Water Contaminants And Speciation

For a first order reaction, the concentration of the contaminant

C(t)

after time

t

is given by:

C(t)%20%3D%20C_0%20e%5E%7B-kt%7D%2C

where

C_0

is the initial concentration,

k

is the degradation constant, and

t

is time. The contaminant concentration becomes half in 10 years, so:

%5Cfrac%7BC_0%7D%7B2%7D%20%3D%20C_0%20e%5E%7B-k%20%5Ccdot%2010%7D%2C

which simplifies to:

e%5E%7B-k%20%5Ccdot%2010%7D%20%3D%20%5Cfrac%7B1%7D%7B2%7D.

Taking the natural logarithm of both sides:

-10k%20%3D%20%5Cln%20%5Cleft(%20%5Cfrac%7B1%7D%7B2%7D%20%5Cright)%2C

k%20%3D%20%5Cfrac%7B%5Cln%202%7D%7B10%7D%20%3D%200.0693%20%5C%2C%20%5Ctext%7Byear%7D%5E%7B-1%7D.

Now, the contaminant is travelling at 0.4 m per day, and the well is 2000 m away. The time

t

for the contaminant to reach the well is:

t%20%3D%20%5Cfrac%7B2000%20%5C%2C%20%5Ctext%7Bm%7D%7D%7B0.4%20%5C%2C%20%5Ctext%7Bm%2Fday%7D%7D%20%3D%205000%20%5C%2C%20%5Ctext%7Bdays%7D%20%3D%2013.7%20%5C%2C%20%5Ctext%7Byears%7D.

The concentration of the contaminant at the well after 13.7 years is:

C(13.7)%20%3D%200.5%20%5C%2C%20%5Ctext%7Bmg%2FL%7D%20%5Ccdot%20e%5E%7B-0.0693%20%5Ccdot%2013.7%7D%20%3D%200.5%20%5C%2C%20%5Ctext%7Bmg%2FL%7D%20%5Ccdot%20e%5E%7B-0.949%7D%20%5Capprox%200.18%20%5C%2C%20%5Ctext%7Bmg%2FL%7D.

Thus, the contaminant concentration expected at the well is

0.18%20%5C%2C%20%5Ctext%7Bmg%2FL%7D

Chapter Questions
1 MCQs