Which of the following statements are correct for dilute solutions?
(A). The elevation in boiling point is directly proportional to the molality of the solution.
(B). The elevation in boiling point is inversely proportional to the molality of the solution.
(C). The depression in freezing point is directly proportional to the molality of the solution.
(D). The depression in freezing point is inversely proportional to the molality of the solution.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (C) only
Elevation of boiling point and depression of freezing point are colligative properties: in a dilute solution they depend only on the number of solute particles, which is measured by the molality m. Experiments show that each is directly proportional to the molality:
\( \displaystyle \Delta T_b = K_b\,m \qquad \Delta T_f = K_f\,m \)
Here \( K_b \) (ebullioscopic constant) and \( K_f \) (cryoscopic constant) depend only on the solvent. Doubling the molality doubles both \( \Delta T_b \) and \( \Delta T_f \).
(A) The elevation in boiling point is directly proportional to the molality of the solution. — Correct. This is \( \Delta T_b = K_b\,m \).
(B) The elevation in boiling point is inversely proportional to the molality of the solution. — Incorrect. A more concentrated solution has a lower vapour pressure, so it must be heated more to boil; \( \Delta T_b \) rises with m.
(C) The depression in freezing point is directly proportional to the molality of the solution. — Correct. This is \( \Delta T_f = K_f\,m \).
(D) The depression in freezing point is inversely proportional to the molality of the solution. — Incorrect. More solute particles lower the freezing point further, so \( \Delta T_f \) increases with molality.
NCERT (2026-27 edition):
Elevation of Boiling Point – “Experiments have shown that for dilute solutions the elevation of boiling point (ΔTb) is directly proportional to the molal concentration of the solute in a solution. Thus
\( \Delta T_b \propto m \) or \( \Delta T_b = K_b\,m \)”
Depression of Freezing Point – “… Similar to elevation of boiling point, depression of freezing point (ΔTf) for dilute solution (ideal solution) is directly proportional to molality, m of the solution. Thus,
\( \Delta T_f \propto m \) or \( \Delta T_f = K_f\,m \)”