Solutions and Colligative Properties 1 Question 19
18. The vapour pressure of two miscible liquids $A$ and $B$ are 300 and $500 \mathrm{~mm}$ of $\mathrm{Hg}$ respectively. In a flask 10 moles of $A$ is mixed with 12 moles of $B$. However, as soon as $B$ is added, $A$ starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After $100 \mathrm{~min}$, 0.525 mole of a solute is dissolved which arrests the polymerisation completely. The final vapour pressure of the solution is $400 \mathrm{~mm}$ of $\mathrm{Hg}$. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.
$(2001,4 M)$
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Solution:
- Let after $100 \mathrm{~min}, x$ moles of $A$ are remaining unpolymerised moles of $B=12$
Moles of non-volatile solute $=0.525$
$\Rightarrow \quad$ Mole fraction of $A=\frac{\chi}{\chi+12+0.525}$
Mole fraction of $B=\frac{12}{\chi+12+0.525}$
$\Rightarrow \quad 400=\left(\frac{\chi}{\chi+12.525}\right) \times 300+\left(\frac{12}{\chi+12.525}\right) \times 500$
$\Rightarrow \quad \chi=9.9$
$\Rightarrow$ Moles of $A$ polymerised in $100 \mathrm{~min}=10-9.9=0.10$
$\Rightarrow \quad k=\frac{1}{t} \ln \frac{10}{9.9}=\frac{1}{100} \ln \frac{10}{9.9} \mathrm{~min}^{-1}$
$=1.005 \times 10^{-4} \mathrm{~min}^{-1}$
