You have a solution of two volatile liquids, A and B (assume ideal behavior). Pure liquid A has a vapor pressure of 385.0 torr and pure liquid B has a vapor pressure of 104.0 torr at the temperature of the solution. The vapor at equilibrium above the solution has double the mole fraction of substance A as the solution does. What is the mole fraction of liquid A in the solution?

the mole fraction of A in solution is 0.32

Explanation:

Let's consider a solution of two volatile liquids A and B

Vapor pressure of A is 385.0 torr

Vapor pressure of B  is 104.0 torr

According to Dalton's Law

         ---------- Equation (1)

where are partial pressure of A and B respectively.

Using Roult's Law

 ---------- Equation (2)

where;

the total vapor pressure of the solution

= mole fraction of A and B respectively

= vapor pressures of pure species of A and B

So;

Replacing our given values for and  into equation (2) ; we have:

The sum of mole fractions is equal to 1

Hence;

  ------ Equation (3)

It is given that mole fraction of vapor is equal to twice the mole fraction of liquid .

It is known that; a partial pressure of a component in gaseous phase is equal to mole fraction times the total pressures. As such;

 ------- Equation (4)

Partial Pressure is given as follows :

Thus; from equation 4

Replacing the above value into equation (8)

192.5 = 281

192.5 - 104 =

88.5 =

= 0.32

Thus, the mole fraction of A in solution is 0.32

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