If the molality of a dilute solution is doubled, what is the effect o…

The correct answer is Option (2) → It is unchanged

For a dilute solution the depression of freezing point is proportional to molality, \( \Delta T_f=K_f\,m \). The proportionality constant K_f (molal depression constant) depends only on the nature of the solvent. Doubling m doubles ΔT_f, but K_f stays the same.

Why the other options are incorrect

Option (1) It is halved — Incorrect. K_f is a property of the solvent; the amount of solute does not change it.

Option (3) It is doubled — Incorrect. What doubles is ΔT_f, not the constant K_f.

Option (4) It depends on the nature of the solute — Incorrect. K_f depends on the nature of the solvent, not of the solute.

NCERT (2026-27 edition):
1.6.3 Depression of Freezing Point – “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. The unit of K_f is K kg mol⁻¹.”