Elements $X$ and $Y$ form two non-volatile compounds ( $X Y$ and $X Y_3$ ). When 10 g of $X Y$ is dissolved in 50 g of ethanol, the depression in freezing point ( $\Delta T_f$ ) was 5.333 K . When 10 g of $X Y_3$ is dissolved in 50 g of ethanol, the (was $\left.\Delta T_f\right) 2.2857 \mathrm{~K}$. What are the atomic weights of $X$ and $Y$ respectively?

$$ \left(K_f=2 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right) $$

A solution is prepared by adding 124 g of ethylene glycol (molar mass $=62 \mathrm{~g} \mathrm{~mol}^{-1}$ ) to $x \mathrm{~g}$ of water to get 10 m solution. What is the value of $x$ (in g )?

The following graph is obtained for an ideal solution containing a non-volatile solute $x$-and $y$-axis represent, respectively

What is the approximate molality of $10 \%(w / w)$ aqueous glucose solution?

(Molar mass of glucose $=180 \mathrm{~g} \mathrm{~mol}^{-1}$ )