What is a disproportionation reaction, and which of the following fit the description?
(a) $\mathrm{I}_{2}(s)+\mathrm{KI}(a q) \longrightarrow \mathrm{KI}_{3}(a q)$
(b) $2 \mathrm{ClO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{HClO}_{3}(a q)+\mathrm{HClO}_{2}(a q)$
(c) $\mathrm{Cl}_{2}(g)+2 \mathrm{NaOH}(a q) \longrightarrow$
NaCl $(a q)+\mathrm{NaClO}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$
(d) $\mathrm{NH}_{4} \mathrm{NO}_{2}(s) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)$
(e) $3 \mathrm{MnO}_{4}^{2-}(a q)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow$
$2 \mathrm{MnO}_{4}-(a q)+\mathrm{MnO}_{2}(s)+4 \mathrm{OH}^{-}(a q)$
(f) $3 \mathrm{AuCl}(s) \longrightarrow \operatorname{AuCl}_{3}(s)+2 \mathrm{Au}(s)$