Two volatile liquids X and Y form an ideal solution at 298 K and have vapour pressures equal to 100 mm and 200 mm of Hg respectively in their pure state. The mole fraction of X in the solution is 0.4 and the mole fraction of Y in the vapour phase is $a / 20$. Calculate the value of a.

When $9.2 \times 10^{-3} \mathrm{~kg}$ of formic acid is added to 600 ml of water the freezing point of water is depressed. If $30 \%$ of Formic acid undergoes dissociation what would be the freezing point of the solution? ( $\mathrm{K}_{\mathrm{f}}$ of $\mathrm{H}_2 \mathrm{O}$ is 1.86 K kg mol ; MM of formic acid: 46 amu )

A non-volatile solute A weighing 60 g when dissolved in 212 g of the solvent Xylene reduces its vapour pressure to $60 \%$. What is the Molar mass of A in $\mathrm{g} / \mathrm{mol}$ ? [MM of xylene $=106 \mathrm{~g} / \mathrm{mol}$ ]

For a 1.0 molal solution containing the non-volatile solute Urea, the elevation in boiling point is 2.0 K while the depression in freezing point in a 3.0 molal solution having the same solvent is $4.0 K$. If the ratio $\frac{K_b}{K_f}=\frac{1}{X}$, what is the value of $X$ ?