15. Former Texas congressman Tom Delay was previously employed as an exterminato

Question

15. Former Texas congressman Tom Delay was previously employed as an exterminator. Assume hire Tom's Pest Control Company to apply an insecticide in your house. At a temperature of 25 degree C the rate constant for the first-order decomposition of the insecticide is 7.70 x10^-3 1/min. The EPA regulated maximum safe exposure concentration for the insecticide in 0.0150 M for children, 0.0100 M for dogs, and 0.0040 for cats and other small animals. Tom applies the pesticide to your house with a concentration of 0.0240 M. Tom's environmental safety disclosure guidelines caution that Homeowners should not allow children or pets to re- enter the house until at least four hours after the time of the herbicide application Are the company's guidelines sufficient to meet the EPA safety limits? Explain your answer. Include calculations to justify your conclusion.

Explanation / Answer

for cats and other small animals , the final concentration is least. So ,the maximum time should be taken for cats and other small animals 'case

So,
we'll check , whether , this time is greater than 4 hours or not.
Now ,

initial concentration,Ao = 0.0240 M

final concentration(for cats and other small animals 'case ) , A =0.0040 M

k = 7.70*10^-3 /min

so ,
for first order
equation is :

k*t = ln ( A/Ao)

7.70*10^-3 *t = ln ( 0.004/0.0240 )

solving this ,
t = 232.696 min = 3.878 hours < (4 hrs , as prescribed by the company))

so ,
Company's guideline are sufficeient to meet the safety limits.

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