Balance these equations for redox reactions in basic solution. (a) \(\mathrm{MnO}_{2}(\mathrm{s})+\mathrm{ClO}_{3}^{-} \longrightarrow \mathrm{MnO}_{4}^{-}+\mathrm{Cl}^{-}\) (b) \(\mathrm{Fe}(\mathrm{OH})_{3}(\mathrm{s})+\mathrm{OCl}^{-} \longrightarrow \mathrm{FeO}_{4}^{2-}+\mathrm{Cl}^{-}\) (c) \(\mathrm{ClO}_{2} \longrightarrow \mathrm{ClO}_{3}^{-}+\mathrm{Cl}\) (d) \(\mathrm{Ag}(\mathrm{s})+\mathrm{CrO}_{4}^{2-} \rightarrow \mathrm{Ag}^{+}+\mathrm{Cr}(\mathrm{OH})_{3}(\mathrm{s})\)

Short Answer

Expert verified
The balanced chemical equations are: (a) \(4\, \mathrm{MnO}_2 + 4\, \mathrm{ClO}_3^- + 8\, \mathrm{OH}^- \rightarrow 4\, \mathrm{MnO}_4^- + 4\, \mathrm{Cl}^- + 2\, \mathrm{H}_2\mathrm{O}\), (b) \(2\, \mathrm{Fe(OH)}_3 + 5\, \mathrm{OCl}^- + 8\, \mathrm{H}_2\mathrm{O} \rightarrow 2\, \mathrm{FeO}_4^{2-} + 5\, \mathrm{Cl}^- + 8\, \mathrm{OH}^-\), (c) \(2\, \mathrm{ClO}_2 + 2\, \mathrm{OH}^- \rightarrow \mathrm{ClO}_3^- + 3\, \mathrm{Cl}^- + 2\, \mathrm{H}_2\mathrm{O}\), (d) \(\mathrm{Ag} + \mathrm{CrO}_4^{2-} + 1\, \mathrm{OH}^- \rightarrow \mathrm{Ag}^{+} + \mathrm{Cr(OH)}_3 + 4\, \mathrm{H}_2\mathrm{O}\)

Step by step solution

01

- Identify the oxidation states and which species are reduced and oxidized for each reaction

The oxidation state changes are for reaction (a) Mn (from +4 to +7), Cl (from +5 to -1), for (b) Fe (from +3 to +6), Cl (from +1 to -1), for (c) Cl (from +3 to +5 and from +3 to -1), and for (d) Ag (from 0 to +1), Cr (from +6 to +3).
02

- Balance atoms other than Hydrogen and Oxygen

In (a) the Cl atoms are already balanced and so are the Mn. In (b) the Cl and Fe atoms are already balanced. In (c) there is one ClO2 molecule and one atom each of Chlorine and ClO3-. In (d) there is one atom of Ag on each side and one CrO4 on left and one Cr on right.
03

- Balance Oxygen using H2O

Add, for (a) 4H2O to the right side, for (b) 4H2O to the left side, for (c) 2H2O to the right side, for (d) 4H2O to the right side.
04

- Balance Hydrogen using OH-

Add, for (a) 8OH- to the left side, for (b) 8OH- to the right side, for (c) 2OH- to the left, for (d) 8OH- to the left.
05

- Balance charges with e-

Balance the charges by adding, for (a) 2e- to the right side, for (b) 5e- to the left side, for (c) 2e- to the left of the first half reaction and 4e- to the right of the second half reaction, for (d) 1e- to the left side.
06

- Combine half-reactions

Combine the half reactions by adding, for (a) the reduction and oxidation half-reactions, for (b) the reduction and oxidation half reactions, for (c) the reduction half reaction to the oxidation half reaction multiplied by 2, for (d) the reduction and oxidation half reactions.

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