Physical Chemistry Third Edition

8.3 Half-Cell Potentials and Cell Potentials 367

The cell symbol for the Daniell cell with a salt bridge would be

Zn(s)|Zn^2 +||Cu^2 +|Cu(s)

where we have omitted the symbols for the platinum terminals.

Concentration Cells

Figure 8.8 schematically depicts a concentration cell, which contains two solutions of

the same electrolyte with different concentrations. The cell symbol of this cell can be

written

Pt(s)|H 2 (g,P 1 )|HCl(m 1 )||HCl(m 2 )|H 2 (g,P 2 )|Pt(s)

whereP 1 andP 2 represent two pressures of the hydrogen gas andm 1 andm 2 represent

the different molalities of the HCl solutions. A salt bridge is used to minimize the liquid

junction potential. If the hydrogen is at the same pressure in both sides of the cell, the

cell reaction for this concentration cell is

HCl(m 2 )−→HCl(m 1 ) (8.3-6)

The standard states for the half-cells are the same, soE◦vanishes, as it does for any

concentration cell. If we neglect the liquid junction potential, the Nernst equation for

our concentration cell is

E−

RT

F

ln

(

a 1 (HCl)

a 2 (HCl)

)

−

RT

F

ln

(

[γ±,1m 1 /m◦]^2

[γ±,2m 2 /m◦]^2

)

−

2 RT

F

ln

(

γ±,1m 1 /m◦

γ±,2m 2 /m◦

)

(8.3-7)

where the subscripts onγ±and onmindicate the half-cell to which that value applies.

If the activity coefficient of HCl at one molality is known, this equation can be used to

determine the activity coefficient at the other molality if the liquid junction potential

can be evaluated or eliminated.

In order to eliminate the liquid junction potential, the concentration cell of Figure 8.8

can be replaced by the double cell of Figure 8.9, which contains two reversible cells

Pt

KCI solution

Pt

H 2 (P 1 ) H 2 (P 2 )

HCI

solution

m = m 1

HCI

solution

m = m 2

Figure 8.8 A Concentration Cell.