Given that the freezing point of benzene is $$5.48^{\circ} \mathrm{C}$$ and its $$\mathrm{K}_{\mathrm{f}}$$ value is $$5.12{ }^{\circ} \mathrm{C} / \mathrm{m}$$. What would be the freezing point of a solution of $$20 \mathrm{~g}$$ of propane in $$400 \mathrm{~g}$$ of benzene?

A solute $$\mathrm{X}$$ is found to exist as a dimer in water. A 4 molal solution of $$\mathrm{X}$$ shows a boiling point of $$101.04^{\circ} \mathrm{C}$$. What is the percentage association of $$\mathrm{X}$$ ? ($$\mathrm{K}_{\mathrm{b}}$$ for water $$=0.52 \mathrm{~K} / \mathrm{m}$$).

$$200 \mathrm{ml}$$ of an aqueous solution contains $$3.6 \mathrm{~g}$$ of Glucose and $$1.2 \mathrm{~g}$$ of Urea maintained at a temperature equal to $$27^{\circ} \mathrm{C}$$. What is the Osmotic pressure of the solution in atmosphere units?

$$\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}{ }^{-1} \mathrm{~mol}^{-1}$$ : Molecular Formula: Glucose is $$\mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6$$ and of Urea is $$\mathrm{NH}_2 \mathrm{CONH}_2$$

An aqueous solution of glucose boils at $$100.01^{\circ} \mathrm{C}$$. The number of glucose molecules in a solution containing $$100 \mathrm{~g}$$ of water is _________ [$$\mathrm{K}_{\mathrm{b}}$$ for water is $$0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$$]