If a solution containing `Al^(3+),Ni^(3+) and Mg^(3+)` is first created with `NH_(4)Cl` and then with `NH_(4)OH`, which of the following will precipitate?

Options

A. `Al(OH)_(3)`
B. `Ni(OH)`
C. `Mg(OH)_(2)`
D. `Al(OH)_(3),Ni(OH)_(3) and Mg(OH)_(2)`

Answer

To solve the problem of determining which cation will precipitate when a solution containing \( \text{Al}^{3+}, \text{Ni}^{3+}, \) and \( \text{Mg}^{2+} \) is treated first with \( \text{NH}_4\text{Cl} \) and then with \( \text{NH}_4\text{OH} \), we can follow these steps:

### Step 1: Understand the Cations and Their Groups
- The cations in the solution are \( \text{Al}^{3+}, \text{Ni}^{3+}, \) and \( \text{Mg}^{2+} \).
- In qualitative analysis, cations are divided into groups based on their precipitation behavior with certain reagents.

### Step 2: Identify the Group of Each Cation
- \( \text{Al}^{3+} \) belongs to Group III.
- \( \text{Ni}^{3+} \) belongs to Group IV.
- \( \text{Mg}^{2+} \) belongs to Group VI.

### Step 3: Consider the Precipitation Reaction
- When \( \text{NH}_4\text{Cl} \) is added, it does not cause any precipitation. However, it prepares the solution for the addition of \( \text{NH}_4\text{OH} \).
- \( \text{NH}_4\text{OH} \) (ammonium hydroxide) will react with the cations to form their respective hydroxides.

### Step 4: Compare Solubility Products (Ksp)
- The ability of a cation to precipitate as a hydroxide is inversely related to its solubility product (Ksp).
- The lower the Ksp value, the less soluble the hydroxide, and thus it will precipitate first.

### Step 5: Determine the Ksp Values
- \( \text{Al(OH)}_3 \) (Aluminum hydroxide) has a lower Ksp compared to \( \text{Ni(OH)}_3 \) (Nickel hydroxide) and \( \text{Mg(OH)}_2 \) (Magnesium hydroxide).
- Therefore, \( \text{Al(OH)}_3 \) will precipitate first.

### Step 6: Conclusion
- When the solution is treated with \( \text{NH}_4\text{OH} \), the first hydroxide to precipitate will be \( \text{Al(OH)}_3 \).
- Thus, the answer to the question is that **Aluminum hydroxide (\( \text{Al(OH)}_3 \)) will precipitate**.

### Summary of the Steps
1. Identify the cations and their respective groups.
2. Understand that \( \text{NH}_4\text{Cl} \) does not cause precipitation but prepares for \( \text{NH}_4\text{OH} \).
3. Compare the Ksp values of the hydroxides formed.
4. Conclude that \( \text{Al(OH)}_3 \) precipitates first due to its lower Ksp.