Which set of coefficients correctly balances the following redox reaction in acidic solution? MnO_4^- + Fe^{2+} → Mn^{2+} + Fe^{3+}

• A. 2 MnO_4^- + 10 Fe^{2+} + 8 H^+ → 2 Mn^{2+} + 10 Fe^{3+} + 4 H_2O
• B. 1 MnO_4^- + 3 Fe^{2+} + 4 H^+ → 1 Mn^{2+} + 3 Fe^{3+} + 2 H_2O
• C. 1 MnO_4^- + 5 Fe^{2+} + 4 H^+ → 1 Mn^{2+} + 5 Fe^{3+} + 2 H_2O
• D. 1 MnO_4^- + 5 Fe^{2+} + 8 H^+ → 1 Mn^{2+} + 5 Fe^{3+} + 4 H_2O

Answer: (D)

Verified step by step guidance

1. Identify the oxidation and reduction half-reactions from the overall reaction. Here, MnO_4^- is reduced to Mn^{2+}, and Fe^{2+} is oxidized to Fe^{3+}.
2. Write the half-reactions separately with their respective electrons to balance the changes in oxidation states: Reduction: \(\mathrm{MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O}\) Oxidation: \(\mathrm{Fe^{2+} \rightarrow Fe^{3+} + e^-}\)
3. Balance the electrons lost in oxidation with the electrons gained in reduction by multiplying the oxidation half-reaction by 5 so that 5 electrons are lost, matching the 5 electrons gained in the reduction half-reaction.
4. Add the two half-reactions together, canceling out the electrons, to get the overall balanced redox reaction: \(\mathrm{MnO_4^- + 8H^+ + 5Fe^{2+} \rightarrow Mn^{2+} + 4H_2O + 5Fe^{3+}}\)
5. Verify that the atoms and charges are balanced on both sides of the equation, confirming the correct coefficients for the balanced redox reaction in acidic solution.