Calculate the mole fraction of pure liquid B in solution if total vapour pressure of solution, vapour pressure of pure liquid A and vapour pressure of pure liquid B are 500 mmHg , 400 ~mm Hg and 575 mm Hg respectively at given temperature.

Step-by-step solution

To determine the mole fraction of liquid B, Raoult's law is applied to the ideal solution. The total vapor pressure is expressed as P_ total = (1 - X_B) P_A^0 + X_B P_B^0 , given P_ total = 500 , mmHg , P_A^0 = 400 , mmHg , and P_B^0 = 575 , mmHg . 500 = (1 - X_B) 400 + X_B 575 Simplifying this equation results in 100 = 175 X_B , yielding X_B = 100 175 = 4 7 0.5714 . This value corresponds to option B , confirming the mole fraction of B is B .