855 7015

7178 7345 7516 7691 7870

8054 8241

8433 8630 8831

9036

9247 9462 9683 9908

7

3214 3289

3365 3443 3524

3606 3690 3776 3864 3954

4046 4140 4236

4335 4436

4539 4645 4753 4864

4977

5093 3212 5333 5458 5585

5715 5848 5984 6124 6266

6412 6561 6714 6871 7031

7194 7362 7534 7709 7889

8072 8260

8453 8650 8851

9057 9268 9484 9705 9931

8

3221 3296

3373 3451 3532

3614 3698 3784 3873 3963

405s 4150 4246

4345 4446

4550 4656

4764 4875 4989

5105 5224 5346 5470 5598

5728 S86i 5998 6138 6281

6427

6577 5730 6887

7047

7211

7379 7551 7727 7907

8091 8279 8472 8670 8872

9078 9290 9506

9727

9

3228 3304 3381 3459 3540

3622 3707 3793 3882 3972

4064

4159 4256 4355 4457

4560 4667

4775 4887 5000

S117 5236 5358 5483 5610

5741 5875 6012 6152 6295

6442 6592

6745 6902 7063

7228 7396 7568 7745 7925

8110 8299

8492 8690 8892

9099

9 3 " 9528 9750

995419977

PROPORTIONAL PARTS.

1

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J-2 I 2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

