Thermodynamics of Redox Reactions

The thermodynamics of an oxidation/reduction reaction is the same as that found for any other chemical reaction. The only difference is that the free energies are given in terms of electrical potential with respect to an arbitrary reference state defined by the oxidation/reduction potential of hydrogen. The electrical potental is a measure of the relative energy of an electron on a molecule/atom.

An example of a normal type of redox reaction is:

Fe3+ + Cu+ <-> Fe2+ + Cu2+
This reaction can be broken down into two half reactions:

Fe3+ + e- <-> Fe2+
Cu+ <-> Cu2+ + e-
In this case the iron is reduced from the 3+ state to the 2+ state. In biological oxidations and reductions the electrons are often carried by protons (i.e. the hydrogen atom or hydride, H-). Thus, a general rule for oxidation-reduction is:
Loss of electrons or hydrogen = oxidation
Gain of electrons or hydrogen = reduction

For example, in a battery made of a solution of Fe2+/Fe3+ in one cell and hydrogen in the other, the following reactions will occur (if the concentration of each species is 1 M). The reaction as written is spontaneous. This indicates that the electron is more stable on the Fe2+ than on the Fe3+. The reaction can be written as a sum of two half-reactions:

The initial voltage across the cells will be +0.77 volts. As the iron becomes reduced (and the hydrogen oxidized), the voltage will drop, becoming zero at equilibrium. The net free energy that can be obtained from this reaction is:

The negative sign indicates that the reaction is spontaneous as written.
n is the number of electrons involved in the transfer (one in this case).
F is the Faraday constant = 96,494 C/mol = 96,494 joules/volt-mol.
∂E is the difference between the redox potential of each half-reaction.
The redox potential is the voltage obtained for a redox reaction relative to that of hydrogen, all reactants being at standard state (1 M). The standard half reaction potential (Eao) is measured relative to reduction of hydrogen at pH 0, 25°C and 1 atm H2 gas (i.e. Eao for this reaction is zero).
The free energy change of any reaction is given by the following.

This important equation is called the Nernst equation; it gives the electrical potential that can be obtained from an oxidation-reduction reaction. As with ∂Go, the standard redox potential (∂Eo) is the potential that would be observed when the concentration of the products and reactants are 1 M.

For any two redox pairs the overall redox potential is calculated according to the following (Eodonor = 0 for the reduction of hydrogen).