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16Aqueous Acid-Base
Equi l ibr ia
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CHAPTER OBJECTIVES
• To understand the autoionization reaction of liquid water
• To know the relationship among pH, pOH, and pK w
• To understand the concept of conjugate acid-base pairs
• To know the relationship between acid or base strength and the magnitude
of K a, K b, pK a, and pK b• To understand the leveling effect
• To be able to predict whether reactants or products are favored in anacid-base equilibrium
• To understand how molecular structure determines acid and base strengths
• To be able to use K a and K b values to calculate the percent ionization andpH of a solution of an acid or a base
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CHAPTER OBJECTIVES
• To be able to calculate the pH at any point in an acid-base titration
• To understand how the addition of a common ion affects the position of anacid-base equilibrium
• To understand how a buffer works and how to use theHenderson-Hasselbalch equation to calculate the pH of a buffer
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Chemistry: Principles, Patterns,
and Applications, 1e
16.1 The Autoionization of
Water
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16.1 The Autoionization of Water
• Acids and bases can be defined in different
ways:1. Arrhenius definition: An acid is a substance that dissociates inwater to produce H+ ions (protons), and a base is a substancethat dissociates in water to produce OH – ions (hydroxide); anacid-base reaction involves the reaction of a proton with the
hydroxide ion to form water
2. Brønsted –Lowry definition: An acid is any substance that candonate a proton, and a base is any substance that can accept aproton; acid-base reactions involve two conjugate acid-basepairs and the transfer of a proton from one substance (the acid)
to another (the base)
3. Lewis definition: A Lewis acid is an electron-pair acceptor, anda Lewis base is an electron-pair donor
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16.1 The Autoionization of Water
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Acid-Base Properties of Water
• Water is amphiprotic: it can act as an acid by donatinga proton to a base to form the hydroxide ion, or as a
base by accepting a proton from an acid to form the
hydronium ion, H3O+
• Structure of the water molecule
1. Polar O –H bonds and two lone pairs of electrons on
the oxygen atom
2. Liquid water has a highly polar structure
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The Ion-Product Constant of Liquid Water
• Because water is amphiprotic, one water molecule can react withanother to form an OH – ion and an H3O
+ ion in an autoionization
process:
2H2O(l)⇋H3O+
(aq) + OH – (aq)
• Equilibrium constant K for this reaction can be written as
K = [H3O+] [OH –]
[H2O]2
• When pure liquid water is in equilibrium with hydronium and
hydroxide ions at 25ºC, the concentrations of hydronium ion andhydroxide ion are equal: [H3O
+] = [OH –] = 1.003 x 10 –7 M
• At 25ºC, the density of liquid water is 0.0997 g/mL
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The Ion-Product Constant of Liquid Water
• The concentration of liquid water at 25ºC is
[H2O] = mol/L = (0.997 g/mL) (1 mol/18.02 g) (1000 mL/L) = 55.3 M
• Because the number of dissociated water molecules is very small,the equilibrium of the autoionization reaction lies far to the left, sothe concentration of water is unchanged by the autoionizationreaction and can be treated as a constant
• By treating [H2O] as a constant, a new equilibrium constant, theion-product constant of liquid water (K w), can be defined:
K [H2O]2 = [H3O+] [OH –] or K w = [H3O
+] [OH –]
• Substituting the values for [H3O+] and [OH –] at 25ºC gives
K w = (1.003 x 10 –7) (1.003 x 10 –7) = 1.006 x 10 –14
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The Ion-Product Constant of Liquid Water
• K w varies with temperature, ranging from 1.15 x 10 –15
at0ºC to 4.99 x 10 –13 at 100ºC
• In pure water, the concentrations of the hydronium ion
and the hydroxide ion are the same, so the solution is
neutral
• If [H3O+] > [OH –], the solution is acidic
• If [H3O+] < [OH –], the solution is basic
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The Relationship among pH, pOH, and pK w
• The pH scale is a concise way of describing the H3O+
concentrationand the acidity or basicity of a solution
• pH and H+ concentration are related as follows:
pH = –log10[H+] or [H+] = 10 –pH
• pH of a neutral solution ([H3O+] = 1.00 x 10 –7 M) is 7.00
• pH of an acidic solution is < 7, corresponding to [H3O+] > 1.00 x 10 –7
• pH of a basic solution is > 7, corresponding to [H3O+] < 1.00 x 10 –7
• The pH scale is logarithmic, so a pH difference of 1 between twosolutions corresponds to a difference of a factor of 10 in their
