Question

For a caffeinated drink with a caffeine mass percent of 0.55% and a density of 1.00 g/mL, how many mL of the drink would be required to reach an LD50 of 150 mg/kg body mass if the person weighed 219 lb?

Answer 1

LD50 Caffeine = 150 mg caffeine/ kg of body mass

Answer 2

1lb = 0.454 kg so the body mass is 99.426 kg

Answer 3

Please continue, you're on the right track.

Answer 4

99.426 kg x (150 mg caffeine/ kg of body mass) = A mg caffeine
A mg caffeine x 100 mL caffeinated drink/ 0.55 mg caffeine = B mL caffeinated drink

Answer 5

I notice that you carefully include units in every conversion calculation. This is \(the\) way to analyze this type of problems, well done! :)

Answer 6

So by doing the above work, my answer came out to be 2711618.182. Should it be that high?

Answer 7

\[10.215 g Caffeine \times \frac{ 30.0 mL Caffeine }{ 0.217 g Caffeine } =1412.2 mL Coffee\]
This is the example that the book gave. The 10.215 is the LD50. But I don't know how to set this up without knowing how many mL of coffee I was given. Am I supposed to figure that out with the given 0.55% caffeine mass percent?

Answer 8

Well, sorry that I missed the units when dividing by 0.0055.
Mass percentage means every 100 mL of coffee, there are 0.55 grams of caffeine.
So reorganized:
`99.426 kg x (150 mg caffeine/ kg of body mass) = A mg caffeine`
`A mg caffeine x 100 mL caffeinated drink/ 0.55 mg caffeine = B mL caffeinated drink`
would read:
99.426 kg x (150 mg caffeine/ kg of body mass) = A mg caffeine
A\(\color{red}{/1000~g}\) caffeine x 100 mL caffeinated drink/ 0.55 \(\color{red}{g}\) caffeine = B mL caffeinated drink
This gives 2711.6 mL, which is about 11 cups.

Answer 9

Thank you!

Answer 10

You're welcome! :)