If for a sucrose, elevation in boiling point is `1.0^(@)C`, then what will be the boiling point of `NaCl` solution for same molal concentration?

Options

A. `1.0^(@)C`
B. `2.0^(@)C`
C. `3.0^(@)C`
D. `4.0^(@)C`

Explanation

To solve the problem, we need to understand the concept of boiling point elevation and how it relates to the Van't Hoff factor for different solutes.

### Step-by-Step Solution:

1. **Understand the given data**:
We know that for a sucrose solution, the elevation in boiling point (ΔTb) is 1.0°C. Sucrose is a non-electrolyte, meaning it does not dissociate into ions when dissolved in a solvent. Therefore, its Van't Hoff factor (i) is 1.

2. **Recall the formula for boiling point elevation**:
The boiling point elevation can be calculated using the formula:
\[ \Delta T_b = i \cdot K_b \cdot m \]
where:
- \( \Delta T_b \) = elevation in boiling point
- \( i \) = Van't Hoff factor (number of particles the solute dissociates into)
- \( K_b \) = ebullioscopic constant of the solvent
- \( m \) = molality of the solution

3. **Apply the formula for sucrose**:
For the sucrose solution, we have:
\[ 1.0 = 1 \cdot K_b \cdot m \]
This means that \( K_b \cdot m = 1.0 \).

4. **Consider the NaCl solution**:
Now, we need to find the boiling point elevation for a NaCl solution at the same molal concentration. NaCl is an electrolyte and dissociates into two ions: Na⁺ and Cl⁻. Therefore, its Van't Hoff factor (i) is 2.

5. **Apply the formula for NaCl**:
For the NaCl solution, the boiling point elevation can be expressed as:
\[ \Delta T_b = 2 \cdot K_b \cdot m \]
Since we know \( K_b \cdot m = 1.0 \) from the sucrose solution, we can substitute this into the equation:
\[ \Delta T_b = 2 \cdot 1.0 = 2.0 \]

6. **Determine the boiling point of the NaCl solution**:
The boiling point of the solution (Tb) can be calculated as:
\[ T_b = T_{b, \text{pure solvent}} + \Delta T_b \]
Assuming the boiling point of the pure solvent (water) is 100°C:
\[ T_b = 100°C + 2.0°C = 102.0°C \]

### Final Answer:
The boiling point of the NaCl solution at the same molal concentration is **102.0°C**.

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