hydronium ion concentrations
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The Relationship among pH, pOH, and pK w
• There is an analogous pOH scale to describe the hydroxide ion
concentration of a solution; pOH and [OH –] are related as follows:pH = –log10[OH –] or [OH –] = 10 –pOH
• A neutral solution has [OH –] = 1.00 x 10 –7, so the pOH of a neutralsolution is 7.00
• The sum of the pH and the pOH for a neutral solution at 25ºC is 7.00+ 7.00 = 14.00
pK w = –log K w = –log([H3O+] [OH –]) =
( –log[H3O+]) + ( –log[OH –]) = pH + pOH
• At any temperature, pH + pOH = pK w, and at 25ºC, where K w = 1.01
x 10 –14, pH + pOH = 14.00; pH of any neutral solution is just half thevalue of pK w at that temperature
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Chemistry: Principles, Patterns,
and Applications, 1e
16.2 A Qualitative
Description of Acid-BaseEquilibria
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Conjugate Acid-Base Pairs
• Two species that differ by only a proton constitute a conjugate
acid-base pair.
1. Conjugate base has one less proton than its acid; A – is the conjugatebase of HA
2. Conjugate acid has one more proton than its base; BH+ is theconjugate acid of B
• In the reaction of HCl with water, HCl, the parent acid , donates aproton to a water molecule, the parent base, forming Cl –; HCl andCl – constitute a conjugate acid-base pair.
• In the reverse reaction, the Cl – ion in solution acts as a base toaccept a proton from H3O
+, forming H2O and HCl; H3O+ and H2O
constitute a second conjugate acid-base pair.
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Conjugate Acid-Base Pairs
• Any acid-base reaction must contain two conjugateacid-base pairs, which in this example are HCl/Cl – and
H3O+/H2O
• HCl (aq) + H2O (l) H3O+ (aq) + Cl – (aq) parent acid parent base conjugate acid conjugate base
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Acid-Base Equilibrium Constants:
K a, K b, pK a, and pK b
• The magnitude of the equilibrium constant for an ionization reaction can be
used to determine the relative strengths of acids and bases
• The general equation for the ionization of a weak acid in water, where HA isthe parent acid and A – is its conjugate base, is
HA(aq) + H2O(l) ⇋ H3O+(aq) + A –(aq)
• The equilibrium constant for this dissociation isK = [H3O
+] [A –]
[H2O] [HA]
• The concentration of water is constant for all reactions in aqueous solution,so [H2O] can be incorporated into a new quantity, the acid ionization
constant (K a):K a = K [H2O] = [H3O
+] [A –]
[HA]
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Acid-Base Equilibrium Constants:
K a, K b, pK a, and pK b
• Numerical values of K and K a
differ by the concentration of water (55.3 M); the larger the value K a, the stronger the acid and thehigher the H+ concentration at equilibrium
• Weak bases react with water to produce the hydroxide ion, B(aq) +
H2O(l) ⇋ BH+(aq) + OH –(aq), where B is the parent base and BH+ is
its conjugate acid
• Equilibrium constant for this reaction is the base ionizationconstant (K b); concentration of water is constant and does notappear in the equilibrium constant expression but is included in thevalue of K b
• The larger the value of K b, the stronger the base and the higher theOH – concentration at equilibrium
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Acid-Base Equilibrium Constants:
K a, K b, pK a, and pK b
• The sum of the reactions described by K a
and K b
is theequation for the autoionization of water, and the productof the two equilibrium constants is K w
• For any conjugate acid-base pair, K aK b = K w
• pK a
= –log10K a and pK b = –log10K b
• Smaller values of pK a correspond to larger acidionization constants and stronger acids
• Smaller values of pK b correspond to larger base
ionization constants and stronger bases• At 25ºC, pK a + pK b = 14.00
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Acid-Base Equilibrium Constants:
K a, K b, pK a, and pK b
• There is an inverse relationship between the strength of the parent acid and the strength of the conjugate base;the conjugate base of a strong acid is a weak base, andthe conjugate base of a weak acid is a strong base
• One can use the relative strengths of acids and bases topredict the direction of an acid-base reaction by followinga simple rule: An acid-base equilibrium always favorsthe side with the weaker acid and base
stronger acid + stronger base weaker acid + weaker base
• In an acid-base reaction, the proton always reacts withthe stronger base
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Solutions of Strong Acids and Bases:
The Leveling Effect
• No acid stronger than H3O+ and no base stronger than OH – can exist
in aqueous solution, leading to the phenomenon known as theleveling effect.
