Question

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 809 ppbm to 10.0 ppbm (parts per billion by mass)

Answer 1

76.0 years

Step-by-step explanation:

Step 1: Given data

• Half-life (t1/2): 12.0 y

• Initial concentration of DDT ([A]₀): 809 ppbm

• Final concentration of DDT ([A]): 10.0 ppbm

• Time elapsed (t): ?

Step 2: Calculate the rate constant (k)

We will use the following expression.

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

Step 3: Calculate the time elapsed

For a first-reaction order, we will use the following equation.

ln [A]/[A]₀ = -k × t

t = ln [A]/[A]₀ / (-k)

t = (ln 10.0 ppbm/809 ppbm) / (-0.0578 y⁻¹)

t = 76.0 y