Question

For the redox reaction
\(MnO_4^-+C_2O^{2-}_4+H^+→Mn^{2+}+CO_2+H_2O\)
the correct coefficients of the reactants for the balanced equation are

• A. \(MnO^-_4-16,\ C_2O^{2-}_4-5,\ H^+-2\)
• B. \(MnO^-_4-2,\ C_2O^{2-}_4-16,\ H^+-5\)
• C. \(MnO^-_4-2,\ C_2O^{2-}_4-5,\ H^+-16\)
• D. \(MnO^-_4-5,\ C_2O^{2-}_4-16,\ H^+-2\)

Answer 1

The Correct Option is C

 To balance the redox reaction:

\(MnO_4^- + C_2O_4^{2-} + H^+ → Mn^{2+} + CO_2 + H_2O\)

we need to determine the correct stoichiometric coefficients for each reactant. We'll do this by following these steps:

1. Identify the oxidation and reduction half-reactions.
2. Balance the electrons lost and gained in the half-reactions.
3. Combine the half-reactions while ensuring that the electrons cancel out.
4. Ensure that the mass and charge are balanced for each element.

Step-by-Step Solution:

1. Identify Oxidation and Reduction Half-Reactions:
   • The permanganate ion (\(MnO_4^-\)) is reduced to \(Mn^{2+}\).
   • The oxalate ion (\(C_2O_4^{2-}\)) is oxidized to \(CO_2\).
2. Write the Half-Reactions:
   1. Reduction: \(MnO_4^- → Mn^{2+}\)
   2. Oxidation: \(C_2O_4^{2-} → CO_2\)
3. Balancing the Oxidation Half-Reaction:
   • Balance the carbon atoms: \(C_2O_4^{2-} → 2 CO_2\).
   • The change in oxidation state per oxalate ion is 2 electrons: \(C_2O_4^{2-} → 2 CO_2 + 2 e^-\).
4. Balancing the Reduction Half-Reaction:
   • Balance the oxygen atoms with water: \(MnO_4^- + 4 H_2O → Mn^{2+}\).
   • Balance the hydrogen atoms with hydrogen ions: \(MnO_4^- + 8 H^+ + 5 e^- → Mn^{2+} + 4 H_2O\).
5. Equalize the Electron Transfer:
   • The oxidation half-reaction involves 2 electrons, and the reduction half-reaction involves 5 electrons.
   • Multiply the oxidation half-reaction by 5 and the reduction half-reaction by 2 to equalize the electron transfer:
6. Combine and Simplify:
   • Combine the balanced half-reactions:
7. Check for Balance:
   • Atoms and charge are balanced:
   • Mn: 2 on each side, C: 10 on each side, O: 18 on each side, H: 16 on each side, Charge: +4 on each side.

Therefore, the balanced equation gives the correct coefficients of the reactants as:

\(MnO_4^- - 2, C_2O_4^{2-} - 5, H^+ - 16\)

Thus, the correct answer is the option with these coefficients: Option 3: \(MnO_4^--2,\ C_2O_4^{2-}-5,\ H^+-16\).