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. `(iii) lt (ii) 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 presence of potential reactants.

### Step-by-Step Solution:

1. **Understanding AgBr Dissociation**:
AgBr dissociates in water to form Ag⁺ and Br⁻ ions:
\[ \text{AgBr (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Br}^- (aq) \]

2. **Analyzing Each Solution**:
- **(i) 0.1 M NH₃**:
- NH₃ does not provide Ag⁺ or Br⁻ ions. However, it can react with Ag⁺ to form complex ions (Ag(NH₃)₂⁺), which can increase the solubility of AgBr by reducing the concentration of free Ag⁺ ions in solution. Thus, there is no common ion effect here.

- **(ii) 0.1 M AgNO₃**:
- AgNO₃ dissociates to give Ag⁺ ions. The presence of Ag⁺ ions will decrease the solubility of AgBr due to the common ion effect, shifting the equilibrium to the left. Thus, the solubility of AgBr will be lower in this solution.

- **(iii) 0.2 M NaBr**:
- NaBr dissociates to give Br⁻ ions. The presence of Br⁻ ions will also decrease the solubility of AgBr due to the common ion effect, shifting the equilibrium to the left. Since NaBr provides a higher concentration of Br⁻ (0.2 M) compared to AgNO₃ (0.1 M Ag⁺), the solubility of AgBr will be even lower in this solution compared to that in AgNO₃.

- **(iv) Pure Water**:
- In pure water, there are no common ions present, so AgBr will have its maximum solubility compared to the other solutions.

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

### Final Order of Solubility:
1. 0.2 M NaBr (least soluble)
2. 0.1 M AgNO₃
3. Pure Water
4. 0.1 M NH₃ (most soluble)

Thus, the increasing order of solubility of AgBr in the given solutions is:
\[ \text{0.2 M NaBr} < \text{0.1 M AgNO₃} < \text{Pure Water} < \text{0.1 M NH₃} \]