Sulfide Precipitation in Acidified Solution of Metal Ions

To determine which metal ions will precipitate upon passing $\mathrm{H}_2\mathrm{S}$ gas into an acidified aqueous solution, we analyze the principles of qualitative inorganic analysis and solubility products ($K_{\text{sp}}$):

1. Equilibrium of Hydrogen Sulfide in Acidic Medium:
   Hydrogen sulfide ($\mathrm{H}_2\mathrm{S}$) is a weak diprotic acid that ionizes in aqueous solution:
   $\mathrm{H}_2\mathrm{S}_{(\text{aq})} \rightleftharpoons 2\mathrm{H}^+_{(\text{aq})} + \mathrm{S}^{2-}_{(\text{aq})}$
   In an acidified medium (containing dilute strong acid, such as $\mathrm{HCl}$), the high concentration of $\mathrm{H}^+$ ions suppresses the dissociation of $\mathrm{H}_2\mathrm{S}$ due to the common ion effect. Consequently, the equilibrium concentration of sulfide ions ($[\mathrm{S}^{2-}]$) is kept extremely low.

2. Precipitation Condition:
   A metal sulfide $\mathrm{MS}$ precipitates only if the ionic product exceeds its solubility product:
   $[\mathrm{M}^{2+}][\mathrm{S}^{2-}] > K_{\text{sp}}(\mathrm{MS})$

3. Comparison of Solubility Products ($K_{\text{sp}}$):

   • Group II cations ($\mathrm{Cu}^{2+}, \mathrm{Hg}^{2+}$):
     The solubility products of $\mathrm{CuS}$ and $\mathrm{HgS}$ are extremely small:
     $K_{\text{sp}}(\mathrm{CuS}) \approx 6 \times 10^{-36}$
     $K_{\text{sp}}(\mathrm{HgS}) \approx 1 \times 10^{-52}$
     Because these values are exceptionally low, even the minuscule concentration of $\mathrm{S}^{2-}$ present in the acidified solution is sufficient to exceed the solubility products, resulting in the precipitation of $\mathrm{CuS}$ and $\mathrm{HgS}$.

   • Group IV cations ($\mathrm{Ni}^{2+}, \mathrm{Mn}^{2+}$):
     The solubility products of $\mathrm{NiS}$ and $\mathrm{MnS}$ are considerably higher:
     $K_{\text{sp}}(\mathrm{NiS}) \approx 3 \times 10^{-19}$
     $K_{\text{sp}}(\mathrm{MnS}) \approx 2 \times 10^{-13}$
     Under acidic conditions, the ionic product $[\mathrm{M}^{2+}][\mathrm{S}^{2-}]$ does not exceed their relatively high $K_{\text{sp}}$ values. Hence, $\mathrm{Ni}^{2+}$ and $\mathrm{Mn}^{2+}$ do not precipitate (they precipitate as sulfides only in basic medium, such as in the presence of $\mathrm{NH}_4\mathrm{OH}/\mathrm{NH}_4\mathrm{Cl}$).

Therefore, only $\mathrm{CuS}$ and $\mathrm{HgS}$ will precipitate from the acidified mixture.

Correct Option: (A)