Environmental Engineering Reference
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[133]. In addition, to perform the thermodynamic verification for both samples
studied in this paper, Eq. (93) is:
(93)
diff
ads
vap
q
=D
GH
−D
whereand is the enthalpy of vaporization (equal with minus sign to the enthalpy
of condensation, ). Horvath and Kawazoe noticed the similarity of the data cal-
culated based on Eq. (93) (with the “experimental” isosteric heat of adsorption
obtained from isotherms measured at different temperatures. It should be pointed
out that the HK model has been verified only for one set of experimental data
and we do not find other cases in the literature. Therefore, the calorimetrically
measured enthalpies of adsorption of C
6
H
6
and CCl
4
are shown in Eqs. (94) and
(95). Moreover, these data will be applied to calculate, using the standard method
the enhancement of potential energy in micropores in comparison to the energy of
adsorption on a “flat” surface. Knowing adsorption isotherms and the differential
molar heats of adsorption, the differential molar entropies of adsorbed molecules
() can be calculated by:
�
q
diff
�
�
p
�
(94)
diff
S
=− −
S
R
ln ln
+
R
€
‚
ƒ
p
„
g
ƒ
T
„
0
where is the molar entropy of the gas at the temperature and is the standard
state pressure. It is well known that different standard states can be chosen, and
in our case, the gas at the standard pressure of = 101,325 Pa was applied. Also
some researchers calculated the enthalpy and entropy of adsorption basing on the
potential theory and applying the procedure described previously. Assuming the
fulfillment of the main condition of the potential theory (first of all the tempera-
ture invariance condition that obtained:
1
−
n
�
A
�
aΘ
= + +− = +
T
ab
TE
pot
q
diff
A
L
RT
A
0
+−
L
RT
(
)
€
‚
(95)
pot
pot
n
b
E
FA
ƒ
„
0
pot
1.2.2.15 BIMODAL PORE SIZE DISTRIBUTIONS FOR CARBON
STRUCTURES
Very puzzling results are obtained by analyzing microporosity of various carbona-
ceous materials of different origin and/or treated thermally or chemically since the
difference between the micropore size distribution curves are often insignificant.
The number of peaks on the pore size distribution (PSD) curves and the ranges of
their location as well as their shapes are very similar. Thus, the bimodality of PSD
for many carbonaceous adsorbents is well known fact in the literature. This fact
can be explained by conditions of carbon preparation; for example, by creation of
the porous structure during activation process. It is amazing that different carbon
materials obtained from different precursors have similar (still bimodal) porous
structure with the gap between the peaks reflecting to the filling of primary and
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