Two volatile liquids X and Y form an ideal solution at 298 K and have vapour pressures equal to 100 mm and 200 mm of Hg respectively in their pure state. The mole fraction of X in the solution is 0.4 and the mole fraction of Y in the vapour phase is a/20. Calculate the value of a.

Step-by-step solution

Given the pure vapour pressures P^ _ X = 100 mm Hg and P^ _ Y = 200 mm Hg. The mole fraction of X in the liquid phase is x_ X = 0.4 . Therefore, the mole fraction of Y in the liquid phase is x_ Y = 1 - 0.4 = 0.6 . Using Raoult's Law, the partial pressures of X and Y are: P_ X = x_ X P^ _ X = 0.4 100 = 40 mm Hg P_ Y = x_ Y P^ _ Y = 0.6 200 = 120 mm Hg The total pressure of the solution is P_ total = P_ X + P_ Y = 40 + 120 = 160 mm Hg. The mole fraction of Y in the vapour phase, denoted as y_ Y , is given by: y_ Y =