Question

# 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.

Solution

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}

]