An ideal solution is prepared by mixing 57 g of octane ( C ₈ H ₁₈ ) with an unknown mass of heptane ( C ₇ H ₁₆ ). At a certain temperature, the vapour pressures of pure heptane and pure octane are 105 kPa and 45 kPa , respectively. If the total vapour pressure of the solution is 85 kPa , the mass of heptane in the mixture is _______ g.

Step-by-step solution

Let the mole fraction of heptane be X_H and that of octane be X_O . According to Raoult's Law, the total vapour pressure is given by: P_ total = P_H^ X_H + P_O^ X_O 85 = 105 X_H + 45 (1 - X_H) 85 = 105 X_H + 45 - 45 X_H 40 = 60 X_H X_H = 2 3 Since X_H = 2 3 , the mole fraction of octane is X_O = 1 3 . The ratio of the number of moles of heptane to octane is: n_H n_O = X_H X_O = 2/3 1/3 = 2 Molar mass of octane ( C ₈ H ₁₈ ) = 8 12 + 18 1 = 114 g/mol Number of moles of octane ( n_O ) = 57 114 = 0.5 mol Number of mole