At $0^{\circ} \mathrm{C}$ urea solution has an osmotic pressure of 400 mm . On dilution by $x$ times, its osmotic pressure decreased to 100 mm at $20^{\circ} \mathrm{C}$. The dilution factor $x$ is approximately

Relative lowering of vapour pressure of a dilute solution is 0.5 . What is the mole fraction of the non-volatile solute?

The solubility product of a sparingly soluble $A B_2$ salt is $2.56 \times 10^{-4} \mathrm{M}^3$ at $25^{\circ} \mathrm{C}$. The $K_f$ of water is 1.8 K kg mol ${ }^{-1}$. The depression in freezing point of a standard solution of $A B_2$ is

The observed molar mass determined for $\mathrm{Na}_2 \mathrm{SO}_4$ by freezing point depression method is $50.0 \mathrm{~g} / \mathrm{mol}$. The molecular weight of $\mathrm{Na}_2 \mathrm{SO}_4$ is 142 . What will be the degree of dissociation $\alpha$ for $\mathrm{Na}_2 \mathrm{SO}_4$ in water?