Which of the following shows a balanced redox reaction in acidic solution?

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

Answer: (A)

Verified step by step guidance

1. Identify the oxidation states of manganese and iron in the reactants and products to determine which species are oxidized and which are reduced. For example, in \(\mathrm{MnO_4^-}\), manganese is typically in the +7 oxidation state, and in \(\mathrm{Mn^{2+}}\), it is +2. Iron changes from \(\mathrm{Fe^{2+}}\) to \(\mathrm{Fe^{3+}}\) or vice versa depending on the reaction.
2. Write the half-reactions for oxidation and reduction separately. For the reduction half-reaction, manganese in \(\mathrm{MnO_4^-}\) is reduced to \(\mathrm{Mn^{2+}}\). For the oxidation half-reaction, \(\mathrm{Fe^{2+}}\) is oxidized to \(\mathrm{Fe^{3+}}\).
3. Balance each half-reaction for all elements except hydrogen and oxygen first, then balance oxygen atoms by adding \(\mathrm{H_2O}\) molecules, and balance hydrogen atoms by adding \(\mathrm{H^+}\) ions (since the solution is acidic).
4. Balance the charges in each half-reaction by adding electrons (\(\mathrm{e^-}\)) to the appropriate side so that the total charge is the same on both sides of the half-reaction.
5. Combine the two half-reactions by multiplying them by appropriate coefficients so that the number of electrons lost in oxidation equals the number gained in reduction. Add the half-reactions together, canceling out electrons and any other species that appear on both sides, to get the balanced overall redox reaction.