Chemistry / Unit 11 Chem 2193 worked example, 60 to 90 seconds
Calculating K from E°cell
The idea
Calculating an equilibrium constant from a standard cell potential means combining ΔG° = −nFE°cell and ΔG° = −RT ln K into ln K = nFE°cell/RT, then solving for K by exponentiating both sides.
In practice
For a two-electron reaction with E°cell = 0.463 V at 298 K, ln K = (2)(96,485)(0.463)/[(8.314)(298)] ≈ 36.0, so K ≈ 4.3 × 10¹⁵, an extremely large constant consistent with the strongly favorable, decisively spontaneous potential this cell already reports. The same K could equally be reached through ΔG° first (Chem 2133), the two routes agreeing since both trace back to one electron-transfer reaction.
Where people slip
Using the wrong electron count n, rather than the number matching the balanced overall equation, scales the exponent incorrectly and produces a badly wrong K, often by many orders of magnitude.
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