Which of the following correctly represents the balanced half-reactions for the redox reaction MnO_4^- + Fe^{2+} → Mn^{2+} + Fe^{3+} in acidic solution?

• A. Oxidation: Fe^{2+} → Fe^{3+} + e^-; Reduction: MnO_4^- + 8H^+ + 5e^- → Mn^{2+} + 4H_2O
• B. Oxidation: Fe^{2+} + e^- → Fe^{3+}; Reduction: MnO_4^- + 4H^+ + 5e^- → Mn^{2+} + 2H_2O
• C. Oxidation: Fe^{2+} → Fe^{3+} + e^-; Reduction: MnO_4^- + 2H^+ + 5e^- → Mn^{2+} + H_2O
• D. Oxidation: Fe^{2+} → Fe^{3+} + 2e^-; Reduction: MnO_4^- + 8H^+ + 3e^- → Mn^{2+} + 4H_2O

Answer: (A)

Verified step by step guidance

1. Identify the species being oxidized and reduced. Here, Fe^{2+} is oxidized to Fe^{3+}, and MnO_4^- is reduced to Mn^{2+}.
2. Write the oxidation half-reaction by showing Fe^{2+} losing electrons to become Fe^{3+}. The general form is: \(\mathrm{Fe^{2+} \rightarrow Fe^{3+} + e^-}\).
3. Write the reduction half-reaction for permanganate ion (MnO_4^-) in acidic solution. Start with \(\mathrm{MnO_4^-}\) and add \(\mathrm{H^+}\) ions and electrons to balance oxygen and charge, forming \(\mathrm{Mn^{2+}}\) and water.
4. Balance oxygen atoms by adding \(\mathrm{H_2O}\) molecules on the appropriate side, and balance hydrogen atoms by adding \(\mathrm{H^+}\) ions.
5. Balance the charge by adding electrons (\(e^-\)) to the side that needs them so that both mass and charge are balanced in each half-reaction.