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
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