Given the following unbalanced half-reactions:1) Fe^{2+} → Fe^{3+} + e^-2) MnO_4^- + 8H^+ + 5e^- → Mn^{2+} + 4H_2OWhich of the following is the correctly balanced overall reaction?

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

Answer: (A)

Verified step by step guidance

1. Identify the two half-reactions given: the oxidation half-reaction is \(\mathrm{Fe^{2+} \rightarrow Fe^{3+} + e^-}\) and the reduction half-reaction is \(\mathrm{MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O}\).
2. Balance the electrons lost in the oxidation half-reaction with the electrons gained in the reduction half-reaction. Since the oxidation half-reaction produces 1 electron and the reduction half-reaction consumes 5 electrons, multiply the entire oxidation half-reaction by 5 to equalize the electrons.
3. Write the multiplied oxidation half-reaction: \(\mathrm{5Fe^{2+} \rightarrow 5Fe^{3+} + 5e^-}\) and keep the reduction half-reaction as is.
4. Add the two half-reactions together, canceling out the electrons on both sides to get the overall balanced reaction.
5. Verify that atoms and charges are balanced on both sides of the overall reaction: \(\mathrm{5Fe^{2+} + MnO_4^- + 8H^+ \rightarrow 5Fe^{3+} + Mn^{2+} + 4H_2O}\).