The reaction of MnO₄^– with oxalic acid (H₂C₂O₄) in acidic solution, yielding Mn²⁺ and CO₂ gas, is widely used to determine the concentration of permanganate solutions. (b) Use the data in Appendix D to calculate E° for the reaction. (c) Show that the reaction goes to completion by calculating the values of ∆G° and K at 25 °C. (H₂C₂O₄) in acidic solution, yielding Mn²⁺ and CO₂ gas, is widely used to determine the concentration of permanganate solutions.

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1. Identify the half-reactions involved in the redox process. For the given reaction, the reduction half-reaction is MnO4– + 8H+ + 5e– → Mn2+ + 4H2O, and the oxidation half-reaction is H2C2O4 → 2CO2 + 2H+ + 2e–.
2. Use the standard reduction potentials from Appendix D to find the E° values for each half-reaction. The standard reduction potential for MnO4– to Mn2+ is typically given, and you will need to reverse the sign for the oxidation of H2C2O4 to CO2.
3. Calculate the standard cell potential, E°, for the overall reaction by combining the half-reactions. Use the formula E° = E°(cathode) - E°(anode). Ensure that the number of electrons lost in the oxidation half-reaction equals the number gained in the reduction half-reaction by multiplying the half-reactions by appropriate coefficients.
4. Calculate the standard Gibbs free energy change, ΔG°, using the formula ΔG° = -nFE°, where n is the number of moles of electrons transferred in the balanced equation, F is the Faraday constant (approximately 96485 C/mol), and E° is the standard cell potential.
5. Determine the equilibrium constant, K, at 25 °C using the relationship between ΔG° and K: ΔG° = -RT ln K, where R is the universal gas constant (8.314 J/mol·K) and T is the temperature in Kelvin. Solve for K to show that the reaction goes to completion.