Question

Since October 2004, Jack Daniels Tennessee whisky, produced in Lynchburg, TN, has been bottled at 80 proof (40% alcohol by volume). Given that the density of ethyl alcohol is 0.789 g/cm3, and that of water 1.00 g/cm3, calculate the concentration of the alcohol in (a) percent by weight and (b) molarity (moles per liter).

Answer 1

40% v/v means 40 mL EtOH/100 mL soln.
For EtOH, 40 mL has a mass of 40 mL x 0.789 g/mL = ? grams.
?grams/molar mass EtOH = mols and mols/L = M. The volume is 100 mL which is 0.1 L.

For %w/w you have the conversion of 40 mL EtOH to grams. We want g EtOH/100 g soln. I think you need the density of the solution but you don't show it. We can estimate that 40% v/v means 40 mL EtOH/(40 mL EtOH + 60 mL H2O).
40 mL EtOH = about 31.6g in (31.6g + 60g) soln or (31.6/91.6)*100 = % w/w.
That isn't quite right because it is based on 40 mL EtOH + 60 mL H2O = 100 mL soln and that isn't right. Actually, it occupies only about 96 mL