What is the mole fraction of ethanol (CH3CH2OH) in an aqueous solution that is 67.6% ethanol by mass?

Question

What is the mole fraction of ethanol (CH3CH2OH) in an aqueous solution that is 67.6% ethanol by mass?

Answer 1

Considering 100g of such solution, there is 67.6g ethanol and 32.4g water.  Since the molar masses of ethanol and water are: 46.068 g/mol and 18.015 g/mol, respectively, the moles of ethanol and water in 100g of this solution are:

ethanol: 67.6/46.068 = 1.467 mole

water: 32.4/18.015 = 1.799 mole

Hence the mole fraction of ethanol (CH3CH2OH) in this aqueous solution is:

1.467/(1.467+1.799) = 44.9%