In which of the following solutions the solubility of AgCI will be maximum?

Options

A. `0.1 M AgNO_(3)`
B. water
C. `0.1 M NaCI`
D. 0.1 M KCI

Answer

To determine in which of the following solutions the solubility of AgCl will be maximum, we need to consider the common ion effect and how it affects the solubility of sparingly soluble salts like AgCl.

### Step-by-Step Solution:

1. **Understanding the Dissolution of AgCl**:
- AgCl is a sparingly soluble salt that dissociates in water according to the following equilibrium:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
- The solubility product constant (Ksp) for AgCl is given by:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]

2. **Analyzing the Effect of Common Ions**:
- The presence of a common ion in the solution will affect the solubility of AgCl. The common ion effect states that the solubility of a salt decreases in a solution that already contains one of its constituent ions.
- If we add a soluble salt that provides either Ag⁺ or Cl⁻ ions, it will shift the equilibrium to the left, reducing the solubility of AgCl.

3. **Considering Different Solutions**:
- **Water**: Pure water does not contain any common ions, so AgCl will have its maximum solubility here.
- **AgNO3 Solution**: AgNO3 dissociates into Ag⁺ and NO3⁻. The presence of Ag⁺ will decrease the solubility of AgCl due to the common ion effect.
- **NaCl Solution**: NaCl dissociates into Na⁺ and Cl⁻. The presence of Cl⁻ will also decrease the solubility of AgCl due to the common ion effect.
- **KCl Solution**: Similar to NaCl, KCl dissociates into K⁺ and Cl⁻, which will also decrease the solubility of AgCl.

4. **Conclusion**:
- The maximum solubility of AgCl will be in pure water since it does not contain any common ions that would shift the equilibrium and reduce the solubility of AgCl.

### Final Answer:
The solubility of AgCl will be maximum in pure water.