T08) Find t from Ct, C0 and half-life

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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A patient (75 Kg) is receiving an IV bolus administration of a drug. The plasma concentration was found to be 2.72 mg/L, when the blood was first collected. If the drug follows a first order elimination and the elimination half life (t1/2) is 2.11 hr, then how long will it take to reach the plasma concentration to 0.067 mg/L?


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lb equals 11.3 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`
    `\implies t = ln(C_{0}/C_{t})/k` ..... (1)
    However, the question did not provide k, but we can derive it from:
    `k=0.693/t_{1/2}=0.693/2.11`.
    Plugging values in equation (1),
    `t =(ln(2.72/0.067))/(0.693/2.11)`
    Or, `t = 11.3`
    Thus, required time is `11.3 \quad h`.(Ans).


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