## electrode reaction rate constants

Also contains definitions of: conditional rate constant of an electrode reaction, standard rate constant of an electrode reaction
https://doi.org/10.1351/goldbook.E01961
The electrode reaction rate constants are related to the partial currents by $k_{\mathrm{ox}}=\frac{l_{\text{a}}}{n\ F\ A\ \Pi\: c_{i}^{\nu _{i}}}$ $k_{\mathrm{red}}=\frac{l_{\text{c}}}{n\ F\ A\ \Pi\:c_{i}^{\nu _{i}}}$ where kox and kred are the rate constants for the oxidizing (anodic) and reducing (cathodic) reactions respectively, n is the charge number of the cell reaction, F is the Faraday constant and A is the geometric area of the electrode, the product Π c i ν i includes all the species i which take part in the partial reaction, ci is the volume concentration of species i and ν i is the order of the reaction with respect to species i. The conditional rate constant of an electrode reaction is the value of the electrode reaction rate constant at the conditional (formal) potential of the electrode reaction. When α the transfer coefficient is independent of potential, $k_{\text{c}} = \frac{k_{\text{ox}}}{\text{e}^{\frac{\alpha _{\text{a}}\ (E- E_{\text{c}}^{0'})\ n\ F}{\nu \ R\ T}}} = \frac{k_{\text{red}}}{\text{e}^{\frac{-\alpha _{\text{c}}\ (E- E_{\text{c}}^{0'})\ n\ F}{\nu \ R\ T}}}$ where αa and αc are the anodic and cathodic transfer coefficients respectively, E is the electric potential difference, E c is the conditional (formal) potential, ν is the stoichiometric number, R is the gas constant and T is the thermodynamic temperature. Similar rate constants can be defined using activities in place of concentrations in the first two equations, and the standard electrode potential in place of the conditional potential in the latter two equations. This type of rate constant is called the standard rate constant of the electrode reaction. The observable electrode rate constant is the constant of proportionality expressing the dependence of the rate of the electrode reaction on the interfacial concentration of the chemical species involved in the reaction.
Sources:
PAC, 1974, 37, 499. 'Electrochemical nomenclature' on page 515 (https://doi.org/10.1351/pac197437040499)
PAC, 1980, 52, 233. 'Electrode Reaction Orders, Transfer Coefficients and Rate Constants. Amplification of Definitions and Recommendations for Publication of Parameters' on page 236 (https://doi.org/10.1351/pac198052010233)