Balance the following oxidation–reduction reactions that occur in basic solution. a. $\mathrm{Al}(s)+\mathrm{MnO}_{4}^{-}(a q) \rightarrow \mathrm{MnO}_{2}(s)+\mathrm{Al}(\mathrm{OH})_{4}-(a q)$ b. \(\mathrm{Cl}_{2}(g) \rightarrow \mathrm{Cl}^{-}(a q)+\mathrm{OCl}^{-}(a q)\) c. $\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \rightarrow \mathrm{NH}_{3}(g)+\mathrm{AlO}_{2}^{-}(a q)$

Oxidation half-reaction: \(\mathrm{Al}(s) \rightarrow \mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)\) Reduction half-reaction: \(\mathrm{MnO}_{4}^{-}(a q) \rightarrow \mathrm{MnO}_{2}(s)\) Notice that the Aluminum and Manganese atoms are already balanced.

Oxidation half-reaction (Balanced): \(\mathrm{Al}(s) \rightarrow \mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)\) Reduction half-reaction (Balanced): \(\mathrm{MnO}_{4}^{-}(a q) + 2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{MnO}_{2}(s) + 4\mathrm{OH}^{-}(a q)\)

Oxidation half-reaction (Balanced): \(\mathrm{Al}(s) \rightarrow \mathrm{Al}(\mathrm{OH})_{4}^{-}(a q) + 3\mathrm{e}^{-}\) Reduction half-reaction (Balanced): \(3\mathrm{e}^{-} + \mathrm{MnO}_{4}^{-}(a q) + 2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{MnO}_{2}(s) + 4\mathrm{OH}^{-}(a q)\)

Overall equation (Balanced): \(\mathrm{Al}(s)+ \mathrm{MnO}_{4}^{-}(a q) + 2 \mathrm{H}_{2} \mathrm{O}(l) \rightarrow \mathrm{MnO}_{2}(s) + \mathrm{Al}(\mathrm{OH})_{4}^{-}(a q)\) b. \(\mathrm{Cl}_{2}(g) \rightarrow \mathrm{Cl}^{-}(a q)+\mathrm{OCl}^{-}(a q)\) Following the same steps for this reaction: Oxidation half-reaction (Balanced): \(\mathrm{Cl}^{-}(a q) \rightarrow \mathrm{OCl}^{-}(a q)+2\mathrm{e}^{-}\) Reduction half-reaction (Balanced): \(\mathrm{Cl}_{2}(g) + 2\mathrm{e}^{-} \rightarrow 2\mathrm{Cl}^{-}(a q)\) Overall equation (Balanced): \(\mathrm{Cl}_{2}(g) + 2\mathrm{OH}^{-}(a q) \rightarrow \mathrm{Cl}^{-}(a q)+\mathrm{OCl}^{-}(a q) + \mathrm{H}_{2}\mathrm{O}(l)\) c. \(\mathrm{NO}_{2}^{-}(a q)+\mathrm{Al}(s) \rightarrow \mathrm{NH}_{3}(g)+\mathrm{AlO}_{2}^{-}(a q)\) Following the same steps for this reaction: Oxidation half-reaction (Balanced): \(\mathrm{Al}(s) \rightarrow \mathrm{AlO}_{2}^{-}(a q)+3\mathrm{e}^{-}\) Reduction half-reaction (Balanced): \(6\mathrm{NO}_{2}^{-}(a q) + 18\mathrm{H}_{2}\mathrm{O}(l) + 12\mathrm{e}^{-} \rightarrow 6\mathrm{NH}_{3}(g)+12\mathrm{OH}^{-}(a q)\) Note that we need to multiply the oxidation half-reaction by 4 to equalize the number of electrons in both half-reactions: Overall equation (Balanced): \(4\mathrm{Al}(s) +6\mathrm{NO}_{2}^{-}(a q) +18\mathrm{H}_{2}\mathrm{O}(l) \rightarrow 6\mathrm{NH}_{3}(g)+ 4\mathrm{AlO}_{2}^{-}(a q) +12\mathrm{OH}^{-}(a q)\)