Isokinetic behaviour in gas phase catalytic hydrodechlorination of chlorobenzene over supported nickel

Article abstract of DOI:10.1016/j.molcata.2006.12.007

The kinetics of the hydrodechlorination (HDC) of chlorobenzene has been measured over Ni supported on a range of substrates (MgO, SiO₂, Al₂O₃, Ta₂O₅, MgO, activated carbon (AC) and graphite) of varying BET area (9-843 m² g^-1) where the Ni loading was in the range 1.5-20.3% (w/w) with catalyst preparation by impregnation and deposition-precipitation. The results of a comprehensive TEM analysis is presented wherein it is demonstrated that the supported Ni phase is present in a range of sizes and morphologies. Compensation behaviour is established for chlorobenzene HDC over these catalysts with an associated isokinetic temperature (T_iso) at 669 ± 2 K. Application of the Selective Energy Transfer (SET) model also arrived at the same calculated T_iso (669 K). The SET model is based on the premise of resonance between a vibrational mode of the catalyst and a vibrational mode of the reactant with a transferral of resonance energy from the catalyst to the reactant to generate the activated complex with subsequent reaction. In this reaction system, resonance results from energy transfer from the catalytic Ni-H vibration (at 940 cm^-1) to the out-of-plane C-H vibration (at 740 cm^-1) of the reactant. The consequence of lumping together experimental kinetic measurements that show slight variations is discussed and rationalized.

Full text of DOI:10.1016/j.molcata.2006.12.007

Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
Isokinetic behaviour in gas phase catalytic hydrodechlorination
of chlorobenzene over supported nickel
Mark A. Keanea,∗, Ragnar Larssonb
a Chemical Engineering, School of Engineering and Physical Sciences, Heriot-Watt University,
Edinburgh EH14 4AS, Scotland, United Kingdom
b Chemical Engineering II, University of Lund, PO Box 124, SE 221 00 Lund, Sweden
Received 20 November 2006; received in revised form 4 December 2006; accepted 5 December 2006
Available online 9 December 2006
Abstract
The kinetics of the hydrodechlorination (HDC) of chlorobenzene has been measured over Ni supported on a range of substrates (MgO, SiO2,
Al2O3, Ta2O5, MgO, activated carbon (AC) and graphite) of varying BET area (9–843 m2 g−1) where the Ni loading was in the range 1.5–20.3%
(w/w) with catalyst preparation by impregnation and deposition-precipitation. The results of a comprehensive TEM analysis is presented wherein it is
demonstrated that the supported Ni phase is present in a range of sizes and morphologies. Compensation behaviour is established for chlorobenzene
HDC over these catalysts with an associated isokinetic temperature (Tiso) at 669 2 K. Application of the Selective Energy Transfer (SET) model
also arrived at the same calculated Tiso (669 K). The SET model is based on the premise of resonance between a vibrational mode of the catalyst
and a vibrational mode of the reactant with a transferral of resonance energy from the catalyst to the reactant to generate the “activated complex”
with subsequent reaction. In this reaction system, resonance results from energy transfer from the catalytic Ni–H vibration (at 940 cm−1) to the
out-of-plane C–H vibration (at 740 cm−1) of the reactant. The consequence of lumping together experimental kinetic measurements that show
slight variations is discussed and rationalized.
© 2006 Elsevier B.V. All rights reserved.
Keywords: Compensation behaviour; Isokinetic temperature; Selective Energy Transfer model; Catalytic hydrodechlorination; Chlorobenzene; Supported Ni catalysts
1. Introduction
[3]. The Tiso predicted from the SET model (655 K) was very
close to the value determined experimentally (658 K). In terms
of reaction mechanism, we proposed a haloarene/catalyst inter-
action where the arene molecule is co-planar with the surface
and the slow step is an activation of the out-of-plane vibrations
of the C–H bond(s).
This result raised the question: will such an agreement
also hold for the hydrodehalogenation of a common reac-
tant promoted by a family of catalysts of similar or related
composition? Indeed, we can flag a number of studies [4–10]
where such a combination has delivered an isokinetic response.
We have accordingly, as an extension to our earlier work,
taken the hydrodechlorination (HDC) of chlorobenzene as a
model reaction promoted by a series of supported Ni catalyts;
the raw kinetic data are provided in Table 1. A consensus is
emerging from the literature that catalytic hydrodehalogenation
is structure sensitive, dependent on metal particle size and
electronic structure [11–16]. We consider, in this study, an
array of substrates ranging from a basic MgO to conventional
Al2O3 and SiO2 as well as Ta2O5, a highly refractive oxide
In a previous paper [1], we have reported an isokinetic
response for the catalytic hydrodehalogenation of a series of
halogenated benzene derivatives over a common nickel/silica
catalyst. An isokinetic effect arises where the Arrhenius plots
(ln k versus 1/T) for a series of very similar reactions intersect
at a common temperature (the isokinetic temperature, Tiso). We
demonstrated that the Tiso for the hydrodehalogenation reac-
tions could be accounted for using the Selective Energy Transfer
(SET) model [2]. The basis for the SET model is the occurrence
of a state of resonance between a vibrational mode of the catalyst
system and a complimentary vibrational mode of the reacting
molecule. We identified the critical reactant vibrational mode as
an out-of-plane C–H vibration with optimum resonance energy
transfer from the catalyst (Ni–H) vibrational mode at 940 cm−1
∗
Corresponding author. Tel.: +44 0131 451 4719
E-mail address: M.A.Keane@hw.ac.uk (M.A. Keane).
1381-1169/$ – see front matter © 2006 Elsevier B.V. All rights reserved.
doi:10.1016/j.molcata.2006.12.007

