In which of the following solution, AgCl has minimum solubility ?

Options

A. `0.05 M AgNO_3`
B. `0.01 M CaCI_2`
C. `0.01 M NaCI`
D. `0.01 M NH_4OH`

Answer

To determine in which solution AgCl has minimum solubility, we need to consider the common ion effect and the solubility product (Ksp) of AgCl.

### Step-by-Step Solution:

1. **Understand the solubility product (Ksp)**:
AgCl is a sparingly soluble salt, and its solubility can be described by the equilibrium:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
The solubility product constant (Ksp) for this equilibrium is given by:
\[ K_{sp} = [\text{Ag}^+][\text{Cl}^-] \]

2. **Identify the common ion effect**:
The common ion effect states that the solubility of a salt is reduced in a solution that already contains one of the ions present in the salt. For AgCl, if either Ag\(^+\) or Cl\(^-\) is added to the solution, the solubility of AgCl will decrease.

3. **Analyze different solutions**:
Consider the following solutions:
- Pure water
- A solution containing NaCl
- A solution containing AgNO₃
- A solution containing KCl

In solutions containing NaCl or KCl, Cl\(^-\) ions are present, which will reduce the solubility of AgCl due to the common ion effect. In a solution containing AgNO₃, Ag\(^+\) ions are present, which will also reduce the solubility of AgCl.

4. **Determine which solution has the highest concentration of common ions**:
- In pure water, the solubility of AgCl is at its maximum.
- In NaCl or KCl solutions, the presence of Cl\(^-\) ions will decrease the solubility of AgCl.
- In AgNO₃ solution, the presence of Ag\(^+\) ions will decrease the solubility of AgCl even further.

5. **Conclusion**:
The solution in which AgCl has the minimum solubility is the one that contains the highest concentration of the common ion. Therefore, AgCl will have minimum solubility in a solution of AgNO₃.

### Final Answer:
AgCl has minimum solubility in a solution containing AgNO₃.