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Cell Potential and Free Energy

Cell potential and free energy are tied together by ΔG° = −nFE°cell (n is the moles of electrons, F is Faraday's constant). A positive standard cell potential means a favorable (spontaneous) reaction. The cell potential is intensive — scaling the balanced equation does not change it — whereas ΔG is extensive (it scales).

UNIT 9 TOPIC 9.9 • CELL POTENTIAL AND FREE ENERGY ΔG° = −nFE°cell WHAT THE SYMBOLS MEAN ΔG° standard Gibbs free energy change (J·mol⁻¹) n moles of electrons transferred F Faraday constant = 96,485 C·mol⁻¹ E°cell standard cell potential (V) GALVANIC CELL (EXAMPLE) V e⁻ salt bridge Zn²⁺ Cu²⁺ Zn(s) anode oxidation (−) Cu(s) cathode reduction (+) Zn(s) | Zn²⁺(aq) ‖ Cu²⁺(aq) | Cu(s) KEY IDEA Cell potential and Gibbs free energy change are directly related. A positive E°cell gives a negative ΔG°, so the reaction is spontaneous under standard conditions. BUILT FROM HALF-CELLS E°cell = E°cathode − E°anode Both from standard reduction potentials. ΔG° = −nFE°cell n = moles of e⁻ transferred RULE OF THUMB E°cell > 0 → ΔG° < 0 spontaneous E°cell = 0 → ΔG° = 0 equilibrium E°cell < 0 → ΔG° > 0 nonspontaneous CONNECTING THE THREE E°cell ΔG° spontaneity > 0 < 0 spontaneous = 0 = 0 equilibrium < 0 > 0 nonspont. WORKED EXAMPLE Galvanic Zn/Cu cell: E°cell = +1.10 V, n = 2 ΔG° = −nFE°cell = −(2)(96,485 C·mol⁻¹)(1.10 V) = −212,267 J·mol⁻¹ ≈ −212 kJ·mol⁻¹ ΔG° < 0 → spontaneous The cell reaction is thermodynamically favorable. AP Chemistry · Unit 9 · Applications of Thermodynamics
Cell potential and free energy are linked by ΔG° = −nFE°cell. A positive standard cell potential means a favorable (spontaneous) reaction. The potential is intensive — scaling the balanced equation does not change it — while ΔG is extensive.
Cell Potential Linker · Open the sandbox →

The traps scale the cell potential when the equation is multiplied (it is intensive, unchanged), read a more negative potential as more favorable (more positive is favorable), add the two reduction potentials (cell potential is cathode minus anode), or drop the minus sign in ΔG° = −nFE°. Positive E° → negative ΔG° → favorable.

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Lesson
Cell Potential & Free Energy ›

ΔG° = −nFE°cell links potential to favorability; E° is intensive and a positive E° is favorable. The lesson computes and reasons about the sign, then closes with a ten-scenario check.

Skill check · 10 scenarios
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Diagnostic
10-item topic check ›

Ten items spanning the Topic 9.9 misconceptions: cell potential wrongly scaled (it is intensive) with the favorability sign inverted, and the cell-potential/free-energy computation (cathode minus anode, minus-sign) mishandled.

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Targeted Practice
Drill a single misconception ›

Pick one of the failure modes you missed and drill it on its own. The round is adaptive: two correct in a row clears the misconception and moves you to the next.

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