Caffeine has a half-life of about 6.000 hours in the body (this is real data!) a
ID: 706328 • Letter: C
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. 1. What is k for the elimination of caffeine from the body? 2. 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? 3.Explanation / Answer
1) t1/2 = 0.693/k
k = 0.693/6 = 0.1155 hour-1
2) Given A = 20 mg, Ao = 95, Find t
Using the equation
ln A = ln Ao - kt
Ao = 95 x 2 = 190 mg
t = 9, k = 0.1155
ln A = ln 95 - 0.1155 x 9 mg
ln A = 4.554 - 1.0395
ln A = 3.5145
A = e3.5145 = 33.6 mg
3) Equation : ln A = ln Ao - kt
ln A = 20, ln Ao = 95, k = 0.1155, Find t
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