Question

Consider a person who has consumed a quart (32oz.) of 3.2% (v/v) beer. What is the millimolar concentration of alcohol in the aqueous portion of this person’s body? Assume the alcohol is fully distributed and has not begun to be metabolized or excreted.

Hint: the human body contains approximately 40L of water, the density of ethanol is 0.789g mL-1, and 32 fluid ounces equals 0.94633L

Answer 1

We have 32 oz = 0.94633 L; therefore, 1 = (1 oz)*(0.94633 L/32 oz). The density of ethanol is 0.789 g/mL.

The concentration of beer is 3.2%(v/v), i.e, 3.2 oz beer per 100 oz fluid. Since the person consumed 32 oz alcohol, the volume of beer consumed = (3.2 oz/100 oz)*(32 oz) = 1.024 oz = (1.024 oz)*(0.94633 L/32 oz) = 0.030282 L.

Mass of ethanol consumed (beer contains ethanol) = (0.030282 L)*(1000 mL/1 L)*(0.789 g/mL) = 23.892498 g.

Molar mass of ethanol, C₂H₆O = (2*12.01 + 6*1.008 + 1*15.9994) g/mol = 46.0674 g/mol.

Mole(s) of ethanol corresponding to 23.892498 g ethanol = (23.892498 g)/(46.0674 g/mol) = 0.518642 mole.

Volume of water in the body = 40 L; therefore, millimolar concentration of ethanol in the body liquid is (0.518642 mole)/(40 L)*(1000 millimolar/1 mol/L) = 12.96605 mM ≈ 13.0 mM (ans).