### 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 3 hr is 2.84 mg/mL, and concentration at 13.1 hr is 1.731 mg/mL, then determine the elimination rate constant of the drug. Assume that the drug follows a first order kinetics. Click on the button below to see the answer and explanations

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lb equals 0.049 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 (13.1 hr and 3 hr) is 10.1 hr.
\implies k =(ln(2.84/1.731))/10.1
Or, k = 0.049
Thus, the rate constant is 0.049 \quad h^{-1}. (Ans).

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