DDT (molar mass = 354.49 g/mol) was a widely used insecticide that was banned fr
ID: 823056 • Letter: D
Question
DDT (molar mass = 354.49 g/mol) was a widely used insecticide that was banned from use in the United States in 1973. This ban was brought about due to the persistence of DDT in many different ecosystems, leading to high accumulations of the substance in many birds of prey. The insecticide was shown to cause a thinning of egg shells, pushing many birds towards extinction. If a 20-L drum of DDT was spilled into a pond, resulting in a DDT concentration of 2.73x10^-5M, how long would it take for the levels of DDT to reach a concentration of 1.41x10^-7M (a level that is generally assumed safe in mammals)? Assume the decomposition of DDT is a first-order process with a half-life of 56.0 days.
Time = days
Explanation / Answer
initial concentration =2.73x10^-5M
final concentration=1.41x10^-7M
as decay is first order so halflife time = 0.693/k
so k =0.693/56 =0.012375 per day
first order decay [Cf]/[Ci]= exp^-kt
so ln [Cf]/[Ci = -kt
ln 1.41x10^-7/2.73x10^-5 =- 0.012375t
give t =425.52 days
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