The metabolism of an antibiotic, A,is a first-order rate process. The rate constant, k, for this process depends on temperature and body weight, but for a 70 kg man at `37^(@)` C its value is `k = 3.0 xx10^(-5) S^(-1)` . How long after taking the first pill containing 400 mg of antibiotic must this man take the second pill to keep the concentration at 200 mg per 100 kg body weight? [ Asume instantaneous uniform distribution of the antibiotic throughout the body.]

Options

A. `0.7 xx10^(4)` s
B. `1.5 xx10^(4)` s
C. `1.4 xx10^(4)` s
D. `3.5 xx10^(4)` s

Answer

D

Explanation

The minium weight required to be maintained by a 70 kg man is `(200xx70)/(100)=140 mg`
`rarrt=(1)/(k) ln (400/(140)=(1.05)/(3xx10^(-5)))=3.5 xx10^(4) sec`