Butler-Volmer Equation for Electrochemical Reaction

At the electrode surface, the redox reaction occurs: . The reaction rates of the forward direction and backward direction depend on the applied potential at the electrode:

,

,

where (in V) is the standard potential of the redox reaction, (in V) is the applied potential, is the gas constant ( J/K mol), is the Faraday constant ( C/mol), (in K) is the temperature, is the number of electrons transferred, is the standard heterogeneous rate constant (in m/s), and is the transfer coefficient ( in this case).

The net current at the electrode is the sum of the currents in the forward (cathodic current) and backward directions (anodic current).

Then , where (m​​) is the surface area of the electrode, [Ox] and [Red] are the concentrations of the oxidant and reductor, and, replacing and , we have

.

This is called the Butler–Volmer equation, the fundamental relationship between current and applied potential.

This Demonstration shows that and change rapidly when the potential differs significantly from the standard potential . When the standard rate constant is very large, the current changes rapidly near the standard potential and the system is in a reversible state. When is small, the system is in an irreversible state.