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Liquids A and B form ideal solution over...

Liquids A and B form ideal solution over the entire range of composition. At temperature T, equimolar binary solution of liquids A and B has vapour pressure 45 torr. At the same temperature, a new solution of A and B having mole fractions `x_(A) and x_(B)`, respectively, has vapours pressure of 22. torr. The value of `x_(A)//x_(B)` in the new solution is ______.
(Given that the vapour pressure of pure liquid A is 20 torr at temperature T).

Text Solution

Verified by Experts

The correct Answer is:
A
`45=P_(A)^(@)xx(1)/(2)+P_(B)^(@)xx(1)/(2)`
`P_(A)^(@)+P_(B)^(@)=90` …..(1)
Given `P_(A)^(@)=200` torr
`P_(B)^(@)=70` torr
`rArr 22.5` torr `=20 x_(A)+70(1-x_(A))`
`=70-50x_(A)`
`x_(A)=((70-22.5)/(50))=0.95`
`x_(B)=0.05`
So `(x_(A))/(x_(B))=(0.95)/(0.05)=19` .
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