Nernst equation

The Nernst equation can be used to calculate the equilibrium constant of a galvanic cell in standard condition. It can also be used to calculate the cell potential in non-standard conditions given the current temperature and the reaction quotient.

$$\begin{array}{rl}{\xi }^{\circ }& =\frac{RT}{nF}\ln K\\ & =\frac{0.0257}{n}\ln K\\ \xi & ={\xi }^{\circ }-\frac{RT}{nF}\ln Q\\ & ={\xi }^{\circ }-\frac{0.0257}{n}\ln Q\end{array}$$

where $n$ is the number of moles of $\mathrm{e}{}^{-}$ exchanged between the oxidizing reducing agent and the oxidizing agent (i.e. number of moles of electrons on either side of balanced redox half-reactions).

Derivation

\begin{align}\Delta G & = \Delta G ^\circ + RT \ln Q \\ - nF \xi & = -nF\xi^\circ + RT \ln Q \\ \xi & = \xi^\circ - \frac{RT}{nF} \ln Q \end{align}