Which of the following pair of acid radicals can be distinguished by using dil `H_(2)SO_(4)`?

Options

A. `C_(2)O_(4)^(2-)` and `NO_(3)^(Θ)`
B. `NO_(3)^(Θ)` and `NO_(2)^(Θ)`
C. `Cl^(Θ)` and `Br^(Θ)`
D. `HCO_(3)^(Θ)` and `CO_(3)^(2-)`

Explanation

To solve the problem of distinguishing between pairs of acid radicals using dilute H₂SO₄, we will analyze each pair given in the options.

### Step-by-Step Solution:

1. **Identify the Acid Radicals**: The pairs of acid radicals provided in the question are:
- Option 1: Oxalate ion (C₂O₄²⁻) and Nitrate ion (NO₃⁻)
- Option 2: Nitrate ion (NO₃⁻) and Nitrite ion (NO₂⁻)
- Option 3: Chloride ion (Cl⁻) and Bromide ion (Br⁻)
- Option 4: Bicarbonate ion (HCO₃⁻) and Carbonate ion (CO₃²⁻)

2. **Analyze Option 1 (C₂O₄²⁻ and NO₃⁻)**:
- When oxalate ion (C₂O₄²⁻) is treated with dilute H₂SO₄, no gas or vapors are evolved.
- The nitrate ion (NO₃⁻) also does not react with dilute H₂SO₄.
- **Conclusion**: No distinction can be made between oxalate and nitrate ions using dilute H₂SO₄.

3. **Analyze Option 2 (NO₃⁻ and NO₂⁻)**:
- The nitrate ion (NO₃⁻) does not react with dilute H₂SO₄.
- The nitrite ion (NO₂⁻) reacts with dilute H₂SO₄ to form HNO₂, which then undergoes disproportionation to produce HNO₃ and NO gas.
- The NO gas evolved will turn into NO₂ gas in the presence of air, which is light brown in color.
- **Conclusion**: Nitrate and nitrite ions can be distinguished using dilute H₂SO₄.

4. **Analyze Option 3 (Cl⁻ and Br⁻)**:
- Both chloride (Cl⁻) and bromide (Br⁻) ions do not react with dilute H₂SO₄.
- **Conclusion**: No distinction can be made between chloride and bromide ions using dilute H₂SO₄.

5. **Analyze Option 4 (HCO₃⁻ and CO₃²⁻)**:
- Both bicarbonate ion (HCO₃⁻) and carbonate ion (CO₃²⁻) react with dilute H₂SO₄ to produce carbon dioxide (CO₂) gas, which evolves with effervescence.
- **Conclusion**: No distinction can be made between bicarbonate and carbonate ions using dilute H₂SO₄.

### Final Answer:
The only pair of acid radicals that can be distinguished using dilute H₂SO₄ is **Nitrate ion (NO₃⁻) and Nitrite ion (NO₂⁻)**. Therefore, the correct option is **Option 2**.