The vapour pressure of two miscible...
Question
The vapour pressure of two miscible liquids A and B are 300 and 500 mm of Hg respectively. In a flask 10 moles of A is mixed with 12 moles of B. However, as soon as
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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 Hg. Estimate the rate constant of the polymerisation reaction. Assume negligible volume change on mixing and polymerisation and ideal behaviour for the final solution.

SSC CGL
Chemistry
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The vapour pressure of two miscible liquids A and B are 300 and 500 mm of 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.
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Let after 100 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}{x+12+0.525} )
[
begin{array}{l}
Rightarrow quad 400=left(frac{chi}{x+12.525}right) times 300+left(frac{12}{x+12.525}right) times 500
Rightarrow quad chi=9.9
end{array}
]
( Rightarrow ) Moles of ( A ) polymerised in 100 min ( =10-9.9=0.10 )
[
begin{aligned}
Rightarrow quad k &=frac{1}{t} ln frac{10}{9.9}=frac{1}{100} ln frac{10}{9.9} min ^{-1}
&=1.005 times 10^{-4} mathrm{min}^{-1}
end{aligned}
]

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