`"Ore" overset("Calcination")to "Residue" overset("dil.HNO"_(3))tounderset("Metal"(M)+Zn^(2+)(aq.))underset(darr"Zn dust")("aq. solution")`
above metallurgy is possible when ore is :-

Options

A. `ZnCO_(3)`
B. `CaCO_(3). MgCO_(3)`
C. `CuCO_(3). Cu(OH)_(2)`
D. PbS

Answer

To solve the problem, we need to identify the ore that, when subjected to calcination, produces a residue that can be treated with dilute nitric acid (HNO3) to yield a metal and zinc ions in solution. Let's break down the steps:

### Step 1: Understanding Calcination
Calcination is a thermal treatment process where an ore is heated in the absence of air to remove volatile impurities. For carbonates, this typically results in the formation of metal oxides and the release of carbon dioxide.

### Step 2: Analyzing the Options
We have the following options:
1. ZnCO3
2. CaCO3
3. MgCO3
4. PbS

### Step 3: Performing Calcination on Each Ore
Let's analyze each option through calcination:

1. **ZnCO3 (Zinc Carbonate)**:
- Upon calcination:
\[ \text{ZnCO}_3 \rightarrow \text{ZnO} + \text{CO}_2 \uparrow \]
- Residue: ZnO

2. **CaCO3 (Calcium Carbonate)**:
- Upon calcination:
\[ \text{CaCO}_3 \rightarrow \text{CaO} + \text{CO}_2 \uparrow \]
- Residue: CaO

3. **MgCO3 (Magnesium Carbonate)**:
- Upon calcination:
\[ \text{MgCO}_3 \rightarrow \text{MgO} + \text{CO}_2 \uparrow \]
- Residue: MgO

4. **PbS (Lead Sulfide)**:
- Upon calcination:
\[ \text{PbS} + \text{O}_2 \rightarrow \text{PbO} + \text{SO}_2 \uparrow \]
- Residue: PbO

### Step 4: Treating Residue with Dilute HNO3
Now, we need to see which of these residues can react with dilute HNO3 to form an aqueous solution containing a metal ion:

1. **ZnO + HNO3**:
- Produces:
\[ \text{ZnO} + 2\text{HNO}_3 \rightarrow \text{Zn(NO}_3)_2 + \text{H}_2\text{O} \]
- Result: Aqueous Zn(NO3)2

2. **CaO + HNO3**:
- Produces:
\[ \text{CaO} + 2\text{HNO}_3 \rightarrow \text{Ca(NO}_3)_2 + \text{H}_2\text{O} \]
- Result: Aqueous Ca(NO3)2

3. **MgO + HNO3**:
- Produces:
\[ \text{MgO} + 2\text{HNO}_3 \rightarrow \text{Mg(NO}_3)_2 + \text{H}_2\text{O} \]
- Result: Aqueous Mg(NO3)2

4. **PbO + HNO3**:
- Produces:
\[ \text{PbO} + 2\text{HNO}_3 \rightarrow \text{Pb(NO}_3)_2 + \text{H}_2\text{O} \]
- Result: Aqueous Pb(NO3)2

### Step 5: Reaction with Zinc Dust
Next, we need to see which of these aqueous solutions can react with zinc dust to produce a metal:

- **Zn(NO3)2**: No reaction (zinc cannot displace itself).
- **Ca(NO3)2**: No reaction (calcium cannot be displaced).
- **Mg(NO3)2**: No reaction (magnesium cannot be displaced).
- **Pb(NO3)2**:
- Produces:
\[ \text{Pb(NO}_3)_2 + \text{Zn} \rightarrow \text{Pb} + \text{Zn(NO}_3)_2 \]
- Result: Produces lead metal.

### Conclusion
The correct ore that satisfies all the conditions is **PbS** (Lead Sulfide), which upon calcination gives PbO, reacts with dilute HNO3 to form Pb(NO3)2, and finally, zinc dust displaces lead to form lead metal.

### Final Answer
The ore is **PbS**.