A biochemist studying the breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with a half-life of 12 yr. How long does it take DDT in a soil sample to decrease from 275 ppbm to 10. ppbm (parts per billion by mass)?

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23-08-2022
Chemistry

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A biochemist studying the breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with a half-life of 12 yr. How long does it take DDT in a soil sample to decrease from 275 ppbm to 10. ppbm (parts per billion by mass)?

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mahima6824soni mahima6824soni · Answer 1 · 2022-09-03T15:59:25+02:00

The DDT will take 57 year in a soil sample to decompose from 275 ppbm to 10.0 ppbm (parts per billion by mass).

What is DDT?

The full form of DDT is Dichlorodiphenyltrichloroethane.

12-year half-life

Decomposition of DDT from 275 ppbm to 10 ppbm in a soil sample (parts per billion by mass)

First, we must solve the first-order half-life equation for k to determine the reaction's rate constant, or k. The time must then be calculated using the first-order integrated rate law expression.

It is known that t1/2 = ln2

Or k = ln2/t1/2

= ln2/12 = 5.776210-2 yr-1

The 1st order integrated rate law can be written as,

ln = -kt

ln = -(5.776210-2 yr-1) t

t = 57.37 yr or 57 yr (rounded)

Thus, the time taken to decompose DDT is 57 years.

Learn more about DDT, here:

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