Balance the following redox reaction under acidic aqueous conditions using the smallest whole-number coefficients possible. What is the coefficient of HSO3-? MnO4-(aq) + HSO3-(aq)... Balance the following redox reaction under acidic aqueous conditions using the smallest whole-number coefficients possible. What is the coefficient of HSO3-? MnO4-(aq) + HSO3-(aq) → Mn2+(aq) + SO4^2-(aq) Read more

Steps to Solve

1. Identify Redox Components The half-reactions need to be identified. The reduction reaction involves the conversion of $MnO_4^-$ to $Mn^{2+}$ and the oxidation reaction involves the conversion of $HSO_3^-$ to $SO_4^{2-}$.

2. Determine Oxidation States Determine the changes in oxidation states for the redox components:

   • In $MnO_4^-$, Mn is in the +7 oxidation state, and it is reduced to +2 in $Mn^{2+}$.
   • In $HSO_3^-$, sulfur is in the +4 oxidation state and is oxidized to +6 in $SO_4^{2-}$.

3. Write the Half-Reactions Write the half-reactions based on the oxidation states:

   • Reduction: $$ MnO_4^- + 8H^+ + 5e^- \rightarrow Mn^{2+} + 4H_2O $$
   • Oxidation: $$ HSO_3^- + H_2O \rightarrow SO_4^{2-} + 2H^+ + 2e^- $$

4. Balance Electrons To balance the number of electrons lost and gained, multiply the oxidation half-reaction by 5 and the reduction half-reaction by 2:

   • Reduction: $$ 2MnO_4^- + 16H^+ + 10e^- \rightarrow 2Mn^{2+} + 8H_2O $$
   • Oxidation: $$ 5HSO_3^- + 5H_2O \rightarrow 5SO_4^{2-} + 10H^+ + 10e^- $$

5. Combine the Half-Reactions Add the two half-reactions together, ensuring all components are balanced: $$ 2MnO_4^- + 5HSO_3^- + 6H^+ \rightarrow 2Mn^{2+} + 5SO_4^{2-} + 3H_2O $$

6. Determine the Coefficient of $HSO_3^-$ The coefficient of $HSO_3^-$ in the balanced equation is 5.