The Foundations of Chemistry

THE RELATIONSHIP OF E^0 cellTO
G^0 AND K

In Section 17-12 we studied the relationship between the standard Gibbs free energy

change, 
G^0 , and the thermodynamic equilibrium constant, K.

G^0 RTlnK

There is also a simple relationship between 
G^0 and the standard cell potential, E^0 cell, for

a redox reaction (reactants and products in standard states).

G^0 nFE^0 cell

G^0 can be thought of as the negative of the maximum electrical workthat can be obtained

from a redox reaction. In this equation, nis the number of moles of electrons transferred

in the overall process (mol e/mol rxn), and Fis the faraday, 96,485 J/Vmol e.

Combining these relationships for 
G^0 gives the relationship between E^0 cellvalues and

equilibrium constants.

nFE^0 cellRTlnK

G^0 
G^0

After multiplying by 1, we can rearrange.

nFE^0 cellRTlnK or E^0 cell

RT

n

l

F

nK

 or lnK

nF

R

E

T

0

cell

If any one of the three quantities 
G^0 , K,and E^0 cellis known, the other two can be calcu-

lated using these equations. It is usually much easier to determine Kfor a redox reaction

from electrochemical measurements than by measuring equilibrium concentrations

directly, as described in Chapter 17. Keep in mind the following for all redox reactions

at standard conditions.

Forward Reaction 
G^0 KE^0 cell

product-favored (spontaneous)   1 

at equilibrium 0    10 (all substances at standard conditions)

reactant-favored (nonspontaneous)  1 

EXAMPLE 21-9 Calculation of 
G^0 from Cell Potentials

Calculate the standard Gibbs free energy change, 
G^0 , in J/mol at 25°C for the following reac-

tion from standard electrode potentials.

3Sn^4 2Cr88n3Sn^2 2Cr^3 

Plan

We evaluate the standard cell potential as we have done before. Then we apply the relation-

ship 
G^0 nFE^0 cell.

21-21

884 CHAPTER 21: Electrochemistry

 











Recall from Chapter 15 that
G^0 can
be expressed in joules per mole of
reaction.Here we ask for the number
of joules of free energy change that
corresponds to the reaction of 2 moles
of chromium with 3 moles of tin(IV)
to give 3 moles of tin(II) ions and 2
moles of chromium(III) ions.