Conversion factors

Question

If the caffeine concentration in a particular brand of soda is 2.33 mg/oz, drinking how many cans of soda would be lethal? Assume that 10.0 g of caffeine is a lethal dose, and there are 12 oz in a can.

Answer 1

If there is 2.33 mg / ounce, the conversion factor to ounces is 1 ounce / 2.33mg. If you multiply this by 10 g (10000 mg caffeine, you get 4292 oz of soda. As there are 12 oz to a can, you would have to drink 4292 / 12 = 358 cans of soda to get a lethal dose.

Answer 2

concentration x volume of can = dose per can. 2.33 mg/oz * 12 oz = X mg/can

known lethal dose 10.0 grams = 10,000 mg (to get the same units)

Lethal dose divided by dose per can = 10000 mg/X mg/can = the number of cans of soda needed to kill