88
M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
Table 1 (Continued )
Table 1
Collation of the experimental chlorobenzene HDC kinetic data
Catalyst
103/T (K−1
)
ln(kexp mol h−1 g−1
)
Eexp (kJ mol−1
)
ln Aexp
Catalyst
103/T (K−1
)
ln(kexp mol h−1 g−1
)
Eexp (kJ mol−1
)
ln Aexp
1.912
2.008
2.114
−8.004
−9.546
Ni/SiO2-I
1.686
1.745
1.808
1.859
1.912
2.008
2.114
−3.252
−3.669
−4.069
−4.145
−4.876
−5.460
−6.298
59.1
8.71
−11.127
Ni/Ta2O5 1.686
1.745
−4.223
−5.184
−5.712
−6.320
−6.897
−8.021
−9.543
99.5
15.91
1.808
1.859
1.912
2.008
Ni/SiO2-II
1.686
1.745
1.808
1.859
1.912
2.008
2.114
−3.111
−3.398
−3.712
−4.056
−4.442
−5.107
−5.894
−2.883
−3.165
−3.589
−3.867
−4.175
−4.834
−5.504
−3.789
−4.023
−4.482
−4.852
−5.298
−6.078
−6.969
−3.806
−4.078
−4.421
−4.785
−5.224
−5.993
−6.927
−3.895
−4.551
−5.023
−5.612
−5.983
−6.912
−7.809
−3.545
−3.945
−4.321
−4.817
−5.184
−6.021
−6.985
−2.887
−3.066
−3.343
−3.743
−4.025
−4.396
−4.893
−4.913
−5.768
−6.856
−7.541
54.7
51.3
63.3
61.5
75.5
67.1
40.4
119.1
8.11
7.58
2.114
that exhibits many of the qualities of TiO2 [17]. The use of
graphite, a material known [18] to induce strong metal/support
interactions and a high surface area activated carbon (AC)
with little or no metal/support interaction have also been
investigated.
Ni/SiO2-III 1.686
1.745
1.808
1.859
1.912
2.008
2.114
2. Experimental details
2.1. Catalyst preparation and characterization
Ni/SiO2-IV 1.686
9.22
1.745
1.808
1.859
1.912
2.008
2.114
Two Ni/SiO2 catalysts were prepared by impregnation of a
Cab-O-Sil 5 M silica (surface area = 194 m2 g−1) with aqueous
solutions of Ni(NO3)2 to deliver a Ni content of 4.6% (w/w)
(denoted Ni/SiO2-I) and 8.9% (w/w) (denoted Ni/SiO2-II).
Prior to reaction, the catalyst precursors were activated in a
100 cm3 min−1 stream of dry H2 (99.9%) at a temperature ramp
(10 K min−1, controlled using a Eurotherm 91e temperature
programmer) to a final temperature of 723 K. The temperature
was maintained for 18 h where the catalyst bed temperature was
independently monitored using an on-line data logging system
(Pico Technology, model TC-08) and found to be constant to
within 1 K. In addition, Ni/SiO2-II was calcined (10 K min−1
in 100 cm3 min−1 stream of air) at 873 K prior to reduction
and the activated form is denoted Ni/SiO2-III. Two further
Ni/SiO2 catalysts were prepared by deposition-precipitation
as described elsewhere [19] and activated as above without
precalcination: 1.5% (w/w) (denoted Ni/SiO2-IV) and 20.3%
(w/w) (denoted Ni/SiO2-V). This synthesis route involves
the precipitation of a nickel(II) phase onto the silica support
by basification of a nickel salt solution/silica suspension via
the decomposition of urea. Nickel loaded Al2O3, Ta2O5, and
MgO (Sigma–Aldrich) were also prepared by impregnation
with aqueous Ni(NO3)2 and reduced without precalcination.
Butanolic Ni(NO3)2 solutions were used to impregnate
activated carbon (G-60, 100 mesh, NORIT) and graphite
(synthetic 1–2 ␮m powder, Sigma–Aldrich) supports. Aqueous
solutions were not employed as the carbon support materials
are hydrophobic, leading to difficulties with surface wetting
that can impact on the ultimate metal dispersion [20]. The Ni
content of the catalyst precursors (75–150 ␮m mesh range)
was measured by ICP-OES (Vista-PRO, Varian Inc.) where
the analysis was reproducible to within 2%; Ni content of
each sample is given in Table 2. The activated samples were
Ni/SiO2-V
Ni/Al2O3
Ni/MgO
Ni/AC
1.686
1.745
1.808
1.859
1.912
2.008
2.114
8.85
1.686
1.745
1.808
1.859
1.912
2.008
2.114
11.36
10.17
5.35
1.686
1.745
1.808
1.859
1.912
2.008
2.114
1.686
1.745
1.808
1.859
1.912
2.008
2.114
Ni/graphite 1.686
19.20
1.745
1.808
1.859

