Which of the following statement(s) is(are) correct ?

Options

A. Soluble sulphide gives black precipitate with `AgNO_(3)` solution which is soluble in hot dilute nitric acid
B. Soluble sulphide produces a yellow precipitate with a susponsion of a cadmium carbonate.
C. Sulphide ion reacts with sodium nitroprusside and gives a purple colouration
D. Free `H_(2)S` gasa reacts with form preipitate with tertradrooxide plumbates (II) solution

Explanation

To determine which of the statements regarding soluble sulfides and their reactions are correct, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement A: Soluble sulfide gives black precipitate with silver nitrate solution which is soluble in hot dilute nitric acid.**
- When soluble sulfides (like sodium sulfide, Na2S) react with silver nitrate (AgNO3), they form a black precipitate of silver sulfide (Ag2S).
- The reaction can be represented as:
\[ 2 \text{Ag}^+ + \text{S}^{2-} \rightarrow \text{Ag}_2\text{S} \downarrow \]
- This black precipitate of silver sulfide is soluble in hot dilute nitric acid, leading to the formation of silver nitrate, sulfur, nitric oxide, and water:
\[ \text{Ag}_2\text{S} + 4 \text{HNO}_3 \rightarrow 2 \text{AgNO}_3 + \text{S} + 2 \text{NO} + 2 \text{H}_2\text{O} \]
- **Conclusion:** Statement A is correct.

2. **Statement B: Soluble sulfide produces a yellow precipitate with suspension of cadmium carbonate.**
- When soluble sulfides react with cadmium ions (from cadmium carbonate), a yellow precipitate of cadmium sulfide (CdS) is formed.
- The reaction can be represented as:
\[ \text{Cd}^{2+} + \text{S}^{2-} \rightarrow \text{CdS} \downarrow \]
- **Conclusion:** Statement B is correct.

3. **Statement C: Sulfide ion reacts with sodium nitroprusside and gives purple coloration.**
- When sodium nitroprusside (Na4[Fe(CN)5NOS]) is added to a solution containing sulfide ions, a purple complex is formed, indicating the presence of sulfide ions.
- The reaction can be represented as:
\[ \text{Na}_2\text{S} + \text{Na}_4[\text{Fe(CN)}_5\text{NOS}] \rightarrow \text{purple complex} \]
- **Conclusion:** Statement C is correct.

4. **Statement D: Free H2S gas reacts to form precipitate with tetraoxide plumbates solution.**
- Hydrogen sulfide (H2S) gas reacts with lead(IV) oxide (PbO2) or lead(II) salts to form lead sulfide (PbS), which is a black precipitate.
- The reaction can be represented as:
\[ \text{H}_2\text{S} + \text{Pb}^{2+} \rightarrow \text{PbS} \downarrow + 2\text{H}^+ \]
- **Conclusion:** Statement D is correct.

### Final Conclusion:
All statements A, B, C, and D are correct.