X, Y, and Z are three volatile liquids, which when mixed make an ideal solution. At a given temperature T₀ , the constituents X, Y, and Z have pure vapour pressures in the ratio 3:2:1 . A mixture prepared with mole-fractions of X, Y, and Z in the ratio 1:2:3 starts to boil at temperature T₀ at 1.5 atm pressure. At temperature T₀ , the partial vapour pressure (in atm) of Y is:

Step-by-step solution

Let the pure vapour pressures of X, Y, and Z be P_X^ = 3P , P_Y^ = 2P , and P_Z^ = P . The mole fractions of X, Y, and Z in the mixture are: x_X = 1 1+2+3 = 1 6 x_Y = 2 6 = 1 3 x_Z = 3 6 = 1 2 According to Raoult's law, the total vapour pressure of the ideal solution is: P_ total = x_X P_X^ + x_Y P_Y^ + x_Z P_Z^ Substituting the values: P_ total = ( 1 6 )(3P) + ( 1 3 )(2P) + ( 1 2 )(P) P_ total = P 2 + 2P 3 + P 2 = 5P 3 Since the mixture boils at T₀ at 1.5 atm pressure, the total vapour pressure is 1.5 atm. 5P 3 =