The solution having maximum boiling point is

Options

A. 0.1 M `C_6H_12O_6`
B. 0.1 M `CaCl_2`
C. 0.1 M `NaCl`
D. 0.5 M `AlCl_3`

Answer

To determine which solution has the maximum boiling point, we need to analyze the effect of non-volatile solutes on the boiling point of a solvent. 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 breaks into)
- \(K_b\) = ebullioscopic constant of the solvent (for water, \(K_b\) is approximately 0.512 °C kg/mol)
- \(m\) = molality of the solution

### Step-by-Step Solution:

1. **Identify the Solutions**: We have four solutions, which are non-volatile. Let's assume they are:
- Solution A: Non-electrolyte (e.g., glucose)
- Solution B: NaCl (sodium chloride)
- Solution C: CaCl2 (calcium chloride)
- Solution D: AlCl3 (aluminum chloride)

2. **Determine the van 't Hoff Factor (i)**:
- For Solution A (non-electrolyte), \(i = 1\).
- For NaCl, it dissociates into Na\(^+\) and Cl\(^-\), so \(i = 2\).
- For CaCl2, it dissociates into Ca\(^{2+}\) and 2Cl\(^-\), so \(i = 3\).
- For AlCl3, it dissociates into Al\(^{3+}\) and 3Cl\(^-\), so \(i = 4\).

3. **Calculate the Molality (m)**: Assume all solutions have the same molality for comparison purposes. Let's say \(m = 0.1\) mol/kg for all solutions.

4. **Calculate the Boiling Point Elevation (\(\Delta T_b\))**:
- For Solution A:
\[ \Delta T_b = 1 \cdot K_b \cdot 0.1 = 1 \cdot 0.512 \cdot 0.1 = 0.0512 \, \text{°C} \]
- For NaCl:
\[ \Delta T_b = 2 \cdot K_b \cdot 0.1 = 2 \cdot 0.512 \cdot 0.1 = 0.1024 \, \text{°C} \]
- For CaCl2:
\[ \Delta T_b = 3 \cdot K_b \cdot 0.1 = 3 \cdot 0.512 \cdot 0.1 = 0.1536 \, \text{°C} \]
- For AlCl3:
\[ \Delta T_b = 4 \cdot K_b \cdot 0.1 = 4 \cdot 0.512 \cdot 0.1 = 0.2048 \, \text{°C} \]

5. **Determine the Maximum Boiling Point**: The solution with the highest \(\Delta T_b\) will have the maximum boiling point. Here are the calculated elevations:
- Solution A: 0.0512 °C
- NaCl: 0.1024 °C
- CaCl2: 0.1536 °C
- AlCl3: 0.2048 °C

Therefore, the solution with the maximum boiling point is **AlCl3**.

### Conclusion:
The solution having the maximum boiling point is **AlCl3**.