The solubility of AgCl will be miniumum in

Options

A. 0.001 M `AgNO_(3)`
B. pure water
C. 0.01 M `CaCl_(2)`
D. 0.01 M NaCl.

Explanation

To determine the solution in which the solubility of AgCl (silver chloride) will be minimum, we need to analyze the effect of common ions on the solubility equilibrium of AgCl.

### Step-by-Step Solution:

1. **Understanding the Dissociation of AgCl:**
- AgCl dissociates in water as follows:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
- The solubility product constant (Ksp) for AgCl is given by:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]

2. **Identifying the Effect of Common Ions:**
- The presence of a common ion in solution will shift the equilibrium to the left according to Le Chatelier's principle, thereby decreasing the solubility of AgCl.

3. **Analyzing Each Solution:**
- **Pure Water:**
- Contains no common ions. Therefore, AgCl will have its normal solubility.
- **AgNO3 (0.001 M):**
- Dissociates into Ag\(^+\) and NO3\(^-\):
\[ \text{AgNO}_3 \rightarrow \text{Ag}^+ + \text{NO}_3^- \]
- The presence of Ag\(^+\) ions will decrease the solubility of AgCl.
- **CaCl2 (0.01 M):**
- Dissociates into Ca\(^{2+}\) and Cl\(^-\):
\[ \text{CaCl}_2 \rightarrow \text{Ca}^{2+} + 2\text{Cl}^- \]
- The Cl\(^-\) ions will also decrease the solubility of AgCl due to the common ion effect.
- **NaCl (0.01 M):**
- Dissociates into Na\(^+\) and Cl\(^-\):
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
- Similar to CaCl2, the presence of Cl\(^-\) ions will decrease the solubility of AgCl.

4. **Comparing the Solutions:**
- Among the solutions, NaCl and CaCl2 both provide Cl\(^-\) ions, but CaCl2 provides twice as many Cl\(^-\) ions due to its dissociation into 2 Cl\(^-\) ions for every formula unit.
- Therefore, the solution with the highest concentration of common ions (Cl\(^-\)) will lead to the least solubility of AgCl.

5. **Conclusion:**
- The solubility of AgCl will be minimum in **CaCl2 (0.01 M)** due to the higher concentration of common ions (Cl\(^-\)) compared to the other solutions.

### Final Answer:
The solubility of AgCl will be minimum in **CaCl2 (0.01 M)**.