Principle involved: Boiling point elevation

The elevation in boiling point is given by $\Delta T_b = i K_b m$ where:

• $i$ = van’t Hoff factor
• $K_b$ = ebullioscopic constant of water
• $m$ = molality

For dilute aqueous solutions, comparing on the basis of molarity is sufficient here since all are very dilute. So we compare the value of $i \times C$.

Find van’t Hoff factor for each solute

• $Na_2SO_4$ dissociates as $Na_2SO_4 \rightarrow 2Na^+ + SO_4^{2-}$ Hence, $i \approx 3$

• Glucose is a non-electrolyte, so $i = 1$

• Urea is also a non-electrolyte, so $i = 1$

• $KNO_3$ dissociates as $KNO_3 \rightarrow K^+ + NO_3^-$ Hence, $i \approx 2$

Compare effective particle concentration $i \times C$

• A: $0.01\,M\; Na_2SO_4$ $iC = 3 \times 0.01 = 0.03$

• B: $0.015\,M$ glucose $iC = 1 \times 0.015 = 0.015$

• C: $0.015\,M$ urea $iC = 1 \times 0.015 = 0.015$

• D: $0.01\,M\; KNO_3$ $iC = 2 \times 0.01 = 0.02$

Conclusion

Since boiling point elevation is maximum for the solution with largest $iC$, we get: $0.03 > 0.02 > 0.015$

Therefore, the solution with the highest boiling point is: A: $0.01\,M\; Na_2SO_4$