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HC is a 55 year old female on a continuous infusion of an antibiotic. The total...

HC is a 55 year old female on a continuous infusion of an antibiotic. The total dose that will be given is 1500 mg over 16 hours. The volume of distribution is 51 L and the drug half life is 6.5 hours.

What is the plasma drug concentration if a blood sample is taken 17 hours after the infusion began? Note: Please provide your answer in units of mg/L.

____

Solutions

Expert Solution

Half life of the drug is 6.5 hours.

Half life of a first order reaction is,

t1/2= 0.693/k

So, k= 0.693/t1/2

k= 0.693/ (6.5 *60*60)s

k= 2.96 * 10-5s-1

Total dose given in 16 hours is 1500 mg. So, to find the concentration of the drug after 17 hours, we have to do the following.

From the equation for first order reaction,

ln [A]t = ln[A]0 -kt

[A]0=1500 mg

t=1 hour = 3600 s

k = 2.96 * 10-5 s-1

So,

ln [A]t= ln [1500] - 2.96 * 10-5s-1 * 3600 s

ln [A]t= 7.21

[A]t= e7.21 = 1574 mg

Drug concentration after 17 hours is 1574 mg.

queen_honey_blossom answered 2 years ago
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