Environmental Engineering Reference
In-Depth Information
similarly. The simplified mathematical form of the Langmuir equation can
be expressed as:
11 1
qq qC
e
(11.1)
o
o
e
where q
e
is the amount of adsorbate adsorbed (mol.g
-1
), C
e
is the equi-
librium molar concentration of the dye (mol. L
-1
), q
o
is the maximum
adsorption capacity over unit mass of the adsorbent (mol.g
-1
) and b is the
energy of adsorption (L.mol
-1
). The Langmuir constants q
o
and b are calcu-
lated from the slopes and intercept of 1/q
e
against 1/C
e
that gives a straight
line at each temperature, thereby confirming that the Langmuir isotherm
is followed in the adsorption process. The Langmuir constant 'b' obtained
by the above expression is helpful in determining various thermodynamic
parameters and also the favorability of the adsorption process.
11.5.1.2
Freundlich Isotherm Model
In the Freundlich model, it is considered that the binding affinities on the
adsorbent surface vary with the interactions between the adsorbed mol-
ecules. Consequently, the sites with stronger affinity are occupied first. The
equation describing the Freundlich model represents adsorption of solutes
from a liquid to a solid surface. This experimental model can be applied
to non-ideal adsorption on heterogeneous surfaces as well as multilayer
adsorption. The Freundlich model is chosen to estimate the adsorption
intensity of the adsorbate on the adsorbent surface [74, 5]. The mathemati-
cal expression for the Freundlich adsorption isotherm model is:
log q
e
= logK
F
+ (1/n) logC
e
(11.2)
Here C
e
denotes the equilibrium concentration (M) of the adsorbate and
q
e
, the amount adsorbed (g.mol
-1
) and K
F
and n are the Freundlich con-
stants related to the adsorption capacity and adsorption intensity of the
adsorbate-adsorbent system, respectively. Thus, the Freundlich adsorption
isotherm plot is sketched by taking log C
e
on abscissa and log q
e
on the ordi-
nate. When the experimental data obtained in terms of log C
e
and log q
e
, fit
into straight lines with regression coefficients close to unity, the Freundlich
adsorption isotherm is assumed to be verified. Values of K
F
and n are derived
from the intercepts and slope of these straight lines, respectively.
11.5.1.3
Tempkin Isotherm Model
The Tempkin isotherm model [76] describes the effect of some indirect
interactions amongst adsorbate particles. The model assumes that the
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