The solution of which does not produce precipitate when treated with `K_(2)CO_(3)` is

Options

A. `BaCl_(2)`
B. `CaBr_(2)`
C. `MgCl_(2)`
D. `Na_(2)SO_(4)`

Explanation

To determine which solution does not produce a precipitate when treated with K2CO3, we will analyze the reactions of various compounds with potassium carbonate.

### Step-by-Step Solution:

1. **Understanding the Reaction**:
When a solution containing a metal salt is treated with K2CO3, a carbonate may form. The solubility of the resulting carbonate will determine whether a precipitate is formed or not.

2. **Analyzing Each Option**:
- **Option A**: Barium chloride (BaCl2) + K2CO3
- Reaction: BaCl2 + K2CO3 → BaCO3 (s) + 2 KCl
- Barium carbonate (BaCO3) is insoluble in water and will precipitate as a white solid.

- **Option B**: Calcium bromide (CaBr2) + K2CO3
- Reaction: CaBr2 + K2CO3 → CaCO3 (s) + 2 KBr
- Calcium carbonate (CaCO3) is also insoluble in water and will precipitate as a white solid.

- **Option C**: Magnesium chloride (MgCl2) + K2CO3
- Reaction: MgCl2 + K2CO3 → MgCO3 (s) + 2 KCl
- Magnesium carbonate (MgCO3) is slightly soluble but will still precipitate as a white solid.

- **Option D**: Sodium sulfate (Na2SO4) + K2CO3
- Reaction: Na2SO4 + K2CO3 → Na2CO3 (aq) + K2SO4 (aq)
- Sodium carbonate (Na2CO3) and potassium sulfate (K2SO4) are both soluble in water, so no precipitate will form.

3. **Conclusion**:
The solution that does not produce a precipitate when treated with K2CO3 is **Option D: Sodium sulfate (Na2SO4)**.

### Final Answer:
**Option D: Sodium sulfate (Na2SO4)** does not produce a precipitate when treated with K2CO3.

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