Page 259 - Soil and water contamination, 2nd edition

246 Soil and Water Contamination

Assuming a linear Freundlich isotherm , Equation (13.12) can be rewritten as:

k ads
k (13.13)
des
K d
Subsequently, substitution of Equation (13.13) into Equation (13.11) yields:
dC C
w k C s (13.14)
dt ads w K d
The term on the right between brackets represents the concentration of a chemical in
solution at equilibrium with C . If the system is not too far from equilibrium or C is barely
s s
affected by the adsorption –desorption reaction (which is true for large K values), this term
d
may be approximated by the final equilibrium concentration. The differential equation then
reads:
dC w
k ads w C eq C (13.15)
dt
-3
where C = the equilibrium concentration [M L ]. The analytical solution of Equation
eq
(13.15) reads (see also Box 11.I):
C Ct C C e k ads t (13.16)
w eq 0 eq

Example 13.2 Sorption kinetics

Stormy winds agitate the water in a lake, and the turbulent conditions resuspend the
PCB-contaminated lake bed sediments into the water column. As a result, the suspended
-1
sediment concentration in the water increases to 50 mg l and the PCB concentration in
-1
the suspended sediment increases to 22 mg kg . The initial dissolved PCB concentration
-1
before the resuspension of the bed material was 18 ng l . Calculate the dissolved PCB
concentration in the lake water 4 hours after the resuspension event, given the first-order
5
-1
-1
adsorption rate constant k = 0.2 h and the distribution coefficient K = 1.1·10 l kg .

ads d
Assume that the suspended sediment concentration and the PCB concentration in the
suspended sediment have increased instantaneously.
Solution
First, calculate the equilibrium concentration of the PCB in the dissolved phase. To do
so, first calculate the total PCB concentration (dissolved and adsorbed) in the water (see
Equation 13.3):
C tot C w C s SS 18 22 50 1118 ng l -1
At equilibrium, the following applies:
C C C SS C C K SS C 1 ( K SS )
tot w s w w d w d
In the above equation, C represents the equilibrium concentration, so we may therefore
w
write:
C tot 1118 -1
C 172 ng l
eq 5 6
1 K d SS 1 1 . 1 10 50 10

10/1/2013 6:45:12 PM
Soil and Water.indd 258 10/1/2013 6:45:12 PM
Soil and Water.indd 258