To calculate the exchange current density i0 for the oxidation of iron in a 0.1 M solution of Fe2+/Fe3+ at 25C, we can use the Butler-Volmer equation, which relates the current density i to the overpotential and the exchange current density i0 .i = i0 * exp * F * / R / T - exp - * F * / R / T Where:i = current density A/m i0 = exchange current density A/m = charge transfer coefficient dimensionless, typically around 0.5 for metal redox reactions F = Faraday's constant 96485 C/mol = overpotential V R = gas constant 8.314 J/mol K T = temperature K We are given the overpotential as 0.2 V, and the temperature T as 25C, which is equivalent to 298.15 K. We will assume = 0.5 for this calculation.First, we need to find the current density i at the given overpotential. We can use the Nernst equation to find the cell potential E at the given concentration of Fe2+/Fe3+:E = E0 - R * T / n * F * ln [Fe3+] / [Fe2+] Where:E0 = standard potential +0.77 V n = number of electrons transferred 2 for Fe2+/Fe3+ redox couple [Fe3+] = concentration of Fe3+ 0.1 M [Fe2+] = concentration of Fe2+ 0.1 M E = 0.77 - 8.314 * 298.15 / 2 * 96485 * ln 0.1 / 0.1 E = 0.77 VNow, we can find the current density i using Ohm's law:i = E / i = 0.77 / 0.2i = 3.85 A/mNow, we can use the Butler-Volmer equation to find the exchange current density i0 :3.85 = i0 * exp 0.5 * 96485 * 0.2 / 8.314 / 298.15 - exp -0.5 * 96485 * 0.2 / 8.314 / 298.15 Solving for i0, we get:i0 1.28 A/mSo, the exchange current density for the oxidation of iron in a 0.1 M solution of Fe2+/Fe3+ at 25C with a standard potential of +0.77 V and an overpotential of 0.2 V is approximately 1.28 A/m.