Derive the relation between the standard EMF of a cell and the equilibrium constant of its reaction. Calculate K and ΔrG° for a cell reaction with n = 2 and E°cell = 0.236 V at 298 K. (F = 96500 C mol⁻¹)

1. 1 · Start from the Nernst equation. E_cell = E°cell − (2.303RT/nF) log Q.
2. 2 · Apply equilibrium. At equilibrium E_cell = 0 and Q = K.
3. 3 · Derive the relation. E°cell = (2.303RT/nF) log K; at 298 K, log K = nE°cell ÷ 0.059.
4. 4 · Find K. log K = (2 × 0.236) ÷ 0.059 = 0.472 ÷ 0.059 = 8, so K = 1 × 10⁸.
5. 5 · Find ΔrG°. ΔrG° = −nFE°cell = −2 × 96500 × 0.236 = −45548 J mol⁻¹ ≈ −45.5 kJ mol⁻¹.
6. 6 · Interpret. ΔrG° is negative and K > 1, so the reaction is spontaneous and lies far to the right.

Scoring tip: Keep the negative sign on ΔrG°, and change J to kJ only in the last line.