In which of the following solvents will `AgBr` has highest solubility?

Options

A. (a) `10^(-3)M NaBr`
B. (b) `10^(-3)M NH_(4)OH`
C. (c) Pure water
D. (d) `10^(-3)M HBr`

Explanation

To determine in which solvent AgBr has the highest solubility, we will analyze the effect of different solvents on the solubility of AgBr.

### Step-by-Step Solution:

1. **Understanding the Dissociation of AgBr**:
- AgBr is a sparingly soluble salt that dissociates in water to form Ag⁺ (silver ions) and Br⁻ (bromide ions).
- The dissociation can be represented as:
\[ \text{AgBr (s)} \rightleftharpoons \text{Ag}^+ (aq) + \text{Br}^- (aq) \]

2. **Identifying the Common Ion Effect**:
- The common ion effect states that the solubility of a salt decreases in a solution that already contains one of the ions of the salt.
- In this case, if we have a solvent that contains Br⁻ ions (like NaBr or HBr), the presence of these ions will shift the equilibrium to the left, reducing the solubility of AgBr.

3. **Analyzing the Solvents**:
- **NaBr**: Contains Br⁻ ions, which will decrease the solubility of AgBr due to the common ion effect.
- **HBr**: Also contains H⁺ and Br⁻ ions, leading to the same common ion effect as NaBr, thus decreasing AgBr solubility.
- **Pure Water**: Does not contain any common ions, so AgBr will have some solubility, but it will not be as high as in other solvents.
- **NH₄OH (Ammonium Hydroxide)**: When AgBr is added to NH₄OH, it forms a complex ion Ag(NH₃)₂⁺ and Br⁻. This complex formation increases the solubility of AgBr because it removes Ag⁺ ions from the solution, shifting the equilibrium to the right.

4. **Conclusion**:
- Among the given solvents, NH₄OH will provide the highest solubility for AgBr due to the formation of a complex ion and the absence of common ions that would decrease solubility.
- Therefore, the solvent in which AgBr has the highest solubility is **NH₄OH**.

### Final Answer:
The solvent in which AgBr has the highest solubility is **NH₄OH**.

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