Question

An ideal solution is made up from the volatile liquids A and B, for which P_Aº = 125 Torr and P_Bº = 58.1 Torr at 298.15 K. As the pressure is reduced the first vapor (first bubble) is observed at a total pressure of 79.2 Torr.

(a) What is the mol fraction of B in the liquid when the first vapor forms?

(b) What is the mol fraction of substance A in the vapor phase when the first vapor forms?

Answer 1

Data Given : P^o_A=125 Torr ; P^o_B=58.1 Torr ; P=79.2 Torr

(a) Now to solve this , we will make use of Roult's Law.

Roult's law for component A,

Y_AP =X_A* P^o_A .............(1)

Where,

Y_A =Mole fraction of component A in vapour phase

P= Total pressure

X_A =mole fraction of component A in liquid phase

P^o_A= Vapour pressure of component A

Similarly we can write Roult's Law for B,

Y_BP =X_B* P^o_B .............(2)

Now for a Binary mixture we have two additional mixture

X_A + X_B = 1             .................(3)

Y_A + Y_B = 1    .........(4)

Adding equation (1) and (2)

(Y_A+Y_B) P =X_A* P^o_A + X_B* P^o_B

substituting Y_A+Y_B =1 and X_A=1-X_B in above eqation

P =(1-X_B)* P^o_A + X_B* P^o_B

Substituing all the known values in above equation

79.2 = (1-X_B)*125+X_B*58.1

On solving above equation we get , X_B=0.6846

(b) Substituting, value of X_B=0.6846 in equation in equation (3)

            X_A=1-X_B = 1-0.6846 = 0.3154

Substituting all the known values in equation (1)

Y_A*79.2= 0.3154*125

From above equation , Y_A=0.4978