Physical Chemistry , 1st ed.

we can easily combine these two equations and derive the expression

E°

R

nF

T

ln K (8.32)

This expression can also be derived from the Nernst equation by considering

the following: at equilibrium,E0 (that is, there is no potential difference be-

tween the cathode and the anode). But also at equilibrium, the expression Qis

exactly the equilibrium constant Kfor the reaction. Therefore, the Nernst

equation becomes

0 E° 

R

nF

T

ln K

which rearranges to

E°

R

nF

T

ln K

which is equation 8.32. Voltages of reactions at standard conditions can there-

fore be used to determine the equilibrium position of that reaction (at which

point Eequals 0).

Example 8.7

Using electrochemical data, what is the solubility product constant,Ksp,of

AgBr at 25°C?

Solution

The chemical reaction representing the solubility of AgBr is

AgBr (s) Ag^ (aq) Br^ (aq)

This can be written as the combination of two reactions from Table 8.2:

AgBr (s) e^ →Ag (s) Br^ (aq) E°0.07133 V

Ag (s) →Ag^ (aq) e^ E°

0.7996 V

Therefore, for the overall reaction E° is 0.728 V. Using equation 8.32 (and

assuming molar quantities):

0.728 V  ln Ksp

Convince yourself that n1 in this example. All of the units on the right

side except J/C cancel, and we should recognize this fraction to be equal to a

volt unit, which cancels with the volt unit on the left side of the equation.

Rearranging to isolate the natural logarithm ofKsp:

ln Ksp 28.4

Taking the inverse logarithm of both sides, we get our final answer:

Ksp4.63    10

13

At 25°C,Kspfor AgBr is measured as 5.35     10

13 , giving you an idea how

closely it can be calculated using the electrochemical values.

( 0.728)(1)(96,485)



(8.314)(298)

(8.314 KJ)(298 K)

(1 mol e^ )(96,485 moCle )

JQPJ

222 CHAPTER 8 Electrochemistry and Ionic Solutions