Book Problem 15.21

[704578485]

Problem 15.21 of the book involves a scenario in which you administer to a patient 20.mg of a beta blocking drug. The reaction that eliminates the drug from the body is a first order reaction with a k of 7.6x10^-3 min^-1. The question ask what mass of the beta drug will still be in the body after 5 hours. The answer the book gives is 2.0mg and I cannot see how they are getting that answer.

[Erin Murashige 1L]

I think you use the formula ln[A]t/[A]0=-kt. Then k will be the 7.6 x 10^-3 and t will be 300 minutes since it is 5 hours. Then after simplifying the equation you'll get that 10% of the initial drug concentration remains in the body. Then 10% of 20 mg will be 2.0 mg.

[Gurkriti Ahluwalia 1K]

note that in solving for this the ln's DO NOT cancel, instead you use the inverse operation (e^) to get rid of the lns, and then divide both sides by A0 to get At=10% of A initial.

[Beza Ayalew 1I]

the solution doesn't plug in 20mg as the initial concentration, but if you do that the same values come out, and i found doing that easier to grasp because you can just directly solve for the final concentration

[torieoishi1A]

First start with the equation: ln(A/A(initial)=-kt
Then plug in k(7.6x10^-3/min) and t (5 hours but use 300 min)
Second you will now have: ln(A/A(initial)=-2.28
Cancel out on by using e: (A/A(initial)=e^-2.28
A(initial)= 20mg
Solve for A which is 2.0 mg

[Gwyneth Huynh 1J]

So to clarify, can we substitute mass for concentration? Or are we supposed to find the ratio of the initial and final concentration and use that to find the final mass?