Chemistry Chemistry 232232

Applications of Aqueous Equilbria

The BrThe Brøønsted Definitionsnsted Definitions

Brønsted Acid proton donor

Brønsted Base proton acceptor

Conjugate acid - base pair an acid and its conjugate base or a base and its conjugate acid

Example Acid-Base ReactionsExample Acid-Base Reactions

Look at acetic acid dissociatingCH3COOH(aq) CH3COO-(aq) + H+(aq)

Brønsted acid Conjugate base

Look at NH3(aq) in waterNH3(aq) + H2O(l) NH4

+(aq) + OH-(aq) Brønsted base conjugate acid

Representing Protons in Aqueous Representing Protons in Aqueous SolutionSolution

CH3COOH(aq) CH3COO-(aq) + H+(aq)

CH3COOH(aq) + H2O(l) CH3COO-(aq) + H3O+(aq)

HCl (aq) Cl-(aq) + H+(aq)

HCl(aq) + H2O(l) Cl-(aq) + H3O+(aq)

What is HWhat is H++ (aq)? (aq)?

+H O

H

HH3O+

HO

H

H +OH

H

H5O2+

+H

HO

OH2H2O

H2O

+

H

H

H+

H9O4+

Representing ProtonsRepresenting Protons

Both representations of the proton are equivalent.

H5O2+ (aq), H7O3

+ (aq), H9O4+ (aq) have

been observed.

We will use H+(aq)!

The Autoionization of Water The Autoionization of Water

Water autoionizes (self-dissociates) to a small extent

2H2O(l) H3O+(aq) + OH-(aq)

H2O(l) H+(aq) + OH-(aq) These are both equivalent definitions of the

autoionization reaction. Water is acting as a base and an acid in the above reaction water is amphoteric.

The Autoionization The Autoionization EquilibriumEquilibrium

From the equilibrium chapter

)OH(a

)OH(a )OH(a or

)OH(a

)OHa( )H(a = K

2

3

2c

But we know a(H2O) is 1.00!

The Defination of KThe Defination of Kww

Kw = a(H+) a(OH-)

Ion product constant for water, Kw, is the product of the activities of the H+ and OH-

ions in pure water at a temperature of 298.15 K

Kw = a(H+) a(OH-) = 1.0x10-14 at 298.2 K

The pH scaleThe pH scale Attributed to Sørenson in 1909

We should define the pH of the solution in terms of the hydrogen ion activity in solution

pH -log a(H+)

Single ion activities and activity coefficients can’t be measured

Determination of pHDetermination of pH

What are we really measuring when we measure the pH?

pH -log a(H+)

a (H+) is the best approximation to the hydrogen ion activity in solution.

How do we measure a(H+)?

For the dissociation of HCl in water

HCl (aq) Cl-(aq) + H+(aq) We measure the mean activity of the acid

a(HCl) = a(H+) a(Cl-)

a(H+) a(Cl-) = (a(HCl))2

Under the assumption

a(H+) = a(Cl-) We obtain

a´(H+) = (a(HCl))1/2 = a(HCl)

Equilibria in Aqueous Solutions Equilibria in Aqueous Solutions of Weak Acids/ Weak Basesof Weak Acids/ Weak Bases

By definition, a weak acid or a weak base does not ionize completely in water ( <<100%). How would we calculate the pH of a solution of a weak acid or a weak base in water?

To obtain the pH of a weak acid solution, we must apply the principles of chemical equilibrium.

Equilibria of Weak Acids in Equilibria of Weak Acids in WaterWater: The K: The Kaa Value Value

Define the acid dissociation constant Ka

For a general weak acid reaction

HA (aq) H+ (aq) + A- (aq)

HAa

Aa HaKa

Equilibria of Weak Acids in Equilibria of Weak Acids in WaterWater

For the dissolution of HF(aq) in water.

HF (aq) H+ (aq) + F- (aq)

HFa

Fa HaKa

The small value of Ka indicates that this acid is only ionized to a small extent at equilibrium.

The Nonelectrolyte ActivityThe Nonelectrolyte Activity

HF (aq) H+ (aq) + F- (aq) The undissociated HF is a nonelectrolyte

a(HF) = (HF) m[HF] m[HF]

(HF) 1

4a 10x1.7

HFm

Fa HaK

Equilibria of Weak Bases in Equilibria of Weak Bases in WaterWater

To calculate the percentage dissociation of a weak base in water (and the pH of the solutions)

CH3NH2 (aq) + H2O CH3NH3+(aq) + OH- (aq)

We approach the problem as in the case of the weak acid above, i.e., from the chemical equilibrium viewpoint.

