What is the relationship between the standard Gibbs free energy change (ΔG°) and the standard cell potential (E°cell) of an electrochemical cell?
Answer and explanation
Correct answer: B. ΔG° = -n F E°cell
- Step 1: Electrical work done by an electrochemical cell in one second equals the product of total electrical charge transferred and electrical potential: .
- Step 2: According to thermodynamics, the maximum electrical work done by a system at constant temperature and pressure equals the decrease in its Gibbs free energy: .
- Step 3: Under standard conditions, .
- Step 4: For a spontaneous galvanic cell reaction, is positive, which makes negative.
Answer
ΔG° = -n F E°cell
Why not the others: 'ΔG° = +n F E°cell' misses the essential negative sign relating free energy decrease to work output; 'ΔG° = -R T ln(E°cell)' incorrectly substitutes for the equilibrium constant ; 'ΔG° = -n F / E°cell' has incorrect dimensional units.
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