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CONCENTRATION CELLS 335

Inserting values into Equation (7.48):

0.0257 V 0.02
emf = ln
2 0.002
emf = 0.0129 V ln(10)
emf = 0.0129 V × 2.303

emf = 29.7mV

so the emf for this two-electron concentration cell is about 30 mV. For an analogous
one-electron concentration cell, the emf wouldbe59mV.

SAQ 7.18 The concentration cell Zn|[Zn 2+ ](c = 0.0112 mol dm −3 )|[Zn 2+ ]
(c = 0.2mol dm −3 )|Zn is made. Calculate its emf, assuming all activity
coefficients are unity.

Justification Box 7.2

Let the redox couple in the two half-cells be O + ne = R. An expression for the emf
−
of the cell is

emf = E (RHS) E (LHS)
The Nernst equation for the O,R couple on the RHS of the cell is:

RT a (O) RHS
E O,R = E O + ln
O,R
nF a (R) RHS
and the Nernst equation for the same O,R couple on the LHS of the cell is:
RT a (O) LHS
E O,R = E O + ln
O,R
nF a (R) LHS
Substituting for the two electrode potentials yields an emf of the cell of

RT a (O) RHS O RT a (O) LHS
O
emf = E O,R + ln − E O,R − ln
nF a (R) RHS nF a (R) LHS
It will be seen straightaway that the two E O terms cancel to leave
RT a (O) RHS RT a (O) LHS
emf = ln − ln
nF a (R) RHS nF a (R) LHS
A good example of a concentration cell would be the iron system in the worked example
above, in which a (R) = a (Cu) = 1; accordingly, for simplicity here, we will assume that
the reduced form of the couple is a pure solid.