• Any species that is a stronger acid than the conjugate acid of water (H3O
+) is leveled to the strength of H3O+ in aqueous solution
because H3O+ is the strongest acid that can exist in equilibrium with
water.
• In aqueous solution, any base stronger than OH – is leveled to thestrength of OH – because OH – is the strongest base that can exist inequilibrium with water
• Any substance whose anion is the conjugate base of a compoundthat is a weaker acid than water is a strong base that reactsquantitatively with water to form hydroxide ion
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Polyprotic Acids and Bases
• Polyprotic acids contain more than one ionizable proton,and the protons are lost in a stepwise manner.
• The fully protonated species is always the strongest acidbecause it is easier to remove a proton from a neutralmolecule than from a negatively charged ion; the fullydeprotonated species is the strongest base.
• Acid strength decreases with the loss of subsequentprotons, and the pK a increases.
• The strengths of the conjugate acids and bases arerelated by pK a + pK b = pK w, and equilibrium favorsformation of the weaker acid-base pair.
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Acid-Base Properties of Solutions
of Salts
• A salt can dissolve in water to produce a neutral, basic, or acidic
solution, depending on whether it contains the conjugate base of aweak acid as the anion (A –) or the conjugate acid of a weak base as
the cation (BH+), or both.
• Salts that contain small, highly charged metal ions produce acidic
solutions in water.
• The most important parameter for predicting the effect of a metal ion
on the acidity of coordinated water molecules is the charge-to-radius
ratio of the metal ion.
• The reaction of a salt with water to produce an acidic or basicsolution is called a hydrolysis reaction, which is just an acid-base
reaction in which the acid is a cation or the base is an anion.
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Chemistry: Principles, Patterns,
and Applications, 1e
16.3 Molecular Structure
and Acid-Base Strength
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• The acid-base strength of a molecule depends stronglyon its structure.
• The stronger the A –H or B –H+ bond, the less likely thebond is to break to form H+ ions, and thus the less acidicthe substance.
• The larger the atom to which H is bonded, the weaker the bond.
• Acid strengths of binary hydrides increase as we go
down a column of the periodic table.
Bond Strengths
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• The conjugate base (A – or B) contains one more lonepair of electrons than the parent acid (AH or BH+).
• Any factor that stabilizes the lone pair on the conjugatebase favors dissociation of H+ and makes the parent acida stronger acid.
• Acid strengths of binary hydrides increase as we go fromleft to right across a row of the periodic table.
Stability of the Conjugate Base
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• Atoms or groups in a molecule other than those to whichH is bonded can induce a change in the distribution of electrons within the molecule, called an inductiveeffect; this can have a major effect on the acidity or basicity of the molecule.
• Inductive effect can weaken an O –H bond and allowhydrogen to be more easily lost as H+ ions.
Inductive Effects
Ch i t P i i l P tt
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Chemistry: Principles, Patterns,
and Applications, 1e
16.4 Quantitative
Aspects of Acid-BaseEquilibria
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Determining K a and K b
• The ionization constants K a
and K b
are equilibrium
constants that are calculated from experimentally
measured concentrations.
• What does the concentration of an aqueous solution of a
weak acid or base exactly mean? – A 1 M solution is prepared by dissolving 1 mol of acid or base in
water and adding enough water to give a final volume of exactly 1 L.
– If the actual concentrations of all species present in the solution
were listed, it would be determined that none of the values is exactly
1 M because a weak acid or a weak base always reacts with water
to some extent.
