The Foundations of Chemistry

log Qcell,so the correction factor becomes more negative. Thus, the overall Ecelldecreases

(the reaction becomes less favorable). Eventually the cell potential approaches zero (equi-

librium), and the cell “runs down.” The cell is completely run down (Ecell0) when the

term 

0.0

n

592

log Qcellis equal in magnitude to E^0 cell.

We can also find the cell potential for a nonstandard cell by first finding E^0 cellor the

overall standard cell reaction, and then using the Nernst equation to correct for nonstan-

dard concentrations. The next example illustrates this approach.

EXAMPLE 21-7 The Nernst Equation

A cell is constructed at 25°C as follows. One half-cell consists of a chlorine/chloride, Cl 2 /Cl,

electrode with the partial pressure of Cl 2 0.100 atm and [Cl]0.100 M.The other half-

cell involves the MnO 4 /Mn^2 couple in acidic solution with [MnO 4 ]0.100 M,[Mn^2 ]

0.100 M,and [H]0.100 M.Apply the Nernst equation to the overall cell reaction to deter-

mine the cell potential for this cell.

Plan

First we determine the overall cell reaction and its standardcell potential, E^0 cell, as in Examples

21-3 and 21-4. Then we apply the Nernst equation to the overall cell.

Solution

The MnO 4 /Mn^2 half-reaction has the more positive reduction potential, so we write it first.

Then we write the Cl 2 /Clhalf-reaction as an oxidation, balance the electron transfer, and add

the two half-reactions and their potentials to obtain the overall cell reaction and its E^0 cell.

E^0

2(MnO 4 8H 5 e88nMn^2 4H 2 O) 1.507 V

5(2Cl88nCl 2  2 e) 1.360 V

2MnO 4 16H10Cl88n2Mn^2 8H 2 O5Cl 2 E^0 cell0.147 V

In the overall reaction, n10. We then apply the Nernst equation to this overall reaction by

substituting appropriate concentration and partial pressure values. Because Cl 2 is a gaseous

component, its term in the Nernst equation involves its partial pressure, PCl 2.

EcellE^0 cell 

0.0

n

592

log

0.147 V

0.0

1

5

0

92

log

0.147 V

0.0

1

5

0

92

log(1.00 1021 )

0.147 V

0.0

1

5

0

92

(21.00) 0.017 V

You should now work Exercises 80 and 84.

The method illustrated in Example 21-7, applying the Nernst equation to the overall

cell reaction, usually involves less calculation than correcting the separate half-reactions

as in Example 21-6. We interpret our results as follows: The positive cell potentials in

Examples 21-6 and 21-7 tell us that each of these cell reactions is spontaneous in the direc-

(0.100)^2 (0.100)^5



(0.100)^2 (0.100)^16 (0.100)^10

[Mn^2 ]^2 (PCl 2 )^5



[MnO 4 ]^2 [H]^16 [Cl]^10

880 CHAPTER 21: Electrochemistry

See the Saunders Interactive
General Chemistry CD-ROM,
Screen 21.7, Electrochemical Cells at
Nonstandard Conditions.

Remember that, in evaluating Q
in the Nernst equation, (1) molar
concentrations are used for dissolved
species, and (2) partial pressures of
gases are expressed in atmospheres.

Now solve Example 21-6 by applying
the Nernst equation to the overallcell
reaction to determine the cell
potential.