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

Answer:

73 cups of coffee are needed for lethal dose.

Step-by-step 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:

$x = \frac{200\,mg}{1\,kg}\times 54.431\,kg$

$x = 10886.2\,mg$

And the number of cups of coffee is:

$n = \frac{10886.2\,mg}{150\,mg}$

$n = 72.575$

73 cups of coffee are needed for lethal dose.