Chemistry · Unit 9: Applications of Thermodynamics · 45 min read · Updated 2026-05-13
Cell Potential and Free Energy — AP Chemistry
AP Chemistry · Unit 9: Applications of Thermodynamics · 45 min read
1. The Core Relationship Between E°cell and ΔG°★★☆☆☆⏱ 15 min
Each variable has a clear meaning: $n$ is the total number of moles of electrons transferred in the balanced full reaction, always a positive integer. Faraday's constant is approximated as $9.65 \times 10^4$ C/mol for AP Chemistry calculations. The negative sign creates the consistent spontaneity rule: positive $E^\circ_{\text{cell}}$ gives negative $\Delta G^\circ$ (spontaneous), while negative $E^\circ_{\text{cell}}$ gives positive $\Delta G^\circ$ (non-spontaneous).
2. Relating E°cell to the Equilibrium Constant K★★★☆☆⏱ 20 min
We can combine the relationship $\Delta G^\circ = -RT \ln K$ with $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ to get a direct connection between $E^\circ_{\text{cell}}$ and the equilibrium constant $K$. This lets us predict how far a reaction will go at equilibrium directly from cell potential data.
The same spontaneity rules apply here: $E^\circ_{\text{cell}} > 0$ means $\log K > 0$, so $K > 1$, meaning products are favored at equilibrium. $E^\circ_{\text{cell}} < 0$ means $K < 1$, so reactants are favored.
3. Summarizing Spontaneity Rules★★☆☆☆⏱ 10 min
All three thermodynamic quantities ($E^\circ_{\text{cell}}$, $\Delta G^\circ$, $K$) give consistent information about the spontaneity of a redox reaction under standard conditions. The table below summarizes all sign relationships:
Common Pitfalls
Why: The negative sign is required to match the sign conventions for $\Delta G$ (negative = spontaneous) and $E^\circ_{\text{cell}}$ (positive = spontaneous). Without it, all signs are flipped.
Why: $n$ is the total moles of electrons transferred in the full balanced reaction, which must cancel out between oxidation and reduction half-reactions.
Why: The simplified log form is derived assuming 298 K (25°C), so it is not valid at other temperatures.
Why: $E^\circ_{\text{cell}}$ only describes spontaneity under standard conditions. Non-standard conditions can make the reaction spontaneous.