Environmental Engineering Reference
In-Depth Information
heat of adsorption of all the molecules in the layer decreases linearly with
surface coverage due to adsorbent-adsorbate interactions. Moreover,
the adsorption process is characterized by a uniform distribution of the
binding energies, up to maximum binding energy. The linear form of the
Tempkin isothermal model is expressed as:
q
e
= k
1
lnk
2
+ k
1
lnC
e
(11.3)
where q
e
is the amount of adsorbate adsorbed per unit mass of adsor-
bent at equilibrium (mol.g
-1
), C
e
is the final concentration at equilibrium
(mol. L
-1
), k
1
is the Tempkin isotherm energy constant (L.mol
-1
) related to
the heat of adsorption [77] and k
2
is the Tempkin isotherm constant. Thus,
a plot of ln C
e
as function of amount adsorbed at equilibrium gives straight
lines suggesting the uniform distribution of binding energy arising due to
interaction of the adsorbate molecules. The straight lines obtained from the
graphs are also helpful in determining the Tempkin isotherm constants.
11.5.1.4
Dubinin-Radushkevich (D-R) Isotherm Model
Dubinin and Radushkevich have made a great contribution to Surface
Science by, developing an isothermal model based on the heterogeneous
characteristics of the adsorbents which is helpful in understanding the
interaction between adsorbate and adsorbent [78]. The isotherm model
suggested by Dubinin and Radushkevich [79] has been used to describe
liquid-phase adsorption and on the basis of the Dubinin-Radushkevich
equation adsorption energy can be estimated. The model, which is com-
monly known as the D-R Adsorption Model, is also chosen to estimate the
characteristic porosity and the apparent free energy of adsorption. It sug-
gests that adsorption data can be analyzed to distinguish between chemical
and physical adsorption by employing the following equation:
ln C
ads
= ln X
m
- β
2
(11.4)
where C
ads
is the amount of dye adsorbed per unit weight of adsorbent
(mol.g
-1
), X
m
is the maximum adsorption capacity (mol.g
-1
), β is the activ-
ity coefficient (mol
2
. J
-2
) related to mean adsorption energy and
is the
Polanyi potential, which is given as:
1
)
(11.5)
RT 1n(1+
C
e
where R is the universal gas constant (J.mol
-1
. K
-1
), T is the temperature
(K) and C
e
is the concentration at equilibrium (mol. L
-1
). Polanyi sorp-
tion potential (
) is the work required to remove a molecule to infinity
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