Biomedical Engineering Reference
In-Depth Information
Integration of
Eqn (9.23)
leads to
RT
Z
E
max
K
A
C
A
ln
e
þ K
A
C
A
f
s0
n
s
K
A
C
A
¼RT
f
s
0
n
s
E
max
0
Es
RT
Es
RT
de
q
A
¼
E
s
RT
e
þ K
A
C
A
(9.24)
0
¼ RT
f
s
0
n
s
1
þ K
A
C
A
K
A
C
A
ln
E
max
RT
e
þ K
A
C
A
where
DH
0
ad
RT
K
A
¼ K
A
e
(9.25)
Substituting
Eqn (9.22)
into
Eqn (9.24)
, we obtain a generalized logarithm coverage.
K
A
C
A
1
þ K
A
C
A
q
A
¼
ln
E
max
RT
E
max
RT
e
e
þ K
A
C
A
Eqn
(9.26)
may be referred to as ExLan (
Ex
ponential distribution
Lan
gmuir) model. The
higher limit on the adsorption heat is generally at least a few times higher than
RT
. Without
loosing much utility, one can assume that
E
max
/N
1
because of the fast decrease in the expo-
nential function. Taking this limit on
Eqn (9.26)
, we obtain an expression that has exactly the
same number of parameters as the Langmuir isotherm,
q
A
¼ K
A
C
A
ln
þðK
A
C
A
Þ
1
(9.27)
which is effectively still a one parameter nonideal isotherm expression. There is no increase
in the number of parameters as compared with the Langmuir isotherm.
½
1
Example 9-1
Adsorption of phenol on activated carbon from aqueous solutions. A
comparison of nonideal isotherm and ideal isotherm.
Table E9-1.1
shows the experimental data collected in an undergraduate lab run for the
adsorption of phenol on activated carbon. Examine the suitability of Langmuir isotherm
and exponential energy distribution nonideal isotherm to describe the experimental data.
TABLE E9-1.1
Equilibrium Concentrations of Phenol in Aqueous Solution and in
Activated Carbon
Phenol concentration in aqueous
solution
Phenol concentration is activated
carbon
C
A
, mg/L
C
As
, mg/g
0
0
1.5
53.0
2.0
62.4
5.1
82.8
6.6
105.0
22.9
137.0
51.6
172.2
80.2
170.9
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