Which of the following metal sulphide is soluble in hot and dil `HNO_(3)`?

Options

A. `Ag_(2)S`
B. `PbS`
C. `CdS`
D. `HgS`

Answer

To determine which metal sulfide is soluble in hot and dilute nitric acid (HNO₃), we will analyze each of the given options one by one.

### Step 1: Analyze Silver Sulfide (Ag₂S)
1. **Reaction with HNO₃**: When silver sulfide (Ag₂S) reacts with hot and dilute nitric acid, it produces silver nitrate (AgNO₃), nitrogen oxides (NO or NO₂), sulfur (S), and water (H₂O).
2. **Balanced Equation**: The balanced reaction is:
\[ 4 \text{HNO}_3 + \text{Ag}_2\text{S} \rightarrow 2 \text{AgNO}_3 + 2 \text{NO}_2 + 2 \text{H}_2\text{O} + \text{S} \]
3. **Conclusion**: Ag₂S is soluble in hot and dilute HNO₃.

### Step 2: Analyze Lead Sulfide (PbS)
1. **Reaction with HNO₃**: Lead sulfide (PbS) reacts similarly with nitric acid to produce lead nitrate (Pb(NO₃)₂), sulfur (S), nitrogen oxides (NO or NO₂), and water (H₂O).
2. **Balanced Equation**: The balanced reaction is:
\[ 8 \text{HNO}_3 + 3 \text{PbS} \rightarrow 3 \text{Pb(NO}_3\text{)}_2 + 3 \text{S} + 2 \text{NO}_2 + 4 \text{H}_2\text{O} \]
3. **Conclusion**: PbS is also soluble in hot and dilute HNO₃.

### Step 3: Analyze Cadmium Sulfide (CdS)
1. **Reaction with HNO₃**: Cadmium sulfide (CdS) reacts with nitric acid to form cadmium nitrate (Cd(NO₃)₂), sulfur (S), nitrogen oxides (NO), and water (H₂O).
2. **Balanced Equation**: The balanced reaction is:
\[ 4 \text{HNO}_3 + \text{CdS} \rightarrow \text{Cd(NO}_3\text{)}_2 + \text{S} + 2 \text{NO} + 2 \text{H}_2\text{O} \]
3. **Conclusion**: CdS is soluble in hot and dilute HNO₃.

### Step 4: Analyze Mercury Sulfide (HgS)
1. **Reaction with HNO₃**: Mercury sulfide (HgS) does not react with dilute nitric acid to form soluble products. Instead, it is generally insoluble in hot and dilute HNO₃.
2. **Conclusion**: HgS is not soluble in hot and dilute HNO₃. It is only soluble in aqua regia, which is a mixture of nitric acid and hydrochloric acid.

### Final Conclusion
The metal sulfides that are soluble in hot and dilute nitric acid are:
- Silver sulfide (Ag₂S)
- Lead sulfide (PbS)
- Cadmium sulfide (CdS)

**Correct Answer**: Options 1, 2, and 3 (Ag₂S, PbS, CdS) are soluble in hot and dilute HNO₃.

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