In your lab you are studying the kinetics of the degradation of a pain killer in
ID: 993058 • Letter: I
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 1.61 M. After 12.96 hours the concentration was found to be 0.8050 M. In another 12.96 hours the concentration was found to be 0.4025 M (t = 25.92 hours overall). If another experiment were set up where the initial concentration of the pain killer was 0.279 M, how long would it take for the pain killer concentration to reach 0.0121 M?
A: 36.6 B: 42.8 C: 50.1 D: 58.7 E: 68.6
Explanation / Answer
This is of first order reaction, since the time taken is same for the concentration will reduced to half in each step.
For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial concentration = 1.61 M
M= concentration left after time t =0.8050 M
t = time = 12.96 hr
Plug the values we get rate constant , k = ( 2.303 /t )x log ( Mo / M)
k = ( 2.303 /12.96 )x log ( 1.61/0.8050)
k = 0.0535 hr-1
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calculation of time taken :
For a first order reaction rate constant , k = ( 2.303 /t )x log ( Mo / M)
Where
Mo = initial concentration = 0.279 M
M= concentration left after time t =0.0121 M
t = time = ?
Plug the values we get time taken, t = ( 2.303 /k )x log ( Mo / M)
= ( 2.303 /0.0535 )x log ( 0.279/0.0121)
= 58.7 hr
Therefore the time taken is 58.7 hr