Which of the following anion does not prodcue prepitate with `BaCl_(2)` solution however gives precipitate with `AgNO_(3)`?

Options

A. `CO_(3)^(2-)(aq.)`
B. `C_(2)O_(4)^(2-)(aq.)`
C. `MnO_(4)^(-)(aq.)`
D. `S^(2-)(aq.)`

Explanation

To solve the question of which anion does not produce a precipitate with BaCl₂ solution but does produce a precipitate with AgNO₃, we will analyze each anion provided in the options: CO₃²⁻, C₂O₄²⁻, MnO₄⁻, and S²⁻.

### Step-by-Step Solution:

1. **Identify the Anions**: The anions given are CO₃²⁻ (carbonate), C₂O₄²⁻ (oxalate), MnO₄⁻ (permanganate), and S²⁻ (sulfide).

2. **Reactions with BaCl₂**:
- **CO₃²⁻**: When CO₃²⁻ reacts with BaCl₂, it forms BaCO₃, which is a precipitate.
- **C₂O₄²⁻**: When C₂O₄²⁻ reacts with BaCl₂, it forms BaC₂O₄, which is also a precipitate.
- **MnO₄⁻**: When MnO₄⁻ reacts with BaCl₂, it does not produce a precipitate because BaMnO₄ is water-soluble.
- **S²⁻**: When S²⁻ reacts with BaCl₂, it does not produce a precipitate because BaS is water-soluble.

3. **Reactions with AgNO₃**:
- **CO₃²⁻**: When CO₃²⁻ reacts with AgNO₃, it forms Ag₂CO₃, which is a precipitate.
- **C₂O₄²⁻**: When C₂O₄²⁻ reacts with AgNO₃, it forms Ag₂C₂O₄, which is a precipitate.
- **MnO₄⁻**: When MnO₄⁻ reacts with AgNO₃, it forms AgMnO₄, which is water-soluble, so no precipitate is formed.
- **S²⁻**: When S²⁻ reacts with AgNO₃, it forms Ag₂S, which is a precipitate.

4. **Conclusion**:
- From the analysis, we find that MnO₄⁻ does not produce a precipitate with BaCl₂ (it is soluble) and does not produce a precipitate with AgNO₃ (it is also soluble).
- S²⁻ does not produce a precipitate with BaCl₂ (it is soluble) but does produce a precipitate with AgNO₃ (Ag₂S).
- Therefore, the anion that does not produce a precipitate with BaCl₂ but does produce a precipitate with AgNO₃ is **S²⁻**.

### Final Answer:
The answer is **S²⁻ (option D)**.