A biochemist studying breakdown of the insecticide DDT finds that it decomposes by a first-order reaction with a half-life of 12.0 yr. How long does it take DDT in a soil sample to decompose from 655 ppbm to 10.0 ppbm (parts per billion by mass) ?

Given that,

Half life = 12years

How long does it take to decompose form 655ppbm to 10ppbm.

Rate of decay is given as

Q=Qo• exp (-λt)

at t=0 Qo=655

Then, Q=10

λ is decay rate and it is

λ = In2 / t½

λ = In2/12

λ=0.05776

Therefore,

Q=Qo• exp (-λt)

10=655exp (-0.05776t)

10/655=exp (-0.05776t)

0.01527=exp (-0.05776t)

Take In of both sides

In (0.01527) = -0.05776t

-4.182=-0.05776t

Then, t=-4.182/-0.05776

t=72.4years

Then the time to decay to 10ppbm is 72 years and 3 months

Or 72 years approximately