The least soluble compound (salt) of the following is

Options

A. CsCl` (K_(sp) = 10^(-12))`
B. HgS `(K_(sp) = 1xx 10^(-52))`
C. `PbCl_(2) (K_(sp) = 1.7 xx 10^(-5))`
D. `ZnS (K_(sp) = 1.2 xx 10^(-23))`

Answer

To determine the least soluble compound from the given options, we will calculate the solubility of each compound based on their solubility product constant (Ksp) values.

### Step-by-Step Solution:

1. **Identify the Compounds and Their Ksp Values:**
- Option 1: CsCl3, Ksp = \(10^{-12}\)
- Option 2: HgS, Ksp = \(10^{-52}\)
- Option 3: PbCl2, Ksp = \(1.7 \times 10^{-5}\)
- Option 4: ZnS, Ksp = \(1.2 \times 10^{-23}\)

2. **Calculate the Solubility for Each Compound:**

- **For CsCl3:**
- Dissociation: \(CsCl_3 \rightarrow Cs^+ + 3Cl^-\)
- Let the solubility of CsCl3 be \(s\).
- Ksp = \(s \cdot (3s)^3 = 27s^4\)
- Given Ksp = \(10^{-12}\), we have:
\[ 27s^4 = 10^{-12} \implies s^4 = \frac{10^{-12}}{27} \implies s = \left(\frac{10^{-12}}{27}\right)^{1/4} \]
- Solubility \(s \approx 10^{-3}\) (approximately).

- **For HgS:**
- Dissociation: \(HgS \rightarrow Hg^+ + S^{2-}\)
- Let the solubility be \(s\).
- Ksp = \(s^2\)
- Given Ksp = \(10^{-52}\), we have:
\[ s^2 = 10^{-52} \implies s = 10^{-26} \]

- **For PbCl2:**
- Dissociation: \(PbCl_2 \rightarrow Pb^{2+} + 2Cl^-\)
- Let the solubility be \(s\).
- Ksp = \(s \cdot (2s)^2 = 4s^3\)
- Given Ksp = \(1.7 \times 10^{-5}\), we have:
\[ 4s^3 = 1.7 \times 10^{-5} \implies s^3 = \frac{1.7 \times 10^{-5}}{4} \implies s \approx 1.69 \times 10^{-2} \]

- **For ZnS:**
- Dissociation: \(ZnS \rightarrow Zn^{2+} + S^{2-}\)
- Let the solubility be \(s\).
- Ksp = \(s^2\)
- Given Ksp = \(1.2 \times 10^{-23}\), we have:
\[ s^2 = 1.2 \times 10^{-23} \implies s = \sqrt{1.2 \times 10^{-23}} \approx 3.46 \times 10^{-12} \]

3. **Compare the Solubility Values:**
- CsCl3: \(s \approx 10^{-3}\)
- HgS: \(s = 10^{-26}\)
- PbCl2: \(s \approx 1.69 \times 10^{-2}\)
- ZnS: \(s \approx 3.46 \times 10^{-12}\)

4. **Determine the Least Soluble Compound:**
- The solubility values indicate that HgS has the least solubility at \(10^{-26}\).

### Conclusion:
The least soluble compound among the given options is **HgS**.