Geoscience Reference
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where:
V
the constant volume of examined contaminant solution with initial
concentration
C
0
, used to inundate the ground samples of mass
m
0
in laboratory
research;
m
0
¼
¼
the mass of the examined ground samples; and
C
0
¼
the initial
concentration of the examined contaminant solution.
For the nonlinear model of sorption kinetics, taking into consideration (
9
) and
using the auxiliary dimensionless expression
½
a
1
¼ð
a
0
V
Þ=
m
0
,(
8
) can be written
in the form:
@
C
@
C
N
t
¼
k
1
þ
k
2
a
1
ð
C
0
C
Þ
(10)
Then, taking into consideration (
4
) and using also the auxiliary dimensionless
expression
,(
10
) can be written for the nonlinear kinetics of
sorption process as the final relationship:
½
a
2
¼
1
=ð
a
0
K
2
Þ
@
C
@
C
N
a
1
ð
a
1
¼
V
m
0
K
2
(11)
t
¼
k
1
þ
k
1
C
0
C
Þ
a
1
a
2
¼
For the linear kinetics of sorption process, taking into consideration (
9
) and
using the auxiliary dimensionless expression
½
a
1
¼ð
a
0
V
Þ=
m
0
,(
3
) can be written
in the form:
@
C
@
t
¼
k
1
C
þ
k
2
a
1
ð
C
0
C
Þ
(12)
Now, taking into consideration (
5
) and using auxiliary dimensionless expression
½
a
3
¼
1
=ð
a
0
K
1
Þ
,(
12
) can be written as the final relationship as follows:
@
C
@
a
2
ð
a
2
¼
V
m
0
K
1
(13)
t
¼
k
1
C
þ
k
1
C
0
C
Þ
a
1
a
3
¼
3 Results of Analytical Calculations
3.1 Determination of the Rate Constants of Adsorption (k
1
)
and Desorption (k
2
) for the Nonlinear and Linear
Models of Sorption Kinetics
In this section, two practical cases of determination of the rate constants of
adsorption (
k
1
) and desorption (
k
2
) are presented for the nonlinear and linear models
of sorption kinetics in relation to the nonlinear and linear sorption isotherms widely
applied in practice (Seidel-Morgenstern
2004
; Chiang
2005
). So, the analytical