The plot given below shows P - T curves (where P is the pressure and T is the temperature) for two solvents X and Y and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute S in equal amount (in kg ) of these solvents, the elevation of boiling point of solvent X is three times that of solvent Y . Solute S is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent Y , the degree of dimerization in solvent X is \ \ \ \ .

Chemistry · Solutions and Colligative Properties

JEE Advanced 2018 — Paper 1 — Question 26

The plot given below shows $\mathrm{P}-\mathrm{T}$ curves (where $P$ is the pressure and $T$ is the temperature) for two solvents $\mathbf{X}$ and $\mathbf{Y}$ and isomolal solutions of NaCl in these solvents. NaCl completely dissociates in both the solvents. On addition of equal number of moles of a non-volatile solute $\mathbf{S}$ in equal amount (in kg ) of these solvents, the elevation of boiling point of solvent $\mathbf{X}$ is three times that of solvent $\mathbf{Y}$ . Solute $\mathbf{S}$ is known to undergo dimerization in these solvents. If the degree of dimerization is 0.7 in solvent $\mathbf{Y}$ , the degree of dimerization in solvent $\mathbf{X}$ is $\_\_\_\_$ .

Answer: 0.05

Numerical answer — enter this value.

Step-by-step solution

$2 = 2 \times K_{b(x)}m$ $1 = 2 K_{b(y)}m$ $\frac{K_{b(x)}}{K_{b(y)}} = 2$

$\Delta T_{b(x)} = \left(1-\frac{\alpha}{2}\right)K_{b(x)}m$ $\Delta T_{b(y)} = \left(1-\frac{\alpha}{2}\right)K_{b(y)}m$

$2S \rightleftharpoons S_2$ $1-\alpha$ $\quad \quad$ $\frac{\alpha}{2}$ $i = 1-\alpha + \frac{\alpha}{2}$ $i = 1-\frac{\alpha}{2}$

$3 = \frac{\Delta T_{b(x)}}{\Delta T_{b(y)}} = \frac{\left(1-\frac{\alpha_1}{2}\right)K_{b(x)}}{\left(1-\frac{0.7}{2}\right)K_{b(y)}}$ $3 = \frac{\left(1-\frac{\alpha_1}{2}\right) \times 2}{\left(1-\frac{0.7}{2}\right)}$

$\left(1-\frac{\alpha_1}{2}\right) = \frac{3 \times 0.65}{2} = 1.5 \times 0.65$ $\alpha_1 = 0.05$

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Exam: JEE Advanced 2018
Paper: Paper 1
Subject: Chemistry
Chapter: Solutions and Colligative Properties
Topic: Abnormal Colligative Properties - van't Hoff Factor

Liquids A and B form ideal solution over the entire range of composition. At temperature T , equimolar binary solution of liquids A and B…

Answer: 0.05

Step-by-step solution

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