The total vapour pressure P (in mm Hg ) of an ideal binary solution containing two volatile liquids A and B is given by the equation: P = 500 - 200 x_ A where x_ A is the mole fraction of liquid A in the solution. If the solution contains a mole fraction of A equal to 0.25 , the mole fraction of A in the vapour phase is 1 Z . The value of Z is ________.

Step-by-step solution

The total pressure of an ideal binary solution is given by: P = P_ B ^ + (P_ A ^ - P_ B ^ )x_ A Comparing this with the given equation P = 500 - 200 x_ A : P_ B ^ = 500 mm Hg P_ A ^ - P_ B ^ = -200 P_ A ^ = 300 mm Hg Given x_ A = 0.25 , the partial vapour pressure of A is: P_ A = P_ A ^ x_ A = 300 0.25 = 75 mm Hg The total vapour pressure at x_ A = 0.25 is: P = 500 - 200(0.25) = 450 mm Hg The mole fraction of A in the vapour phase ( y_ A ) is: y_ A = P_ A P = 75 450 = 1 6 Comparing with 1 Z , we get Z = 6 . Answer: