$$20 \%$$ of acetic acid is dissociated when its $$5 \mathrm{~g}$$ is added to $$500 \mathrm{~mL}$$ of water. The depression in freezing point of such water is _________ $$\times 10^{-3}{ }^{\circ} \mathrm{C}$$.

Atomic mass of $$\mathrm{C}, \mathrm{H}$$ and $$\mathrm{O}$$ are 12,1 and 16 a.m.u. respectively.

[Given : Molal depression constant and density of water are $$1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$ and $$1 \mathrm{~g} \mathrm{~cm}^{-3}$$ respectively.]

25 mL of an aqueous solution of KCl was found to require 20 mL of 1 M $$\mathrm{AgNO_3}$$ solution when titrated using $$\mathrm{K_2CrO_4}$$ as an indicator. What is the depression in freezing point of KCl solution of the given concentration? _________ (Nearest integer).

(Given : $$\mathrm{K_f=2.0~K~kg~mol^{-1}}$$)

Assume 1) 100% ionization and 2) density of the aqueous solution as 1 g mL$$^{-1}$$

At $$27^{\circ} \mathrm{C}$$, a solution containing $$2.5 \mathrm{~g}$$ of solute in $$250.0 \mathrm{~mL}$$ of solution exerts an osmotic pressure of $$400 \mathrm{~Pa}$$. The molar mass of the solute is ___________ $$\mathrm{g} \mathrm{~mol}^{-1}$$ (Nearest integer)

(Given : $$\mathrm{R}=0.083 \mathrm{~L} \mathrm{~bar} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$$)

Lead storage battery contains $38 \%$ by weight solution of $\mathrm{H}_{2} \mathrm{SO}_{4}$. The van't Hoff factor is $2.67$ at this concentration. The temperature in Kelvin at which the solution in the battery will freeze is ________. (Nearest integer).

Given $\mathrm{K}_{f}=1.8 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$