Which of the following 0.1 m aqueous solution is likely to have the highest boiling points ?

Options

A. `Na_(2)SO_(4)`
B. KCl
C. Glucose
D. Urea

Answer

To determine which of the following 0.1 m aqueous solutions is likely to have the highest boiling point, we need to consider the colligative properties of solutions, specifically the elevation of boiling point. The elevation in boiling point 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 (water in this case)
- \(m\) = molality of the solution

Since the molality (m) is the same for all solutions (0.1 m) and the solvent is the same (water), the only variable that affects the boiling point elevation is the van 't Hoff factor (i).

### Step-by-Step Solution:

1. **Identify the van 't Hoff factor (i) for each solute**:
- **Na2SO4**: Dissociates into 2 Na⁺ and 1 SO₄²⁻, thus:
\[ i = 2 + 1 = 3 \]
- **KCl**: Dissociates into 1 K⁺ and 1 Cl⁻, thus:
\[ i = 1 + 1 = 2 \]
- **Glucose (C6H12O6)**: Does not dissociate (non-electrolyte), thus:
\[ i = 1 \]
- **Urea (NH2CONH2)**: Also does not dissociate (non-electrolyte), thus:
\[ i = 1 \]

2. **Calculate the boiling point elevation for each solute**:
- For **Na2SO4**:
\[ \Delta T_b = 3 \cdot K_b \cdot 0.1 \]
- For **KCl**:
\[ \Delta T_b = 2 \cdot K_b \cdot 0.1 \]
- For **Glucose**:
\[ \Delta T_b = 1 \cdot K_b \cdot 0.1 \]
- For **Urea**:
\[ \Delta T_b = 1 \cdot K_b \cdot 0.1 \]

3. **Compare the boiling point elevations**:
- The boiling point elevation is highest for Na2SO4 (3), followed by KCl (2), and then both glucose and urea (1).

4. **Determine the solution with the highest boiling point**:
- Since Na2SO4 has the highest value of \(i\), it will have the highest boiling point elevation. Therefore, the boiling point of the Na2SO4 solution will be the highest among the given options.

### Conclusion:
The 0.1 m aqueous solution that is likely to have the highest boiling point is **Na2SO4**.

---