T06) Find half life 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 1 hr is 2.5 mg/mL, and concentration at 9.1 hr is 0.707 mg/mL, then determine the elimination half life of the drug. Assume that the drug follows a first order kinetics.


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lb equals 4.44 h 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 (9.1 hr and 1 hr) is 8.1 hr.
    `\implies k =(ln(2.5/0.707))/8.1`
    Or, `k = 0.156`
    Thus, the rate constant is `0.156 \quad h^{-1}`.
    Now, to calculate the half life from rate constant: `t_{1/2}=0.693/k=0.693/(0.156 \quad h^(-1))=4.44 \quad h` (Ans).