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


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For an intravenously administered drug, if the concentration at 2 hr is 2.85 mg/mL, and concentration at 6.7 hr is 1.018 mg/mL, then determine the elimination rate constant of the drug. Assume that the drug follows a first order kinetics.


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lb equals 0.219 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 (6.7 hr and 2 hr) is 4.7 hr.
    `\implies k =(ln(2.85/1.018))/4.7`
    Or, `k = 0.219`
    Thus, the rate constant is `0.219 \quad h^{-1}`. (Ans).


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