2

3 3

3 3 3 3 3

3 3 3 3 3

3 3 3 4 4

4 4 4 4 4

4 4 4 4 S

3

2

2

2

2

2

2

3 3 3 3

3 3 3 3 3

3 3 3 3 3

4 4 4 4 4

4 4 4 4 4

4 S S 5 S

5

s 5 5 5

6 6 6 6 6

6 6 7 7 7

4

3

3 3 3 3

3 3 3 4 4

4 4 4 4 4

4 4 4 4 5

5 S 5 S 5

5 S 5 6 6

6 6 6 6 6

7 7 7 7 7

7 8 8 8 8

8 8 9 9 9

. 1 _ _

4 4 4 4 4

4 4 4 4

s

5 5 5 S S

5 S S 6 6

6 6 6 6 6

7 7 7 7 7

7 8 8 8 8

8 8 9 9 9

9 9 10

10

10

10

II

II

II

II

6

4

5 5 5 5

S 5 5 S S

6 6 6 6 6

6 6 7 7 7

7 7 7 8 8

8 8 8 8 9

9 9 9 9 ID

10

10

10

II

II

II

II

12

12

12

12

13

13 13 14

7

5 5 5 6 6

6 6 6 6 6

6 7 7 7 7

7 7 8 8 8

8 8 9 9 9

9 9 10

10

10

10

II

II

11

ir

12

12

12

12

13

13 13 14 14 14

IS 15 15 16 16

8

6 6 6 6 6

7 7 7 7 7

7 8 8 8 8

8 9 9 9 9

9 10

10

10

10

10

II

II

II

II

12

12

12

13

13

13

13

14

14

14

15

IS

IS 16

I6

17

17

17 18

9

7 7 7 7 7

7 8 8 S 8

3 9 9 9 9

9 10

10

10

10

n u n II

12

12

12

12

13

13

13 14 14 14 IS

IS IS la i5

16

17

17

17 18

I3

19

19 20

20

iS'SO

INDEX OF AUTHORS

AGREE, S . F . , 46, 88

ANTWEILER, N . J., 152

ABBHBNIUS, SV., 1

BAWDBN, A . T . , 113

BEATTIE, J . A., 102

BELCHBB, D . , 88

BiiLMAN, E., 91, 93 BJEBRUM, N . , 6

BORNSTETN, R . , 1 1 9

BOSCH, W . , 96

BouLAD, J. H., 135 BBITTON, H . T . S., 100, 123, 125

BBONSTED, J. N., 4

BYE, J., 134

CALLAK, T . , 123

CAMPBELL, M . A., 93

CANDLA, C , 134

CHRETIEN, A., 134

CLARK, W . M . , 4, 25, 26, 32, 51, 78, 87,

100 COHEN, B . , 26

COWPEBTHWAITE, I . A. , 1 1 4

Cox, D. C , 114

DAVIES, C . W . , 127

BEARING, W . C , 96

DEB YE, P., 2, 3, 4 DESHUSSES, J., 134

DESHUSSES, L . , 134

DOLE, M . , 100, 101, 102, 114

DRAKE, N . L . , 26

Dnoz, M. E., 82, 83 DUBOIS-RETMOND, 76

DuToiT, P., 121, 134

ERVING, W . W . , 84

FAWC3ETT, E . H . , 4 6

FBNWICK, F . , 99, 113

F I N N , A. N., 101

FouLK, C. W., 113

94,

FREAK, G . A., 134

F R U M K I N , A. , 152

FuRMAN, N . H., 79, 94, 99, 100, 111, 113, •--•146

GARMAN, R . L . , 82, 83, 123

GILLESPIE, L . J., 39

GOODE, K . H . , 82

GUGGENHEIM, E . A., 89

GYBMANT, A . , 44

HABER, F . , 100

HAGER, 0 . B. , 82

HAMER, W . J., 88

HAMILTON, E . H . , 101

HARDEN, W . C , 26

HARMS, J., 135

HENGEVELD, G . , 135

HEYBOVSKY, J., 136, 140, 153, 158

HITCHCOCK, D . I., 89, 90

HOAR, T . P , 97

HoHN, H., 136 HORROBIN, S., 123

HOSTETTER, J . C , 1 1 3

HOVORKA, F . , 96

HUBBARD, D . , 101

HiJCKEL, E., 2, 3, 4 HuLETT, G. A., 86 HuRwiTz, S. H., 45

ILKOVIC, D . , 143

IMMIG, H . , 134, 135

ITANO, A . , 134

JANDER, G , 123, 125, 134, 135

JONES, P . T., 114

KAMEDA, T . , 46, 89, 134

KAMIENSKI , B . , 112

KLBMENSIEWICZ, Z. , 100

KLUMPAR, J., 136

KOCERT, H . , 134

183

184 I N D E X OF AUTHORS

KoLTHOFF, I. M., 20, 25, 32, 33, 37, 41, 43, 44, 46, 51, 52, 79, 89, 94, 96, 99, 100, 111, 116, 125, 134, 135, 136, 139, 143, 148, 165

