Passage: Two volatile liquids A and B form an ideal solution. Consider a 5 molal solution of B in A inside a closed container having a total vapour pressure of 100 mm Hg at 300 K. The vapour pressure of pure A at 300 K is 105 mm Hg. Assume that A and B behave as ideal gases in the vapour phase. Given: The gas constant R = 0.08 L atm K ⁻¹ mol ⁻¹ Molar mass of A is 50 g mol ⁻¹ Molar mass of B is 57 g mol ⁻¹ Density of

Step-by-step solution

For a 5 molal solution of B in A, there are 5 moles of B in 1000 g of A. Moles of A = 1000 50 = 20 mol. Mole fraction of B, x_B = 5 20 + 5 = 0.2 Mole fraction of A, x_A = 1 - 0.2 = 0.8 Using Raoult's law for the total vapour pressure: P_T = P_A^ x_A + P_B^ x_B 100 = 105 0.8 + P_B^ 0.2 100 = 84 + 0.2 P_B^ 0.2 P_B^ = 16 P_B^ = 80 mm Hg The molar volume of pure B in the liquid phase ( V_ m,l ) is: V_ m,l = Molar mass of B Density of liquid B = 57 0.5 = 114 mL/mol = 0.114 L/mol Assuming pure B behaves as an ideal gas i