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.

Verified step by step guidance

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.

Key Concepts

Standard Electrode Potential (E°)

The standard electrode potential (E°) is a measure of the tendency of a chemical species to be reduced, measured under standard conditions. It is crucial for predicting the direction of redox reactions and calculating the overall cell potential. In this context, E° values for the half-reactions involving MnO4– and oxalic acid will help determine the feasibility of the reaction.

Gibbs Free Energy (∆G°)

Gibbs Free Energy (∆G°) is a thermodynamic quantity that indicates the spontaneity of a reaction at standard conditions. A negative ∆G° value suggests that a reaction is spontaneous and will proceed to completion. In this case, calculating ∆G° for the reaction will provide insight into whether the reaction between MnO4– and oxalic acid is thermodynamically favorable.

Equilibrium Constant (K)

The equilibrium constant (K) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It is related to Gibbs Free Energy by the equation ∆G° = -RT ln(K). A large K value indicates that products are favored at equilibrium, which, when calculated for the reaction, will confirm whether it goes to completion.