Explanation:
Bromine water is an oxidising agent It oxidises \(\mathrm{SO}_{2}\) to \(\mathrm{SO}_{3}\) and itself gets reduced to colourless \(\mathrm{HBr}\).
\[\begin{array}{l}
{\rm{B}}{{\rm{r}}_2} + {{\rm{H}}_2}{\rm{O}} \to 2{\rm{HBr}} + [{\rm{O}}]\\
{\rm{Orange}}\,\,\,\,\,\,\,\,\,\,\,{\rm{Colourless}}\\
{\rm{red}}
\end{array}\]
\({\rm{S}}{{\rm{O}}_2} + [{\rm{O}}] \to {\rm{S}}{{\rm{O}}_3}\)
\({{\rm{H}}_2}{\rm{O}} + {\rm{S}}{{\rm{O}}_3} \to {{\rm{H}}_2}{\rm{S}}{{\rm{O}}_4}\)
\({{\rm{H}}_2}\;{\rm{S}}\) is also oxidised by bromine water but in this case, decolourisation is also accompanied by the formation of sulphur.
\({{\rm{H}}_2}\;{\rm{S}} + [{\rm{O}}] \to {{\rm{H}}_2}{\rm{O}} + {\rm{S}}\)
