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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

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ConditionI:
`x_(A)=0.5, x_(B)=0.5`
`p_(A)^(@)=20` Torr and `P_("soln")=45` Torr
Using Raoult's law
`P_("soln")=P_(A)^(@)x_(A)=P_(B)^(@)x_(B)`
`45=(20)(0.5)+P_(B)^(@)(0.5)`
`p_(B)^(@)=70` Torr
Condition II,
`x_(A)=?" "x_(B)=?`
`P_("soln")=22.5`
Using Raoult's Law
`P_(M)=P_(A)^(@)x_(A)+P_(B)^(@)(1-x_(A))`
`22.5=(2)(X_(A)+40(1-X_(A))`
`50x_(A)=47.5`
`x_(A)=47.5/50=19/20`
`x_(A)=19/20,x_(B)+1/20`
`(x_(A))/(x_(B))=(19/20)/(1/20)=19`
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