# 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...

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

mlsiasebs | College Teacher | (Level 1) Associate Educator

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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