Environmental Engineering Reference
In-Depth Information
where
q
=
mass ratio of the solid phase - mass of adsorbed solute per mass of adsorbent
C
e
=
equilibrium concentration of solute (mass
/
volume)
=
K
,
n
experimental constants (some values are provided in Table 3.2).
The Langmuir-Freundlich equation is similar in form to the Langmuir isotherm.
When the adsorbate occupies
n
sites, it is modified to:
(
BP
)
1
/
n
q
=
(
BP
)
1
/
n
,
(3.17)
1
+
where
B
is a constant and
P
is the total pressure.
This equation is the Langmuir-Freundlich isotherm; it differs from the Langmuir
isotherm in two ways. First, it does not assume that the energy of adsorption is the same
for all surface sites. In reality, the energy of adsorption will vary because real surfaces
are heterogeneous. The isotherm expression tries to account for this by assuming that the
frequency of sites associated with a free energy of adsorption decreases exponentially
with increasing free energy. Second, it is assumed that each adsorbate occupies
n
sites.
When the term in the denominator is close to 1, (
BP
)
1
/
n
1, the equation simplifies
to the Freundlich isotherm:
x
m
=
KC
1
/
n
e
q
=
,
(3.18)
where
x
=
mass of solute adsorbed
m
=
mass of adsorbent.
The Langmuir and Freundlich isotherms are the most common isotherms; it is likely
that the constants in these isotherms for many sorbate-sorbent pairs have already been
measured (see Tables 3.1 and 3.2, respectively).
Example 3.3: determining Freundlich-isotherm constants
Problem:
Treated and filtered wastewater can be recycled for use in irrigation. An important
issue is odor removal prior to reuse. For a wastewater that has an initial concentration
of 10 ppm of these compounds, the following test results are obtained when activated
carbon is used to adsorb them:
Carbon added (mg
/
L)
0.0
0.4
1.0
6.0
Concentration (ppm)
10
6.9
4.5
1.5
Using the Freundlich isotherm, determine the minimum amount of activated carbon
required to reduce the concentration to 0.20 ppm.
Solution:
A
mass carbon added) vs
log(concentration at equilibrium) gives a straight line. A linear regression of the data
plot
(Figure
3.16)
of
log(concentration
adsorbed
/
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