Which of the following statements is incorrect?

The correct answer is Option (1) → Two sucrose solutions of the same molality prepared in different solvents have the same depression in freezing point

For a dilute solution the depression of freezing point is \( \Delta T_f=K_f\,m \). The molality m is the same for both sucrose solutions, but K_f depends on the solvent (for example, 1.86 K kg mol⁻¹ for water and 5.12 K kg mol⁻¹ for benzene). So the two depressions are different.

Option (1) Two sucrose solutions of the same molality prepared in different solvents have the same depression in freezing point — An incorrect statement. Equal molality gives equal ΔT_f only in the same solvent; a different solvent has a different K_f.

Option (2) The osmotic pressure (π) of a dilute solution is given by π = CRT, where C is the molarity of the solution — A correct statement. Osmotic pressure is proportional to the molar concentration C at temperature T, with R the gas constant.

Option (3) For a solution of volatile liquids, the partial vapour pressure of each component is directly proportional to its mole fraction in the solution — A correct statement. This is Raoult’s law, p₁ = p₁⁰x₁.

Option (4) The order of osmotic pressure of 0.01 M aqueous solutions is BaCl₂ > KCl > CH₃COOH > sucrose — A correct statement.

• Osmotic pressure depends on the number of solute particles.

• \( \ce{BaCl2} \) gives 3 ions (i = 3), KCl gives 2 (i = 2), acetic acid, a weak electrolyte, dissociates only slightly (i a little above 1), and sucrose does not dissociate (i = 1).

NCERT (2026-27 edition):
1.6.3 Depression of Freezing Point – “Similar to elevation of boiling point, depression of freezing point (ΔT_f) for dilute solution (ideal solution) is directly proportional to molality, m of the solution. Thus,

    \( \displaystyle \Delta T_f=K_f\,m \qquad (1.34) \)

The proportionality constant, K_f, which depends on the nature of the solvent is known as Freezing Point Depression Constant or Molal Depression Constant or Cryoscopic Constant.”