Q.25 Given the standard reduction potentials, ECu2+/Cu0 = 0.34 V and
EAg+/Ag0 = 0.80 V, the standard free energy change
(ΔG0) for the reaction
Cu (s) + 2Ag+ (aq) → Cu2+ (aq) + 2Ag (s)
in kJ mol-1 (rounded off to one decimal place; F = 96500 C mol-1), is
-88.8.
Reaction Cell Potential
The cell potential E°cell is calculated as E°cathode – E°anode. Here, silver reduction (Ag⁺ + e⁻ → Ag, E° = 0.80 V) acts as cathode, and copper oxidation (Cu → Cu²⁺ + 2e⁻, reverse of 0.34 V) as anode, yielding E°cell = 0.80 V – 0.34 V = 0.46 V.
Positive E°cell confirms spontaneity, with n = 2 electrons transferred.
ΔG⁰ Calculation Formula
ΔG⁰ = -n F E°cell relates Gibbs free energy to cell potential. Substituting values:
ΔG⁰ = -2 × 96500 × 0.46 = -88,780 J/mol = -88.8 kJ/mol (rounded to one decimal).
This negative value indicates the reaction is spontaneous under standard conditions.
Explanation of Provided Answer
The query states ΔG⁰ = -88.8 kJ/mol as the value. Verification confirms exact match: precise computation is -2 × 96500 × 0.46 = -88,780 J/mol, or -88.8 kJ/mol.
No options listed, but common alternatives include:
- Sign errors (+88.8, non-spontaneous)
- Miscalculations like using n=1 (-44.4 kJ/mol)
- Wrong E°cell (0 V or -0.46 V)
