Question

As with any drug, aspirin (acetylsalicylic acid) must remain in the bloodstream long enough to be effective. Assume that the removal of aspirin from the bloodstream into the urine is a first-order reaction, with a half-life of about 3 hours. The instructions on an aspirin bottle say to take 1 or 2 tablets every 4 hours. If a person takes 1 aspirin tablet, how much aspirin remains in the bloodstream when it is time for the second dose? (A standard tablet contains 400. mg of aspirin.)

Answer 1

180 mg

Step-by-step explanation:

For a first-order reaction, we can calculate the amount of aspirine (A) at a certain time (t) using the following expression.

`A=A_(0).e^(-k.t)`

where,

k: rate constant

A₀: initial amount

If we know the half-life (
`t_(1/2)`) we can calculate the rate constant.

`k=(ln2)/(t_(1/2)) =(ln2)/(3h) =0.2h^(-1)`

When t = 4 h and A₀ = 400 mg, A is:

`A=400mg.e^{-0.2h^(-1)* 4h} =180mg`