The correct order of increasing solubility of AgCI in
(A) water (B) 0.1 M NaCI
(C ) 0.1 M `BaCI_2` (D) 0.1 M `NH_3` is

Options

A. `A lt B lt C lt D`
B. `B lt C lt A lt D`
C. `C lt B lt D lt A`
D. `C lt B lt A lt D`

Answer

To determine the correct order of increasing solubility of AgCl in the given solutions (A) water, (B) 0.1 M NaCl, (C) 0.1 M BaCl2, and (D) 0.1 M NH3, we can analyze the solubility of AgCl in each solution based on the common ion effect and complex formation.

### Step-by-Step Solution:

1. **Understanding AgCl Solubility**:
- AgCl (silver chloride) is a sparingly soluble salt. Its solubility can be affected by the presence of other ions in solution.

2. **Analyzing Ammonia (NH3)**:
- When AgCl is added to ammonia, it forms a complex ion: Ag(NH3)2Cl. This complex formation significantly increases the solubility of AgCl in ammonia.
- Therefore, AgCl is highly soluble in 0.1 M NH3.

3. **Analyzing Water**:
- Water is a universal solvent, and while AgCl is not highly soluble in pure water, it is more soluble than in solutions containing common ions.
- Thus, AgCl will have moderate solubility in water.

4. **Analyzing Sodium Chloride (NaCl)**:
- NaCl provides Cl⁻ ions, which contribute to the common ion effect. The presence of Cl⁻ ions decreases the solubility of AgCl due to the common ion effect.
- The concentration of Cl⁻ in 0.1 M NaCl is 0.1 M, which reduces the solubility of AgCl compared to pure water.

5. **Analyzing Barium Chloride (BaCl2)**:
- BaCl2 dissociates to give 2 Cl⁻ ions for each formula unit, resulting in a Cl⁻ concentration of 0.2 M.
- The higher concentration of Cl⁻ ions in BaCl2 compared to NaCl leads to a greater common ion effect, further reducing the solubility of AgCl.

6. **Conclusion**:
- Based on the analysis, the order of increasing solubility of AgCl is:
- (C) 0.1 M BaCl2 < (B) 0.1 M NaCl < (A) water < (D) 0.1 M NH3
- Therefore, the correct order of increasing solubility is: **C < B < A < D**.

### Final Answer:
The correct order of increasing solubility of AgCl is: **C < B < A < D**.