Aqueous Acid-Base Equilibria

71
7/28/2019 Aqueous Acid-Base Equilibria http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 1/71 16 Aqueous Acid-Base Equilibria 

Transcript of Aqueous Acid-Base Equilibria

Page 1: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 1/71

16Aqueous Acid-Base 

Equi l ibr ia 

Page 2: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 2/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 3: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 3/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 4: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 4/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Chemistry: Principles, Patterns,

and Applications, 1e 

16.1 The Autoionization of 

Water  

Page 5: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 5/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 6: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 6/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

16.1 The Autoionization of Water  

Page 7: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 7/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 8: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 8/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 9: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 9/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 10: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 10/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 11: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 11/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 12: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 12/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 13: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 13/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Chemistry: Principles, Patterns,

and Applications, 1e 

16.2 A Qualitative

Description of Acid-BaseEquilibria 

Page 14: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 14/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 15: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 15/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 16: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 16/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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]

Page 17: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 17/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 18: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 18/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 19: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 19/71Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 20: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 20/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 21: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 21/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 22: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 22/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 23: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 23/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Chemistry: Principles, Patterns,

and Applications, 1e 

16.3 Molecular Structure

and Acid-Base Strength

Page 24: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 24/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

• 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 

Page 25: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 25/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

• 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 

Page 26: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 26/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

•  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

Page 27: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 27/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Chemistry: Principles, Patterns,

and Applications, 1e 

16.4 Quantitative

Aspects of Acid-BaseEquilibria

Page 28: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 28/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 29: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 29/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 30: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 30/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 –]

Page 31: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 31/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 32: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 32/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 33: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 33/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 34: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 34/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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%

Page 35: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 35/71

Page 36: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 36/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 37: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 37/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 38: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 38/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Chemistry: Principles, Patterns,

and Applications, 1e 

16.5 Acid-Base Titrations 

Page 39: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 39/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 40: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 40/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 41: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 41/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 42: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 42/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 43: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 43/71

Page 44: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 44/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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.

Page 45: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 45/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 46: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 46/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 47: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 47/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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+]) 

Page 48: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 48/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 49: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 49/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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. 

Page 50: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 50/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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. 

Page 51: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 51/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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 

Page 52: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 52/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Titrations of Polyprotic Acids or Bases 

I di

Page 53: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 53/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 54: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 54/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Indicators 

I di t

Page 55: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 55/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 56: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 56/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 57: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 57/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 58: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 58/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

Indicators 

I di t

Page 59: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 59/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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,

Page 60: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 60/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

y p , ,

and Applications, 1e 

16.6 Buffers

16 6 B ff

Page 61: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 61/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 62: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 62/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 63: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 63/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 64: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 64/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

The Common Ion Effect

C l l ti th H f B ff

Page 65: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 65/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 66: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 66/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 67: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 67/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 68: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 68/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 69: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 69/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 70: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 70/71

Copyright © 2007 Pearson Education, Inc., publishing as Pearson Benjamin Cummings 

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

Page 71: Aqueous Acid-Base Equilibria

7/28/2019 Aqueous Acid-Base Equilibria

http://slidepdf.com/reader/full/aqueous-acid-base-equilibria 71/71

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.