Question

What is the mole fraction of water in a solution containing water and ethanol that is 470% water by mass?

Answer 1

Water by mass = 47%

The solution contains 47 grams of H₂O

So weight % of C₂H₅OH is 53 grams

Molecular mass of C₂H₅OH = 46 grams/mole.

Molar mass of water is 18 grams/mole.

Moles of C₂H₅OH = 53 grams of C₂H₅OH /Molar mass of C₂H₅OH

                                 = 53 g/46g/mole = 1.1522 mole

Moles of water = 47grams of H₂O / molar mass of H₂O

=47g/18 g/mole = 2.6111moles

Mole fraction of H₂O = Moles of water/(Moles of water + moles of ethyl alcohol)

                                      = 2.6111moles /(2.6111moles +1.1522moles)

                                      = 0.6938

Mole fraction of H₂O = 0.694