Explanation:
\(\begin{aligned}& \mathrm{S}^{2-}+\left(\mathrm{CH}_{3} \mathrm{COO}\right)_{2} \mathrm{~Pb} \rightarrow \underset{\text { Black ppt }}{\mathrm{PbS}} \downarrow+2 \mathrm{CH}_{3} \mathrm{COO}^{-}\end{aligned}\)
\({{\text{S}}^{{\text{2 - }}}}{\text{ + N}}{{\text{a}}_{\text{2}}}\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{5}}}{\text{NO}}} \right] \to \)
\(\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{\mathop {\left[ {{\text{Fe(CN}}{{\text{)}}_{\text{5}}}{\text{NOS}}} \right]}\limits_{{\text{Violet}}\,\,{\text{ppt}}} ^{{\text{4 - }}}}{\text{ + 2N}}{{\text{a}}^{\text{ + }}}\)
Hence, they can be distinguished by both the reagents as only \(\mathrm{S}^{2-}\) gives precipitate with these reagents, while \(\mathrm{SO}_{3}^{2-}\) does not.