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).

Explanation

For ideal solution
`p=p_(A)^(2)x_(A)+p_(B)^(@)x_(B)`
`45=P_(A)^(@)xx(1)/(2)+p_(B)^(@)xx(1)/(2)`
`p_(A)^(@)+p_(B)^(@)=90` torr
Given `p_(A)^(@)=20` torr, `:. p_(B)^(@)=70` torr
For new solution :
`p=p_(A)^(@)x_(A)+p_(B)^(@)x_(B)`
`22.5=20x_(A)+70(1-x_(A))`
`=70-50x_(A)`
`x_(A)=(70-22.5)/(50)=0.95`
`x_(B)=0.05`
`:. (x_(A))/(x_(B))=(0.95)/(0.05)=19`.