Which of the following is the correctly balanced equation for the redox reaction between MnO_4^- and Fe^{2+} in acidic aqueous solution?

• A. Fe^{2+} + MnO_4^- + 2 H^+ → Fe^{3+} + Mn^{2+} + H_2O
• B. 2 Fe^{2+} + MnO_4^- + 4 H^+ → 2 Fe^{3+} + MnO_2 + 2 H_2O
• C. 5 Fe^{2+} + MnO_4^- → 5 Fe^{3+} + Mn^{2+}
• D. 5 Fe^{2+} + MnO_4^- + 8 H^+ → 5 Fe^{3+} + Mn^{2+} + 4 H_2O

Answer: (D)

Verified step by step guidance

1. Identify the oxidation and reduction half-reactions. Manganese in MnO_4^- is reduced to Mn^{2+}, and Fe^{2+} is oxidized to Fe^{3+}.
2. Write the half-reactions separately. For reduction: \(\mathrm{MnO_4^- + 8 H^+ + 5 e^- \rightarrow Mn^{2+} + 4 H_2O}\); for oxidation: \(\mathrm{Fe^{2+} \rightarrow Fe^{3+} + e^-}\).
3. Balance the electrons transferred in both half-reactions by multiplying the oxidation half-reaction by 5 so that the electrons lost and gained are equal.
4. Add the two half-reactions together, canceling out the electrons and any species that appear on both sides to get the overall balanced redox equation.
5. Verify that the atoms and charges are balanced on both sides of the final equation, ensuring the number of atoms and total charge are equal.