Kinetics #1. A microorganism degrades benzene with a first order rate constant o

Question

Kinetics #1. A microorganism degrades benzene with a first order rate constant of 0.0371 day 1 a. What is the half-life of benzene? b. If a groundwater contaminated with 37 mg/L of benzene is treated by injecting the microorganism into the aquifer, how long will it take for the benzene level in the groundwater to drop below 3 mg/L? below 1 mg/L? Kinetics #2. In a laboratory study, you examine the degradation of two unknown chemicals (A and B) my measuring their concentration in solution over time. The results are shown in the attached table. For each of the two chemicals, determine: c, the order of the degradation reaction d. the reaction rate constants for the degradation of A and of B e. the corresponding halflives of A and B in the solution

Explanation / Answer

For the 1st order rate constant, half-life,

t1/2=ln2 / k0.693 / k

here rate constant k = 0.0371 day-1

then half time =

t1/2= 0.693 / k

= 0.693/ 0.0371 day-1

= 18.68 days

For 1st order reaction:

ln[A]=kt+ln[A]o.

here [A]= 3 mg/ L

[A0]= 37 mg/L

k = 0.0371 day-1

ln[A]=kt+ln[A]o.

ln 3 = 0.0371 day-1 * t+ln 37

1.099 = 0.0371 day-1 * t+ 3.61

-2.511 = = 0.0371 day-1 * t

t = 67.98 days

here [A]= 1 mg/ L

[A0]= 37 mg/L

k = 0.0371 day-1

ln[A]=kt+ln[A]o.

ln 1 = 0.0371 day-1 * t+ln 37

0.0 = 0.0371 day-1 * t+ 3.61

-3.61 = = 0.0371 day-1 * t

t = 97.3 days

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