In a solvent $\mathbf{S}$, a compound $\mathbf{B}$ is partially dissociated into $\mathbf{C}$ and $\mathbf{D}$ as given below :

$$ \mathbf{B} \rightleftharpoons 2 \mathbf{C}+2 \mathbf{D} $$

$\mathbf{B}, \mathbf{C}$ and $\mathbf{D}$ are non-volatile in nature. The molar mass of $\mathbf{B}$ is 10 times the molar mass of $\mathbf{S}$. The standard boiling point and the standard enthalpy of vaporization of $\mathbf{S}$ are 400 K and $10 R \mathrm{~J} \mathrm{~mol}^{-1}$, respectively ( $R$ is the gas constant in $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ). A solution of $\mathbf{B}$ in $\mathbf{S}$ with an initial concentration of $\mathbf{B}$ as $0.25 \%$ (mass/mass) has a boiling point of 408 K at 1 bar pressure. In this solution, the mole percent of $\mathbf{B}$ that has been dissociated is $\_\_\_\_$ .

Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of pure $\mathbf{A}$ at 300 K is 105 mm Hg . Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as ideal gases in the vapour phase.

Given :

The gas constant $R=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{A}$ is $50 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{B}$ is $57 \mathrm{~g} \mathrm{~mol}^{-1}$

Density of liquid $\mathbf{B}$ at 300 K is $0.5 \mathrm{~g} / \mathrm{mL}$

$1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$

At 300 K , the ratio of the molar volume of pure $\mathbf{B}$ in vapour phase to its molar volume in liquid phase is $\_\_\_\_$ .

Two volatile liquids $\mathbf{A}$ and $\mathbf{B}$ form an ideal solution. Consider a 5 molal solution of $\mathbf{B}$ in $\mathbf{A}$ inside a closed container having a total vapour pressure of 100 mm Hg at 300 K . The vapour pressure of pure $\mathbf{A}$ at 300 K is 105 mm Hg . Assume that $\mathbf{A}$ and $\mathbf{B}$ behave as ideal gases in the vapour phase.

Given :

The gas constant $R=0.08 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{A}$ is $50 \mathrm{~g} \mathrm{~mol}^{-1}$

Molar mass of $\mathbf{B}$ is $57 \mathrm{~g} \mathrm{~mol}^{-1}$

Density of liquid $\mathbf{B}$ at 300 K is $0.5 \mathrm{~g} / \mathrm{mL}$

$1 \mathrm{~atm}=760 \mathrm{~mm} \mathrm{Hg}$

The mole fraction of $\mathbf{B}$ in vapour phase which is in equilibrium with this solution is $\_\_\_\_$ .

At 300 K , an ideal dilute solution of a macromolecule exerts osmotic pressure that is expressed in terms of the height $(h)$ of the solution (density $=1.00 \mathrm{~g} \mathrm{~cm}^{-3}$ ) where $h$ is equal to 2.00 cm . If the concentration of the dilute solution of the macromolecule is $2.00 \mathrm{~g} \mathrm{dm}^{-3}$, the molar mass of the macromolecule is calculated to be $\boldsymbol{X} \times 10^4 \mathrm{~g} \mathrm{~mol}^{-1}$. The value of $\boldsymbol{X}$ is __________.

Use: Universal gas constant $(R)=8.3 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}$ and acceleration due to gravity $(g)=10 \mathrm{~m} \mathrm{~s}^{-2}$