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Determining K a and K b
– The extent of the reaction depends on the value of K a
or K b
, the
concentration of the acid or base, and the temperature.
– Only the total concentration of both the ionized and unionized species
is equal to 1 M.
– The analytical concentration (C) is defined as the total concentration of
all forms of an acid or base that are present in solution, regardless of their state of protonation.
– Thus; a 1 M solution has an analytical concentration of 1 M, which is
the sum of the actual concentrations of unionized acid or base and the
ionized form.
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Determining K a and K b
– In addition to the analytical concentration of the acid or base,
one must be able to measure the concentration of a least one of
the species in the equilibrium constant expression in order to
determine the value of K a or K b.
– Two common ways to obtain the concentrations
1. By measuring the electrical conductivity of the solution, which is
related to the total concentration of ions present
2. By measuring the pH of the solution, which gives [H+] or [OH –]
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Determining K a and K b
• Procedure for determining K a for a weak acidand K b for a weak base
1. The analytical concentration of the acid or base is the initial
concentration
2. The stoichiometry of the reaction with water determines thechange in concentrations
3. The final concentrations of all species are calculated from the
initial concentrations and the changes in the concentrations
4. Inserting the final concentration into the equilibrium constant
expression enables the value of K a or K b to be calculated
Calculating Percent Ionization from
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Calculating Percent Ionization from
K a or K b
• Need to know the concentrations of all species in solution
• The reactivity of a weak acid or a weak base is very different from the
reactivity of its conjugate base or acid; need to know the percent
ionization of a solution of an acid or base in order to understand a
chemical reaction
• Percent ionization is defined as
percent ionization of acid = [H+]
CHA
percent ionization of base = [OH –]
CB
x 100
x 100
Calculating Percent Ionization from
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Calculating Percent Ionization from
K a or K b • To determine the concentrations of species in
solutions of weak acids and bases, use a tabular method1. Make a table that lists the following values for each of thespecies involved in the reaction
a. Initial concentration
b. The change in concentration on preceding to equilibrium( – x or + x )
c. The final concentration—sum of the initial concentration andthe change in concentration
d. In constructing the table, define x as the concentration of theacid that dissociates
2. Solve for x by substituting the final concentrations from thetable into the equilibrium constant expression
Calculating Percent Ionization from
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Calculating Percent Ionization from
K a or K b
3. Calculate the concentrations of the speciespresent in the solution by inserting the value of x intothe expressions in the last line of the table (finalconcentration)
4. Calculate the pH = –log[H3O+]
5. Use the concentrations to calculate the fraction of the original acid that is ionized (the concentration of
the acid that is ionized divided by the analytical or initial concentration of the acid times 100%
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Determining K eq from K a and K b
• The value of the equilibrium constant for the reaction of a
weak acid with a weak base can be calculated from K a(or pK a), K b (or pK b), and K w
• One can quantitatively determine the direction andextent of reaction for a weak acid and a weak base by
calculating the value of K for the reaction
• The equilibrium constant for the reaction of a weak acidwith a weak base is the product of the ionizationconstants of the acid and the base divided by K w
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Determining K eq from K a and K b
• Calculations
1. Write the dissociation reactions for a weak acid and a weak base andthen sum them:
Acid HA⇋ H+ + A – K a
Base B + H2O⇋ HB+ + OH – K b
Sum HA + B + H2O⇋ H+ + A – + HB+ + OH – K sum = K aK b
2. Obtain an equation that includes only the acid-base reaction by simplyadding the equation for the reverse of the autoionization of water
(H+ + OH – ⇋ H2O), for which K = 1/K w, to the overall reaction andcanceling
HA + B + H2
O⇋ H+ + A – + HB+ + OH – K sum
= K a
K b
H+ + OH – ⇋ H2O 1/K w
HA + B ⇋ A – + HB+ K = (K aK b)/K w
Chemistry: Principles Patterns
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Chemistry: Principles, Patterns,
and Applications, 1e
16.5 Acid-Base Titrations
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16.5 Acid-Base Titrations
• In acid-base titrations, a buret is used to deliver
measured volumes of an acid or base solution of knowntitration (the titrant) to a flask that contains a solution of a
base or an acid, respectively, of unknown concentration
(the unknown).
