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)}