Question

Caffeine has a half-life of about 6.000 hours in the body (this is real data!) and is eliminated by a first-order process.

What is k for the elimination of caffeine from the body?

There are about 95.0 mg of caffeine per 8 oz. cup of coffee. If you drank two cups of

coffee with lunch at 12:00 PM, how much caffeine is in your body at 9:00 PM?

If you want to make sure you have 20 mg or less of caffeine in your body by 11:00 PM, what is the latest you could have a cup of coffee, rounded to the nearest hour?

Answer 1

T1/2 = half life time = 6 hr

k = 0.693/T1/2

= 0.693/6

= 0.1155 hr-1

first order kinetics

k = (1/t)ln(a0/a)

t = time taken = 9 hr

a0 = initial amount of caffeine taken = 95*2 = 190 mg

a = amount of caffeine left in the body at 9 PM = ?

0.115 = (1/9)ln(190/a)

a = amount of caffeine left in the body at 9 PM = 67.5 mg

If you want to make sure you have 20 mg or less of caffeine in your body by 11:00 PM

the amount of caffiene must be present in a cup of coffee =

t = time = 11 hr

a0 = the amount of caffiene must be present in a cup of coffee = ?

a = minimum amount of caffeine must be in the body by 11 PM = 20 mg

0.115 = (1/11)ln(a0/20)

a0 = 71 mg

the amount of caffiene must be present in a cup of coffee = 71 mg