Question

The half-life of nicotine in most humans is about 2 hrs, whereas the half-life of cotinine, a by-product of nicotine that is a used as a biomarker for tobacco use, is 20 hrs. Assuming there is a concentration of 20 µM for both substances in your bloodstream after tobacco use (t₀), and the detection limit for both substances is 1 µM, how long would it be before nicotine and cotinine are undetectable? Show all work

Answer 1

Remember first the equation of rate for this situation : A = A0e^-kt

Where A is the final concentration or quantity, A0 os the initial one, k is the constant of velocity and t is the time. Now when you conider a half life, you get ln(2) = kt.

Then, ln(2) = k(2h) for nicotine. K= 0.3466

And ln(2) = k(20h) for cotinine. K= 0.0347

Now the time so that the final concentration of each is 1uM: t = ln(A/A0) / -k

Nicotine: t= ln(1uM/20uM) / -0.3466 = 8.64h

Cotinine: t= ln(1uM/20uM) / -0.0347 = 86.33h