In which of the following the solubility of AgCl will be minimum ?

Options

A. `0.1 M NaNO_(3)`
B. Water
C. `0.1 M NaCl`
D. `0.1 M NaBr`

Explanation

To determine in which of the following solutions the solubility of AgCl will be minimum, we need to consider the common ion effect. The common ion effect states that the solubility of a salt is reduced when a common ion is added to the solution.

### Step-by-Step Solution:

1. **Identify the Salt and Its Ions**:
- AgCl dissociates in water to form Ag⁺ (silver ion) and Cl⁻ (chloride ion).
- The solubility of AgCl can be affected by the presence of either Ag⁺ or Cl⁻ ions in the solution.

2. **Consider Different Solutions**:
- We will analyze the solubility of AgCl in different solutions:
- Pure Water
- 0.1 M NaNO₃
- 0.1 M NaCl

3. **Analyze Pure Water**:
- In pure water, there are no additional ions present. Thus, AgCl will have its normal solubility.

4. **Analyze 0.1 M NaNO₃**:
- NaNO₃ dissociates into Na⁺ and NO₃⁻ ions.
- There are no common ions (Ag⁺ or Cl⁻) present, so the solubility of AgCl will remain relatively unchanged.

5. **Analyze 0.1 M NaCl**:
- NaCl dissociates into Na⁺ and Cl⁻ ions.
- The presence of Cl⁻ ions (a common ion) will suppress the ionization of AgCl due to the common ion effect.
- Therefore, the solubility of AgCl will be significantly reduced in this solution.

6. **Conclusion**:
- Among the three solutions, the solubility of AgCl will be minimum in 0.1 M NaCl due to the common ion effect from the Cl⁻ ions.

### Final Answer:
The solubility of AgCl will be minimum in **0.1 M NaCl**.