Vapour pressures of two miscible liquids A and B are 300 and 500mm Hg respectively. In a flask, 10mol of A is mixed with 12mol of B . However, as soon as B is added, A starts polymerisation follows first order kinetics. After 100min, 0.525mol of a solutedissolved,which arrests the polymerisation completely. Final vapour pressure of the solution is 400mm Hg. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.

Vapour pressures of two miscible liquids A and B are 300 and 500mm Hg

1.	Vapour pressures of two miscible liquids A and B are 300 and 500mm Hg respectively. In a flask, 10mol of A is mixed with 12mol of B . However, as soon as B is added, A starts polymerisation follows first order kinetics. After 100min, 0.525mol of a solutedissolved,which arrests the polymerisation completely. Final vapour pressure of the solution is 400mm Hg. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.
Answer» Solution :Given , initial moles of A = 10 , initial moles of B = 12 . Let the number of moles of A = n when polymerizationis arrested . Moles of solute added = 0.525. `therefore` Total number of moles = `(n+12+0.525)=(n+12.525)` `therefore " Mole FRACTION of A "(x_(A))=(n)/(n+12.525)and ` Mole fraction of B`(x_(b))=(12)/(n+12.525) ` The total vapour pressure of the solution `p_(A)^(0)X_(A)+p_(B)^(0)X_(B)` or,`400=300xx(n)/(n+12.525)+500xx(12)/(n+12.525) "or, " n = 9.9` For a first ORDER reaction , `k=(2.303)/(t)log.([A]_(0))/([A])` or,`k=(2.303)/(100)log.(a)/(a-x)=(2.303)/(100)log.(10)/(9.9)[because a-x=n=9.9]` or,` k = 1.004xx10^(-4)"min"^(-1)`