• If the concentration of the titrant is known, then the
concentration of the unknown can be determined.
• Plotting the pH changes that occur during an acid-base
titration against the amount of acid or base addedproduces a titration curve; the shape of the curve
provides important information about what is occurring in
solution during the titration.
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Titrations of Strong Acids and Bases
• Before addition of any strong base, the initial [H3O+]
equals the concentration of the strong acid.
• Addition of strong base before the equivalence point, thepoint at which the number of moles of base (or acid)added equals the number of moles of acid (or base)
originally present in the solution, decreases the [H3O+
]because added base neutralizes some of the H3O
+
present.
• Addition of strong base at the equivalence point
neutralizes all the acid initially present and pH = 7.00;the solution contains water and a salt derived from astrong base and a strong acid.
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Titrations of Strong Acids and Bases
• Addition of a strong base after the equivalence causes an excess of
OH – and produces a rapid increase in pH.
• A pH titration curve shows a sharp increase in pH in the region near
the equivalence point and produces an S-shaped curve; the shape
depends only on the concentration of the acid and base, not on their
identity.
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Titrations of Strong Acids and Bases
• For the titration of a monoprotic strong acid with a monobasic strong
base, the volume of base needed to reach the equivalence point can
be calculated from the following relationship:
moles of base = moles of acid
(volume)b (molarity)b = (volume)a (molarity)a
V bM b = V aM a
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Titrations of Weak Acids and Bases
• The pH changes much more gradually around the equivalence point
in the titration of a weak acid or a weak base.
• [H+] of a solution of a weak acid (HA) is not equal to the
concentration of the acid but depends on both its pK a and itsconcentration.
• Only a fraction of a weak acid dissociates, so [H+] is less than [HA];
therefore, the pH of a solution of a weak acid is higher than the pH
of a solution of a strong acid of the same concentration.
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Titrations of Weak Acids and Bases
• Comparing the titration curve of a strong acid with a
strong base with the titration curve of a weak acid and astrong base
1. Below the equivalence point, the two curves are very
different; before any base is added, the pH of the weak acid is
higher than the pH of the strong acid
2. pH changes more rapidly during the first part of the titration in
a weak acid and strong base titration
3. Due to the higher starting pH, the pH of the weak acid at the
equivalence point is greater than 7.00, so solution is basic
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Titrations of Weak Acids and Bases
4. Change in pH for the weak acid/strong base titration aroundthe equivalence point is about half as large as for the strong acid
titration; the magnitude of the change at the equivalence point
depends on the pK a of the acid being titrated
5. Above the equivalence point, the two curves are identical; onceacid has been neutralized, the pH of the solution is controlled
only by the amount of excess of OH – present, regardless of
whether the acid is weak or strong
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Titrations of Weak Acids and Bases
• Calculating the pH of a solution of a
weak acid or base
– If K a or K b and the initial concentration of a weak acid or base
are known, one can calculate the pH of a solution of a weak acid
or base by setting up a table of initial concentrations, changes in
concentrations, and final concentrations
– Define x as [H+] due to the dissociation of the acid
– Insert values for final concentrations into the equilibrium
equation and solve for x and then pH (pH = –log[H+])
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Titrations of Weak Acids and Bases
• Calculating the pH during titration of a
weak acid or base
– Solved in two steps: a stoichiometric calculation followed by
an equilibrium calculation
1. Use stoichiometry of the neutralization reaction to calculate the
amounts of acid and conjugate base present in solution after the
neutralization reaction has occurred
2. Use the equilibrium equation K = [H3O+] [A –] / [H2O] [HA] to
determine [H+] of the resulting solution
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Titrations of Weak Acids and Bases
• Identity of the weak acid or base being titrated strongly
affects the shape of the titration curve.
• The shape of titration curves as a function of the pK a or pK b shows that as the acid or base being titratedbecomes weaker (its pK a or pK b becomes larger), the
pH change around the equivalence point decreasessignificantly.
