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 4 hr is 0.4 mg/mL, and concentration at 10.2 hr is 0.314 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 17.77 h 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 (10.2 hr and 4 hr) is 6.2 hr.
`\implies k =(ln(0.4/0.314))/6.2`
Or, `k = 0.039`
Thus, the rate constant is `0.039 \quad h^{-1}`.
Now, to calculate the half life from rate constant: `t_{1/2}=0.693/k=0.693/(0.039 \quad h^(-1))=17.77 \quad h` (Ans).