Pesticides are routinely sprayed on crops that we eat. There are government regu

Question

Pesticides are routinely sprayed on crops that we eat. There are government regulations to control the minimum time between when the crops are sprayed and the time the crops are sold for consumption. The idea is that this gives the chemical time to break down before consumers eat the food item. If the government safely level for a given pesticide is 0.500 ppm, then how long do you have to wait since the last pesticide application if the last application resulted in 41.0 ppm of the chemical on the crop? The half-life for this pesticide is 36.0 hours. Assume first order kinetics. The units for the answer are hours.

Explanation / Answer

we know that

for first order kinetics

ln[A] = ln [Ao] - kt

so

ln [Ao] - ln [A] = kt

ln [Ao/A] = kt

also

rate constant is given by

k = 0.693 / half life

so

k = 0.693/36

k = 0.01925

now

given

[Ao] = 41 pppm

[A] = 0.5 ppm

so

using those values

we get

ln ( 41 / 0.5) = kt

kt = 4.407

t = 4.407/k

t = 4.407/0.01925

t = 228.92 hours

so

the wait should be for 228.92 hours

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