During operation of an electrochemical cell, chemical energy is transformed into electrical energy. This can be expressed mathematically as the product of the cells emf E measured in volts (V) and the electric charge Q' transferred through the external circuit.
:Electrical energy = EQ
Q is the cell current integrated over time and measured in coulombs (C); it can also be determined by multiplying the total number n of electrons transferred (measured in moles) times Faradays constant (F').
The emf of the cell at zero current is the maximum possible emf. It can be used to calculate the maximum possible electrical energy that could be obtained from a chemical reaction. This energy is referred to as electrical work and is expressed by the following equation:
where work is defined as positive when it increases the energy of the system.
Since the free energy is the maximum amount of work that can be extracted from a system, one can write:
A positive cell potential gives a negative change in Gibbs free energy. This is consistent with the cell production of an electric current from the cathode to the anode through the external circuit. If the current is driven in the opposite direction by imposing an external potential, then work is done on the cell to drive electrolysis.
A spontaneous electrochemical reaction (change in Gibbs free energy less than zero) can be used to generate an electric current in electrochemical cells. This is the basis of all batteries and fuel cells. For example, gaseous oxygen (O) and
hydrogen (H) can be combined in a fuel cell to form water and energy, typically a combination of heat and electrical energy.
Conversely, non-spontaneous electrochemical reactions can be driven forward by the application of a current at sufficient voltage. The electrolysis of water into gaseous oxygen and hydrogen is a typical example.
The relation between the equilibrium constant, K, and the Gibbs free energy for an electrochemical cell is expressed as follows:
Rearranging to express the relation between standard potential and equilibrium constant yields
At T = 298 K, the previous equation can be rewritten using the Briggsian logarithm as follows: