Which of the following acid radical does not produce white ppt. with $\mathrm{Pb}{\left(\mathrm{OAc}\right)}_2$ solution?

None of the acid radicals in the options does produce white ppt. with  $\mathrm{Pb}(\mathrm{OAc}{)}_2$ solution

Either the acid radical is  ${\mathrm{SO}}_3^{2-}$or ${\mathrm{SO}}_4^{2-}$.

These radicals react with barium chloride to produce a white precipitate that can be either barium sulphite or barium sulphate.

$\begin{array}{r}{\mathrm{BaCl}}_2+{\mathrm{SO}}_3^{2-}\to {\mathrm{BaSO}}_3+2{\mathrm{Cl}}^{-}\\ {\mathrm{BaCl}}_2+{\mathrm{SO}}_4^{2-}\to {\mathrm{BaSO}}_4+2{\mathrm{Cl}}^{-}\end{array}$