T05) Find k from C0, Ct and t.

50. Pharmacokinetics 50.2) Plasma concentrations over time 50.2.1) Plasma concentrations over time

T01: Later plasma concentration Normal 1


Total tried:       Correct:       Wrong:

For an intravenously administered drug, if the concentration at 1 hr is 1.54 mg/mL, and concentration at 12.8 hr is 0.095 mg/mL, then determine the elimination rate constant of the drug. Assume that the drug follows a first order kinetics.


Click on the button below to see the answer and explanations

lb equals 0.236 h-1 kg

    For a first order process,
    `C_{t}=C_{0}×e^(-kt)`
    It may be re-organized as:
    `ln(C_{t})=ln(C_{0})-kt`
    `∴ k = ln(C_{0}/C_{t})/t`
    Difference between two time points (12.8 hr and 1 hr) is 11.8 hr.
    `\implies k =(ln(1.54/0.095))/11.8`
    Or, `k = 0.236`
    Thus, the rate constant is `0.236 \quad h^{-1}`. (Ans).