Page 152 - Instant notes

Physical chemistry 138

Activity dependence of cell voltage

Measurement of cell potentials away from the standard state provides a convenient
method for measuring ion activity and activity coefficients (see Topic E2). As ion
concentration is varied in a half-cell to vary ion activity, the equilibrium position of the
half-cell reduction reaction changes, and this causes a change in the half-cell potential.
The relationship between the half-cell potential and activity is given by the Nernst
equation:

for the general half-cell reduction reaction:
−
aA+bB+ne →cC+dD

where are the activities of A, B, C, D raised to the power of their
stoichiometries and n is the number of electrons transferred (see Topic E4). For the
formal cell reaction, aA+bB→cC+dD, the Nernst equation becomes

where Q is the reaction quotient for the cell reaction in terms of their activities (see
Topic B6) and n is the number of electrons in each half-cell reaction used to obtain the
formal cell reaction (see Topic E4). The activity of pure liquids and solids is equal to 1,
which simplifies both Nernst expressions (see Topic C1).

Cells at equilibrium

When a cell is at equilibrium, E cell=0 (the ‘flat battery’ condition) and Q=K, the
equilibrium constant for the reaction (see Topic C1). This gives the expression:

which allows calculation of equilibrium constants (see Topic C1) for cell reactions from
calculated or measured values (see Topic E4).