The post presents the generalized Nernst Equation, used in electrochemistry to convert equilibrium interface potentials to non-standard conditions.

Nernst equation

For a reduction reaction of the form:

$$ {\text{Oxidized}} + n \cdot {e^ – } \rightleftharpoons {\text{Reduced}} $$

The generalized Nernst equation can be written as:

$$ {{\text{E}}^{\text{Rev}}} = {{\text{E}}^{\text{0}}} – \left( {\frac{{R \cdot T}}{{n \cdot F}}} \right) \cdot \ln \left( {\frac{{\prod {{{\left( {{a_{{\text{Red}}}}} \right)}^j}} }}{{\prod {{{\left({{a_{Ox}}} \right)}^k}} }}} \right) $$

Where:

Term	Definition	Value	Units
\(\text{E}^{\text{Rev}}\)	Reversible Potential	–	\(\text{V vs. Reference}\)
\(\text{E}^\text{0}\)	Standard Potential	–	\(\text{V vs. Reference}\)
\(R\)	Universal Gas constant	8.3144621(75)	\(\frac{J}{{\unicode{x2103} \cdot mol}}\)
\(T\)	Temperature	–	\(\unicode{x2103}\)
\(F\)	Faraday’s constant	96,485.3399(24)	\(\frac{C}{eq}\)
\(n\)	Number electrons	–	\(\frac{eq}{mol}\)
\(a_\text{Red}\)	Activity reduced species	–	–
\(a_\text{Ox}\)	Activity oxidized species	–	–
\(j\) and \(k\)	Stoichiometric coefficients	–	–

LaTeX code

# Generalized Nernst Equation

{{\text{E}}^{{Rev}}} = {{\text{E}}^{\text{0}}} - \left( {\frac{{R \cdot T}}{{n \cdot F}}} \right) \cdot \ln \left( {\frac{{\prod {{{\left( {{a_{{\text{Rev}}}}} \right)}^j}} }}{{\prod {{{\left( {{a_{Ox}}} \right)}^k}} }}} \right)}