In a 200 g sample of solution that is 89% by mass ethanol, what is the mole fraction of ethanol?

• A. 0.24
• B. 0.32
• C. 0.50
• D. 0.76

Answer: (D)

Mole fraction tells us what portion of the total moles in a solution comes from a given component. So we convert masses to moles and then compare.

In this 200 g sample, 89% is ethanol, so there are 178 g of ethanol and 22 g of water. Use molar masses to get moles: ethanol (C2H5OH) is about 46.07 g per mole, so n_ethanol ≈ 178 / 46.07 ≈ 3.86 mol. Water has a molar mass of about 18.02 g/mol, so n_water ≈ 22 / 18.02 ≈ 1.22 mol.

Total moles ≈ 3.86 + 1.22 = 5.08 mol. The mole fraction of ethanol is x_ethanol = n_ethanol / total ≈ 3.86 / 5.08 ≈ 0.76.

So the mole fraction of ethanol is about 0.76. This aligns with ethanol being the majority component by mole in this mixture.