The use of standard reduction potentials to predict the course
of a reaction is somewhat limited, in that they are only valid
under standard conditions. However, they can be used to predict
the course of redox reactions under nonstandard conditions.
This process of extrapolation of the properties of a reaction
under one set of conditions to those under another set of conditions
uses the Nernst equation.
|The Nernst Equation
If we know the Gibbs free energy of reaction at
under one set of conditions, it can be used to predict the Gibbs
free energy of reaction, and from that the reduction potential,
under a new set of conditions.
of the Nernst equation
|Consider the reaction:
|The Gibbs free reaction energy
can be related to the standard Gibbs free reaction energy:
|Q is the reaction
|The reduction potentials
may be related to the free energies of reaction:
|Therefore, the Nernst equation
is the result:
The Nernst equation relates the non-equilibrium
properties of a reaction to those at equilibrium. At equilibrium,
the reaction free energy, and hence the potential for the reaction,
is zero, and the reaction quotient, Q, is the equilibrium
constant, K. We can therefore calculate the equilibrium
constant from the standard reduction potential.
The exponential dependence of the equilibrium
constant on the reaction potential means that a change in reaction
potential of one volt results in a change in the equilibrium
constant of seventeen orders of magnitude: hence, E*
= +2 V means K = 1034, E* = 0 V means
K = 1, and E* = -2 V means K = 10-34.
When we introduced half-reactions, we saw that
we could split up the overall potential for a cell into contributions
from the oxidant and the reductant. We can also do this for
the Nernst equation, and therefore write a similar expression
for each of the reduction couples.
pH dependence of reduction potentials
The Nernst equation can be used to determine the
pH dependence of the potential for a given reaction.
|Consider the reaction:
|The Nernst equation gives
is the reduction potential for the Ox/Red couple, E*(Ox/Red),
as the standard reduction potential for the H+/H2
couple is zero, and [H2] is given by the partial
pressure of H2, which is 1 under standard conditions,
and the number of electrons transferred is 2.
|The Nernst equation becomes:
|The definition of pH:
||pH = -log10[H+]
|So the reduction potential
is related to the pH:
In general this equation should be adapted for
the number of electrons transferred.
Stability Fields: Water
The values of the reduction potentials for the H+/H2
and O2,H+/H2O redox couples,
and their pH dependences, can be used to predict where a given
species may be stable in aqueous solution. This stability can
be expressed in terms of the stability field
(aka Pourbaix diagram).
|The Stability Field of Water
When a reducing agent that can reduce water to
H2, or an oxidizing agent which can oxidize water
to O2, is placed in water, the reduction or oxidation
reaction will take place, and the species will decompose, and
hence it is unstable. A species is therefore stable if its reduction
potential lies in the range 0 < E < +1.23 V, 0 V being
E*(H+/H2) and +1.23 V being
the reduction potentials change with pH, and so the range of
stable reduction potentials also changes.
The variation of stable reduction potentials with
pH is shown in the stability field plot, and in water, the stable
species are those which have reduction potentials lying between
the solid black lines.
If the effects of kinetic control are taken
into account, the need for the presence of the overpotential
predicts stability for those species with reduction potentials
in the range between the dashed black lines.
The vertical lines on the diagram have been added
to show the range of pH values commonly found in lakes and streams,
pH values between 4 and 9. Hence the area in the middle of the
diagram represents the area of stability in natural waters.