Two liquids A and B form an ideal solution at temperature T K. At T K, the vapour pressures of pure A and B are 55 and 15 kN m ⁻² respectively. What is the mole fraction of A in solution of A and B in equilibrium with a vapour in which the mole fraction of A is 0.8 ?

Step-by-step solution

For an ideal solution with Raoult's law, the partial pressure of A in vapour is P_A = P_A^0 y_A where y_A = 0.8 is the mole fraction in vapour phase. Thus P_A = 55 0.8 = 44 kNm ⁻² . Using the equilibrium condition y_A = P_A^0 _A P_ total where _A is mole fraction in liquid and P_ total = P_A^0 _A + P_B^0(1- _A) : 0.8 = 55 _A 55 _A + 15(1- _A) 0.8(55 _A + 15 - 15 _A) = 55 _A 44 _A + 12 - 12 _A = 55 _A 12 = 23 _A _A = 0.5217