For a caffeinated drink with a caffeine mass percent of 0.51% and a density of 1.00 g/mL, how many mL of the drink would be required to reach an LD50 of 170 mg/kg body mass if the person weighed 171 lb?

(1) convert body mass in lb to kg

211 lb = (211 lb) * (1 kg/2.2046 lb) = 95.71 kg

(2) calculate the amount of caffeine required for a person of that mass at the LD50

(150 mg/kg) * (95.71 kg) = 14356 mg

(3) convert % (w/w) to % (w/v)

0.61% (w/w) = 0.61 g/100 g = (0.61 g) / ((100 g) / (1.00 g/mL)) = 0.61 g/100 mL

(4) calculate the volume that contains the amount of caffeine calculated

14356 mg = 14.356 g = (14.356 g) / (0.61 g/100 mL) = 2353 mL