Acid-Base Titrations Introduction 3.)Overview Titrations are Important tools in providing...

Acid-Base Titrations

Introduction

3.) Overview Titrations are Important tools in providing quantitative and qualitative data for

a sample.

To best understand titrations and the information they provide, it is necessary to understand what gives rise to the shape of a typical titration curve.

To do this, acid-base equilibria are used to predict titration curve shapes.

Biochemistry, Vol. 41, No. 22, 2002 6945

pKa of His in the His-Asp catalytic dyad that catalyzes the oxidation of glucose 6-phosphate


Titration of Strong Base with Strong Acid

1.) Graph of How pH changes as Titrant is Added Assume strong acid and base completely dissociate

Any amount of H+ added will consume a stoichiometric amount of OH-

Reaction Assumed to go to completion

Three regions of the titration curve- Before the equivalence point, the pH is determined

by excess OH- in the solution

- At the equivalence point, H+ is just sufficient to react with all OH- to make H2O

- After the equivalence point, pH is determined by excess H+ in the solution.

14

w10K

1K



1.) Graph of How pH changes as Titrant is Added Remember, equivalence point is the

ideal goal

Actually measure End Point- Marked by a sudden physical

change: color, potential

Different Regions require different kinds of calculations- Illustrated examples

The “true” titration reaction is:

Titrant Analyte



2.) Volume Needed to Reach the Equivalence Point Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

At equivalence point, amount of H+ added will equal initial amount of OH-

mL00.10V)M02000.0(mL00.50M1000.0)mL(V ee

mmol of HBrat equivalence point

mmol of OH-

being titrated

When 10.00 mL of HBr has been added, the titration is complete. Prior to this point, there is excess OH- present.

After this point there is excess H+ present.



3.) Before the Equivalence Point Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- Equivalence point (Ve) when 10.00 mL of HBr has been added- When 3.00 mL of HBr has been added, reaction is 3/10 complete

M0132.000.300.50

00.50M02000.0

00.10

00.300.10OH

][

Fraction of OH- Remaining

Initial concentration of OH-

Dilution Factor

Initial volume of OH-

Total volume

12.12pHM1058.70132.0

100.1

OH

KH 13

14

-w

][][

Calculate Remaining [OH-]:

Calculate [H+] and pH:



4.) At the Equivalence Point Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- Just enough H+ has been added to consume OH-

- pH determined by dissociation of water

- pH at the equivalence point for any strong acid with strong base is 7.00- Not true for weak acid-base titration

Kw Kw= 1x10-14

00.7pHM1000.1xxK 72w

x x



5.) After the Equivalence Point Titration curve for 50.00 mL of 0.02000 M KOH with 0.1000 M HBr

- Adding excess HBr solution- When 10.50 mL of HBr is added

M1026.850.1000.50

50.0M1000.0H 4

][

Calculate excess [H+]:

Initial concentration

of H+

Dilution factor

Volume of excess H+

Total volume

Calculate volume of excess H+:

mL50.000.1050.10VV eequivalencadded

Calculate pH:

08.3)M1026.8log(H 4 ]-log[pH



6.) Titration Curve Rapid Change in pH Near Equivalence Point

- Equivalence point is where slope is greatest- Second derivative is 0

pH at equivalence point is 7.00, only for strong acid-base- Not True if a weak base-acid is used


Titration of Weak Acid with Strong Base

1.) Four Regions to Titration Curve Before any added base, just weak acid (HA) in water

- pH determined by Ka

With addition of strong base buffer- pH determined by Henderson Hasselbach equation

At equivalence point, all HA is converted into A-

- Weak base with pH determined by Kb

Ka

][

][

HA

AlogpKpH a

Kb



1.) Four Regions to Titration Curve Beyond equivalence point, excess strong base is added to A- solution

- pH is determined by strong base- Similar to titration of strong acid with strong base

2.) Illustrated Example: Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH

- MES is a weak acid with pKa = 6.27

- Reaction goes to completion with addition of strong base

K

727.614awb

104.510/101

1K/K

1K

1K



3.) Volume Needed to Reach the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH

- Reaction goes to completion with addition of strong base- Strong plus weak react completely

mL00.10V)M02000.0(mL00.50M1000.0)mL(V ee

mmol of base mmol of HA



4.) Region 1: Before Base is Added Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH Simply a weak-acid problem

F - x x x

4a

221003.1HxK

x02000.0

x

xF

x

][

Ka Ka= 10-6.27Calculate [H+]:

Calculate pH:

