Question

Observe the following statements.
Statement - I: The boiling point of 0.1 M urea solution is less than that of 0.1 M KCl solution.
Statement - II: Elevation of boiling point is inversely proportional to molar mass of solute.
The correct answer is

• A. Both statements I and II are correct
• B. Statement I is correct, but statement II is not correct
• C. Statement I is not correct, but statement II is correct
• D. Both statements I and II are not correct

Hint:

Colligative properties are defined by the *number* of particles. When comparing solutions of the same molar concentration, the one with the higher van't Hoff factor (\( i \)) will have the greater effect.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:

Boiling point elevation (\( \Delta T_b \)) is a colligative property, meaning it depends on the number of solute particles in the solution. Formula: \( \Delta T_b = i \cdot K_b \cdot m \), where \( i \) is the van't Hoff factor.
Step 2: Detailed Explanation:

Analysis of Statement I:

• Urea is a non-electrolyte, so it does not dissociate. \( i = 1 \). Effective concentration = \( 0.1 \times 1 = 0.1 \, \text{M} \).
• KCl is an electrolyte, dissociating into \( \text{K}^+ \) and \( \text{Cl}^- \). \( i = 2 \). Effective concentration = \( 0.1 \times 2 = 0.2 \, \text{M} \).
• Since \( \Delta T_b \) is directly proportional to the effective concentration (\( i \times C \)), the elevation for KCl is greater than for Urea.
• Higher elevation means higher boiling point. Thus, B.P.(KCl) \textgreater B.P.(Urea).
• Statement I says B.P.(Urea) \textless B.P.(KCl), which is Correct.

Analysis of Statement II:

• Statement II says "Elevation of boiling point is inversely proportional to molar mass of solute."
• Colligative properties depend on the *number of particles*, which relates to the number of moles.
• While the formula \( \Delta T_b = K_b \frac{w_B \times 1000}{M_B \times w_A} \) shows \( M_B \) in the denominator, this implies an inverse relationship only if the *mass percentage* or *mass concentration* is constant.
• However, as a fundamental definition, the property depends on molality (moles). Saying it is purely inversely proportional to molar mass is conceptually incomplete or incorrect without specifying "for a fixed mass of solute". Furthermore, it completely ignores the van't Hoff factor \( i \), which is critical.
• In the context of comparing "0.1 M solutions" (fixed molarity), the molar mass is already factored into the concentration. The difference in BP arises solely from dissociation (i), not molar mass directly. Thus, in this context, Statement II is false or irrelevant.

Step 3: Final Answer:

Statement I is correct, Statement II is not correct.