The composition of vapour over a binary ideal solution is determined by the composition of the liquid. If `X_(A)` and `Y_(A)` are the mole fractions of `A` in the liquid and vapour, respectively, find the value of `X_(A)` for which `Y_(A)-X_(A)` has a maximum. What is the value of the pressure at this composition in terms of `P_(A)^(@)` and `P_(B)^(@)`.

Answer

`X_(A)=((sqrt(P_(A)^(0)P_(B)^(0))-P_(B)^(0)))/((P_(A)^(0)-P_(B)^(0))),P=sqrt(P_(A)^(0)P_(B)^(0))`

Explanation

`P_("benzenen")^(@)=X_(A)PA^(@)+(1-X_(A))P_(B)^(@)`
`(1)/(P_(T))=(Y_(A))/(P_(B)^(0))+((1-Y_(A)))/(P_(B)^(0))`
calculate `(X_(A)-Y_(A)) &` maximise it
`X_(A)=(sqrt(P_(A)^(0)P_(B)^(0))-P_(B)^(0))/((P_(A)^(0)-P_(B)^(0)))`
& `P_(T)=sqrt(P_(A)^(0)P_(B)^(0))`
`X_(A)=((sqrt(P_(A)^(0)P_(B)^(0))-P_(B)^(0)))/((P_(A)^(0)-P_(B)^(0))),P=sqrt(P_(A)^(0)P_(B)^(0))`