The KThe Kbb Value Value

Define the base dissociation constant Kb For a general weak base reaction with water

B (aq) + H2O (aq) B+ (aq) + OH- (aq)

Ba

OHa BaKb

For the above system

Bm

OHaBaKb

Examples of Acid-Base Examples of Acid-Base CalculationsCalculations

Determining the pH of a strong acid (or base solution).

Determining the pH of a weak acid (or base solution).

Calculating the pH of Solutions Calculating the pH of Solutions of Strong Acidsof Strong Acids

For the dissolution of HCl, HI, or any of the other seven strong acids in water

HCl (aq) H+ (aq) + Cl- (aq) HI (aq) H+ (aq) + I- (aq) % eq = 100%

The pH of these solutions can be estimated from the molality and the mean activity coefficient of the dissolved acid

pH -log ( (acid) m[H+])

For the dissolution of NaOH, Ba(OH)2, or any of the other strong bases in water

NaOH (aq) Na+ (aq) + OH- (aq) Ba(OH)2 (aq) Ba2+ (aq) + 2OH- (aq)

% eq = 100%

Calculating the pH of Solution of Calculating the pH of Solution of Strong BasesStrong Bases

The pH of these solutions is obtained by first estimating the pOH from the molality and mean activity coefficient of the dissolved base

pOH -log ( (NaOH) m[OH-])

pOH -log{ (Ba(OH)2) 2 m[Ba(OH)2]}

pH = 14.00 - pOH

Calculating the pH of a Weak Calculating the pH of a Weak Acid SolutionAcid Solution

The pH of a weak acid solution is obtained via an iterative procedure.

We begin by making the assumption that the mean activity coefficient of the dissociated acid is 1.00.

We ‘correct’ the value of (H+) by calculating the mean activity coefficient of the dissociated acid.

Repeat the procedure until (H+) converges.

Measuring the pH of SolutionsMeasuring the pH of Solutions

Because the activity of a single ion cannot be measured, we can only measure our ‘best approximation’ to the hydrogen ion activity.

Let’s assume that we are going to couple a hydrogen electrode with another reference electrode, e.g., a calomel reference electrode.

A Cell for ‘Measuring’ the pHA Cell for ‘Measuring’ the pH

Half-cell reactions.HgCl2 (s) + 2e- Hg (l) + 2 Cl- (aq)

E(SCE) = 0.2415 V

2 H+ (aq) + 2e- H2 (g)

E (H+/H2) = 0.000 V Cell Reaction

HgCl2 (s) + H2 (g) Hg (l) + 2 H+ (aq) + 2Cl- (aq)

Ecell = (0.2415 - 0.0000 V) = 0.2415 V

Pt H2 (g), f=1 H+ (aq) HgCl2 Hg Cl- (aq), 3.5 M Pt

The Nernst EquationThe Nernst Equation

For the above cell

2

cell Hf

Cla Haln

F 2

RTV2415.0E

Note since the concentration of the KCl on one side of the liquid junction is so large, the magnitude of the junction potential should be small!

The Practical Problem The Practical Problem

The activity of the Cl- ion in the cell is not accurately known.

We try to place the cell in a reference solution with an accurately known pH (solution I).

Next place the solution whose pH we are attempting to measure into the cell (solution II).

Assuming that the ELJ and the a(Cl-) are the same in both cases,

I,HalnF

RTII,Haln

F

RTEE III

cellcell

Substituting the definition of the pH into the above expression,

Icell

IIcell

III EETR2.303

FpHpH

Standard SolutionsStandard Solutions

Generally, two solutions are used as references. Saturated aqueous solution of sodium hydrogen

tartarate, pH = 3.557 at 25C. 0.0100 mol/kg disodium tetraborate, pH =

9.180 at 25C.

The Glass ElectrodeThe Glass Electrode

The glass electrode has replaced the hydrogen electrode in the operational definition of the pH.

Glass ElectrodesGlass Electrodes

Measuring the pH – the glass electrode is immersed in the solution of interest.

Inner solution – solution is generally a phosphate buffer with a sufficient quantity of Cl- (aq).

Silver-silver chloride electrode is sealed within the cell and a calomel electrode is used as the reference electrode.

Glass Electrodes and pHGlass Electrodes and pH

The potential difference across the special glass membrane arises to equilibrate the hydronium ions inside the membrane with those outside the membrane.