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Titrations of Weak Acids and Bases
• The midpoint of a titration is defined as the point at which exactlyenough acid (or base) has been added to neutralize one-half of theacid (or base) originally present and occurs halfway to theequivalence point.
• At the midpoint of the titration of an acid, [HA] = [A –].
• The pH at the midpoint of the titration of a weak acid is equal to thepKa of the weak acid.
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Titrations of Polyprotic Acids or Bases
• When a strong base is added to a solution of a polyprotic
acid, the neutralization reaction occurs in stages.
1. The most acidic group is titrated first, followed by the next
most acidic, and so forth
2. If the pK a values are separated by at least three pK a units,
then the overall titration curve shows well-resolved ―steps‖corresponding to the titration of each proton
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Titrations of Polyprotic Acids or Bases
I di
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Indicators
• Most acid-base titrations are not monitored by recordingthe pH as a function of the amount of the strong acid or base solution used as a titrant
• Instead, an acid-base indicator is used, and they are
compounds that change color at a particular pH and if carefully selected, undergo a dramatic color change atthe pH corresponding to the equivalence point of thetitration
• Acid-base indicators are typically weak acids or baseswhose changes in color correspond to deprotonation or protonation of the indicator itself
I di t
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Indicators
I di t
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Indicators
• The chemistry of indicators are described by the general
equation Hn(aq)⇋ H+(aq) + n –
(aq), where the protonated
form is designated by Hn and the conjugate base by n –
• The ionization constant for the deprotonation of indicator
Hn is K in = [H+] [n –] / [Hn]
• The value of pK in determines the pH at which the
indicator changes color
I di t
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Indicators
• A good indicator must have the following properties:
1. Color change must be easily detected
2. Color change must be rapid
3. Indicator molecule must not react with the substance beingtitrated
4. The indicator should have a pK in that is within one pH unit of
the expected pH at the equivalence point of the titration
• Synthetic indicators have been developed that meet theabove criteria and cover the entire pH range
• An indicator does not change color abruptly at aparticular pH but undergoes a pH titration like any other acid or base
I di t
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Indicators
• Choosing the correct indicator for an acid-base
titration
1. For titrations of strong acids and strong bases (and vice
versa), any indicator with a pKin between 4 and 10 will do
2. For the titration of a weak acid, the pH at the equivalencepoint is greater than 7, and an indicator such as phenolphthalein
or thymol blue, with pKin > 7, should be used
3. For the titration of a weak base, where the pH at the
equivalence point is less than 7, an indicator such as methyl red
or bromcresol blue, with pKin < 7, should be used
I di t
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Indicators
I di t
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Indicators
• Paper or plastic strips that
contain combinations of
indicators estimate the pH of a
solution by simply dipping a
piece of pH paper into it andcomparing the resulting color
with standards printed on the
container
Chemistry: Principles, Patterns,
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y p , ,
and Applications, 1e
16.6 Buffers
16 6 B ff
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16.6 Buffers
• Buffers are solutions that maintain a relatively constantpH when an acid or a base is added; they protect or ―buffer‖ other molecules in solution from the effects of the added acid or base
• Buffers contain either a weak acid (HA) and its conjugate
base (A –) or a weak base (B) and its conjugate acid(BH+)
• Buffers are critically important for the proper functioningof biological systems; every biological fluid is buffered to
maintain its physiological pH
Th C I Eff
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The Common Ion Effect
• The ionization equilibrium of a weak acid (HA) is affected
by the addition of either the conjugate base of the acid
(A –) or a strong acid (a source of H+); LeChâtelier’s
principle is used to predict the effect on the equilibrium
position of the solution
• Common-ion effect—the shift in the position of an
equilibrium on addition of a substance that provides an
ion in common with one of the ions already involved in
the equilibrium; equilibrium is shifted in the direction that
reduces the concentration of the common ion
Th C I Eff t
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The Common Ion Effect
• Buffers are characterized by the following:
