Question

Caffeine has a half-life of approximately 5 h. Suppose you drink a cup of coffee that contains 200 mg of caffeine. How long will it take until there is less than 10 mg of caffeine left in your bloodstream?

Answer 1

25 hours

Explanation:

Half-life describes the time it takes a compound to react or decay.

Half-lives

Half-lives are how long it takes for 50% of the original sample to react, decay, or otherwise dissipate. For example, it takes one half-life for a sample of 100g to become 50g. Then, it takes an additional half-life to become 25g.

The question states that we start with 200mg and want to see how long it takes for there to be less than 10mg of caffeine left. So the first thing we need to do is find how many half-lives this will require. One of the easiest ways to do this is to divide the original sample mass by 2 until the desired mass is reached. For instance, 200/2 = 100, 100/2 = 50, 50/2 = 25. Then, continue this pattern.

• 200 / 2⁵ = 6.25

It requires 5 half-lives to have less than 10mg of caffeine present.

Solving for Time

Now we know that we need 5 half-lives, but the question asks how long this will require. So, to find the time in hours, simply multiply the number of half-lives by the length of the half-life.

• 5 half-lives * 5 hours = 25

So, it will take approximately 25 hours for there to be less than 10mg. Note that at 25 hours, there will be around 6.25 mg. This means that it will take slightly less than 25 hours for there to be exactly 10mg.