The concentration of a drug in the body is often expressed in units of milligrams per kilogram of body weight.
a) The initial dose of a drug in an animal was 25.0 mg/kg body weight. After 2.00 hours, the concentration had dropped to 15.0 mg/kg body weight. If the drug is eliminated metabolically by a first-order process, what is the rate constant for the process in units of mn‒1
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To find the relationship between concentration and time, we need to use the integrated rate laws. For a first order reaction, the equation is
ln ([A]t/[A]o) = - kt
Where [A] is the amount of the substance at time t and time zero. k is the rate constant and t is the elapsed time. For concentration, we are worried about the ratio between the two species so the amount can be in a variety of units as long as they are both in the same units.
ln (15/25) = - k(2 hr)
Since we want k to be in inverse minutes, it's easiest to change the time to minutes before we calculate the value of k
ln (15/25) = -k (120 min)
k = 0.00426 min^-1
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