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 equimolar binary solution of liquids A and B
`x_(A) = 0.5 , x_(B) = 0.5 and p_(A)^(@) = 20 torr`
`p_("total") = x_(A)P_(A)^(@) + x_(B)p_(B)^(@)`
`45 = 0.5 xx 20 + 0.5 xx p_(B)`
`0.5 p_(B)^(@) = 45 - 10 = 35`
`therefore " " p_(B)^(@) = 35 xx 2 = 70 torr`
If mole fraction are `x_(A)` and `x_(B)` for the new solution,
`22.5 = 20x_(A) + 70 x_(B)`
`22.5 = 20x_(A) + 70(1-x_(A))`
`50x_(A) = 70 - 22.5 = 47.5`
`x_(A) = (47.5)/(50) = 0.95`
`x_(B) = 1-0.95 = 0.05`
`therefore " "(x_(A))/(x_(B)) = (0.95)/(0.05) = 19.00`