The vapor pressure of pure benzene and methyl benzene at $$27^{\circ} \mathrm{C}$$ is given as 80 Torr and 24 Torr, respectively. The mole fraction of methyl benzene in vapor phase, in equilibrium with an equimolar mixture of those two liquids (ideal solution) at the same temperature is _________ $$\times 10^{-2}$$ (nearest integer)

A solution containing $$10 \mathrm{~g}$$ of an electrolyte $$\mathrm{AB}_2$$ in $$100 \mathrm{~g}$$ of water boils at $$100.52^{\circ} \mathrm{C}$$. The degree of ionization of the electrolyte $$(\alpha)$$ is _________ $$\times 10^{-1}$$. (nearest integer)

[Given : Molar mass of $$\mathrm{AB}_2=200 \mathrm{~g} \mathrm{~mol}^{-1}, \mathrm{~K}_{\mathrm{b}}$$ (molal boiling point elevation const. of water) $$=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$, boiling point of water $$=100^{\circ} \mathrm{C} ; \mathrm{AB}_2$$ ionises as $$\mathrm{AB}_2 \rightarrow \mathrm{A}^{2+}+2 \mathrm{~B}^{-}]$$

When '$$x$$' $$\times 10^{-2} \mathrm{~mL}$$ methanol (molar mass $$=32 \mathrm{~g}$$' density $$=0.792 \mathrm{~g} / \mathrm{cm}^3$$) is added to $$100 \mathrm{~mL}$$. water (density $$=1 \mathrm{~g} / \mathrm{cm}^3$$), the following diagram is obtained.

$$x=$$ ________ (nearest integer).

[Given : Molal freezing point depression constant of water at $$273.15 \mathrm{~K}$$ is $$1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$]

Considering acetic acid dissociates in water, its dissociation constant is $$6.25 \times 10^{-5}$$. If $$5 \mathrm{~mL}$$ of acetic acid is dissolved in 1 litre water, the solution will freeze at $$-x \times 10^{-2}{ }^{\circ} \mathrm{C}$$, provided pure water freezes at $$0{ }^{\circ} \mathrm{C}$$.

$$x=$$ _________. (Nearest integer)

$$\begin{aligned} \text{Given :} \quad & \left(\mathrm{K}_{\mathrm{f}}\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}-1 \\ & \text { density of acetic acid is } 1.2 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of water }=18 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { molar mass of acetic acid= } 60 \mathrm{~g} \mathrm{~mol}^{-1} \text {. } \\ & \text { density of water }=1 \mathrm{~g} \mathrm{~cm}^{-3} \end{aligned}$$

Acetic acid dissociates as $$\mathrm{CH}_3 \mathrm{COOH} \rightleftharpoons \mathrm{CH}_3 \mathrm{COO}^{\ominus}+\mathrm{H}^{\oplus}$$