Consider equimolal aqueous solutions of `NaHSO_(4)` and NaCl with `DeltaT_(b)` and `DeltaT'_(b)` as their respective boiling point elevation . The value of `underset(m to1)("lim") (DeltaT_(b))/(DeltaT'_(b))` will be :

Options

A. 1
B. 1.5
C. 3.5
D. `2/3`

Explanation

To solve the problem, we need to find the ratio of the boiling point elevation (\( \Delta T_b \)) of an equimolal aqueous solution of \( \text{NaHSO}_4 \) to that of \( \text{NaCl} \) as the molarity approaches 1.

### Step-by-Step Solution:

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

2. **Identify the Van't Hoff Factor for Each Solute**:
- For \( \text{NaHSO}_4 \):
\[ \text{NaHSO}_4 \rightarrow \text{Na}^+ + \text{HSO}_4^- \]
This dissociates into 3 ions: \( \text{Na}^+ \), \( \text{H}^+ \), and \( \text{SO}_4^{2-} \). Therefore, \( i = 3 \).

- For \( \text{NaCl} \):
\[ \text{NaCl} \rightarrow \text{Na}^+ + \text{Cl}^- \]
This dissociates into 2 ions: \( \text{Na}^+ \) and \( \text{Cl}^- \). Therefore, \( i = 2 \).

3. **Set Up the Ratios for Boiling Point Elevation**:
Using the boiling point elevation formula for both solutions:
\[ \Delta T_b = i_{\text{NaHSO}_4} \cdot m \cdot K_b = 3 \cdot m \cdot K_b \]
\[ \Delta T'_b = i_{\text{NaCl}} \cdot m \cdot K_b = 2 \cdot m \cdot K_b \]

4. **Calculate the Ratio**:
We want to find the limit of the ratio as \( m \) approaches 1:
\[ \frac{\Delta T_b}{\Delta T'_b} = \frac{3 \cdot m \cdot K_b}{2 \cdot m \cdot K_b} \]
The \( m \) and \( K_b \) cancel out:
\[ \frac{\Delta T_b}{\Delta T'_b} = \frac{3}{2} \]

5. **Final Answer**:
Therefore, the value of \( \lim_{m \to 1} \frac{\Delta T_b}{\Delta T'_b} \) is:
\[ \frac{3}{2} = 1.5 \]

### Conclusion:
The final answer is \( 1.5 \).

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