1. the pH range over which they can maintain a constant pH—depends strongly on the chemical properties of the weak acid or base used to prepare the buffer (on K )
2. their buffer capacity , the amount of strong acid or base thatcan be absorbed before the pH changes significantly—dependssolely on the concentration of the species in the buffered solution(the more concentrated the buffer solution, the greater its buffer capacity)
3. observed change in the pH of the buffer is inversely
proportional to the concentration of the buffer
Th C I Eff t
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The Common Ion Effect
C l l ti th H f B ff
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Calculating the pH of a Buffer
• The pH of a buffer can be calculated from theconcentrations of the weak acid or the weak base usedto prepare it, the concentration of the conjugate base or acid, and the pK a or pK b of the weak acid or base
• An alternative method used to calculate the pH of a
buffer solution is based on a rearrangement of theequilibrium equation for the dissociation of a weak acid
• Ionization reaction is HA⇋H+ + A – and the equilibriumconstant expression is
K a = [H+] [A –] or [H+] = K a[HA]
[HA] [A –]
C l l ti th H f B ff
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Calculating the pH of a Buffer
• Taking the logarithm of both sides and multiplying bothsides by –1 gives
–log[H+] = –logK a – log([HA]/[A –]) = – logK a + log([A –]/[HA])
• Replacing the negative logarithms gives
pH = pK a + log([A –
]/[HA]) or pH = pk a + log([base]/[acid])Both forms of the Henderson-Hasselbalch equation
• Henderson-Hasselbalch equation is valid for solutionswhose concentrations are at least a hundred times
greater than the value of their K a’s
C l l ti th H f B ff
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Calculating the pH of a Buffer
• Three special cases where the Henderson-Hasselbalchequation is interpreted without the need for calculations
1. [base] = [acid]. Under these conditions, [base]/[acid] = 1.Because log 1 = 0, pH = pK a, regardless of the actualconcentrations of the acid and base (corresponds to the midpoint inthe titration of a weak acid or base)
2. [base]/[acid] = 10. Because log 10 = 1, pH = pK a
+ 1
3. [base]/[acid] = 100. Because log 100 = 2, pH = pK a+ 2
• Each time the [base]/[acid] ratio is increased by 10, thepH of the solution increases by one unit; if the[base]/[acid] ratio is 0.1, then pH = pK a – 1, so each
additional factor-of-10 decrease in the [base]/[acid] ratiocauses the pH to decrease by one pH unit
C l l ti th H f B ff
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Calculating the pH of a Buffer
• The Henderson-Hasselbalch equation can also be used
to calculate the pH of a buffer solution after the addition
of a given amount of strong acid or base
• A buffer that contains equal amounts of the weak acid
(or weak base) and its conjugate base (or acid) insolution is equally effective at neutralizing either added
base or added acid
The Relationship between Titrations
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and Buffers
• A strong correlation exists between the effectiveness of
a buffer solution and the titration curves
• In a titration of a weak acid with a strong base;
– the region around pK a corresponds to the midpoint of the titration,
when half the weak acid has been neutralized; this portion of the
titration curve corresponds to a buffer because it exhibits the smallestchange in pH per increment of added strong base (horizontal nature of
the curve in this region);
– the flat portion of the curve extends only from a pH value of one unit
less than the pK a to a pH value of one unit greater than the pK a ; that is
why buffer solutions have a pH that is within ±1 pH units of the pK a of
the acid component of the buffer;
The Relationship between Titrations
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and Buffers
– in the region of the titrationcurve at the lower left, before
the midpoint, the acid-base
properties of the solution are
dominated by the equilibrium
for dissociation of the weak
acid, corresponding to K a;
– in the region of the titration
curve at the upper right, after
the midpoint, the acid-base
properties of the solution are
dominated by the equilibriumfor reaction of the conjugate
base of the weak acid with
water, corresponding to K b.
Blood: A Most Important Buffer
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Blood: A Most Important Buffer
• Metabolic processes produce large amounts of acids and bases, but
organisms are able to maintain a constant internal pH because their fluids contain buffers.
• pH is not uniform throughout all cells and tissues of a mammal; even
within a cell, different compartments can have very different pH
values.
• Because no single buffer system can effectively maintain a constant
pH value over the physiological range of 5 to 7.4, biochemical
systems use a set of buffers with overlapping ranges; most
important of these is the CO2/HCO3 – system, which dominates the
buffering action of blood plasma.