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 ___

Engineering

Chemistry

Elevation in Boiling Point

Question

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 ____.

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$\frac{2}{1} = \frac{2 \times K_{b_{1}} \times m}{2 \times K_{b_{2}} \times m}$

$\frac{2}{1} = \frac{K_{b_{1}}}{K_{b_{2}}}$

${ΔT}_{b_{1}} = 3 {ΔT}_{b_{2}}$

$i_{1} K_{b_{1}} m = i_{2} K_{b_{2}} m$

i₁ × 2 = 3i₂

2A —→ A₂

_{$1 - α i_{1} K_{b_{1}} m = i_{2} K_{b_{2}} m i = \frac{1 - α + \frac{α}{2}}{1}$}

_{$∴ i_{2} = 1 - \frac{α_{2}}{2}$}

= 1 – 0.35 = 0.65

$i_{1} = 3 \times \frac{0 .65}{2} = 0.325 \times 3$

$1 - \frac{α_{1}}{2} = 0.325 \times 3$

$1 - \frac{α_{1}}{2} = 0.975$

α₁ = 0.05