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 0.33 mg/mL, and concentration at 8.7 hr is 0.222 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 0.059 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 (8.7 hr and 2 hr) is 6.7 hr.
`\implies k =(ln(0.33/0.222))/6.7`
Or, `k = 0.059`
Thus, the rate constant is `0.059 \quad h^{-1}`. (Ans).