Physical Chemistry Third Edition

368 8 The Thermodynamics of Electrochemical Systems

HCl

Solution

m
m 1

HCl

Solution

m
m 2

Ag

AgCl

Ag

Pt

H 2 (P 1 )

Pt

H 2 (P 2 )

Figure 8.9 A Double Cell Equivalent to a Concentration Cell.

with hydrogen electrodes. Assuming that the pressure of hydrogen is equal toP◦in

both cells, the Nernst equation for the left-hand cell is

E(left cell) 0 .2223V−

2 RT

F

ln(γ±,1m 1 /m◦)

and that of the right-hand cell is

E(right cell)− 0 .2223 V+

2 RT

F

ln(γ±,2m 2 /m◦)

so that the potential difference of the double cell is equal to that of Eq. (8.3-7) without

the liquid junction potential. Another possibility is to build just one cell, like half of

the double cell, and then to measure its potential difference once when filled with a

solution of molalitym 1 , and once when filled with a solution of molalitym 2.

Exercise 8.8

Find the potential difference of the concentration cell of Figure 8.8 if in solution 1 the molality is

0.500 mol kg−^1 withγ±,1equal to 0.757, and in solution 2 the molality is 0.200 mol kg−^1 with

γ±,2equal to 0.767.

The Temperature Dependence of the Cell Voltage

We have already studied the temperature dependence of∆G◦. From Eqs. (7.6-9) and

(8.2-14), if∆H◦can be assumed to be temperature-independent,

E◦(T 2 )

T 2

−

E◦(T 1 )

T 1

−

∆H◦

nF

[

1

T 2

−

1

T 1

]

(8.3-8)