Physical Chemistry Third Edition

8.3 Half-Cell Potentials and Cell Potentials 365

Cells with Liquid Junctions

Some pairs of half-cells cannot be combined to make a cell with a single liquid solution

because a single solution in contact with both electrodes would allow undesired chem-

ical reactions at the electrode surfaces or in the solution. Consider the cell with the

half-reactions

Zn(s)−→Zn^2 ++ 2 e−

Cu^2 ++ 2 e−−→Cu(s)

If the Cu^2 +ions were in the solution that contacts the zinc electrode the oxidation and

reduction half-reactions would both take place at the zinc electrode without transferring

electrons through an external circuit. Two separate solutions are needed. A cell with

two compartments can be constructed, as shown in Figure 8.6. This cell is known as

theDaniell cell, and these cells were once used commercially. The left compartment

contains a zinc electrode and a solution of zinc sulfate, and the right compartment

contains a copper electrode and a solution of copper(II) sulfate. The two solutions

are separated by a porous barrier that keeps theliquid junctionbetween the solutions

confined to one location. Ions can diffuse through the liquid filling its pores, but the

two solutions cannot mix by flowing together.

Pt

Porous

barrier

Zn

ZnSO 4

solution

CuSO 4

solution

Cu

Pt

Figure 8.6 The Daniell Cell.

A cell with a liquid junction is called acell with transference. In a cell symbol, a liquid

junction is sometimes represented by a vertical broken line, but it can be represented by

an unbroken vertical line like that representing any other phase boundary. The presence

of the liquid junction makes it impossible to bring the cell to equilibrium with a counter

voltage. Ions can diffuse through the liquid junction even if the cell is on open circuit or

has a counter voltage to stop the flow of current. These irreversible diffusion processes

can produce excess positive ions on one side of the liquid junction and excess negative

ions on the other side. This makes a contribution to the potential difference of the cell,

called theliquid junction potential, denoted byELJ.

EXAMPLE 8.4

a.Write the cell reaction equation and the cell symbol for the Daniell cell.

b.Write the Nernst equation for the Daniell cell.

c.Find the standard-state potential difference of the Daniell cell, neglecting the liquid junc-

tion potential. In which direction will the cell reaction proceed spontaneously under stan-

dard conditions?

Solution

a.If we omit the electrons the cell reaction equation is

Zn(s)+Cu^2 +−→Zn^2 ++Cu(s)

and the cell symbol is Zn(s)|Zn^2 +|Cu^2 +|Cu(s), where we represent the liquid junction by

a vertical line segment, as with any other phase boundary. We have omitted the symbols

for the platinum terminals.

b.If the pressure is not greatly different fromP◦, the activities of the solid electrodes can

be approximated by unity, and the Nernst equation is

EE◦+ELJ−

RT

2 F

ln

(

a(Zn^2 +)

a(Cu^2 +)

)

whereELJrepresents the liquid junction potential.