R3.2.14 Gibbs free energy and cell potential (Higher Level Only) Notes

Gibbs Free Energy and Standard Cell Potentials

The Equation: $ΔG^\circ = −nFE^\circ_{\text{cell}}$

1. The equation $$ΔG^\circ = −nFE^\circ_{\text{cell}}$$ links two fundamental concepts in chemistry: Gibbs free energy change ($ΔG^\circ$) and standard cell potential ($E^\circ_{\text{cell}}$).
2. Let’s break it down step by step to understand how it works.

$ΔG^\circ$ (Standard Gibbs Free Energy Change):

1. $ΔG^\circ$ represents the maximum amount of energy available to do useful work from a chemical reaction under standard conditions (298 K, 1 atm, and 1 M concentrations for all solutions).
2. The sign of $ΔG^\circ$ determines spontaneity:
   1. Negative $ΔG^\circ$:The reaction is spontaneous under standard conditions.
   2. Positive $ΔG^\circ$:The reaction is non-spontaneous under standard conditions.
   3. $ΔG^\circ=0$: The system is at equilibrium.

$E^\circ_{\text{cell}}$ (Standard Cell Potential):

1. $E^\circ_{\text{cell}}$ measures the voltage of an electrochemical cell under standard conditions.
2. It is calculated as the difference between the standard electrode potentials of the cathode (reduction) and the anode (oxidation): $$E^{\ominus}{\text{cell}} = E^{\ominus}_{\text{cathode}} - E^{\ominus}_{\text{anode}}$$
   1. A positive $E^\circ_{\text{cell}}$ corresponds to a negative $ΔG^\circ$, indicating a spontaneous reaction.
   2. Conversely, a negative $E^\circ_{\text{cell}}$ means $ΔG^\circ$ is positive, and the reaction is non-spontaneous.

n (Number of Electrons Transferred):

$n$ represents the number of moles of electrons transferred in the balanced redox reaction.