contestada

A biochemist 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)?

Respuesta :

dsdrajlin

Answer:

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.

[tex]A(t)=A_{0}e^{-k.t} \\10.0ppbm=413ppbm.e^{-0.0578y^{-1}t } \\t=64.4y[/tex]

mahima6824soni

The DDT will take 64.4 years in a soil sample to decompose from 413 ppbm to 10.0 ppbm (parts per billion by mass).

What is DDT?

The full form of DDT is Dichlrodiphenyltrichloroethane.

It is a colorless, tasteless, odorless very harmful insecticides.

Given that, it decomposes by a first order reaction with a half life of 12.0 years.

By the equation of first order half life

[tex]k = \dfrac{ln^ 2}{t^1/2} = \dfrac{ln^ 2}{12.0 y} = 0.0578\; y^-^1[/tex]

Now from the radioactive decay formula, we can find the time taken in decay

A₀ = 413 ppbm

A(t) = 10.0 ppbm

[tex]A(t) = A_0^e^-^k^.^t\\\\10.0\;ppbm=413\;ppbm.e^-^0^.^0^5^7^8^y^-^1^t\\\\t=64.4\;y[/tex]

Thus, the time taken in decomposing the DDT is 64.4 years.

Learn more about DDT, here:

https://brainly.com/question/18046263

Otras preguntas