The Definition of a Buffer The Definition of a Buffer

Buffer a reasonably concentrated solution of a weak acid and its conjugate base that resists changes in the pH when an additional amount of strong acid or strong base is added to the solutions.

How would we calculate the pH of a buffer solution?

HCOOHm

HCOOa HaKa

HCOOHm

HCOOa HalogKlogpK aa

HCOOHmlogHCOOalogHalogpKa

note pH = -log a(H+)

Define pKa = -log (Ka )

The Buffer EquationThe Buffer Equation

HCOOHm

)HCOO(alogpHpKa

Substituting and rearranging

HCOOHm

)HCOO(alogpKpH a

The Generalized Buffer The Generalized Buffer EquationEquation

The pH of the solution determined by the ratio of the weak acid to the conjugate base. This equation (the Henderson-Hasselbalch equation) is often used by chemists, biochemists, and biologists for calculating the pH of a solution of a weak acid and its conjugate base!

acid weakm

)base .conj(alogpKpH a

Note: The Henderson-Hasselbalch equation is really only valid for pH ranges near the pKa of the weak acid!

Buffer CH3COONa (aq) and CH3COOH (aq))

CH3COOH (aq) ⇄ CH3COO- (aq) + H+ (aq)

The Equilibrium Data Table

n(CH3COOH) n(H+) n(CH3COO-)

Start A 0 B

Change -eq + eq +eq

m (A-eq) (eq) (B+ eq)

The pH of the solution will be almost entirely due to the original molalities of acid and base!!

]A[m

BmlogpKpH a

This ratio will be practically unchanged in the presence of a small amount of added strong acid or base

The pH of the solution changes very little after adding strong acid or base (i.e., it is buffered)

How does the pH change after the addition of strong acid or base?

Example of Buffer Example of Buffer CalculationsCalculations

How do we calculate the pH of a buffer solution?

The pH of a Buffer SolutionThe pH of a Buffer Solution

The major task in almost all buffer calculations is to obtain the ratio of the concentrations of conjugate base to weak acid!

Using the Ka of the appropriate acid, the pH of the solution is obtained from the Henderson-Hasselbalch equation.

Adding Strong Acid or Base to Adding Strong Acid or Base to Buffer Solutions Buffer Solutions

To obtain the pH after the addition of a strong acid or base, we must calculate the new amount of weak acid and conjugate base from the reaction of the strong acid (or base) to the buffer system.

The pH of the solution may again be calculated with the Henderson-Hasselbalch equation.

Solubility EquiSolubility Equilibria libria

Examine the following systems

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq)

BaF2 (s) ⇌ Ba2+ (aq) + 2 F- (aq)

Using the principles of chemical equilibrium, we write the equilibrium constant expressions as follows

10

sp 10x8.1Cla AgaK

1AgCla note

AgCla

Cla AgaK

622sp 10x0.1Fa BaaK

Calculate the solubility of a solid in the presence of a common ion.

Examples of KExamples of Kspsp Calculations Calculations

Calculate the solubility of a sparingly soluble solid in water.

Calculate the solubility of a solid in the presence of an inert electrolyte.

Solubility of Sparingly Soluble Solubility of Sparingly Soluble Solids in WaterSolids in Water

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq) We approach this using the principles of

chemical equilibrium. We set up the equilibrium data table, and calculate the numerical value of the activity of the dissolved ions in solution.

The Common Ion EffectThe Common Ion Effect

What about the solubility of AgCl in solution containing NaCl (aq)?

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq)

NaCl (aq) Na+ (aq) + Cl- (aq)

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq)

Equilibrium is displaced to the left by LeChatelier’s principle (an example of the common ion effect).

Solubility in the Presence of Solubility in the Presence of an Inert Electrolytean Inert Electrolyte

What happens when we try to dissolve a solid like AgCl in solutions of an inert electrolyte (e.g., KNO3 (aq))?

We must now take into account of the effect of the ionic strength on the mean activity coefficient!

The Salting-In EffectThe Salting-In Effect

AgCl (s) ⇌ Ag+ (aq) + Cl- (aq). We designate the solubility of the salt in the

absence of the inert electrolyte as so = m(Ag+) = m(Cl-) at equilibrium.

2o

2

102

sp

s

10x8.1ClmAgm

Cla AgaK

For a dilute solution

2osp sK1

Designate s as the solubility of the salt in the presence of varying concentrations of inert electrolyte.

o2

sp

sssK