教甄◆化學專業/化工科題庫下載題庫

24. After people take the medicine X, it can be absorbed into the body through pathway A→B and enter the blood. Medicine in the blood can reduce its concentration through decomposition (B→C) or excretion (B→D), as shown in the figure below:

Assume that the process A→B is much faster than those of B→C and B→D. Therefore, each time a medicine with a dose of [X]_o is taken, it can be regarded as immediately producing a concentration of [X]_b (= 0.020 mM) of X in the blood. Assume that B→C and B→D are both first-order processes, and their rate constants are k₁ (= 0.075 h^-1 ) and k₂ (= 0.025 h^-1 ), respectively. If a person takes the same dose ([X]_o) of the medicine every t hour, answer the following questions.
(A) Just after taking the medicine for the n^th time, its concentration in the blood is equal to [P]_n. Express [P]_n as a function of [X]_b, k₁, k₂ and t.    3%
(B) Continue to take the medicine every 6 hours for a long period of time (n→∞), calculate [P]_∞ (in mM)?    3%
(C) Find the half-life of the medicine in the blood.    2%
(D) What proportion of the decrease in medicine concentration in the blood is caused by decomposition?    2%