Abiochemist studying breakdown of the insecticide ddt finds that it decomposes by a first order reaction with a half life of 12.0 years. how long does it take ddt in a soil sample to decompose from 413 ppbm to 10.0 ppbm (parts per billion by mass)?

64.4 years

Explanation:

The half-life (t1/2) for the first order breakdown of DDT is 12.0 years. The rate constant (k) is:

k = ln 2 / t1/2 = ln 2 / 12.0 y = 0.0578 y⁻¹

We can find the time (t) for an initial concentration A₀ = 413 ppbm to decrease to A(t) = 10.0 ppbm, using the following expression.