For `0.1` m aq. Solution of given electrolytes correct order of their increasing order of boiling point :

Options

A. `CH_(3)COOH lt HCOOH lt NaCl lt Na_(2)SO_(4)`
B. `HCL lt HCOOH lt NaCl lt Na_(2)SO_(4)`
C. `HCOOH lt CH_(3)COOH lt NaCl lt Na_(2)SO_(4)`
D. `Na_(2)SO_(4) lt NaCl lt HCOOH lt CH_(3)COOH`

Answer

To determine the correct order of increasing boiling points for a 0.1 molar aqueous solution of the given electrolytes, we can follow these steps:

### Step 1: Understand the Boiling Point Elevation Formula
The boiling point elevation (\( \Delta T_b \)) can be calculated using the formula:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where:
- \( i \) = van 't Hoff factor (number of particles the solute dissociates into)
- \( K_b \) = ebullioscopic constant of the solvent (water in this case)
- \( m \) = molality of the solution

Since \( K_b \) and \( m \) are constant for all solutions in this case, the boiling point elevation depends only on the van 't Hoff factor \( i \).

### Step 2: Determine the van 't Hoff Factor for Each Electrolyte
1. **For Na₂SO₄**:
- Dissociates into 2 Na⁺ and 1 SO₄²⁻.
- \( i = 3 \)

2. **For NaCl**:
- Dissociates into 1 Na⁺ and 1 Cl⁻.
- \( i = 2 \)

3. **For HCOOH (Formic Acid)**:
- A weak acid that partially dissociates.
- Assume \( i \approx 1 \) (as it does not fully dissociate).

4. **For CH₃COOH (Acetic Acid)**:
- Another weak acid that also partially dissociates.
- Assume \( i \approx 1 \) (as it does not fully dissociate).

### Step 3: Compare the van 't Hoff Factors
Now we can summarize the van 't Hoff factors:
- Na₂SO₄: \( i = 3 \)
- NaCl: \( i = 2 \)
- HCOOH: \( i \approx 1 \)
- CH₃COOH: \( i \approx 1 \)

### Step 4: Order the Electrolytes by Increasing Boiling Point
Since the boiling point elevation is directly proportional to \( i \):
- The lowest boiling point will correspond to the electrolyte with the lowest \( i \), and the highest boiling point will correspond to the electrolyte with the highest \( i \).

Thus, the order of increasing boiling point is:
1. HCOOH (i ≈ 1)
2. CH₃COOH (i ≈ 1)
3. NaCl (i = 2)
4. Na₂SO₄ (i = 3)

### Final Order
The correct order of increasing boiling points is:
\[ \text{HCOOH} \approx \text{CH}_3\text{COOH} < \text{NaCl} < \text{Na}_2\text{SO}_4 \]