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BME 100L
Fall 2009
Exam 1
1. 20 mg of a prodrug is infused into the liver at the beginning of a treatment. Within the liver,
the prodrug is metabolized to form the drug. The metabolism can be modeled as a first order
chemical reaction.
where A represents the prodrug and B represents the drug.
The rate constant of metabolism, k,
is 5 hour
1
. Determine
(a) the rate of change of [A],
(b) the rate of change of [B],
(c) the halflife of the prodrug in the liver,
(d) how [B] changes with time by solving the differential equations.
Solution:
]
A
[
k
dt
]
A
[
d
]
A
[
k
dt
]
B
[
d
[A] = [A]
0
exp(kt)
[B] = [A]
0
 [A] = [A]
0
[1  exp(kt)] = (20/V)*[1  exp(5*t)]
where V is the liver volume.
t
1/2
= ln(2)/k = 0.138 hr
2. In the following reactions, k
1
, k
1
, k
2
, and k
2
are known.
(a) Determine the ratios between [A] and [B] and between [A] and [C], in terms of k
1
, k
1
, k
2
, and
k
2
, when all reactions are at equilibrium.
(b) If both k
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 Fall '07
 YUAN

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