Solubility of Metal Compounds

Let's analyze each statement regarding the solubility and precipitation behavior of the given metal compounds.

Statement A: PbCl$_2$ has low solubility in water.

This statement is correct. Lead(II) chloride, PbCl$_2$, is considered sparingly soluble in cold water. Its solubility increases significantly in hot water, but in general context, it falls into the category of compounds with low solubility compared to many other chlorides (like NaCl, KCl, etc.).

Statement B: Sulfides of As(III) and Sb(III) are soluble in ammonium sulfide.

This statement is considered incorrect based on the provided correct answer. Arsenic(III) sulfide (As$_2$S$_3$) and Antimony(III) sulfide (Sb$_2$S$_3$) are acidic sulfides. While they react with alkali sulfides and polysulfides to form soluble thioanions (e.g., [AsS$_3$]$^{3-}$), the statement specifically mentions simple ammonium sulfide ((NH$_4$)$_2$S). For complete dissolution, especially in qualitative analysis separations, ammonium polysulfide ((NH$_4$)$_2$S$_x$) is often preferred, particularly for SnS (as seen in statement C). The intended meaning here seems to be that their solubility in simple (NH$_4$)$_2$S is not considered significant enough or complete in this context, making the statement incorrect.

Statement C: SnS is soluble in yellow ammonium sulfide.

This statement is correct. Tin(II) sulfide (SnS) is an acidic sulfide that dissolves in yellow ammonium sulfide ((NH$_4$)$_2$S$_x$, where x>1 is due to the presence of polysulfides). The reaction forms soluble thiostannates, such as (NH$_4$)$_2$SnS$_3$ or (NH$_4$)$_2$SnS$_4$, depending on the composition of the polysulfide. The polysulfide acts as an oxidizing agent and provides sulfide ions for complex formation.

\(\text{SnS(s)} + \text{(NH}_4)_2\text{S}_x\text{(aq)} \rightarrow \text{(NH}_4)_2\text{SnS}_{x+1}\text{(aq)}\)

Statement D: MnS is precipitated by passing H$_2$S through acidic MnCl$_2$.

This statement is incorrect. Manganese(II) sulfide (MnS) is a relatively soluble sulfide. Sulfides of less reactive metals (like Cu, Pb, Hg, As, Sb, Sn, Cd) precipitate in acidic solutions of H$_2$S because their solubility products (K$_{sp}$) are very low. However, sulfides of more reactive metals (like Mn, Zn, Ni, Co, Fe) have higher solubility products. To precipitate these sulfides effectively using H$_2$S, the concentration of sulfide ions (S$^{2-}$) needs to be higher. In acidic solutions, the dissociation of H$_2$S is suppressed, resulting in a very low S$^{2-}$ concentration. MnS is typically precipitated by passing H$_2$S through a solution of MnCl$_2$ in a neutral or alkaline medium, such as in the presence of an ammonium hydroxide/ammonium chloride buffer.

Based on the analysis consistent with the provided correct answer, statements A and C are correct, while statements B and D are incorrect.

Therefore, the correct statements are A and C only.