Question

Vessel-1 contains $w_2$ g of a non-volatile solute $X$ dissolved in $w_1$ g of water. Vessel-2 contains $w_2$ g of another non-volatile solute $Y$ dissolved in $w_1$ g of water. Both the vessels are at the same temperature and pressure. The molar mass of $X$ is 80\% of that of $Y$. The van’t Hoff factor for $X$ is 1.2 times that of $Y$ for their respective concentrations. The elevation of boiling point for solution in Vessel-1 is \_\_\_\_\_ \% of the solution in Vessel-2.

Hint:

For colligative properties, compare molar mass, van’t Hoff factors, and solute concentrations to calculate the relative effects.

Answer 1

1. Expression for elevation of boiling point in Vessel-1 ($(\Delta T_b)_I$): $$(\Delta T_b)_I = i_X \times \frac{w_2}{M_X} \times \frac{1000}{w_1} \times K_B.$$ 2. Expression for elevation of boiling point in Vessel-2 ($(\Delta T_b)_{II}$): $$(\Delta T_b)_{II} = i_Y \times \frac{w_2}{M_Y} \times \frac{1000}{w_1} \times K_B.$$ 3. Ratio of elevations: $$\frac{(\Delta T_b)_I}{(\Delta T_b)_{II}} = \frac{i_X}{i_Y} \times \frac{M_Y}{M_X}.$$ 4. Substituting $M_X = 0.8 M_Y$ and $i_X = 1.2 i_Y$: $$\frac{(\Delta T_b)_I}{(\Delta T_b)_{II}} = \frac{1.2}{1} \times \frac{1}{0.8}.$$ $$\frac{(\Delta T_b)_I}{(\Delta T_b)_{II}} = 1.5.$$ 5. Percentage increase: $$(\Delta T_b)_I = 150\% \text{ of } (\Delta T_b)_{II}.$$