99.3)M1003.1log(Hlog-pH 4 ][

10

3



5.) Region 2: Before the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH Adding OH- creates a mixture of HA and A- Buffer Calculate pH from [A-]/[HA] using Henderson-Hasselbach equation

Calculate [A-]/HA]:

Relative Initial quantities (HA≡1) 1 - -

Relative Final quantities -10

3

10

7

Amount of added NaOH is 3 mL with equivalence point is 10 mL

90.5

107

103

log27.6HA

AlogpKpH a

][

][Calculate pH:

Simply ratio of volumesSimply the differenceof initial quantities

10

3

2

1



5.) Region 2: Before the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH pH = pKa when the volume of titrant equals ½Ve

2

1Relative Initial quantities (HA≡1) 1 - -

Relative Final quantities - 2

1

aaa pK

21

21

logpKHA

AlogpKpH

][

][

2

1



5.) Region 3: At the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH Exactly enough NaOH to consume HA

The solution only contains A- weak base

Relative Initial quantities (HA≡1) 1 1 - -

Relative Final quantities - - 1 1

Kb

a

wb K

KK

F - x x x

a

wb

2

K

KK

xF

x



5.) Region 3: At the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH

Calculate Formal concentration of [A-]:

A- is no longer 0.02000 M, diluted by the addition of NaOH

M0167.000.1000.50

00.50M02000.0'F


of HA

Dilution factor

Initial volume of HA

Total volume

pH at equivalence point is not 7.00



5.) Region 3: At the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH

M1076.1OHx1086.1x0167.0

x

1086.110

101

K

KK

xF

x

5--82

827.6

14

a

wb

2

][

Calculate [OH-]:

Calculate pH:

25.90167.0

101log

x

KlogHlog-pH

14w

][

pH will always be above 7.00 for titration of a weak acidbecause acid is converted into conjugate base at the equivalence point

Acid-Base Titrations Titration of Weak Acid with Strong Base

5.) Region 4: After the Equivalence Point Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH Adding NaOH to a solution of A-

- NaOH is a much stronger base than A-

- pH determined by excess of OH-

M...

.M. 410661

10100050

10010000

][OH-

Calculate excess [OH-]:


of OH-

Dilution factor

Volume of excess OH-

Total volume

Calculate volume of excess OH-:

mL10.000.1010.10VV eequivalencadded

Calculate pH:

22.101066.1

1000.1log

OH

KlogHlog

4

14w

][][-pH

Amount of added NaOH is 10.10 mL with equivalence point is 10 mL


5.) Titration Curve Titration of 50.00 mL of 0.02000 M MES with 0.1000 M NaOH Two Important Features of the Titration Curve

Equivalence point: [OH-] = [HA]Steepest part of curve

Maximum slope

pH=pKa

Vb = ½Ve

Minimum slope

Maximum Buffer Capacity


5.) Titration Curve Depends on pKa or acid strength Inflection point or maximum slope decreases with weaker acid

- Equivalence point becomes more difficult to identify

Strong acid large slope change in titration curve

Easy to detect equivalence point

weak acid small slope change in titration curve

Difficult to detect equivalence point


5.) Titration Curve Depends on acid concentration Inflection point or maximum slope decreases with

lower acid concentration- Equivalence point becomes more difficult to

identify- Eventually can not titrate acid at very low

concentrations

High concentration large slope change in titration curve

Easy to detect equivalence point

Low concentration small slope change in titration curve

Difficult to detect equivalence pointAt low enough concentration, can not detect change

Titration in Polyprotic Systems

1.) Principals for Monoprotic Systems Apply to Diprotic and Triprotic Systems Multiple equivalence points and buffer regions Multiple Inflection Points in Titration Curve


Kb2

Two equivalence points Kb1

Acid-Base Titrations End Point Determination

1.) Indicators: compound added in an acid-base titration to allow end point detection Common indicators are weak acids or bases Different protonated species have different colors

pK = 1.7 pK = 8.9


2.) Choosing an Indicator Want Indicator that changes color in the vicinity of the equivalence point

and corresponding pH The closer the two match, the more accurate determining the end point will

be

Bromocresol green will change colorSignificantly past the equivalence point resulting in an error.

Bromocresol purple color change brackets the equivalence point and is a good indicator choice


2.) Choosing an Indicator

The difference between the end point (point of detected color change) and the true equivalence point is the indicator error

Amount of indicator added should be negligible

Indicators cover a range of pHs


3.) Example:

a) What is the pH at the equivalence point when 0.100 M hydroxyacetic acid is titrated with 0.0500 M KOH?

b) What indicator would be a good choice to monitor the endpoint?

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