Question

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 xᴀ and xв, respectively, has vapour pressure of 22.5 Torr. The value of xᴀ/xв
in the new solution is ____.
(given that the vapour pressure of pure liquid A is 20 Torr at temperature T)

Answer 1

Answer:

According to Raoult's Law:

PT=PA0XA+PB0XB

Case 1: Equimolar solution of A & B

45=PA0×21+PB0×21

⟹PA0+PB0=90 torr

⟹PB0=90−PA0

⟹PB0=70 torr

Case 2: Solution has a total vapor pressure of 22.5 torr

22.5=20×XA+70×XB

XA+XB=1

⟹XB=1−XB

⟹22.5=20×XA+70×(1−XA)

⟹XA=0.95

⟹XB=0.05

So, XBXA=0.050.95

⟹XBXA=19