KRAFT, J., 134

LAITINEN, H . A . , 86, 136, 139, 160

LAMER, V. K , 4

LAMMERT, 0 . M., 93

LANDOLT, H . , 119

LARSSON, E . L. , 128

LATIMER, W . M . , 66

LEWIS, G . N . , 2, 3, 56

LINDERSTROM-LAXC, K . , 95

LiNGANB, J. J., 136, 143, 148, 160 LIPSCOMB, G . T . , 84

LoRCH, A. E., 89 LuBS, H. A., 26, 32, 34, 35 LUND, H . , 43, 91

LUTHER, R . , 78

M u s , J., 144 MACDOUGALL, F . H . , 2, 4, 56

MACINNES, D . A. , 88, 102, 114

MAJER, V . , 155

MAJOIU, P . B . , 134

MEYER, K . F . , 45

MicHAELis, L., 42, 44 MORGAN, J. L. R., 93

MUELLER, E . F . , 160

MiiLLER, E., 112, 114, 134 MURGULESCU, I . G . , 1 3 4

NEJEDLY, V. , 146

NERNST, W . , 55

OSTENBERG, Z. , 4 5

OSTWALD, W . , 7 8

P A X , Y . D . , 165 PERLEY, G . A . , 99

PFUNDT, 0. , 125, 134, 135

PiNKHOF, J., I l l POGGENDORF, 76

RAB, N . , 130 RANDALL, M . , 2

RICHARDS, W . T . , 97

RIGHELLATO, E . C . , 127

RiPAN, R., 134 ROBERTS, E . J., 99

ROBERTS, H . S., 113

ROSBNBLUM, C , 2 0

ROTH, W . A. , 119

ROTHER, E . , 134

SCHINDLER, T. D., 89 SciionsTEiN, H., 123 SCHULZ, G. , 91 SERFASS, E . J., 83

SHEDLOVSKY, T . , 88

S M I T H , G . F . , 82

SoRENSEN, S. P . L,, 32, 33, 36, 95 STACKELBERG, M . V . , 152

STONE, H . W . , 90

SULLIVAN, V. R., 82

TAYLOR, A. C , 89, 90

TiLici, R. R., 134 TRE.\DWELL, W . D . , I l l , 123

UNMACK, A. , 6, 89, 96

URMANCZY, A. , 96

VAN NAME, R . G. , 113

VAN SLYKB, D . D . , 20

VAN SUCHTELEN, F . H . H . , 134

VBIBBL, S., 86

VIÊSCHHOUWER, J. J., 33, 35, 36

VON K I S S , A., 96

WALBUM, L . E . , 33

WALPOLB, H . , 44

WBISS, L . , I l l

WIDMARK, E . M . P . , 128

WILLARD, H . H . , 82, 113

WILSON, E . B . , JR., 113

INDEX OF SUBJECTS

Acetic acid, conductometric titration, 126

neutralization curve, 107 Acid exponent, 8 Acid salts, reaction of, 14 Acidity, 11 Acids, 4

Bronsted definition of, 4 ionization constants of, 10

Cj. Neutralization reactions Activity, of ions, 1, 2, 56

of metals in amalgams, 58 Activity coefficient, 2, 16, 21, 48, 49,

50, 57, 66, 72 Activity constants, 15

table of, for acids and bases, 10 Adsorption, effect on colorimetric

method, 52 effect on conductometric titrations,

133 effect on quinhydrone electrode, 96

Alcohol, effect on indicators, 52 in amperometric titrations, 169 in conductometric titrations, 127

Alizarine yellow, 29 Alkaloids, influence on hydrogen elec

trode, 91 Ammonium salts, conductometric titra

tion, 131 Amperometric titrations, 165

advantages and limitations, 107 performance of, 170

Analysis of polarographic waves, 153 Anions, polarographic determination,

148 Anodic waves, 150 Antimony-antimonious oxide electrode,

99 Aprotonic solvents, 5 Aromatic compounds, influence on hy

drogen electrode, 91

Arsenic trioxide, amperometric titration, 167

influence on hydrogen electrode, 91 Asymmetry potential, 101

Barium acetate as reagent, 134 Bases, 4

Bronsted definition of, 4 ionization constants of, 10

Battery, 77 Bicolorimeter, 39 Bimetallic electrode systems, 112 Bismuth oxyperchlorate as reagent, 135 Borax, as standard p H solution, 90

conductometric titration, 128 effect on quinhydrone electrode, 96 for buffers, 34

Boric acid for buffers, 33 Bromate, polarographic determination,

148 Bromcresol green, 28, 29, 40

indicator constant, 41 salt correction, 48

Bromcresol purple, 41 Bromphenol blue, 28, 29, 40

dichromatism, 26 indicator constant, 41 salt correction, 50

Bromphenol red, 28 Brorathymol blue, 28, 29, 40

as isohydric indicator, 46 indicator constant, 41 salt correction, 50

Buffer capacity, 20 Buffer solutions, 17

effect of dilution, 21 effect of temperature, 19, 37 mateiials for, 33 of Clark and Lubs, 32, 34, 35 of Kolthoff and Vleeschhouwer, 35, 36 of Sorensen, 36

185

186 I N D E X OF SUBJECTS

Calcium ferrocyanide as reagent, 135 Calomel electrode, as reference elec

trode, 85 theory of, 61

Capillaries for dropping mercury electrode, 159

Capillary electrometer, 79 Catalytic hydrogen waves, 151 Cations, polarographic determination,

148 Charging current, 141 Chemical potential, 56 Chloride, amperometric titration, 170

conductometric titration, 134 polarographic determination, 150 potentiometric titration, 109

Chlorphenol red, 28, 29, 40 iiidicator constant, 41 salt correction, 50

Cobalt, amperometric titration, 167 Colorimeter, Gillespie, 39

Walpole, 44 wedge, 39

Colorimetric determination of pH, cj. Hydrogen-ion determination (colorimetric)

Concentration polarization, 137, 138 Condenser current, 141 Conductance, equivalent, 119

specific, 119 Conductometric titrations, 118

acid-base titrations, 125 complex formation reactions, 131 limitations, 121, 132 performance, 121 precipitation reactions, 131 replacement titrations, 130

