**Practice Problem 12**

Use the relationship between *G*^{o} and *E*^{o} for an electrochemical reaction to
derive the relationship between the standard-state cell potential and the equilibrium
constant for the reaction.

**Answer**

We can start with the equation that describes the relationship between the standard-state free energy of reaction and the standard-state cell potential for an electrochemical cell:

* G ^{o} = -nFE^{o}*

We can then write the relationship between the standard-state free energy fo reaction and the equilibrium constant for the reaction:

*G*^{o}
= - *RT* ln *K*

Substituting one of these equations into the other gives:

*-nFE ^{o }*= -

We now multiply both sides of this equation by -1:

*nFE ^{o }*=

Solving for the ln *K* term gives the following equation: