Physical Chemistry Third Edition

376 8 The Thermodynamics of Electrochemical Systems

For the standard-state reaction,

∆H◦−nFE◦+nF T

(

∂E◦

∂T

)

P

(8.5-7)

A chemical reaction does not have to be an oxidation-reduction reaction for us to

calculate its equilibrium constant. It is only necessary to be able to write the reaction

as the sum of an oxidation half-reaction and a reduction half-reaction.

EXAMPLE 8.9

Find the solubility product constant of AgI at 298.15 K from electrochemical data.

Solution

The reaction equation is

AgI(s)−→Ag++I−

This reaction equation can be written as the sum of the oxidation and reduction half-reaction

equations:

AgI(s)+e−−→Ag(s)+I− E◦− 0 .1519 V

Ag(s)−→Ag++e− E◦− 0 .7986 V

AgI(s)−→Ag++I− E◦− 0 .9505 V

The solubility product constant is

Kspexp

(

( 1 )(96485 C mol−^1 )(− 0 .9505 V)

(9.3145 J K−^1 mol−^1 )(298.15 K)

)

e−^36.^99  8. 6 × 10 −^17

Many solubility product constants are so small that their values cannot be determined

by chemical analysis. Electrochemical data provide the practical means to evaluate

them.

Exercise 8.14

a.Using electrochemical data, find the solubility product constant for mercury(I) iodide, Hg 2 I 2.

b.Find the volume of a saturated solution of Hg 2 I 2 that contains 1.00 mol of Hg 2 I 2. Assuming

that the ocean has an average depth of 1.00 mile, estimate the area of ocean that contains this

volume of water.

PROBLEMS

Section 8.5: Thermodynamic Information from
Electrochemistry

8.22 a.Using half-cell potentials, find the value of the
equilibrium constant for the reaction at 298.15 K:
I 2 (aq)+I−
I− 3

b. Find the final concentrations if 100 mL of a

0.00100 mol kg−^1 solution of I 2 and 100 mL of a

0.00100 mol kg−^1 solution of KI are mixed and allowed

to equilibrate. Assume thatγ(I 2 ) 1 .00 and use the

Davies equation to estimate the activity coefficients of

the ions.