The thermodynamic criterion for determining the spontaneity of a reaction is ∆G, Gibbs free energy, the maximum amount of useful work produced by a chemical reaction. In an electrochemical cell, the work done is dependent on the number of coulombs and the energy available. Thus, ∆G and EMF are related as follows:
∆G = −nFEcell
where n is the number of moles of electrons exchanged, F is Faraday’s constant, and Ecell is the EMF of the cell. Keep in mind that if Faraday’s constant is expressed in coulombs (J/V), then ∆G must be expressed in J, not kJ.
If the reaction takes place under standard conditions, then the ∆G is the standard Gibbs free energy and Ecell is the standard cell potential. The above equation then becomes:
∆G° = −nFE°cell
Recall that in the chapter on thermochemistry we derived the following equation:
∆G° = −RT ln Keq
where R is the gas constant 8.314 J/(K•mol), T is the temperature in K, and Keq is the equilibrium constant for the reaction. Combining this with the equation above, we get:
∆G° = −nFE°cell = −RT ln Keq
or simply:
nFE°cell = RT ln Keq
If the values for n, T, and Keq are known, then the E°cell for the redox reaction can be readily calculated.