Environmental Engineering Reference
In-Depth Information
gives the slope and the intercept of a straight-line fit, and the constants
n
and
K
can be
found. Taking logarithms of both sides of the isotherm gives:
log
x
m
1
n
=
log
K
+
log
C
e
.
The value of the slope in the plot is 1
/
n
, and the intercept is log(
K
). Therefore
n
=
0.73 (unitless) and
K
L carbon). Now that the constants are known,
the isotherm can be solved for the mass
=
0.91 (ppm
/
mg
·
volume of carbon required to reduce the
concentration to 0.2 ppm. Remember that
x
is not concentration, but concentration
adsorbed
(
C
e
is concentration at equilibrium). Therefore:
98 mg
/
/
L of carbon are required for a concentration of 0.2 ppm.
1
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
log(equilibrium concentration)
Figure 3.16
Log-log plot, Example 3.3.
Mixture isotherms
Langmuir has also considered the dissociative adsorption for the case of each molecule
occupying two sites. In this case two sites are needed for both adsorption and desorption,
and hence the rates are proportional to (1
X
)
2
and
X
2
−
(where
X
=
q
/
a
) for adsorption
and desorption, respectively. The resulting isotherm for gas sorption is:
(
B
P
)
1
/
2
q
=
(
B
P
)
1
/
2
,
(3.19)
1
+
where, as before,
B
is a constant and
P
is pressure. Knaebel [9] lists a number of single-
component and mixture isotherms. Single-component and mixture equilibrium data are
available (refer to references in Chapter 7, Adsorption).
3.5
Equilibrium-limited analysis
As stated previously, the degree of separation in an equilibrium-limited process is restricted
to a single contact. So, this process is normally carried out in sequential stages to improve
Search WWH ::
Custom Search