Which of the following pairs of cations ca be separated by adding `NH_(4)Cl,NH_(4)OH` and then `(NH_(4))_(2)CO_(3)` to the mixture?

Options

A. `Ca^(2+),Mg^(2+)`
B. `Ba^(2+),Sr^(2+)`
C. `Sr^(2+),Ca^(2+)`
D. `Ba^(2+),Ca^(2+)`

Answer

To solve the problem of which pairs of cations can be separated by adding `NH₄Cl`, `NH₄OH`, and then `(NH₄)₂CO₃` to the mixture, we need to analyze the behavior of each cation in the presence of these reagents.

### Step-by-Step Solution:

1. **Identify the Cations**: The pairs of cations given are:
- (a) Calcium (Ca²⁺) and Magnesium (Mg²⁺)
- (b) Barium (Ba²⁺) and Strontium (Sr²⁺)
- (c) Strontium (Sr²⁺) and Calcium (Ca²⁺)
- (d) Barium (Ba²⁺) and Calcium (Ca²⁺)

2. **Understanding the Reagents**:
- `NH₄Cl` (Ammonium Chloride) provides `NH₄⁺` ions.
- `NH₄OH` (Ammonium Hydroxide) provides hydroxide ions (OH⁻).
- `(NH₄)₂CO₃` (Ammonium Carbonate) provides carbonate ions (CO₃²⁻).

3. **Reactions with Ammonium Hydroxide**:
- When `NH₄OH` is added, it can precipitate certain cations as hydroxides. However, for the purpose of separation, we focus on the carbonate precipitation.

4. **Reactions with Ammonium Carbonate**:
- Calcium (Ca²⁺) reacts with `(NH₄)₂CO₃` to form calcium carbonate (CaCO₃), which is insoluble and precipitates out.
- Magnesium (Mg²⁺) does not form a precipitate with `(NH₄)₂CO₃` under these conditions, remaining in solution.
- Barium (Ba²⁺) and Strontium (Sr²⁺) both form their respective carbonates (BaCO₃ and SrCO₃), which are also insoluble and precipitate out.

5. **Analysis of Each Pair**:
- **Pair (a) Ca²⁺ and Mg²⁺**: Ca²⁺ precipitates as CaCO₃, while Mg²⁺ remains in solution. **They can be separated.**
- **Pair (b) Ba²⁺ and Sr²⁺**: Both Ba²⁺ and Sr²⁺ precipitate as BaCO₃ and SrCO₃ respectively. **They cannot be separated.**
- **Pair (c) Sr²⁺ and Ca²⁺**: Both Sr²⁺ and Ca²⁺ precipitate as SrCO₃ and CaCO₃ respectively. **They cannot be separated.**
- **Pair (d) Ba²⁺ and Ca²⁺**: Both Ba²⁺ and Ca²⁺ precipitate as BaCO₃ and CaCO₃ respectively. **They cannot be separated.**

6. **Conclusion**: The only pair that can be separated using the given reagents is **Calcium (Ca²⁺) and Magnesium (Mg²⁺)**.

### Final Answer:
The correct answer is **(a) Calcium (Ca²⁺) and Magnesium (Mg²⁺)**.