# What is the Nernst equation?

Feb 6, 2016

${E}_{c e l l} = {E}_{c e l l}^{\circ} - \frac{R T}{n F} \ln Q$

#### Explanation:

The Nernst Equation is used to determine the cell potential ${E}_{c e l l}$ of a galvanic cell. It is given by:

${E}_{c e l l} = {E}_{c e l l}^{\circ} - \frac{R T}{n F} \ln Q$

Where, ${E}_{c e l l}^{\circ}$ is the cell potential at standard conditions,

$Q$ is the reaction quotient ,

$n$ is the number of electrons exchanged between the cathode and the anode,

$R = 8.3145 \frac{J}{m o l \cdot K}$ is the universal gas constant ,

and $F = 96485 \frac{C}{\text{mol } {e}^{-}}$ is Faraday's constant .

For example, consider the following cell at ${25}^{\circ} C$, where the reaction is:

$2 A l \left(s\right) + 3 M {n}^{2 +} \left(a q\right) \to 2 A {l}^{3 +} \left(a q\right) + 3 M n \left(s\right)$

$\left[M {n}^{2 +}\right] = 0.50 M$ and $\left[A {l}^{3 +}\right] = 1.50 M$.

$Q = \frac{{\left[A {l}^{3 +}\right]}^{2}}{{\left[M {n}^{2 +}\right]}^{3}}$

and $n = 6$ in this case.

${E}_{c e l l}^{\circ} = 0.48 V$

${E}_{c e l l} = 0.48 - \frac{8.3145 \times 298}{6 \times 96485} \ln \left(\frac{{\left(1.50\right)}^{2}}{{\left(0.50\right)}^{3}}\right) = 0.47 V$

Here is a video that explains in details the Nernst Equation and its uses:
Electrochemistry | The Concentration Cell.