$A$ cylinder containing an ideal gas ($0.1 \; mol$ in $1.0 \; dm^{3}$) is in thermal equilibrium with a large volume of $0.5 \; m$ (molal) aqueous solution of ethylene glycol at its freezing point. If the stoppers $S_{1}$ and $S_{2}$ (as shown in the figure) are suddenly withdrawn,the volume of the gas in litres after equilibrium is achieved will be ............ $litre$.
(Given: $K_{f}$ (water) $= 2.0 \; K \; kg \; mol^{-1}$,$R = 0.08 \; dm^{3} \; atm \; K^{-1} \; mol^{-1}$,freezing point of water $= 273 \; K$)

For $0.1 \ M$ solutions of urea and $Al_2(SO_4)_3$,which of the following statements is correct? $(a)$ $i$ for urea is $1$ and $i$ for $Al_2(SO_4)_3$ is $5$. $(b)$ $Al_2(SO_4)_3$ has a higher elevation in boiling point. $(c)$ $Al_2(SO_4)_3$ has a higher depression in freezing point. $(d)$ Urea has a higher vapor pressure.

At $T \ K$,the vapour pressure of pure benzene $(C_6H_6)$ and toluene $(C_7H_8)$ are $75 \ mm \ Hg$ and $22 \ mm \ Hg$ respectively. $23.4 \ g$ of benzene and $64.4 \ g$ of toluene are mixed to form an ideal solution. If the vapours are in equilibrium with the liquid mixture,the mole fraction of toluene in the vapour phase is (Atomic weight: $C=12, H=1$).

Evaluate the following statements for their correctness.
$(A)$ The elevation in boiling point temperature of water will be same for $0.1 \ M \ NaCl$ and $0.1 \ M$ urea.
$(B)$ Azeotropic mixtures boil without change in their composition.
$(C)$ Osmosis always takes place from hypertonic to hypotonic solution.
$(D)$ The density of $32 \% \ H_2SO_4$ solution having molarity $4.09 \ M$ is approximately $1.26 \ g \ mL^{-1}$.
$(E)$ $A$ negatively charged sol is obtained when $KI$ solution is added to silver nitrate solution.
Choose the correct answer from the options given below:

Assertion : If one component of a solution obeys Raoult's law over a certain range of composition,the other component will not obey Henry's law in that range.
Reason : Raoult's law is a special case of Henry's law.

Calculate the osmotic pressure in $atm$ of an aqueous solution of urea at $37\,^oC$,which has a freezing point of $0.52\,^oC$. Assume molality and molarity are numerically equal. $(K_f = 1.86\,^oC\, m^{-1})$