Constants, concentration, 15 indicator, 24 thermodynamic, 15

Copper, amperometric titration, 167 Cresol purple, 28, 29 Cresol red, 40 Current-voltage curves, characteristics

of, 136 maxima on, 151 with concentration polarization, 138 with dropping mercury electrode, 141 without polarization, 137

Cyanogen, polarographic determination, 149

Debye-Huckel equation, 2, 3 Dichromatism, 26 Differential titrations, 113 Diffusion coefficients of ions, 146 Diffusion currents, 139

effect of concentration, 145 effect of diffusion coefficient, 145 effect of drop time, 144, 145 effect of temperature, 146 factors which determine, 143

Dilution correction, in amperometric titrations, 171

in conductometric titrations, 123 Dinitrophenols, 43 Dissociation, of acids and bases, 4

of electrolytes, 2, 4 of indicators, 23 of water, 6

Double layer, 55

Electrocapillary curve, 142 Electrocapillary maximum, 142 Electrocapillary zero, 142 Electrochemical potential, 56 Electrode, air, 96

bimetallic, 112 calomel, 61, 84 Carborundum, 112 ceric-cerous, 64, 66 depolarized, 137, 138 dichromate-chromic, 65 dropping mercury, 140 ferric-ferrous, 63 glass, 100 higher oxide, 66, 98 hydrogen, 59, 87 indicator, 104, 109, 140 metal, potential of, 55 metal-metallic oxide, 98 oxygen, 96 permanganate-manganous, 65 polarized, 113, 137 quinhydrone, 64, 86, 91 reference, 73, 84

for voltammetry, 161, 162 rotating, 139

construction of, 161 in amperometric titrations, 171 residual current with, 143

stannic-stannous, 64

I N D E X OF SUBJECTS 187

Electrode, table of normal potentials, 67 uranyl-uranous, 64

Electrolysis cells for voltammetry, 161 Electrolytes, dissociation of, 1 Electrolytic solution tension, 55 Electromotive force of cells, 69

determination of, 76 Electron-tube conductance meter, 124 Electron-tube potentiometer, 82 Equation, Debye-Hiickel, 2, 3

Ilkovic, 143 of polarographic wave, 153

Equivalence point, location of, in poten-tiometric titrations, 109

Equivalence potential, 104 in neutralization reactions, 104, 107 in oxidation-reduction reactions, 105,

110 in precipitation reactions, 105, 109

Equivalent conductance, 119

Ferrocyanide, amperometric titration, 167

Formal potential, 68 Free energy of cell reaction, 70

Galvanometers, 79 alternating-current,

Glass electrode, 100 123

Half-wave potential, 141, 154 diagram of, 155

Higher oxide electrode, 65, 98 Hydrochloric acid, for buffers, 33

neutralization curve, 107 Hydrogen, catalytic reduction of, 151 Hydrogen electrode, 59, 87

cells for, 87 checking of, 90 correction for pi'essure, 60 deposition of coat, 89 interfering factors, 90 poisoning of, 91 theory of, 59

Hydrogen generators, 89 Hydrogen-ion determination (colori-

metric), 32 adsorption, effect of, 52 approximate value, 37 protein effect, 51 salt effect, 47

Hydrogen-ion determination, sources of error, 45

with buffer solutions, 37 with one-color indicators, 41 with two-color indicators, 39 without buffer solutions, 38

Hydrogen-ion determination (potentio-metric), 87

with antimony-antimonious oxide

electrode, 99 with glass electrode, 100 with hydrogen electrode, 59, 87 with mercury-mercuric oxide elec

trode, 98 with metal-metallic oxide electrodes,

98 with oxygen electrode, 97 with quinhydrone electrode, 91 with silver-silver oxide electrode, 98

