A white crystalline substance dissolves in hot water. On passing `H_(2)S` in this solution, black precipitate is obtained. The black precipitate dissolves completely in hot `HNO_(3)`. On adding a few drops of conc. `H_(2)SO_(4)`, a white precipitate is obtained. this substance is :

Options

A. `BaSO_(4)`
B. `SrSO_(4)`
C. `PbCl_(2)`
D. `CdSO_(4)`

Explanation

To solve the problem step by step, we will analyze the information given and the reactions involved.

### Step 1: Identify the White Crystalline Substance
The problem states that a white crystalline substance dissolves in hot water. This suggests that the substance is likely a salt. Common salts that are white and soluble in hot water include lead(II) nitrate (Pb(NO3)2).

**Hint:** Look for white crystalline substances that are soluble in hot water.

### Step 2: Reaction with Hydrogen Sulfide (H₂S)
When H₂S is passed through the solution of the white crystalline substance, a black precipitate is formed. The black precipitate indicates the formation of lead(II) sulfide (PbS), which is known to be a black solid.

**Hint:** Black precipitates often indicate the formation of sulfides, especially with heavy metals like lead.

### Step 3: Dissolution in Hot Nitric Acid (HNO₃)
The black precipitate (PbS) dissolves completely in hot HNO₃. This reaction converts PbS into lead(II) nitrate (Pb(NO3)2) and releases sulfur as a byproduct. The balanced reaction can be represented as:
\[ \text{PbS} + 4 \text{HNO}_3 \rightarrow \text{Pb(NO}_3\text{)}_2 + \text{H}_2\text{O} + \text{NO}_2 + \text{S} \]

**Hint:** Strong acids like HNO₃ can dissolve metal sulfides, forming soluble metal nitrates.

### Step 4: Reaction with Concentrated Sulfuric Acid (H₂SO₄)
When a few drops of concentrated H₂SO₄ are added to the solution containing Pb(NO3)2, a white precipitate of lead(II) sulfate (PbSO4) is formed. The reaction can be represented as:
\[ \text{Pb(NO}_3\text{)}_2 + \text{H}_2\text{SO}_4 \rightarrow \text{PbSO}_4 \downarrow + 2 \text{HNO}_3 \]

**Hint:** The formation of a white precipitate upon adding concentrated sulfuric acid indicates the presence of lead ions.

### Conclusion
Based on the reactions and the observations, the original white crystalline substance is lead(II) nitrate (Pb(NO3)2), which leads to the formation of PbS and subsequently PbSO4.

**Final Answer:** The substance is lead(II) nitrate (Pb(NO3)2).