The addition of `K_(2)CO_(3) (aq)` to the following solution is expected to produce a precipitate in every case but that one which does not produce precipitate is:

Options

A. `BaCl_(2) (aq)`
B. `CaCr_(2) (aq)`
C. `Na_(2)SO_(4) (aq)`
D. `Pb(NO_(3))_(2)(aq)`

Answer

To solve the problem of which solution does not produce a precipitate when K2CO3 (potassium carbonate) is added, we will analyze the solubility of the carbonates formed from the given solutions.

### Step-by-Step Solution:

1. **Identify the Solutions**: The question implies that there are multiple solutions being considered. Let's assume they are:
- A) BaCl2 (Barium Chloride)
- B) CaCl2 (Calcium Chloride)
- C) Na2SO4 (Sodium Sulfate)
- D) Pb(NO3)2 (Lead Nitrate)

2. **Reactions with K2CO3**:
- When K2CO3 is added to each of these solutions, the following reactions occur:
- **BaCl2 + K2CO3 → BaCO3 (s) + 2 KCl**
- Barium carbonate (BaCO3) is insoluble and will precipitate.
- **CaCl2 + K2CO3 → CaCO3 (s) + 2 KCl**
- Calcium carbonate (CaCO3) is also insoluble and will precipitate.
- **Na2SO4 + K2CO3 → Na2CO3 (aq) + K2SO4**
- Sodium carbonate (Na2CO3) is soluble in water and will not precipitate.
- **Pb(NO3)2 + K2CO3 → PbCO3 (s) + 2 KNO3**
- Lead carbonate (PbCO3) is insoluble and will precipitate.

3. **Conclusion**:
- From the above reactions, we can see that BaCl2, CaCl2, and Pb(NO3)2 will all produce precipitates when K2CO3 is added, while Na2SO4 will not produce a precipitate because Na2CO3 is soluble in water.

4. **Final Answer**:
- The solution that does not produce a precipitate when K2CO3 is added is **C) Na2SO4**.