What is electrochemistry? (b) Derive the Nernst equation and explain all terms.

The change in Gibbs free energy ($\Delta G$) for a reaction is related to the cell potential ($E$) by the equation:

$$\Delta G = -nFE$$

where $n$ is the number of moles of electrons transferred, and $F$ is Faraday's constant.

The Gibbs free energy change under non-standard conditions is related to the standard Gibbs free energy change ($\Delta G^{\circ}$) and the reaction quotient ($Q$) by:

$$\Delta G = \Delta G^{\circ} + RT \ln Q$$

where $R$ is the ideal gas constant and $T$ is the absolute temperature.

We also know that $\Delta G^{\circ} = -nFE^{\circ}$, where $E^{\circ}$ is the standard cell potential. Substituting these into the equation from Step 2:

$$-nFE = -nFE^{\circ} + RT \ln Q$$

Divide the entire equation by $-nF$:

$$E = E^{\circ} - \frac{RT}{nF} \ln Q$$

This is the Nernst equation.

Explanation of terms:

• $E$: The cell potential (or electrode potential) under non-standard conditions, measured in volts (V).
• $E^{\circ