As the cell reaction in an electrochemical cell progresses,
electrons move through a wire connecting the two electrodes
until the equilibrium point of the cell reaction is reached,
at which point the flow of electrons ceases.
As long as the reaction has not reached equilibrium, the electrons
being driven through the external circuit may be used to do
work.
The work that transfer of a given number of electrons may do
depends upon the potential difference between the two electrodes.
This potential difference is called the cell
potential, and is measured in volts. (When the cell potential
is large, transfer of a given number of electrons can do more
electrical work than when the cell potential is small.)
Note that when the cell reaction
is at equilibrium, the cell potential is zero and no work can
be done.
The maximum amount of electrical work a galvanic cell can do
at constant temperature and pressure is given by ΔG, the
change in the Gibbs energy of the system from the starting situation
to the final situation. (In practice this will usually be equal
to the Standard Gibbs Energy of Reaction,
ΔGšr , for the cell reaction, which is given
by the sum of the standard molar Gibbs energies of the products,
minus the sum of the standard molar Gibbs energies of the reactants,
each standard molar Gibbs energy being multiplied by its stoichiometric
coefficient.)
Thus to make thermodynamic measurements upon the cell by measuring
the work it can do, it is necessary to ensure that the cell
is operating reversibly, as only then does it produce the maximum
amount of work, which can be equated with ΔG.
Furthermore, another thermodynamic property, the Reaction
Gibbs Energy, ΔGr , (which is entirely
different from the standard reaction Gibbs energy, ΔGšr
, defined above) must be evaluated at a specified composition
of the reaction mixture. This makes it necessary to ensure that
the cell is operating reversibly at a specific, unchanging composition.
Both requirements may be satisfied by measuring the cell potential
when a precisely equal opposing potential is being applied,
ensuring that the cell reaction is occurring under conditions
of thermodynamic reversibility and that the composition of the
cell is constant. (It may make more sense to think of this in
terms of measuring the minimum potential that needs to be applied
to halt the cell reaction, and equating this value with the
cell potential. When the opposing and cell potentials are precisely
equal, the driving force for the reaction has been neutralised,
and no current flows; the cell reaction is poised to occur,
but no change is actually taking place - hence the composition
remains constant.) The resulting potential difference is called
the zero-current cell potential,
designated E.
The relationship between the reaction Gibbs energy, ΔGr
, and the zero-current cell potential, E, is given by

where ν is the number of electrons transferred in the
reaction, and F, the Faraday constant, has the approximate value
96 485.3 C mol-1.
Note that a negative reaction Gibbs energy (spontaneous cell
reaction) corresponds to a positive zero-current cell potential.
The equation also implies that the cell potential is proportional
to the slope of the Gibbs energy with respect to the extent
of reaction (the definition of ΔGr ). i.e.
the driving force of the cell (the cell potential) is greater
the further from equilibrium the cell reaction is (as
the slope of a graph of Gibbs energy against extent of reaction
tends to zero the closer one gets to the point of equilibrium,
which corresponds to the Gibbs energy minimum.)
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