The vapour pressure of pure liquid A at 300 K is 76.7 kPa and that of pure liquid B is 52.0 kPa. These two compounds form ideal liquid and gaseous mixtures. Consider the equilibrium composition of a mixture in which the mole fraction of A in the vapour is 0.350. Calculate the total pressure of the vapour and the composition of the liquid mixture.

•Mole of fraction of A in liquid, m = 0.267

•Mole of fraction of B in liquid =0.733

•Total vapour pressure = 58.6kPa

Explanation:

Given:

T_A = 300K

Vapour pressure of A = 76.7kPa

Vapour pressure of B = 52.0kPa

Let's take m as the mole fraction of A in liquid.

Mole fraction of B in liquid will now be given as: (1-m)

Let's now use the expression from Raoult's law, we now have:

m * 76.7 + (1-m) * 52

= 76.7m + 52 - 52m

= 24.7m + 52

Using Raoult's law of partial pressure, we have:

m * 76.7 = 76.7m kpa

Using Dalton's law o partial pressure, we also have:

0.350 * (24.7m +52) kPa

= 0.350 * (24.7m+52) = 76.7m

Solving for m we have

8.65m + 18.2 = 76.7m

68.05m = 18.2

m = 18.2 / 68.05

m = 0.267

Therefore, we solve for the following:

•Mole of fraction of A in liquid, m = 0.267.

•Mole of fraction of B in liquid, (1-m)

= (1-0.267) = 0.733

•Total vapour pressure = (24.7m+52)

= (24.7*0.267)+52

= 58.6kPa

gas and liquid