How Is Standard Cell Potential Related to Gibbs Energy? (HL)

Standard cell potential and standard Gibbs energy change are related by $\Delta G^\circ = -nFE_{\text{cell}}^\circ$. A positive $E_{\text{cell}}^\circ$ therefore gives a negative $\Delta G^\circ$, so the redox reaction is thermodynamically spontaneous under standard conditions.

This relationship is Reactivity 3.2.14 and is additional higher level (AHL) content in IB Chemistry.

In the equation:

• $\Delta G^\circ$ is the standard Gibbs energy change in $\text{J mol}^{-1}$.
• $n$ is the number of moles of electrons transferred according to the balanced overall equation.
• $F$ is the Faraday constant, .

The equation represents the maximum electrical work available from a cell under standard conditions. Its negative sign connects spontaneous electron transfer with a decrease in Gibbs energy.

For a cell with $E_{\text{cell}}^\circ = +1.10\ \text{V}$ and two moles of electrons transferred:

$$\Delta G^\circ = -(2)(96\,485)(1.10)$$ $$\Delta G^\circ = -212\,267\ \text{J mol}^{-1} \approx -212\ \text{kJ mol}^{-1}$$

The units confirm the relationship: $\text{mol e}^{-}$ and $\text{C mol}^{-1}$ combine with $\text{J C}^{-1}$ to give energy per mole of reaction. The negative result confirms spontaneity. For the same , a more positive cell potential produces a more negative Gibbs energy change.

Reaction scaling explains the different roles of $n$ and potential. If the balanced overall equation is doubled, both $n$ and $\Delta G^\circ$ double because Gibbs energy is an extensive property. However, $E_{\text{cell}}^\circ$ remains unchanged because potential measures energy transferred per unit charge rather than total energy.

A common misconception is multiplying an electrode potential by a stoichiometric coefficient. Electrode potentials are intensive properties, so they are never scaled. Balance the half-equations to find $n$, but calculate $E_{\text{cell}}^\circ$ from the unmodified electrode potentials.

Exam technique: State the formula, obtain $n$ from the balanced redox equation, convert joules to kilojoules when required, include units, and interpret the sign using the term spontaneous.