Chapter 16

Equilibria in Aqueous Systems

Buffers

•! buffers are solutions that resist changes in pH when an acid or base is added

•! they act by neutralizing the added acid or base

•! but just like everything else, there is a limit to what they can do, eventually the pH changes

•! many buffers are made by mixing a solution of a weak acid with a solution of soluble salt containing its conjugate base anion

Making a Buffer Solution from a Weak Acid

How Acid Buffers Work

HA(aq) + H2O(l) ! A!

(aq) + H3O+

(aq)

•! buffers work by applying Le Châtelier’s Principle to weak acid equilibrium

•! buffer solutions contain significant amounts of the weak acid molecules, HA – these molecules react with added base to neutralize it !!you can also think of the H3O

+ combining with the OH! to make H2O; the H3O

+ is then replaced by the shifting equilibrium

•! the buffer solutions also contain significant amounts of the conjugate base anion, A! - these ions combine with added acid to make more HA and keep the H3O

+ constant

Common Ion Effect

HA(aq) + H2O(l) ! A!

(aq) + H3O+

(aq)

•! adding a salt containing the anion, NaA, that is

the conjugate base of the acid (the common ion)

shifts the position of equilibrium to the left

•! this causes the pH to be higher than the pH of

the acid solution

!!lowering the H3O+ ion concentration

The Effect of Added Acetate Ion on the Dissociation of Acetic Acid

[CH3COOH]initial [CH3COO-]added % Dissociation* pH

* % Dissociation = [CH3COOH]dissoc

[CH3COOH]initial x 100

0.10 0.00

0.10 0.050

0.10

0.10 0.10

0.15

1.3

0.036

0.018

0.012

2.89

4.44

4.74

4.92

How a Buffer Works

Buffer with equal

concentrations of conjugate base and acid

OH- H3O+

Buffer after addition of H3O+

H2O + CH3COOH H3O+ + CH3COO-

Buffer after addition of OH-

CH3COOH + OH- H2O + CH3COO-

The Henderson-Hasselbalch Equation

HA + H2O H3O+ + A-

Ka = [H3O+] [A-]

[HA]

[H3O+] =

Ka [HA]

[A-]

- log[H3O+] = - log Ka + log

[A-]

[HA]

pH = pKa + log [base]

[acid]

Buffering Effectiveness •! a good buffer should be able to neutralize moderate

amounts of added acid or base

•! however, there is a limit to how much can be added before the pH changes significantly

•! the buffering capacity is the amount of acid or base a buffer can neutralize

•! the buffering range is the pH range the buffer can be effective

•! the effectiveness of a buffer depends on two factors (1) the relative amounts of acid and base, and (2) the absolute concentrations of acid and base

Effectiveness of Buffers

•! a buffer will be most effective when the [base]:

[acid] = 1

!!equal concentrations of acid and base

•! effective when 0.1 < [base]:[acid] < 10

•! a buffer will be most effective when the [acid]

and the [base] are large

•! we have said that a buffer will be effective when

0.1 < [base]:[acid] < 10

•! substituting into the Henderson-Hasselbalch we can calculate the maximum and minimum pH at which the buffer will be effective

!!"

#$$%

&+=

][HA

][AlogppH

-

aK

Lowest pH

( )

1ppH

10.0logppH

!=

+=

a

a

K

K

Highest pH

( )

1ppH

10logppH

+=

+=

a

a

K

K

therefore, the effective pH range of a buffer is pKa ± 1

when choosing an acid to make a buffer, choose

one whose is pKa is closest to the pH of the buffer

Buffering Range

Buffering Capacity

•! buffering capacity is the amount of acid or base that can be added to a buffer without destroying its effectiveness

•! the buffering capacity increases with increasing absolute concentration of the buffer components

•! as the [base]:[acid] ratio approaches 1, the ability of the buffer to neutralize both added acid and base improves

•! buffers that need to work mainly with added acid generally have [base] > [acid]

•! buffers that need to work mainly with added base generally have [acid] > [base]

How Much Does the pH of a Buffer

Change When an Acid or Base Is Added?

•! though buffers do resist change in pH when acid or base are added to them, their pH does change

•! calculating the new pH after adding acid or base requires breaking the problem into 2 parts

1.! a stoichiometry calculation for the reaction of the added chemical with one of the ingredients of the buffer to reduce its initial concentration and increase the concentration of the other !! added acid reacts with the A! to make more HA

!! added base reacts with the HA to make more A!

