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 5 hr is 1.51 mg/mL, and concentration at 14.2 hr is 0.42 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 0.139 h-1 kg
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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 (14.2 hr and 5 hr) is 9.2 hr.
`\implies k =(ln(1.51/0.42))/9.2`
Or, `k = 0.139`
Thus, the rate constant is `0.139 \quad h^{-1}`. (Ans).