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:
(in V) is the standard potential of the redox reaction,
(in V) is the applied potential,
is the gas constant (
is the Faraday constant (
(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).
) is the surface area of the electrode, [Ox] and [Red] are the concentrations of the oxidant and reductor, and, replacing
, we have
This is called the Butler–Volmer equation, the fundamental relationship between current and applied potential.
This Demonstration shows that
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.