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. 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.

### Step-by-step Solution:

1. **Understanding the Common Ion Effect**:
- The solubility of a salt decreases when a common ion is added to the solution. For AgCl, the dissociation can be represented as:
\[ \text{AgCl (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Cl}^- (aq) \]
- If we add a solution that contains either Ag⁺ or Cl⁻ ions, the equilibrium will shift to the left according to Le Chatelier's principle, resulting in decreased solubility of AgCl.

2. **Identifying Solutions**:
- We need to evaluate the provided solutions for the presence of Ag⁺ or Cl⁻ ions. The presence of these ions will reduce the solubility of AgCl.

3. **Analyzing the Options**:
- If one of the options contains a salt that provides Ag⁺ ions (like AgNO₃), that solution will have the greatest effect on reducing the solubility of AgCl.
- For example, a 0.05 M AgNO₃ solution will provide a significant concentration of Ag⁺ ions.

4. **Conclusion**:
- Among the options provided, the solution with 0.05 M AgNO₃ will lead to the minimum solubility of AgCl due to the common ion effect, as it increases the concentration of Ag⁺ ions in the solution.

### Final Answer:
- AgCl has minimum solubility in a 0.05 M AgNO₃ solution.

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