The absorption of a drug by an organism often follows simple kinetics though the mechanism is very c — Physical Chemistry — Kinetics Chemistry Question
Drug kinetics
The absorption of a drug by an organism often follows simple kinetics though the mechanism is very complicated. Consider a drug delivered orally in a common capsule. Let [A]s be its concentration in the stomach and assume that the rate of its introduction into the blood stream is first order with respect to this [A]s. Also assume that the rate by which the drug is metabolized or removed from the blood stream is proportional to its concentration in the blood, [A]b.
Give the plot of [A]s as a function of time and write the equation representing d[A]b/dt.
Model Answer
A_s --k1--> A_b --k2--> products (1)
d[A]_s / dt = -k_1 [A]_s (2)
Integration of Eq. 2 gives [A]_s = [A]_0 exp(-k_1 t), where [A]_0 is the concentration of the drug in the stomach at zero time.
Equation representing d[A]_b / dt:
d[A]_b / dt = k_1 [A]_s - k_2 [A]_b
[VISUAL]
After one hour 75 % of [A]s have been removed from the stomach. What percentage of the initial [A]s will remain in the stomach two hours after taking the drug?
Model Answer
At t = 1 hour, [A]s / [A]0 = 1 - 0.75 = 0.25.
Since 1/4 of the initial amount remains after one hour, (1/4)^2 = 1/16 = 0.0625 will remain after 2 hours, which corresponds to 4 half lives. That is 6.25 % of [A]s is left.