Question

The rate at which a certain drug is eliminated by the body follows first-order kinetics, with a half life of 29 minutes. Suppose in a particular patient the concentration of this drug in the bloodstream immediately after injection is 1.8/μgmL. What will the concentration be 145 minutes later? Round your answer to 2 significant digits.

Answer 1

The first order rate law is given as

ln [A] = -kt + ln [A]₀

where [A] denotes the concentration of the drug at time t and [A]₀ is the concentration at t = 0. k is the first order rate constant and is related to the half life as

k = 0.693/t_1/2

where t_1/2 denotes the half life of the reaction.

Therefore,

ln [A]/[A]₀ = -kt

======> ln [A]/(1.8 µg/mL) = -0.693/(29 min)*(145 min)

======> ln [A]/(1.8 µg/mL) = -3.465

======> [A]/(1.8 µg/mL) = exp(-3.465)

======> [A]/(1.8 µg/mL) = 0.03127

======> [A] = 0.03127*(1.8 µg/mL)

======> [A] = 0.056286 µg/mL ≈ 0.056 µg/mL

The concentration of the drug in the bloodstream 145 minutes after the injection = 0.056 µg/mL (ans).