Hydrogen-ion exponent, 6, 7 Hydrogen ions, concentration, in acids, 7

in buffer solutions, 17 in salts, 11

Hydrogen peroxide, polarographic determination, 149

Hydrogen sulfide, as reagent, 135

influence on hydrogen electrode, 91 Hydrolysis constant, 12 Hydrolysis of salts, 11

effect of temperature, 15 Hydroxonium ions, 4, 6 Hydroxyl ions, 6

anodic depolarization by, 151 interference with quinhydrone elec

trode, 94

Ilkovic equation, 143 Indicator constants, 23, 24, 41, 43

of one-color indicators, 43 , of two-color indicators, 41

Indicator electrode, in potentiometric titrations, 104

in voltammetry, 140 Indicator exponent, 24 Indicator solutions, preparation of, 25 Indicators, color change interval, 23, 24

concentration and color, 28 table of, 29

isohydric, 46 medium and color, 30 one-color, 41, 43

188 INDEX OF SUBJECTS

Indicators, properties of, 25 protein effect on, 51 salt effect on, 41, 43, 47, 49, 50 temperature and color, 30 two-color, 39, 41

Indifferent electrolyte, effect of, on current-voltage curves, 147

lodate, polarographic determination, 148 Ionic strength, 3

Cj. Salt effect Ionization constants of acids and bases,

10 Ionization product of water, 6 Ions, mobility table of, 119

Lead, amperometric titration, 166 polarographic determination, 148

Lead nitrate as reagent, 134 Limiting current, 147 Liquid junction potential, 71 Lithium halides as reagent, 135 Lithium oxalate as reagent, 134 Lithium sulfate as reagent, 134

Maxima on current-voltage curves, 151 suppression of, 153

Mercuric perchlorate as reagent, 134 Mercury-mercuric oxide electrode, 98 Metal-metallic ion electrodes, 55

normal potentials, 68, 68 Metal-metallic oxide electrodes, 98 Methyl orange, 26, 29, 40


Methyl red, 26, 28, 29, 40 effect on unbuffered solution, 46 indicator constant, 41 salt correction, 50 suppression of maxima, 149, 153

Methyl yellow, 27, 28, 29 Migration current, 147 Mobility of ions, table of, 119

Neutral red, 26, 29 Neutralization reactions, 104,106,125 Nickel, amperometric titration, 167 Nitrate, polarographic determination,

148 Nitric oxide, polarographic determina

tion, 149

Nitrite, polarographic determination, 148

Nitrophenols, conductometric titration, 128

indicator constant, 43 Null-point instruments, 78

Organic compounds, influence on hydrogen electrode, 91

polarographic determination, 148 Oxalate, amperometric titration, 167 Oxidation potential, 61

formal, 68 table of standard, 67, 68

Oxidizing agents, influence on hydrogen electrode, 91

influence on quinhydrone electrode, 96

Oxygen, polarographic determination, 149

removal of, from hydrogen, 90 in voltammetry, 163

Oxygen electrode, 96

pH, cf. Hydrogen-ion determination Phenol, conductometric titration, 128 Phenol red, 28, 29, 40

indicator constant, 41 salt correction, 48 structure changes of, 26

Phenolphthalein, color change interval, 29

conductometric titration, 128 pH determination with, 44 salt correction, 50 structure change, 27

Pinachrom, 43 Platinization of hydrogen electrode, 89 Platinum microeleotrode, 161

technique, 164 Polarization, concentration, 137 Polarogram, 140, 159 Polarograph, 140, 158 Polarographic determination, anions,

148 catalytic hydrogen waves, 151 cations, 148 organic compounds, 149 uncharged substances, 149

Polarographic spectrum, 155

INDEX OF SUBJECTS 189

Polarographic wave, 140 anodic, 150 cathodic, 148

Polarographic waves, analysis of, 153 Polarography, equipment used in, 157

technique, 163 Potassium biphthalate for buffers, 33 Potassium chloride for buffers, 33 Potassium citrate (mono), as pH

standard, 90 for buffers, 33

Potassium cyanide in polarography, 148 Potassium ferricyanide as reagent, 135 Potassium ferrocyanide as reagent, 135 Potassium phosphate (mono) for buf

fers, 33 Potassium phthalate (mono) as pH

standard, 90 Potential, asymmetry, 101

chemical, 56 diagram of, 74 electrochemical, 56 equivalence, 104, 105, 107, 109, 110 formal, 68 half-wave, 141, 154, 155 liquid junction, 71 normal, 58

table of, 67, 68 of amalgam electrodes, 58 of calomel electrode, 61 of ferric-ferrous electrode, 63 of higher oxide electrode, 65 of hydrogen electrode, 59, 87 of metal electrode, 55 of quinhydrone electrode, 65, 92 oxidation, 61 phase-boundary, 57 Cf. Electrode

Potentials, oxidation, table of, 67, 68 Potentiometer, 79 Potentiometric measurement of joH, cf.

