The solubility of mercurous chloride in water will be given as :

Options

A. `K_(sp)(Hg_(2)Cl_(2))`
B. `sqrt(K_(sp)(Hg_(2)Cl_(2))//4)`
C. `(K_(sp)(Hg_(2)Cl_(2)))/4]^(1/2)`
D. `K_(sp)(Hg_(2)Cl_(2))^(1/3)`

Explanation

To find the solubility of mercurous chloride (Hg2Cl2) in water, we can follow these steps:

### Step-by-Step Solution:

1. **Write the Dissociation Equation:**
Mercurous chloride (Hg2Cl2) dissociates in water as follows:
\[ \text{Hg}_2\text{Cl}_2 (s) \rightleftharpoons \text{Hg}_2^{2+} (aq) + 2\text{Cl}^- (aq) \]

2. **Define Solubility:**
Let the solubility of mercurous chloride be \( S \) mol/L. This means that at equilibrium:
- The concentration of \(\text{Hg}_2^{2+}\) will be \( S \)
- The concentration of \(\text{Cl}^-\) will be \( 2S \) (since two chloride ions are produced for each formula unit of mercurous chloride that dissolves).

3. **Write the Expression for Ksp:**
The solubility product constant (\( K_{sp} \)) for the dissociation reaction is given by:
\[ K_{sp} = [\text{Hg}_2^{2+}][\text{Cl}^-]^2 \]
Substituting the concentrations we defined:
\[ K_{sp} = (S)(2S)^2 \]

4. **Simplify the Expression:**
Simplifying the expression gives:
\[ K_{sp} = S \cdot 4S^2 = 4S^3 \]

5. **Solve for Solubility (S):**
Rearranging the equation to find \( S \):
\[ S = \left( \frac{K_{sp}}{4} \right)^{\frac{1}{3}} \]

6. **Final Expression:**
Thus, the solubility of mercurous chloride in water can be expressed as:
\[ S = \left( \frac{K_{sp}}{4} \right)^{\frac{1}{3}} \]

### Conclusion:
The solubility of mercurous chloride in water is given by the expression \( S = \left( \frac{K_{sp}}{4} \right)^{\frac{1}{3}} \).