Delta G = -nFE: Cell Potential and Spontaneity

ΔG = -nFE connects thermodynamics to electrochemistry. A positive cell potential means a negative ΔG, so the reaction is spontaneous. Use ΔG° = -nFE° at standard conditions.

Variables

• n: moles of electrons transferred in the balanced reaction.
• F: Faraday constant, 96,485 C per mole of electrons (about 10^5 for MCAT estimates).
• E: cell potential in volts. Volts times coulombs gives joules.

Sign rules

Do not multiply E° by n when you combine half-reactions. Potential is intensive, so E°cell = E°cathode - E°anode no matter how you scale the equation. ΔG does scale with n.

Link to K

At equilibrium ΔG = 0, so E = 0. Combining ΔG° = -RT ln K and ΔG° = -nFE° gives E° = (RT/nF) ln K. At 25 °C this is about E° = (0.0592/n) log K. A positive E° means K > 1.

Worked example

Zn + Cu²⁺ → Zn²⁺ + Cu has E° = 1.10 V and n = 2.

ΔG° = -(2)(96,485)(1.10) ≈ -212,000 J/mol, about -212 kJ/mol. It is negative, so it is spontaneous, and K is much greater than 1.

Common traps

• Using kJ with volts. Convert J to kJ before comparing.
• Doubling E° when you double the equation.
• Dropping the negative sign.

One-minute recap

• ΔG = -nFE; spontaneous when E > 0.
• E° scales with nothing; ΔG scales with n.
• Positive E° means K > 1.