The vapour pressure of two miscible liquids $(A)$ and $(B)$ are $300$ and $500:mm$ of $Hg$ respectively. In a flask $10:mole$ of $(A)$ is mixed with $12:mole$ of $(B)$. However, as soon as $(B)$ is added,$(A)$ starts polymerising into a completely insoluble solid. The polymerisation follows first-order kinetics. After $100:minute,:0.525:mole$ of a solute is dissolved which arrests the polymerisation completely. The final vapour pressure of the solution is $400:mm$ of $Hg$. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.