Question

An aqueous solution of \(\mathrm{SO}_{2}\) reduces (a) aqueous \(\mathrm{KMnO}_{4}\) to \(\mathrm{MnSO}_{4}(a q)\), (b) acidic aqueous \(\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}\) to aqueous \(\mathrm{Cr}^{3+}\), (c) aqueous \(\mathrm{Hg}_{2}\left(\mathrm{NO}_{3}\right)_{2}\) to mercury metal. Write balanced equations for these reactions.

Short answer

The balanced equations for the given reactions are: (a) \(8H^{+} + 5SO_{2} + 2KMnO_{4} \to 5MnSO_{4} + 8H_{2}O\) (b) \(6SO_{2} + 14H^{+} + 2K_{2}Cr_{2}O_{7} \to 4Cr^{3+} + 6SO_{4}^{2-} + 7H_{2}O\) (c) \(2Hg_{2}(NO_{3})_{2} + 4H^{+} + 2SO_{2} \to 4Hg + 2SO_{4}^{2-} + 6H^{+}\)

Step-by-step solution

Identify the products for each reaction

(a) KMnO4 + SO2 -> MnSO4 (b) K2Cr2O7 + SO2 -> Cr3+ + SO4^2- (c) Hg2(NO3)2 + SO2 -> Hg + SO4^2-

Balance the oxygens and hydrogens

(a) KMnO4 + H2O + SO2 -> MnSO4 (b) K2Cr2O7 + 7H2O + 3SO2 -> 2Cr3+ + 3SO4^2- + 14H+ (c) Hg2(NO3)2 + 2H2O + SO2 -> 2Hg + SO4^2- + 4H+

Balance the charges

(a) 8H+ + KMnO4 + 5e- + SO2 -> Mn2+ + 4H2O (b) 6e- + 14H+ + K2Cr2O7 + 3SO2 -> 2Cr3+ + 3SO4^2- + 7H2O (c) 2e- + 4H+ + Hg2(NO3)2 + SO2 -> 2Hg + SO4^2- + 6H+

Combine the half-reaction equations

(a) 8H+ + 5SO2 + 2KMnO4 -> 5MnSO4 + 8H2O (b) 6SO2 + 14H+ + 2K2Cr2O7 -> 4Cr3+ + 6SO4^2- + 7H2O (c) 2Hg2(NO3)2 + 4H+ + 2SO2 -> 4Hg + 2SO4^2- + 6H+