Question

A person takes a single dose of 500 mg of aspiring. The half life of aspirin in the body is 3 hours. At what point will 97% of the aspirin have left the person’s body?

How can I solve this problem? Step by step

Answer 1

Unless a problem states otherwise, I would assume it is a first order rate of decay. Hence, we would use the first order equations that illustrate and relate kinetics,

`t_(1/2) = 0.693/k`

`ln""([A]_t)/([A]_0) = -kt`

The rate constant is,

`3h = 0.693/k`
`therefore k approx 0.231h^-1`

Subsequently we may realize the amount of time this process takes with our knowledge of its kinetics; it takes,

`ln((1-0.97)/1) = -0.231h^-1*t`
`therefore t approx 15.2h`

for that quantity of aspirin to have "left" the body.