Question

Solve by using dimensional analysis: "The lethal dose for caffeine is ~150 – 200 mg/kg of body mass. How much caffeine would be lethal for a 120 lbs. person? Assuming 1 cup of strong coffee contains 150 mg of caffeine, how many cups of coffee would that be?”

Answer 1

73 cups of coffee are needed for lethal dose.

Explanation:

A pound equals 0.453 kilograms. Then, the weight of the person is 54.431 kilograms. The total quantity of caffeine needed for such weight is determined by this simple rule of three:

`x = (200\,mg)/(1\,kg)* 54.431\,kg`

`x = 10886.2\,mg`

And the number of cups of coffee is:

`n = (10886.2\,mg)/(150\,mg)`

`n = 72.575`

73 cups of coffee are needed for lethal dose.