In your lab you are studying the kinetics of the degradation of a pain killer in

Question

In your lab you are studying the kinetics of the degradation of a pain killer in the human liver. You are monitoring the concentration of the pain killer over a period of time. The initial concentration of the pain killer in your experiment was 1.93 M. After 34.15 hours the concentration was found to be 0.9650 M. In another 34.15 hours the concentration was found to be 0.4825 M (t = 68.3 hours overall). If another experiment were set up where the initial concentration of the pain killer was 0.453 M, how long would it take for the pain killer concentration to reach 0.0149 M?

Explanation / Answer

ln(A) = ln(A)0 - kt

ln(0.965) = ln(1.93) - k*(34.15)

k = -(ln(0.965) -  ln(1.93) )/(34.15) = 0.02029

proof

ln(A) = ln(A)0 - kt

ln(0.4825) = ln(0.965) - k*34.15

k =-( ln(0.4825) - ln(0.965) ) /34.15 = 0.02029

so...

ln(0.0149) = ln(0.453) - 0.02029*t

t = (ln(0.0149)- ln(0.453))/(-0.02029)

t = 168.2863 hours

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