Which of the following solutions in water has highest boiling point?

Options

A. 1 M NaCl
B. 1 M `MgCl_2`
C. 1 M urea
D. 1 M glucose

Explanation

To determine which solution in water has the highest boiling point, we can use the concept of boiling point elevation. The boiling point elevation can be calculated using the formula:

\[ \Delta T_b = i \cdot K_b \cdot m \]

Where:
- \(\Delta T_b\) is the boiling point elevation,
- \(i\) 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-by-Step Solution:

1. **Identify the Solutions**: Let's consider the solutions we are comparing. For example, we can take:
- Magnesium chloride (MgCl₂)
- Urea
- Glucose

2. **Determine the van 't Hoff Factor (i)**:
- For **MgCl₂**: It dissociates into 1 Mg²⁺ ion and 2 Cl⁻ ions, giving a total of 3 particles. Thus, \(i = 3\).
- For **Urea**: It does not dissociate in solution, so \(i = 1\).
- For **Glucose**: Similar to urea, glucose does not dissociate, so \(i = 1\).

3. **Compare the van 't Hoff Factors**:
- MgCl₂ has \(i = 3\),
- Urea has \(i = 1\),
- Glucose has \(i = 1\).

4. **Conclusion**: Since the boiling point elevation (\(\Delta T_b\)) depends on the value of \(i\) when the molality (\(m\)) and \(K_b\) are constant, the solution with the highest \(i\) will have the highest boiling point. Therefore, the solution with the highest boiling point is the one with MgCl₂, as it has the highest van 't Hoff factor of 3.

5. **Final Answer**: The solution in water that has the highest boiling point is the one containing **MgCl₂**.