1
56
T.N. Pham et al. / Journal of Catalysis 314 (2014) 149–158
2
2
2
1
1
1
1
40
20
00
80
60
40
20
Table 4
Activation enthalpies and entropies for ketonization of acetic, propionic, and butyric
acid over Ru/TiO
2
catalyst.
Activation enthalpy,
H (kJ/mol)
Activation entropy,
S (J/mol K)
D
D
Acetic acid
Propionic acid
Butyric acid
156.4
181.5
220.0
3.4
32.4
78.2
than that of the two adsorbed acids and more interestingly, the
entropy gain increases with the length of the alkyl chain. That is,
there seems to be a correlation between entropy and enthalpy.
In fact, as shown in Fig. 10a, the well-known compensation
effect [40–42] is clearly apparent in these data. Bond et al.
[
43,44] have suggested that the compensation effect may be a
result of using apparent activation enthalpy and entropy. However,
we must emphasize that in this work, the compensation effect is
observed with true enthalpy and entropy (see Fig. 10b).
Acetic
Propionic
Butyric
Carboxylic acid
Many years ago, Everett [45] made the observation of the com-
monly observed linear relationship between entropy and enthalpy
of adsorption, which can be interpreted taking into account that a
greater binding energy of the molecule to the surface would
restrict its vibrational and rotational degrees of freedom. This is
not the case in our system, in which no compensation effect is
observed for the adsorption. In fact, the heats of adsorption
remained constant as a function of the alkyl chain length, but the
entropy of adsorption did increase due to a greater number of
degrees of freedom with increasing chain length. By contrast, the
compensation effect was in fact observed for the enthalpies and
entropies of activation, when the transition state was involved,
which gives us more information about the nature of this species
and, consequently, sheds light on the reaction mechanism.
Fig. 9. Ketonization activation energies as a function of carbon chain length. Error
bars indicate 95% confidence interval.
exclude the CꢂC bond stretch along the reaction coordinate). This
0
#
K
value reflects the enthalpy and entropy of activation, which
can be readily calculated from data at varying temperatures using
the Eyring–Polanyi expression:
k
h
B
T
#
#
À
Á
2
ꢂ
DH
=RT
DS
=R
#
rate ¼
e
e
½2RCOOH ꢄꢃ
ð18Þ
It is important to note that the rate in transition state analysis is
on a per catalytic active site basis, which is calculated as follows:
As mentioned above, the ketonization can either go through an
early or a late transition state, depending on the position of the
energy peak along the reaction coordinate. The early transition
state involves the formation of the C–C bond between the two
adsorbed carboxylates, leading to the formation of the b-ketoacid
Number of catalyst sites ¼Catalyst mass ðgÞ
2
ꢁ
ꢁ
ꢁ
Catalyst surface area ðm =gÞ
2
Ti cation density ðTi sites=nm Þ
1
8
2
2
10 nm =m
(
RCOꢀꢀꢀRCOO) intermediate, as proposed in our earlier study [16].
To obtain the catalyst surface area in this expression, BET mea-
surements were conducted on the catalyst. The density of Ti cat-
ions was obtained from prior surface science studies [38].
In contrast, the late transition state involves the decarboxylation
of b-ketoacid (RCORꢀꢀꢀCOO), as suggested by Renz et al. [46].
The observed trend in activation enthalpy is an increase in the
following order, acetic < propionic < butyric. We believe that this
trend supports the idea of an early transition state, since we can
expect that increasing the alkyl chain length would enhance the
energy requirement to overcome the increasing steric repulsion
of bulkier alkyl groups that make the formation of the C–C bond
more difficult. In other words, larger molecules imply larger spatial
hindrance to overcome to reach the appropriate coupling configu-
ration, and therefore a higher energy requirement. In contrast, in
the case of the late transition state, one would not expect a higher
enthalpy barrier with increasing alkyl chain length. The decarbox-
ylation of b-ketoacid only involves the redistribution of electrons
within the ketone and acid functional group [47], which is not only
a relatively simple process from an energy requirement point of
view, but also independent of the alkyl chain length.
In some kinetics studies, the barriers derived from fitting
pseudo first-order rate expressions are ‘‘apparent’’ values, relative
to the gas phase [18,39]. It is important to note that since we use a
full LH equation to fit the reaction rate measurements, the rate
constant thus derived includes the true enthalpy and entropy of
activation for the C–C bond formation (or breaking) with respect
to the surface adsorbed species (single elementary step (5)). There-
#
#
fore, the values of
DH and DS in Eq. (18) refer to the differences
between the H and S values of the transition state and those of the
adsorbed reactants (i.e., two adsorbed acid molecules).
The goodness of the kinetic fitting for a second-order LH model
with respect to adsorbed acid coverage is consistent with the pro-
posed mechanism that involves two adsorbed carboxylate species
on the surface that form a b-ketoacid intermediate, as previously
discussed [3,10,24].
The positive activation entropy for all three acids with respect
to the adsorbed state indicates that the bidentate carboxylates go
through a transition state with an entropy gain. This is indicative
of a structure for the activated complexes with more degrees of
freedom than the sum of the two adsorbates.
During the catalytic cycle, the transition state could undergo a
transformation to a less restricted adsorption configuration such
as monodentate linkage to the surface, but the increase in
entropy is most probably related to intramolecular configura-
Table 4 summarizes the resulting activation enthalpies and
entropies of acetic, propionic, and butyric acid, respectively. It is
#
clear that the activation enthalpy (
D
H ) increases monotonically
with increasing alkyl chain length, which can be described as an
increased energy barrier for the rate-limiting step as the size of
the alkyl chain increases. Similarly, the changes in activation entro-
#
pies
D
S
are positive and also increase as a function of carbon
chain length. That is, the entropy of the transition state is higher