If molality of a dilute solution is doubled, what will be the effect on molal depression constant (K_f)?

Unchanged

The correct answer is option 2. Unchanged.

The molal depression constant (\( K_f \)) is a characteristic property of the solvent and represents how much the freezing point of the solvent decreases per molal concentration of solute added. It is a colligative property, meaning it depends only on the nature of the solvent, not on the identity of the solute.

When the molality of a dilute solution is doubled, it means that the concentration of the solute in the solution has increased, but this change does not affect the inherent properties of the solvent. The \( K_f \) value is determined by the solvent-solvent interactions and the nature of the solvent molecules themselves, which do not change when more solute is added.

Therefore, regardless of the concentration of the solute, the \( K_f \) value remains constant for a particular solvent at a given temperature. Hence, doubling the molality of the solution will not alter the \( K_f \) value.