Precipitation of Metal Cations using Hydrogen Sulfide in Dilute Hydrochloric Acid

In qualitative inorganic analysis, the passing of $\text{H}_2\text{S}$ gas in the presence of dilute $\text{HCl}$ is the specific reagent used for the precipitation of Group II cations as their insoluble sulfides.

Theoretical Principle:

1. Common Ion Effect: Dilute $\text{HCl}$ is a strong acid that dissociates completely in water: $\text{HCl(aq)} \rightarrow \text{H}^+(\text{aq}) + \text{Cl}^-(\text{aq})$ The weak diprotic acid $\text{H}_2\text{S}$ ionizes according to the equilibrium: $\text{H}_2\text{S(aq)} \rightleftharpoons 2\text{H}^+(\text{aq}) + \text{S}^{2-}(\text{aq})$ Due to the high concentration of $\text{H}^+$ ions supplied by $\text{HCl}$, the equilibrium of $\text{H}_2\text{S}$ dissociation is shifted strongly to the left (Le Chatelier's principle).

2. Controlled $[\text{S}^{2-}]$ Concentration: This suppression minimizes the sulfide ion concentration $[\text{S}^{2-}]$ in the solution. Consequently, the ionic product exceeds the solubility product ($K_{sp}$) ONLY for metal sulfides that have extremely small $K_{sp}$ values, which corresponds specifically to Group II cations: $\text{Group II Cations: } \text{Hg}^{2+}, \text{Pb}^{2+}, \text{Bi}^{3+}, \text{Cu}^{2+}, \text{Cd}^{2+}, \text{As}^{3+}, \text{Sb}^{3+}, \text{Sn}^{2+}$

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Analysis of Options:

• Option (A) $\text{Ba}^{2+}, \text{Zn}^{2+}$:

  • $\text{Ba}^{2+}$ belongs to Group V and forms a soluble sulfide; it is precipitated as a carbonate in basic medium.
  • $\text{Zn}^{2+}$ belongs to Group IV ($K_{sp}$ of $\text{ZnS} \approx 10^{-24}$). It requires a higher $[\text{S}^{2-}]$, which is provided in basic medium ($\text{H}_2\text{S} / \text{NH}_4\text{OH}$).
  • Result: Neither cation precipitates in dilute $\text{HCl}$.

• Option (B) $\text{Bi}^{3+}, \text{Fe}^{3+}$:

  • $\text{Bi}^{3+}$ is a Group II cation and precipitates as bismuth sulfide ($\text{Bi}_2\text{S}_3$): $2\text{Bi}^{3+} + 3\text{H}_2\text{S} \rightarrow \text{Bi}_2\text{S}_3\downarrow + 6\text{H}^+$
  • $\text{Fe}^{3+}$ is reduced by $\text{H}_2\text{S}$ to $\text{Fe}^{2+}$ with the deposition of sulfur: $2\text{Fe}^{3+} + \text{H}_2\text{S} \rightarrow 2\text{Fe}^{2+} + \text{S}\downarrow + 2\text{H}^+$ $\text{Fe}^{2+}$ sulfide ($\text{FeS}$) has a higher $K_{sp}$ and does not precipitate in an acidic medium.
  • Result: Only $\text{Bi}^{3+}$ forms a metal sulfide precipitate.

• Option (C) $\text{Cu}^{2+}, \text{Pb}^{2+}$:

  • Both $\text{Cu}^{2+}$ and $\text{Pb}^{2+}$ belong to Group II.
  • $\text{Cu}^{2+}$ precipitates as black copper sulfide ($\text{CuS}$, $K_{sp} \approx 10^{-36}$): $\text{Cu}^{2+} + \text{H}_2\text{S} \rightarrow \text{CuS}\downarrow + 2\text{H}^+$
  • $\text{Pb}^{2+}$ precipitates as black lead sulfide ($\text{PbS}$, $K_{sp} \approx 10^{-28}$): $\text{Pb}^{2+} + \text{H}_2\text{S} \rightarrow \text{PbS}\downarrow + 2\text{H}^+$
  • Result: BOTH cations are precipitated.

• Option (D) $\text{Hg}^{2+}, \text{Bi}^{3+}$:

  • Both $\text{Hg}^{2+}$ and $\text{Bi}^{3+}$ belong to Group II.
  • $\text{Hg}^{2+}$ precipitates as black mercuric sulfide ($\text{HgS}$, $K_{sp} \approx 10^{-52}$): $\text{Hg}^{2+} + \text{H}_2\text{S} \rightarrow \text{HgS}\downarrow + 2\text{H}^+$
  • $\text{Bi}^{3+}$ precipitates as dark brown/black bismuth sulfide ($\text{Bi}_2\text{S}_3$, $K_{sp} \approx 10^{-99}$): $2\text{Bi}^{3+} + 3\text{H}_2\text{S} \rightarrow \text{Bi}_2\text{S}_3\downarrow + 6\text{H}^+$
  • Result: BOTH cations are precipitated.

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Conclusion:

The ion pairs in which both cations precipitate in acidic $\text{H}_2\text{S}$ solution are given by options (C) and (D).