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 1.51 M. After 15.58 hours the concentration was found to be 0.7550 M. In another 15.58 hours the concentration was found to be 0.3775 M (t = 31.16 hours overall).

If another experiment were set up where the initial concentration of the pain killer was 0.383 M, how long would it take for the pain killer concentration to reach 0.0205 M?

Also, for this type of problem, how can I determine the order?

Answer 1

In the first experiment , the initial concentration of painkiller was 1.51 M , which reduced to half , i.e. 0.7550 in 15.58 hours , which indicates that the half life periof of the painkiller is 15.58 hours .

In next 15.58 hours , the concentration of the pain killer reduced to half again .

The half life of the reactant did not change with the initial concentration , i.e. it is independent of the initial concentration of the reactant and remains constant , which suggests that the reaction is first order reaction .

t 0.5 = 0.693 / k

k = 0.693 / 15.58

k = 0.04448

Now when the initial concentration is 0.383 M , time required to reach 0.0205 M can be calculated using the formula:

Nt = No (1/2)^{t / t 0.5}

where Nt is the final concentration

No is the initial concentration

t is the amount of time lapsed

t 0.5 is the half life period

putting all the values we get ,

0.0205 = 0.383 (1/2)^{t / 15.58}

t = 65.8 hours

And the reaction is first order as already explained above .