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At a certain temperature, the vapour pre...

At a certain temperature, the vapour pressure of pure ether is `640 mm` and that of pure acetone is `280 mm`. Calculate the mole fraction of each component in the vapour state if the mole fraction of ether in the solution is `0.50.`

Text Solution

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In the given solution, both ether and acetone are volatile, so from Raoult’s Law, we can have vapour pressure of solution `(P_("Total"))`.
Let A : ether and B : acetone.
`P_("Total") =P_A+P_B =P_A^0chi_A+P_B^0chi_B`
`rArr P_("Total")= 646 xx0.5+283xx0.5 =464.5 mm`
Now mole fraction in vapour state is given as follows
`chi_A("vapour") =(P_A)/(P_("Total")) =(P_A^0chi_A)/(P_(" Total"))=(646xx0.5)/(464.5)=0.695`
`chi_B ("vapour")=(P_B)/(P_"Total")=(P_B^0chi_B)/(P_"Total")=(283xx0.5)/(464.5)=0.305`
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