A gaseous mixture of two substances $\mathrm{A}$ and $\mathrm{B}$, under a total pressure of $0.8 \mathrm{atm}$ is in equilibrium with an ideal liquid solution. The mole fraction of substance $\mathrm{A}$ is $0.5$ in the vapour phase and $0.2$ in the liquid phase. The vapour pressure of pure liquid $\mathrm{A}$ is____atm.(Nearest integer)

The osmotic pressure of solutions of PVC in cyclohexanone at $300 \mathrm{K}$ are plotted on the graph. The molar mass of PVC is  $\mathrm{g} {\mathrm{mol}}^{-1}$ (Nearest integer)

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

The number of pairs of the solution having the same value of the osmotic pressure from the following is
(Assume $100\%$ ionization)

A. $0.500 \mathrm{M} {\mathrm{C}}_2{\mathrm{H}}_5\mathrm{OH}\left(\mathrm{aq}\right)$ and $0.25 \mathrm{M} \mathrm{KBr}\left(\mathrm{aq}\right)$
B. $0.100 {\mathrm{M}}_{} {\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]\left(\mathrm{aq}\right)$ and $0.100 \mathrm{M}$ ${\mathrm{FeSO}}_4{\left({\mathrm{NH}}_4\right)}_2{\mathrm{SO}}_4\left(\mathrm{aq}\right)$

C. $0.05 \mathrm{M} {\mathrm{K}}_4\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]$ (aq) and $0.25 \mathrm{M} \mathrm{NaCl}$ $\left(\mathrm{aq}\right)$
D. $0.15 \mathrm{M} \mathrm{NaCl}\left(\mathrm{aq}\right)$ and $0.1 \mathrm{M} {\mathrm{BaCl}}_2\left(\mathrm{aq}\right)$
E. $0.02 \mathrm{M} \mathrm{KCl}.{\mathrm{MgCl}}_2.6{\mathrm{H}}_2\mathrm{O}\left(\mathrm{aq}\right)$ and $0.05 \mathrm{M}$ $\mathrm{KCl}\left(\mathrm{aq}\right)$

Solid Lead nitrate is dissolved in $1$ litre of water. The solution was found to boil at $100.15°\mathrm{C}$. When $0.2\mathrm{mol}$ of $\mathrm{NaCl}$ is added to the resulting solution, it was observed that the solution froze at $-0.8°\mathrm{C}$. The solutbility product of ${\mathrm{PbCl}}_2$ formed is _____ $\times {10}^{-6}$ at $298 \mathrm{K}$. (Nearest integer)

Given : ${\mathrm{K}}_{\mathrm{b}}=0.5\mathrm{K} \mathrm{kg} {\mathrm{mol}}^{-1}$ and ${\mathrm{K}}_{\mathrm{f}}=1.8\mathrm{kg} {\mathrm{mol}}^{-1}$. Assume molality to be equal to molarity in all cases.

Match List-I and List-II

Choose the correct answer from the options given below: