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Butler-Volmer Equation for Electrochemical Reaction

Unlike a chemical reaction, which depends strongly on the temperature (through the Arrhenius equation), an electrochemical reaction depends directly on the applied potential at the electrodes. This Demonstration shows the dependence of the heterogeneous electrochemical rate on the potential as described by the Butler–Volmer equation.

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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.
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