Environmental Engineering Reference
In-Depth Information
from its location in the sorption space, independent of temperature. This
model assumes the heterogeneity of sorption energies within this space.
The slopes of straight-lines of graphs between lnC ads against 2 give activ-
ity coefficient and intercept yields adsorption capacity. The applicability of
the isotherm is related with determination of the nature of the adsorption
process and mean sorption energy is the decisive factor for distinguish-
ing between chemical and physical adsorption. It is given by the following
form:
1
(11.6)
E=
2
It has been postulated that in any adsorbate-adsorbent system, when
mean sorption energy 'E' estimated by the above expression is less than 8
kJ.mol −1 , physisorption dominates the sorption mechanism, whereas if
'E' is between 8 to 16 kJ.mol −1 , chemisorption is the governing factor of
the process [80]. Thus, the calculated values of E play a significant role in
deciding the operative nature of the ongoing adsorption.
11.5.1.5 Thermodynamic Parameters
An isothermal model like the Langmuir model has been proven useful in
the determination of thermodynamics of the adsorption process. Using
Langmuir adsorption data, particularly the Langmuir constant, energy of
adsorption (b), various thermodynamic parameters of the adsorption sys-
tems such as change in Gibb's free energy (ΔG ), change in enthalpy (ΔH )
and change in entropy (ΔS ) are calculated from the following well-known
relations [81]:
ΔG = - R T ln b
(11.7)
HR TT
TT
b
b
(11.8)
21
ln
2
(
)
2
1
1
HG
T
(11.9)
S
where b, b 1 and b 2 are Langmuir constants (L.mol -1 ) at different tem-
peratures (K) and R is universal gas constant (J.mol -1 . K -1 ).
Thus, Gibb's free energy (ΔG ) is calculated at different temperatures
by putting the corresponding values of Langmuir constant 'b' in the
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