Question

Explain the variation of vapour pressures with mole fractions of binary solutions of two volatile liquids forming ideal solutions.

Answer 1

Consider a liquid mixture of two liquid components A and B having vapour pressures `P_1^0` and `P_2^0` and mole fractions x₁ and x₂ respectively.

By Raoult’s law, the vapour pressures P₁ and P₂ are, 

`P_1 = x_1P_1^0 and P_2 = x_2P_2^0`

The vapour pressure of the solution is,

`P_T = P_1 + P_2 = x_1P_1^0 + x_2P_2^0`

`P_T = (1 - x_2) P_1^0 + x_2P_2^0`

`= P_1^0 - x_2P_1^0 + x_2P_2^0`

`= (P_2^0 - P_1^0)x_2 + P_1^0`

The plot of P_T versus x₂ is a straight line III.

The plots of P₁ versus x₁ (I) and P₂ versus x₂ (II) are straight lines passing through the origins.

When `x_1 = 1, x_2 = 0, P_T = P_1^0 and "when"  x = 0, x_2 = 1, P_T = P_2^0`