Arrange the following in increasing order of solubility product:
\[
{Ca(OH)}_2, {AgBr}, {PbS}, {HgS}
\]
Show Hint
- HgS<AgBr<PbS<Ca(OH)2
- PbS<HgS<Ca(OH)2<AgBr
- Ca(OH)2<AgBr<HgS<PbS
- HgS<PbS<AgBr<Ca(OH)2
The Correct Option is C
Approach Solution - 1
The solubility product constant, \(K_{sp}\), is a measure of the solubility of a compound; the smaller the \(K_{sp}\), the less soluble the compound is. To determine the increasing order of solubility product for the given compounds: \(Ca(OH)_2\), \(AgBr\), \(PbS\), and \(HgS\), we compare their \(K_{sp}\) values.
1. \({HgS}\): It has a very low \(K_{sp}\) with a value approximately in the order of \(10^{-54}\), indicating extremely low solubility.
2. \({PbS}\): This compound also has a low \(K_{sp}\) but is slightly more soluble than \(HgS\), with \(K_{sp}\) around \(10^{-28}\).
3. \({AgBr}\): It is more soluble than both \(HgS\) and \(PbS\), with a \(K_{sp}\) around \(10^{-13}\).
4. \({Ca(OH)}_2\): This compound has the highest \(K_{sp}\) among the given compounds, approximately \(10^{-6}\), making it the most soluble.
Based on these \(K_{sp}\) values, the increasing order of solubility product is:
\(HgS<PbS<AgBr<Ca(OH)_2\)
Approach Solution -2
The solubility product constant (Ksp) represents the extent to which a sparingly soluble salt dissociates in water. A smaller value of Ksp indicates lower solubility, while a larger value indicates higher solubility.
Step 2: Write the dissociation equations.
1. \( Ca(OH)_2 \rightarrow Ca^{2+} + 2OH^- \)
2. \( AgBr \rightarrow Ag^+ + Br^- \)
3. \( PbS \rightarrow Pb^{2+} + S^{2-} \)
4. \( HgS \rightarrow Hg^{2+} + S^{2-} \)
Step 3: Compare their solubility products (Ksp).
Experimental values of solubility products (approximate):
- \( K_{sp}[Ca(OH)_2] \approx 5.5 \times 10^{-6} \)
- \( K_{sp}[AgBr] \approx 5 \times 10^{-13} \)
- \( K_{sp}[HgS] \approx 1 \times 10^{-52} \)
- \( K_{sp}[PbS] \approx 3 \times 10^{-28} \)
Step 4: Arrange in increasing order of Ksp (decreasing solubility).
The smaller the Ksp, the less soluble the compound. Therefore:
\[ Ca(OH)_2 < AgBr < HgS < PbS \]
Step 5: Final Answer.
\[ \boxed{Ca(OH)_2 < AgBr < HgS < PbS} \]
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