Question

a biochemist studying the breakdown of the insecticide ddt finds that it decomposes by a first-order reaction with a half-life of 11.6 years. how long (in years) does it take ddt in a soil sample to decrease from 294 ppbm to 19 ppbm (part per billion by mass)? enter to 1 decimal place.

Answer 1

To calculate how long it takes for the DDT concentration in a soil sample to decrease, we can use the half-life formula for first-order reactions. By substituting the given values into the formula, we can determine the total time required.

Step-by-step explanation:

The decomposition of DDT follows a first-order reaction with a half-life of 11.6 years. To determine how long it takes for the concentration of DDT in a soil sample to decrease from 294 ppbm to 19 ppbm, we can use the half-life formula for first-order reactions.

First, let's calculate the number of half-lives required:

Number of half-lives = ln(initial concentration / final concentration) / ln(2)

After determining the number of half-lives, multiply it by the half-life of DDT to get the total time:

Total time = Number of half-lives * Half-life of DDT

Substituting the given values, we get:

Total time = [(ln(294/19)) / ln(2)] * 11.6 years

Calculating this expression gives us the total time it takes for DDT in the soil sample to decrease from 294 ppbm to 19 ppbm.