What is the mole fraction of water in 200 g of a solution that is 89% by mass ethanol (C2H5OH)?

• A. 0.11
• B. 0.24
• C. 0.32
• D. 0.76

Answer: (B)

Mole fraction is the ratio of the number of moles of a component to the total number of moles in the solution. Start from the given mass percentages: water makes up 11% of the mass, and ethanol 89%. In 200 g of solution, water mass is 22 g and ethanol mass is 178 g. Convert to moles using molar masses: water is 18.015 g/mol, so n_water ≈ 22 / 18.015 ≈ 1.22 mol. Ethanol has a molar mass of about 46.068 g/mol, so n_ethanol ≈ 178 / 46.068 ≈ 3.86 mol. The total moles ≈ 1.22 + 3.86 ≈ 5.08 mol. Therefore, x_water = n_water / (n_water + n_ethanol) ≈ 1.22 / 5.08 ≈ 0.24.