The correct relationship between the boiling points of very dilute solution of `Na_2 SO_4 (T_1K)` and `NaCl(T_2K)` having the same molar concentration is

Options

A. `T_1=T_2`
B. `T_1gtT_2`
C. `T_2gtT_1`
D. `T_2lt=T_1`

Answer

To determine the correct relationship between the boiling points of very dilute solutions of Na₂SO₄ (T₁K) and NaCl (T₂K) having the same molar concentration, we can follow these steps:

### Step 1: Understanding Boiling Point Elevation
The boiling point elevation (\( \Delta T_b \)) of a solution is given by the formula:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where:
- \( i \) is the van 't Hoff factor (the number of particles the solute dissociates into),
- \( K_b \) is the ebullioscopic constant of the solvent (water in this case),
- \( m \) is the molality of the solution.

### Step 2: Identify the van 't Hoff Factors
For the two solutes:
- **Na₂SO₄** dissociates into 3 ions: \( 2 \text{Na}^+ \) and \( \text{SO}_4^{2-} \). Thus, \( i = 3 \).
- **NaCl** dissociates into 2 ions: \( \text{Na}^+ \) and \( \text{Cl}^- \). Thus, \( i = 2 \).

### Step 3: Compare the Boiling Point Elevations
Since both solutions have the same molar concentration and are in the same solvent (water), the \( K_b \) and \( m \) values will be the same for both solutions. Therefore, the boiling point elevation can be compared directly based on the van 't Hoff factors:
\[ \Delta T_{b, \text{Na}_2\text{SO}_4} = 3 \cdot K_b \cdot m \]
\[ \Delta T_{b, \text{NaCl}} = 2 \cdot K_b \cdot m \]

### Step 4: Establish the Relationship Between Boiling Points
Since \( \Delta T_b \) for Na₂SO₄ is greater than that for NaCl:
\[ \Delta T_{b, \text{Na}_2\text{SO}_4} > \Delta T_{b, \text{NaCl}} \]
This means that the boiling point of the Na₂SO₄ solution (T₁K) will be higher than that of the NaCl solution (T₂K):
\[ T_1 > T_2 \]

### Conclusion
The correct relationship is:
\[ T_1 > T_2 \]
This indicates that the boiling point of the very dilute solution of Na₂SO₄ is greater than that of NaCl when both have the same molar concentration.

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