Mass percent and molality?

Question

A bottle of wine contains 12.5% ethanol by volume. The density of ethanol (C2H5OH) is 0.789 g/cm3. Calculate the concentration of ethanol in wine in terms of mass percent and molality.

Answer 1

Take a given volume of wine - say 1L (enough to keep you happy for a bit! But don't drink it until after we finish the experiment...).

This consists of 125 mL ethanol and (we can assume) 875 mL water, since it is 12.5% ethanol by volume.

This water weighs 875 g since the density of water is 1.00 g/cm^3. The ethanol weighs (0.789)(125) = 98.6 g, so the toal weight is 875 + 98.6 = 973.6 g. The percentage of ethanol by mass is thus (98.6 / 973.6) * 100 = 10.1%.

Ethanol has a molecular mass of 2*12.0 + 6*1.00 + 1*16.0 = 46.0. So in 1L of wine we have 98.6 g = 98.6 / 46.0 mol = 2.14 mol. So the concentration of ethanol is 2.14 mol / L.