An aqueous solution containing 0.2 g of a non volatile solute ' $A$ ' in 21.5 g of water freezes at 272.814 K . If the freezing point of water is 273.16 K , the molar mass (in $\mathrm{g} \mathrm{mol}^{-1}$ ) of solute $A$ is $\left[\mathrm{K}_f\left(\mathrm{H}_2 \mathrm{O}\right)=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right]$

At $T(\mathrm{~K})$, the vapour pressure of $x$ molal aqueous solution containing a non-volatile solute is $12.078 \mathrm{kPa}_{\mathrm{d}}$, The vapour pressure of pure water at $T(\mathrm{~K})$ is 12.3 kPa . What is the value of $x$ ?

In aqueous glucose solution, the mole fraction of wate is 40 times to mole fraction of glucose. What is the weight percentage $(w / w)$ of glucose in the solution?

Benzoic acid molecules undergo dimerisation in benzene. 2.44 g of benzoic acid when dissolved in 30 g of benzene caused depression in freezing point of 2 K . What is the percentage of association of it?

(Given $K_f\left(\mathrm{C}_6 \mathrm{H}_6\right)=5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$; molar mass of benzoic acid $=122 \mathrm{~g} \mathrm{~mol}^{-1}$ )