Non-standard electrode potential; Fe/Ag cell emf

Non-standard electrode potential

When the concentration of the ions is not 1 M (or the gas pressure is not 1 atm, or temperature is not 25°C), the electrode potential is called a non-standard electrode potential. It is calculated with the Nernst equation: for a reduction half-reaction Mⁿ⁺ + ne⁻ → M, E = E° + (0.0591/n) log [Mⁿ⁺] at 25°C.

Reading of the data

The Ag half reaction is written with "2e⁻" and E° = −0.80 V, which is inconsistent for Ag⁺ (one electron, reduction potential +0.80 V; −0.80 V is its oxidation potential). I read it as Ag⁺ + e⁻ → Ag, E° = +0.80 V, as in the standard Fe–Ag cell. Fe²⁺/Fe: E° = −0.44 V.

Cell

Ag⁺/Ag has the higher reduction potential, so it is the cathode; Fe is the anode.

Anode  : Fe → Fe²⁺ + 2e⁻
Cathode: 2Ag⁺ + 2e⁻ → 2Ag
Cell   : Fe + 2Ag⁺ → Fe²⁺ + 2Ag     (n = 2)
Notation: Fe | Fe²⁺ (0.2 M) || Ag⁺ (0.1 M) | Ag

E°cell = 0.80 − (−0.44) = 1.24 V
Q = [Fe²⁺]/[Ag⁺]² = 0.2/(0.1)² = 20,  log Q = 1.301
E = 1.24 − (0.0591/2)(1.301)
  = 1.24 − 0.0384 = 1.2016 V

Answer: EMF ≈ 1.20 V.

(If the values were taken literally as reduction potentials, −0.44 V and −0.80 V, Ag would be the anode and E° = 0.36 V, which does not match the usual Fe–Ag cell.)