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)^(@).

The composition of vapour over a binary ideal solution is determined b

1.	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» SOLUTION :`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))`