At $50^{\circ} \mathrm{C}$, the vapour pressure of pure benzene is 268 torr. The number of moles of non-volatile solute per mole of benzene required to prepare a solution having a vapour pressure of 167 torr at the same temperature is (molar mass of benzene $=78 \mathrm{~g} \mathrm{~mol}^{-1}$ )

Liquids $A$ and $B$ form an ideal solution. The vapour pressures of $A$ and $B$ are 50 and 32 mm Hg respectively at 300 K . One mole of liquid $A$ is mixed with 1 mole of liquid $B$. What is the approximate mole fraction of $A$ in vapour phase?

' $x^{\prime} \mathrm{g}$ of urea (molar mass $60 \mathrm{gmol}^{-1}$ ) is completely dissolved in ' $y^{\prime} \mathrm{g}$ of pure water and the solution boiled at 373.202 K . If the boiling point of pure water at $1.01^3$ bar is 373.15 K , then $x: y$ is $\left(K_b\left(\mathrm{H}_2 \mathrm{O}\right)=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)$

At 300 K , the osmotic pressure of a decinormal solution of sodium chloride is 4.82 atm . The degree of dissociation of sodium chloride is $x \times 10^{-2}$. The value of $x$ is $\left(R=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$