Which of the following statements, with reference to a solution are correct?
(A) The osmotic pressure of the solution is proportional to the molarity of the solute.
(B) The elevation of the boiling point (\( ΔT_b \)) is directly proportional to the molal concentration of the solute in a solution.
(C) The unit of \( K_b \) is \( K\, kg^{-1}\, mol^{-1} \).
(D) \( ΔT_b = T_b^0-T_b \)
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (A) and (B) only
Osmotic pressure and the elevation of boiling point are colligative properties: they depend on the number of solute particles, not on their nature. The osmotic pressure is written with molarity and the boiling point elevation with molality:
\( \displaystyle \pi = C\,R\,T \qquad \Delta T_b = K_b\,m \)
(A) The osmotic pressure of the solution is proportional to the molarity of the solute. — Correct. In \( \pi = CRT \), C is the molar concentration, so at a fixed temperature \( \pi \propto C \).
(B) The elevation of the boiling point (\(ΔT_b\)) is directly proportional to the molal concentration of the solute in a solution. — Correct. For a dilute solution \( \Delta T_b = K_b\,m \), where m is the molality.
(C) The unit of \(K_b\) is \(K\, kg^{-1}\, mol^{-1}\). — Incorrect. The unit follows from \( K_b = \Delta T_b / m \):
\( \displaystyle \text{unit of } K_b = \frac{\mathrm{K}}{\mathrm{mol\,kg^{-1}}} = \mathrm{K\,kg\,mol^{-1}} \)
The kilogram appears with a positive power, not as kg−1.
(D) \(ΔT_b = T_b^0-T_b\) — Incorrect. A solution with a non-volatile solute boils at a higher temperature than the pure solvent, so \( \Delta T_b = T_b - T_b^{0} \). The printed form would give a negative value.
NCERT (2026-27 edition):
Elevation of Boiling Point – “… Let Tb0 be the boiling point of pure solvent and Tb be the boiling point of solution. The increase in the boiling point ΔTb = Tb − Tb0 is known as 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. … The unit of Kb is K kg mol-1.”
Osmosis and Osmotic Pressure – “… For dilute solutions, it has been found experimentally that osmotic pressure is proportional to the molarity, C of the solution at a given temperature T.”