Vessel-1 contains $\mathbf{w}_2 \mathrm{~g}$ of a non-volatile solute $\mathbf{X}$ dissolved in…

Vessel-1 contains $\mathbf{w}_2 \mathrm{~g}$ of a non-volatile solute $\mathbf{X}$ dissolved in $\mathbf{w}_1 \mathrm{~g}$ of water. Vessel- 2 contains $\mathbf{w}_2 \mathrm{~g}$ of another non-volatile solute $\mathbf{Y}$ dissolved in $\mathbf{w}_1 \mathrm{~g}$ of water. Both the vessels are at the same temperature and pressure. The molar mass of $\mathbf{X}$ is $80 \%$ of that of $\mathbf{Y}$. The van't Hoff factor for $\mathbf{X}$ is 1.2 times of that of $\mathbf{Y}$ for their respective concentrations. The elevation of boiling point for solution in Vessel-1 is ________. $\%$ of the solution in Vessel-2.

Solution

Vessel-I \(\left(\Delta \mathrm{T}_{\mathrm{b}}\right)_{\mathrm{I}}=\mathrm{i}_{\mathrm{x}} \frac{\mathrm{w}_2}{\mathrm{M}_{\mathrm{x}}} \cdot \frac{1}{\mathrm{w}_1} \times 1000 \times \mathrm{K}_{\mathrm{b}}\) \(\mathrm{M}_{\mathrm{X}}=\) Molar mass of ' X ' Vessel-II \(\left(\Delta \mathrm{T}_{\mathrm{b}}\right)_{\mathrm{II}}=\mathrm{i}_{\mathrm{Y}} \frac{\mathrm{w}_2}{\mathrm{M}_{\mathrm{Y}}} \cdot \frac{1}{\mathrm{w}_1} \times 1000 \times \mathrm{K}_{\mathrm{b}}\) \(M_Y=\) Molar mass of ' \(Y\) ' \(\begin{aligned} & \frac{\left(\Delta T_b\right)_{\mathrm{I}}}{\left(\Delta \mathrm{T}_{\mathrm{b}}\right)_{\mathrm{II}}} \times 100=\frac{\mathrm{i}_{\mathrm{x}}}{\mathrm{i}_{\mathrm{Y}}} \cdot \frac{\mathrm{M}_{\mathrm{Y}}}{\mathrm{M}_{\mathrm{x}}} \times 100 \\ & =1.2 \times \frac{100}{80} \times 100 \\ & =150 \% \end{aligned}\)

Asked in: JEE Advanced 2024 (Paper 2)

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