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
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).
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