2.! an equilibrium calculation of [H3O+] using the new

initial values of [HA] and [A!]

Basic Buffers

B:(aq) + H2O(l) ! H:B+(aq) + OH!

(aq)

•! buffers can also be made by mixing a weak

base, (B:), with a soluble salt of its conjugate

acid, H:B+Cl!

H2O(l) + NH3 (aq) ! NH4+

(aq) + OH!

(aq)

The Common Ion Effect

Titration

•! in an acid-base titration, a solution of unknown concentration (titrant) is slowly added to a solution of known concentration from a burette until the reaction is complete

!!when the reaction is complete we have reached the endpoint of the titration

•! an indicator may be added to determine the endpoint

!!an indicator is a chemical that changes color when the pH changes

•! when the moles of H3O+ = moles of OH!, the titration

has reached its equivalence point

Titration

Color Changes for Various Acid-Base Indicators

Acid-Base Indicators

Titration Curve

•! a plot of pH vs. amount of added titrant

•! the inflection point of the curve is the equivalence point of the titration

•! prior to the equivalence point, the known solution in the flask is in excess, so the pH is closest to its pH

•! the pH of the equivalence point depends on the pH of the salt solution !!equivalence point of neutral salt, pH = 7

!!equivalence point of acidic salt, pH < 7

!!equivalence point of basic salt, pH > 7

•! beyond the equivalence point, the unknown solution in the burette is in excess, so the pH approaches its pH

Curve for a strong acid-strong base titration

Acid Type

pKa1

Maximum pH

Minimum pH

Maximum Volume

Minimum Volume

Initial [Acid], M

Initial Acid Volume, mL

Initial [NaOH], M

Titration Curve of Weak Acid with NaOH

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30 35 40 45 50

Volume NaOH Added, mL

pH

pH

0

50

0

Show First Derivative

Curve for a

weak acid-

strong base

titration

Titration of 40.00mL of 0.1000M HPr

with 0.1000M NaOH

[HPr] = [Pr-]

pH = 8.80 at

equivalence point

pKa of HPr

= 4.89

methyl red!

Titrating Weak Acid with a Strong Base

•! the initial pH is that of the weak acid solution

!!calculate like a weak acid equilibrium problem

"!e.g., 15.5 and 15.6

•! before the equivalence point, the solution becomes a buffer

!!calculate mol HAinit and mol A!

init using reaction stoichiometry

!!calculate pH with Henderson-Hasselbalch using mol HAinit and mol A!

init

•! half-neutralization pH = pKa

•! at the equivalence point, the mole HA = mol Base, so the resulting solution has only the conjugate base anion in it before equilibrium is established

!!mol A! = original mole HA

"!calculate the volume of added base like Ex 4.8

!![A!]init = mol A!/total liters

!!calculate like a weak base equilibrium problem

"!e.g., 15.14

•! beyond equivalence point, the OH is in excess

!![OH!] = mol MOH xs/total liters

!![H3O+][OH!]=1 x 10-14

Titrating Weak Acid with a Strong Base

Comparison of Titrations

Various weak acid-strong base titrations

Curve for a

weak base-

strong acid

titration

Titration of 40.00mL of 0.1000M NH3

with 0.1000M HCl

pH = 5.27 at

equivalence point

pKa of NH4+ =

9.25

Weak base-strong acid titration

pKa = 7.19

pKa = 1.85

Curve for the titration of a weak polyprotic acid.

Titration of 40.00mL of 0.1000M

H2SO3 with 0.1000M NaOH

Titration of a polyprotic acid

Solubility Equilibria

•! all ionic compounds dissolve in water to some

degree

!!however, many compounds have such low solubility

in water that we classify them as insoluble

•! we can apply the concepts of equilibrium to

salts dissolving, and use the equilibrium

constant for the process to measure relative

solubilities in water

Solubility Product •! the equilibrium constant for the dissociation of a solid

salt into its aqueous ions is called the solubility product, Ksp

•! for an ionic solid MnXm, the dissociation reaction is:

MnXm(s) ! nMm+(aq) + mXn!(aq)

•! the solubility product would be

Ksp = [Mm+]n[Xn!]m

•! for example, the dissociation reaction for PbCl2 is

PbCl2(s) ! Pb2+(aq) + 2 Cl!(aq)

