If molality of the dilute solution is doubled, the value of molal depression constant $$\left( {{K_f}} \right)$$  will be

Solution :
For a dilute solution, the depression in freezing point $$\left( {\Delta {T_f}} \right)$$  is directly proportional to molality $$(m)$$ of the solution.
$$\Delta {T_f} \propto m\,\,\,\,or\,\,\,\Delta {T_f} = {K_f}m$$
Where, $${{K_f}}$$ is called molal depression constant or freezing point depression constant or cryoscopic constant. The value of $${{K_f}}$$ depends only on nature of the solvent and independent of composition of solute particles, i.e. does not depend on the concentration of solution.