What are the oxidizing and reducing agents in the following redox reactions? (a) \(5 \mathrm{SO}_{3}^{2-}+2 \mathrm{MnO}_{4}^{-}+6 \mathrm{H}^{+} \longrightarrow\) \(5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+3 \mathrm{H}_{2} \mathrm{O}\) (b) \(2 \mathrm{NO}_{2}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\) (c) \(2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}+\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+} \longrightarrow\) \(2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}+2 \mathrm{H}_{2} \mathrm{O}\)

Firstly, identify the oxidation states of the species in the reactants and products. (a) For \(5 \mathrm{SO}_{3}^{2-}+2 \mathrm{MnO}_{4}^{-}+6 \mathrm{H}^{+} \longrightarrow 5 \mathrm{SO}_{4}^{2-}+2 \mathrm{Mn}^{2+}+3 \mathrm{H}_{2} \mathrm{O}\), in SO3^2-, S is in +6 oxidation state and in SO4^2-, it's also +6, so sulfur doesn't change. Mn in MnO4^- is +7 and in Mn^2+ it's +2; Therefore, Mn is reduced. (b) For \(2 \mathrm{NO}_{2}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})+4 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})\), N in NO2 is +4 and in NH3 it's -3; thus N is reduced. H in H2 is in 0 state and in H2O it's +1; thus H is oxidized. (c) For \(2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{4-}+\mathrm{H}_{2} \mathrm{O}_{2}+2 \mathrm{H}^{+} \longrightarrow 2\left[\mathrm{Fe}(\mathrm{CN})_{6}\right]^{3-}+2 \mathrm{H}_{2} \mathrm{O}\), in [Fe(CN)6]^4-, Fe is in +2 state and in [Fe(CN)6]^3-, Fe is is +3; Fe is therefore oxidized. H2O2 is 0 state and in H2O it's +1; H is hence reduced.

Next, assign the oxidizing and reducing agents based on the ions which have been oxidized or reduced. (a) MnO4^- is the oxidizing agent (it is reduced), and SO3^2- is the reducing agent (it is oxidized). (b) NO2 is the oxidizing agent (it is reduced), and H2 is the reducing agent (it is oxidized). (c) [Fe(CN)6]^4- is the reducing agent (it is oxidized), and H2O2 is the oxidizing agent (it is reduced).