In a 78.0-g aqueous solution of methanol, CH4O, the mole fraction of methanol is 0.180. What is the mass of each component?

Molar mass of CH₄O = (12.0 + 1.0×4 + 16.0) g/mol = 32.0 g/mol
Molar mass of H₂O = (1.0×2 + 16.0) g/mol = 18.0 g/mol

Mole ratio CH₄O : H₂O = 0.180 : (1 - 0.180) = 0.180 : 0.820
Mass ratio CH₄O : H₂O = (0.180 × 32) : (0.820 × 18.0) = 5.76 : 14.76

Mass of CH₄O in the solution = (78.0 g) × [5.76/(5.76 + 14.76)] = 21.9 g
Mass of H₂O in the solution = (78.0 - 21.9) g = 56.1 g