At the electrode surface, the redox reaction can be written:
. Assume that there is only reductor in the solution with concentration
When the diffusion is very fast, the current depends only on the kinetics. Because of the fast diffusion, the concentration at the surface of the electrode
is equal to the concentration in the bulk solution:
The reaction rates of the oxidation direction
depend on the applied potential
at the electrode:
(in V) is the standard potential of the redox reaction,
is the applied potential,
is the gas constant (8.314 J/K mol),
is the Faraday constant (96485 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.
Then current is calculated from
is the surface area of the electrode, and
is the concentration of the reductor at the surface of the electrode.
When the kinetics are very fast, the concentration at the surface of electrode
is always zero (
) because the reductor is oxidized very quickly. Then the current depends on the diffusion of the reductor from the bulk solution to the electrode surface. The current in this case depends on the rate of diffusion at the surface
, given by
is the diffusion coefficient.
This Demonstration shows that when the diffusion occurs (
) one must use equation (2) instead of equation (1) to calculate the current. The kinetics-controlled case is simpler than the diffusion-controlled case because the diffusion equation (a partial differential equation) must be solved. In this Demonstration, equation (3), a Cottrell equation, is used for a large electrode with planar diffusion.