The concentration of a drug in the body is often expressed in units of milligrTh

Question

The concentration of a drug in the body is often expressed in units of milligrThe concentration of a drug in the body is often expressed in units of milligrams per kilogram of body weight. The initial dose of a drug in an animal was 24.0 mg/kg body weight. After 1.60 hours, the concentration had dropped to 16.7 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 min-1? Enter your answer in scientific notation:ams per kilogram of body weight. The initial dose of a drug in an animal was 24.0 mg

Explanation / Answer

you have this info
.. order = 1
.. [Ao] = 24.0 mg/kg
.. [At] = 16.70 mg / kg
.. t = 1.6 hr = 96 min
and you want "k"

so.. from that link I gave you
.. ln[At] = -kt + ln[Ao]

rearranging
.. ln[At] - ln[Ao] = -kt

then
.. ln[Ao] - ln[At] = +kt

then since ln(a) - ln(b) = ln(a/b)
.. ln( [Ao] / [At] ) = +kt

and one last time
.. k = ln( [Ao] / [At] ) / t = ln ( 24.0 / 16.70 ) / 96 min = 3.777x10-3 / min

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