•! and its equilibrium constant is

Ksp = [Pb2+][Cl!]2

Molar Solubility

•! solubility is the amount of solute that will dissolve in a given amount of solution

!!at a particular temperature

•! the molar solubility is the number of moles of solute that will dissolve in a liter of solution

!!the molarity of the dissolved solute in a saturated solution

•! for the general reaction MnXm(s) ! nMm+(aq) + mXn!(aq)

Molar Solubility =

Ksp and Relative Solubility

•! molar solubility is related to Ksp

•! but you cannot always compare solubilities of

compounds by comparing their Ksps

•! in order to compare Ksps, the compounds must

have the same dissociation stoichiometry

Solubility-Product Constants (Ksp) of Selected Ionic

Compounds at 250C

Name, Formula Ksp

Aluminum hydroxide, Al(OH)3

Cobalt (II) carbonate, CoCO3

Iron (II) hydroxide, Fe(OH)2

Lead (II) fluoride, PbF2

Lead (II) sulfate, PbSO4

Silver sulfide, Ag2S

Zinc iodate, Zn(IO3)2

3 x 10-34

1.0 x 10-10

4.1 x 10-15

3.6 x 10-8

1.6 x 10-8

4.7 x 10-29

8 x 10-48

Mercury (I) iodide, Hg2I2

3.9 x 10-6

Relationship Between Ksp and Solubility at 250C

No. of Ions Formula Cation:Anion Ksp Solubility (M)

2 MgCO3 1:1 3.5 x 10-8 1.9 x 10-4

2 PbSO4 1:1 1.6 x 10-8 1.3 x 10-4

2 BaCrO4 1:1 2.1 x 10-10 1.4 x 10-5

3 Ca(OH)2 1:2 5.5 x 10-6 1.2 x 10-2

3 BaF2 1:2 1.5 x 10-6 7.2 x 10-3

3 CaF2 1:2 3.2 x 10-11 2.0 x 10-4

3 Ag2CrO4 2:1 2.6 x 10-12 8.7 x 10-5

•! addition of a soluble salt that contains one of the

ions of the “insoluble” salt, decreases the

solubility of the “insoluble” salt

•! for example, addition of NaCl to the solubility

equilibrium of solid PbCl2 decreases the

solubility of PbCl2

PbCl2(s) ! Pb2+(aq) + 2 Cl!(aq) addition of Cl! shifts the equilibrium to the left

The Effect of Common Ion on Solubility

The Effect of pH on Solubility

•! for insoluble ionic hydroxides, the higher the pH, the

lower the solubility of the ionic hydroxide

!!and the lower the pH, the higher the solubility

!!higher pH = increased [OH!]

M(OH)n(s) ! Mn+(aq) + nOH!(aq)

•! for insoluble ionic compounds that contain anions of

weak acids, the lower the pH, the higher the solubility

M2(CO3)n(s) ! 2 Mn+(aq) + nCO32!(aq)

H3O+(aq) + CO3

2! (aq) ! HCO3! (aq) + H2O(l)

Precipitation

•! precipitation will occur when the concentrations of the ions exceed the solubility of the ionic compound

•! if we compare the reaction quotient, Q, for the current solution concentrations to the value of Ksp, we can determine if precipitation will occur

!!Q = Ksp, the solution is saturated, no precipitation

!!Q < Ksp, the solution is unsaturated, no precipitation

!!Q > Ksp, the solution would be above saturation, the salt above saturation will precipitate

•! some solutions with Q > Ksp will not precipitate unless disturbed – these are called supersaturated solutions

The effect of a common ion on solubility

PbCrO4(s) Pb2+(aq) + CrO42-(aq) PbCrO4(s) Pb2+(aq) + CrO4

2-(aq)

CrO42- added

Cr(NH3)63+, a typical complex ion.

M(H2O)42+

M(H2O)3(NH3)2+

M(NH3)42+

NH3

3NH3

The stepwise exchange of NH3 for H2O in M(H2O)42+.

The amphoteric behavior of aluminum hydroxide.

Al(H2O)3(OH)3(s) 3H2O(l) + Al(H2O)3(OH)3(s) Al(H2O)3(OH)4-(s) + H2O(l)

Solubility of amphoteric hydroxides

The general procedure for separating ions in qualitative analysis.

Add

precipitating ion

Cen

trifuge

Add

precipitating ion

Cen

trifuge