Question

DOT (molt mass35449mol) was a widely used insecticide that was banned from use in the United States in 1973. This ban was brought about due to the persistence of DDT in many different com , leading to high accum s of the substance in many buds of prey. The insecticide was shown to cause a thinning of ea shells, pushing many birds towards extinction. If a 20-L drum of DDT was spelled into a pood, multing in a DOT concentration of 9/9 X 10 how long would it take for the levels of DDT to reach a concentration of 1.41 x 10" Ma level that is generally assumed safe in mama m e the decomposition of DDT is a first-order process with a half life of 560 days Time days

Answer 1

The integrated rate equation for a first order process is

In 4= -kt + In 40

Where

At = concentration at timet
(for us
A = 1.41 x 10-7 M
)

A0 = concentration at time t=0
(for us
40 = 9.49 x 10-5 M
)

k = rate constant

Now, the rate constant is related to the half life of a first order process as follows:

In 2 1/2

Given that half life for DDT is 56.0 days,

In 2 tu 0 .693 = 0.01238 days-1 56.0 days

Hence, putting in the values in the integrated rate equation, we can calculate the time t needed to get to the desired concentration of DDT.

In A4 = -kt + In 40 In(1.41 x 10-?M) = -0.01238 days 1 x t + ln(9.49 x 10-5 M) 9.49 x 10-5 0.01238 days 1 x t = ln 6.5118 t=a 0.01238 days-1 - 1 526 days 1.41 x 10-7 = 6.5118

hence, it will take 526 days for the DDT concentration to decrease to acceptable level.

Hence, answer is

Time = 526 days