# What is the Nernst potential?

Oct 25, 2015

$E = {E}^{\circ} - \frac{R T}{n F} \log Q$

#### Explanation:

Nernst equation is derived from the thermodynamic expression of free energy: $\Delta G = \Delta {G}^{\circ} + R T \ln Q$ and we know that $G = - n F E$, therefore, Nernst equation will be:

$E = {E}^{\circ} - \frac{R T}{n F} \log Q$

where $Q$ is the reaction quotient, $R$ is the universal gas constant $R = 8.3145 \frac{J}{m o l . K}$, $F$ is Faraday's constant $F = 96485 \frac{C}{m o l {e}^{-}}$ and $T$ is the temperature in Kelvin.

Example,

RedOx Reaction: $2 A l \left(s\right) + 3 M {n}^{2 +} \to 2 A {l}^{3 +} + 3 M n \left(s\right)$ at ${25}^{\circ} C$

${E}_{c e l l} = {E}_{c e l l}^{\circ} - \frac{0.0591}{6} \log \left({\left[A {l}^{3 +}\right]}^{2} / \left({\left[M {n}^{2 +}\right]}^{3}\right)\right)$

where $0.0591 = \frac{8.3145 \times 298}{96485} \times 2.30$ (the conversion factor between ln and log ")

Here is a video that explains this equation further: