## 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 @E01960@ 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 $$k_{\mathrm{ox}}$$ and $$k_{\mathrm{red}}$$ are the rate constants for the oxidizing (anodic) and reducing (cathodic) reactions respectively, $$n$$ is the @C00993@ of the cell reaction, $$F$$ is the @F02325@ and $$A$$ is the geometric area of the electrode, the product $$\Pi\:c_{i}^{\nu _{i}}$$ includes all the species $$i$$ which take part in the partial reaction, $$c_{i}$$ is the volume concentration of species $$i$$ and $$\nu _{i}$$ is the order of the reaction with respect to species $$i$$. The conditional rate constant of an electrode reaction is the value of the @E01960@ @O04322@ at the @C01240@ of the @E01960@. When $$\alpha$$ the transfer @C01124@ 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 $$\alpha _{\text{a}}$$ and $$\alpha _{\text{c}}$$ are the anodic and cathodic transfer coefficients respectively, $$E$$ is the @E01935@ difference, $$E_{\text{c}}$$ is the @C01240@, $$\nu$$ is the @S06025@, $$R$$ is the @G02579@ and $$T$$ is the @T06321@. Similar rate constants can be defined using activities in place of concentrations in the first two equations, and the @S05912@ in place of the conditional potential in the latter two equations. This type of @O04322@ is called the standard @O04322@ of the @E01960@. The observable electrode @O04322@ is the constant of proportionality expressing the dependence of the rate of the @E01960@ on the @I03083@ of the chemical species involved in the reaction.
Sources:
PAC, 1974, 37, 499. (Electrochemical nomenclature) on page 515 [Terms] [Paper]
PAC, 1980, 52, 233. (Electrode Reaction Orders, Transfer Coefficients and Rate Constants. Amplification of Definitions and Recommendations for Publication of Parameters) on page 236 [Terms] [Paper]