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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
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
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
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