If the caffeine concentration in a particular brand of soda is 2.85 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.

2,375 cans

Explanation:

The strategy here is to use the information given to calculate the lethal dosage contained in the number of cans we will compute.

We know the lethal dosage is

Ld = 10.0 g caffeine

and we also know that the oncentration of caffeine is:

2.85 mg / oz

So our problem simplifies to calculate how many oz will contain the lethal dose, and then given the ounces per can determine how many cans are required.

First convert the lethal dose in grams to mg:

Ld = (10 g x 1000 mg) = 10,000 mg caffeine

10,000 mg x (1 Oz / 2.85 mg) = 28,500 oz

28500 oz x (1 can/12 oz) = 2,375 cans

We could also have calculated it in one step using conversion factors:

Number of cans = 10000 mg x 1 oz / 2.85 mg x 1 can / oz = 2,375 cans