Biomedical Engineering Reference
In-Depth Information
TABLES E9-2.2
Least Square Parameter Estimation for the Freundlich Isotherm with the Highest Coverage
Data Point Not Accounted for in Data-Fitting. The Final Solution Shown Are for c
0
¼
52.21
(mg/L)
m
0.306, Which Were Obtained by
Minimizing the Variance between the Freundlich Model and the Experimental Data, s
L
$mg-phenol/g-Activated Carbon and m
¼
Error
2
(
Aqueous solution
C
A
, mg/L
On activated carbon
C
0
As
, mg/g
Eqn
(9.43)
C
As
,
C
As
LC
0
As
)
2
mg/g
0
0
0
0
1.5
53.0
59.11624
37.40836
2.0
62.4
64.56151
4.672121
5.1
82.8
85.99851
10.23046
6.6
105.0
93.0651
142.4419
22.9
137.0
136.2292
0.594159
51.6
172.2
174.7157
6.328751
80.2
170.9
s
P
i¼1
ðC
As;i
C
0
As;i
Þ
2
s
L
¼
¼
5.79764
7
1
One can observe from
Tables E9-2.1
that the Freundlich model fit is not as good as the
Langmuir fit as shown in Example 9-1. The deviation of the model with the experimental
data is higher at the high coverage region.
Fig. E9-2.1
shows the visual quality of the
fit. Visual inspection of the data shown in
Fig. E9-2.1
reinforces our assessment based
on
Table E9-2.1
.
One can observe from
Table E9-2.2
and
Fig. E9-2.1
that the Freundlich model fit with the
highest coverage data removed has improved quality of fit. Within the region of fit, the
Freundlich isotherm fit and the Langmuir isotherm fit are of similar quality, i.e. both within
the apparent experimental data error.
We next examine the Temkin isotherm fit to the same data. Substituting
Eqn (9.28)
into
Eqn
(9.42)
, we obtain
C
As
¼ f
T
ln
ðK
AT
C
A
Þ
(9.44)
RT
¼ K
A
e
D
H
ad
þ
E
max
E
max
C
As
N
and
K
AT
¼ K
A
e
E
max
where
f
T
¼
RT
. Since the Temkin isotherm is
only valid in the intermediate coverage region, we remove the zero coverage data from
consideration.
Table E9-2.3
shows the least square fit using Temkin isotherm to the experi-
mental data. Visual representation of the fit as compared with Langmuir isotherm fit is shown
in
Fig. E9-2.2
.
One can observe from
Table E9-2.3
and
Fig. E9-2.2
that the Temkin model fit is consistent
with the experimental data. Within the region of fit, the Temkin isotherm fit and the
Langmuir isotherm fit are of similar quality, both within the apparent experimental data
error.
RT
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