Bioremediation is a process where bacteria are deployed to mitigate an environme
ID: 483143 • Letter: B
Question
Bioremediation is a process where bacteria are deployed to mitigate an environmental disaster, such as an oil spill. The efficiency of bacteria for destroying oil (hydrocarbons) depends on many environmental factors. When cleaning a certain oil spill it was found that the bacteria remove oil in a second-order process (with respect to the oil) with a rate constant of 2 times 10^-6 M^-1 s^-1. The initial concentration of the oil is 3.5 times 10^-4 M. How many clays does it take the bacteria to remove 90% of the oil from the water? What is the first half-life for the decomposition of the oil by the bacteria? What is the second half-life for the decomposition of the oil by the bacteria?Explanation / Answer
a)
[A]o = 3.5*10^-4 M
90 % is removed, so remaining is 10%
[A]= 10% of 3.5*10^-4 M = 3.5*10^-5 M
use integrated rate law for 2nd order reaction:
1/[A]o = 1/[A] - k*t
1/(3.5*10^-4) = 1/(3.5*10^-5) - (2*10^-6)*t
(2*10^-6)*t = 2.57*10^4
t = 1.29*10^10 s
= (1.29*10^10)/(24*3600) days
= 1.49*10^5 days
Answer: 1.49*10^5 days
b)
half life of 2nd order reaction is given by,
t1/2 = 1 / (k*[A]o)
t1/2 = 1/(2*10^-6 * 3.5*10^-4)
= 1.43*10^9 seconds
Answer: 1.43*10^9 seconds
c)
after 1st half life concetration, [A]o = (3.5*10^-4)/2 M = 1.75*10^-4 M
t1/2 = 1 / (k*[A]o)
t1/2 = 1/(2*10^-6 * 1.75*10^-4)
= 2.86*10^9 seconds
Answer: 2.86*10^9 seconds
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