Two binary solutions, A and B, are prepared using the same non-volatile solute X and solvent Y. In solution A, the mole fraction of X is 0.5 . In solution B, the mole fraction of X is 0.8 . If 100 g of solution A is mixed with 400 g of solution B, the mass percentage of solute X in the final mixture is ________. (Integer answer) (Given: Molar mass of X = 40 g mol ⁻¹ , Molar mass of Y = 160 g mol ⁻¹ )

Step-by-step solution

For solution A: Mole fraction of X is 0.5 , so mole fraction of Y is 0.5 . Let the total number of moles be 1 . Mass of X = 0.5 40 = 20 g Mass of Y = 0.5 160 = 80 g Total mass of solution A = 20 + 80 = 100 g Mass percentage of X in A = 20 100 100 = 20 % For solution B: Mole fraction of X is 0.8 , so mole fraction of Y is 0.2 . Let the total number of moles be 1 . Mass of X = 0.8 40 = 32 g Mass of Y = 0.2 160 = 32 g Total mass of solution B = 32 + 32 = 64 g Mass percentage of X in B = 32 64 100 = 50 % Mixing the sol