Physical Chemistry Third Edition

8.3 Half-Cell Potentials and Cell Potentials 361

An alternate extrapolation method can also be used. For small values ofmthe

(m/m◦)^1 /^2 term negligible compared to unity and thebmterm is negligible compared

to theαm^1 /^2 term. If these terms are omitted, Eq. (8.2-21) becomes

E+

2 RT

F

ln

(m

m◦

)

E◦+

2 RT

F

αm^1 /^2 (8.2-22)

If the left-hand side of this equation is plotted as a function ofm^1 /^2 the extrapolation

tom0 should be nearly linear for small values ofm^1 /^2 , giving the value ofE◦from

the intercept.

PROBLEMS

Section 8.2: Electrochemical Cells

8.4 a.Find the reversible cell voltage for the cell of Figure 8.2

at 298.15 K if the partial pressure of hydrogen is equal to

712 torr and the molality of the HCl solution is

0.100 mol kg−^1. Assume the hydrogen gas to be ideal

and use the Davies equation to estimate the activity

coefficient of the HCl.

b.Repeat the calculation of part a using the value

of the activity coefficient from Table A.11 of

Appendix A.

8.5Find the reversible voltage of the cell of Figure 8.2 at

298.15 K if the HCl solution has a molality of 1.00 mol kg−^1

and the pressure of the hydrogen gas is 755 torr. Use the

value of the activity coefficient from Table A.11 of

Appendix A.

8.6The cell

Cd|CdCl 2 (6.62 m)|Cl 2 (1.000 atm)|Pt

has a cell voltage equal to 1.8111 V at 25◦C. The

6.62 mol kg−^1 solution of CdCl 2 is saturated and is at

equilibrium with CdCl 2 ·^52 H 2 O and water vapor at 16.5 torr.

The activity coefficient of CdCl 2 at this molality is equal to

0.025. The vapor pressure of pure water at this temperature

is 23.8 torr. FindE◦for the cell and∆G◦for the reaction

Cd(s)+Cl 2 (g)+

5

2

H 2 O(l)−→CdCl 2 ·

5

2

H 2 O(s)

8.3 Half-Cell Potentials and Cell Potentials

Figure 8.3 depicts a cell that has a hydrogen electrode on the left side and acalomel

electrodeon the right side. The calomel electrode contains liquid mercury in contact

with solid calomel (Hg 2 Cl 2 ). A platinum wire extends from the pool of mercury and

acts as a terminal. The solution in this cell is an aqueous solution of HCl, just as in the

cell of Figure 8.2. The reduction half-reaction at the calomel electrode is

Hg 2 Cl 2 (s)+ 2 e−−→2Hg(l)+2Cl− (8.3-1)

The oxidation half-reaction of the hydrogen electrode is the same as in Eq. (8.2-1). The

cell reaction equation is

H 2 (g)+Hg 2 Cl 2 (s)−→2Hg(l)+2H++2Cl−

The standard-state cell voltage is equal to 0.268 V for this cell.

Exercise 8.5

a.Write the Nernst equation for the cell of Figure 8.3.

b.Write an equation analogous to Eq. (8.2-21) that could be used to determine the value of

E◦for the cell of Figure 8.3.