Sammy the stoner has been enjoying the new state marijuana law in Washington a l

Question

Sammy the stoner has been enjoying the new state marijuana law in Washington a little too
much. Now he is worried since he accepted a job at a company out of Washington state and he
found out that the company will be firing employees who fail mandatory drug tests. Assume the
half-life of cannabinol in the body is 7.4 days and that it is metabolized in a first-order process
starting from an initial concentration of 100 ppm (parts per million). For how long does Sammy
have to stay clean in order to reach 2 ppm (a value just below the detection threshold of the
test)?

Explanation / Answer

Rate constant, K = 0.693/(half life) = 0.09365 day(-1)

t = (2.303/K)log (final conc/initial conc.) = 24.59 X log (100/2)=24.59 X 1.689 = 41.78 days

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