Hydrogen-ion determination Potentiometric measurements, tech

nique of, 76 Potentiometric titrations, 104

differential, 113 oxidation-reduction reactions, 105,

109 precipitation reactions, 104, 108 special determinations. 114

Potentiometric titrations, to equivalence potential. 111

with bimetallic electrode system, 112 Pressure, effect on hydrogen electrode,

60 Protein, determination of pH of, 91

effect on colorimetric determinations, 51

effect on indicators, 51 polarographic determination, 151

Quinaldin red, 43 Quinhydrone, preparation of, 93 Quinhydrone electrode, 64, 86, 91

as reference, 86, 88 in potentiometric titrations, 93, 94 influence of boric acid, 96 influence of organic compounds, 94 influence of oxidizing and reducing

agents, 96 salt error, 95 sources of error, 94 temperature coefficient, 92 vessels, 93

Reaction, 6 of buffer solutions, 17 of salts, 11 of weak acids, 7 of weak bases, 7

Reducing agents, influence on hydrogen electrode, 91

influence on quinhydrone electrode, 96

Reference electrodes, 73, 84 for voltammetry, 161, 162

Replacement titrations, conductometric, 130

Residual current, 141

Salicylic acid, conductometric titration, 126

Salt bridge, 73, 85, 86 Salt effect, on colorimetric determina

tions, 41, 43, 47 on indicator constant, 49, 50 on quinhydrone electrode, 95

Salts, hydrolysis of, 11 Selenite, polarographic determination,

148

190 I N D E X OF SUBJECTS

Silver, amperometric titration, 166, 167 conductometrjo titration, 120, 132,

134, 135 potentiometric titration, 109

Silver nitrate, as reagent, 134 Silver-silver chloride electrode, 102, 115 Silver-silver oxide electrode, 98 Sodium chromate, as reagent, 135 Sodium perchlorate as reagent, 135 Sodium sulfide, as reagent, 135 Solutions, for p H standards, 90

preparation of indicator, 25 Solvents, aprotonic, 5

polar, 5 Standard acid mixture, 90 Standard cell, 77 Standard half-cells, 73, 84

for voltammetry, 161, 162 Storage battery, 77 Sulfate, amperometric titration, 167

conductometric titration, 134 Sulfonphthaleins, conductometric titra

tion, 130 structure change, 26

Sulfur dioxide, polarographic determination, 149

Tellurite, polarographic determination, 148

Temperature, effect on buffer solutions, 37

effect on color of indicators, 30 effect on conductance, 119, 122 effect on diffusion current, 146 effect on dissociation of water, 6 effect on hydrolysis of salts, 15 effect on indicator constants, 41,

43 effect on p H of buffers, 19, 37

Temperature coefficient, of calomel electrodes, 86

of hydrogen-calomel cells, 88 of quinhydrone-caiomel ceJis, 92 of standard Weston cell, 78

Tetrabromphenol blue, 26, 28 color change interval, 29

Thallous sulfate as reagent, 134 Thymol blue, 28, 29, 40


Thymolphthalein, salt correction, 50 Titration curves, amperometric, 166

conductometric, 121, 125 potentiometric, 106

Titration vessels, conductometric, 122 Titrations, cf. Amperometric titrations;

Conductometric titrations; Potentiometric titrations

Tropeoiine 00, 26, 29

Unbuffered solutions, pR of, 45, 89, 102 Uranyl acetate as reagent, 134

Vacuum-tube conductance meter, 124 Vacuum-tube potentiometer, 82 Vanillin, conductometric titration of,

128 Voltammetrie determination, cf. Polar

ographic determination Voltammetry, 136

electrolysis cells, 161 equipment, 157 general technique, 163

Water, dissociation, 6 ionization product, 6

Wedge colorimeter, 39 Weston cell, 78 Wheatstone bridge, 123

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