https://doi.org/10.1351/goldbook.09068
Fundamental equation in electrochemistry that describes the dependence of the equilibrium electrode potential on the composition of the contacting phases, written as a reduction: \[E_{\rm{eq}} = E^{\circ}\!-\!(RT/zF)\mathop \sum \limits_i \nu _i \ln(a_i)\] where \(E_{\rm{eq}}\) is the equilibrium electrode potential, \(E^{\circ}\) the standard electrode potential of the reaction, \(R\) the gas constant, \(T\) the thermodynamic temperature, \(F\) the Faraday constant, \(z\) the electron number of an electrochemical reaction, and \(\nu_{\rm{i}}\) are the stoichiometric coefficients (numbers of species) in the equation of the electrode reaction, positive for products and negative for reactants, while \(a_{\rm{i}}\) represents the activities of the species involved (most usually ions).
Notes:
- For a solution containing oxidized (ox) and reduced (red) forms of a redox couple at activities \(a_{\rm{ox}}\) and \(a_{\rm{red}}\), respectively, the equilibrium electrode potential is \[E_{\rm{eq}} = E^{\circ}\!-\!(RT/zF)\ln(a_{\rm{red}}/a_{\rm{ox}})\] where \(E^{\circ}\) is the standard electrode potential of the redox couple.
- In analytical chemistry, concentrations, rather than activities, are often considered (see Note to formal electrode potential) \[E_{\rm{eq}} = E^{\circ\prime}\!-\!(RT/zF)\ln(c_{\rm{red}}/c_{\rm{ox}})\] where \(E^{\circ\prime}\) is the formal potential which can differ from the standard electrode potential owing to the influence of real conditions (pH, ionic strength, concentration of complex forming substances, etc.), and \(c_{\rm{red}}\) and \(c_{\rm{ox}}\) are the amount concentrations of reduced and oxidized species, respectively. At \(\pu{25^{\circ}C}\), and for practical purposes, this equation is often written as \[E_{\rm{eq}} \approx E^{\circ\prime}\!-\!(0.0592/z)\log_{10}(c_{\rm{red}}/c_{\rm{ox}})\] where the factor \(0.0592 \approx (RT/F)/{\rm{log}}_{10}(\rm{e})\) at \(\pu{298.15 K}\).