Which of the following aqueous solution will exhibit highest boiling point?

The correct answer is 0.01 M Na₂SO₄.

Underlying Concept:
Boiling point elevation is a colligative property, which means it depends on the total number of solute particles (ions or molecules) present in the solution rather than their chemical identity.

The elevation in boiling point ($\Delta T_b$) is given by the formula:
$\Delta T_b=i\times K_b\times M$
where:
• $i$ is the van 't Hoff factor (the number of particles into which the solute dissociates),
• $K_b$ is the molal boiling point elevation constant of the solvent (water), and
• $M$ is the molarity (concentration) of the solution.

Since the solvent (water) is the same for all options, $K_b$ remains constant. Therefore, the boiling point elevation is directly proportional to the product of the van 't Hoff factor and the molar concentration of the solution ($i\times M$):
$\Delta T_b\propto i\times M$
The solution with the highest value of $i\times M$ will undergo the greatest elevation in boiling point and will exhibit the highest boiling point.

Step-by-Step Calculation:

1. 0.01 M Urea:
Urea is a non-electrolyte and does not dissociate in water.
• Van 't Hoff factor ($i$) = 1
• $i\times M=1\times 0.01=0.01\text{M}$

2. 0.01 M KNO₃:
Potassium nitrate dissociates completely into two ions:
KNO₃ → K⁺ + NO₃^-
• Van 't Hoff factor ($i$) = 2
• $i\times M=2\times 0.01=0.02\text{M}$

3. 0.01 M Na₂SO₄:
Sodium sulfate dissociates completely into three ions:
Na₂SO₄ → 2Na⁺ + SO₄^2-
• Van 't Hoff factor ($i$) = 3
• $i\times M=3\times 0.01=0.03\text{M}$

4. 0.015 M C₆H₁₂O₆ (Glucose):
Glucose is a non-electrolyte and does not dissociate in water.
• Van 't Hoff factor ($i$) = 1
• $i\times M=1\times 0.015=0.015\text{M}$

Conclusion:
Comparing the effective particle concentrations ($i\times M$):
• 0.01 M Urea = 0.01 M
• 0.01 M KNO₃ = 0.02 M
• 0.01 M Na₂SO₄ = 0.03 M
• 0.015 M C₆H₁₂O₆ = 0.015 M

Since 0.01 M Na₂SO₄ has the highest value of $i\times M$ (0.03 M), it produces the maximum number of solute particles in the solution, resulting in the highest elevation in boiling point. Therefore, it has the highest boiling point among the given options.