Page 137 - Materials Chemistry, Second Edition

120 Practical Design Calculations for Groundwater and Soil Remediation

concentration to drop below 100 mg/kg without any remediation measures
taken.

Strategy:
Only two concentrations at two different days are given. We need to
take a two-step approach to solve the problem. We need to deter-
mine the rate constant first and then the initial concentration.
Solution:
(a) Determine the rate constant, k:
At t = 10 days, insert the concentration value into Equation (4.11):

1,200
= e − k(10)
C i

At t = 25 days, insert the concentration value into Equation (4.11):

1,100
= e − k(25)
C i

By dividing both sides of the first equation by the corresponding
sides of the second equation, we can obtain

1,200 = e − 10 k ÷ e − 25 k = e − 10 k (25)− − k = e 15 k
1,100

Thus, k = 0.0058/day
(b) Estimate the initial concentration (immediately after the spill)
C can be readily determined by inserting the value of k into
i
either of the first two equations:
1,200
= e − (0.0058)(10) = 0.944
C i

So, C = 1,272 mg/kg.
i
(c) For the concentration to drop below 100 mg/kg, it will take:
100 = 0.0786 = e − 0.0058 t

1,272

t = 438 days