Arrange in increasing order of solubility of AgBr in the given solutions :
(i) 0.1 M `NH_(3)` (iI) 0.1M `AgNO_(3)`
(iii) 0.2M NaBr (iv) pure water

Options

A. `(iii)lt(ii)lt(iv)lt(i)`
B. `(ii)lt(iii)lt(i)lt(iv)`
C. `(iii)lt(ii)lt(i)lt(iv)`
D. `(ii)lt(iii)lt(iv)lt(i)`

Answer

To determine the increasing order of solubility of AgBr in the given solutions, we need to analyze how each solution affects the solubility of AgBr based on the common ion effect and the formation of complexes.

### Step-by-Step Solution:

1. **Understanding the Solubility of AgBr**:
AgBr is a sparingly soluble salt which dissociates in water according to the following equilibrium:
\[ \text{AgBr (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Br}^- (aq) \]

2. **Effect of Common Ions**:
- **In 0.1 M AgNO3**: This solution provides Ag⁺ ions. The presence of Ag⁺ shifts the equilibrium to the left (according to Le Chatelier's principle), thus decreasing the solubility of AgBr due to the common ion effect.
- **In 0.2 M NaBr**: This solution provides Br⁻ ions. Similar to AgNO3, the presence of Br⁻ also shifts the equilibrium to the left, further decreasing the solubility of AgBr.

3. **Effect of Complex Formation**:
- **In 0.1 M NH3**: Ammonia can form a complex with Ag⁺ ions, specifically \([Ag(NH_3)_2]^+\). This complex formation effectively removes Ag⁺ from the solution, shifting the equilibrium to the right and increasing the solubility of AgBr.

4. **Pure Water**:
- In pure water, AgBr will dissolve to a certain extent, but there are no common ions or complexing agents present. Thus, the solubility will be higher than in the solutions with common ions but lower than in the ammonia solution.

5. **Ranking the Solubility**:
- **Lowest Solubility**: 0.2 M NaBr (due to high concentration of Br⁻)
- **Next Lowest Solubility**: 0.1 M AgNO3 (due to high concentration of Ag⁺)
- **Next Higher Solubility**: Pure Water (no common ions, moderate solubility)
- **Highest Solubility**: 0.1 M NH3 (due to complex formation)

### Final Order of Increasing Solubility:
1. 0.2 M NaBr (lowest)
2. 0.1 M AgNO3
3. Pure Water
4. 0.1 M NH3 (highest)

### Summary of Increasing Order of Solubility:
0.2 M NaBr < 0.1 M AgNO3 < Pure Water < 0.1 M NH3