M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
89
Table 2
evaluated taking the approach outlined previously [22] where
the molecular diffusion coefficients were calculated using Sat-
terfield’s [23] method. The catalytic system was found to operate
with negligible diffusion retardation of the reaction rate; effec-
tiveness factor (η) > 0.99 at 573 K. The catalyst was supported
on a glass frit and a layer of glass beads above the catalyst bed
served as a heating zone, ensuring that the reactants reached the
reaction temperature before contacting the catalyst. A Model
100 (kd Scientific) microprocessor controlled infusion pump
was used to deliver the chloroarene feed via a glass/PTFE air-
tight syringe and PTFE line at a fixed (calibrated) rate. The
ultra pure (99.999%) H2 was supplied via a Brooks mass flow
controller and the flow rate was monitored using a Humon-
ics (Model 520) digital flowmeter. The catalyst weight (W) to
inlet molar chloroarene flow rate (FCl) ratio spanned the range
¯
Nickel content, BET area and TEM derived mean Ni particle size (d) and size
range associated with the catalysts considered in this study
¯
Catalyst
% Ni
(w/w)
BET area
Ni size
range (nm)
d (nm)
(m2 g−1
)
Ni/SiO2-I
Ni/SiO2-II
Ni/SiO2-III
Ni/SiO2-IV
Ni/SiO2-V
Ni/Al2O3
Ni/MgO
Ni/AC
Ni/graphite
Ni/Ta2O5
4.6
8.9
8.9
1.5
20.3
8.4
8.6
8.3
9.8
7.8
179
176
173
188
170
121
102
843
9
1–24
2–30
4–45
1–4
11
16
21
2
1–7
4
8
1–16
2–25
2–70
5–80
2–28
15
27
29
14
11
−1
1–1420 g h mol where H2 was at least 12 times in excess
Cl
passivated at room temperature in a stream of 1% (v/v) O2/He
(mass flow controlled at 20 cm3 min−1) prior to ex situ analysis.
The BET surface areas were measured using the commercial
CHEMBET 3000 unit (Quantachrome Instruments), employing
a 30% (v/v) N2/He flow; pure N2 (99.9%) served as the inter-
nal standard. At least 2 cycles of nitrogen adsorption–desorption
were employed to determine total surface area using the standard
single point method; BET surface area values were reproducible
to within 3% and the values quoted in this paper are the mean.
XRD analysis (recorded on a Philips X’Pert instrument using
nickel filtered Cu K␣ radiation) established that the supported
Ni phase exhibits an exclusive cubic symmetry with character-
istic peaks at 44.5◦, 51.8◦ and 76.3◦, corresponding to (1 1 1),
(2 0 0) and (2 2 0) planes. Supported Ni particle size was deter-
mined by transmission electron microscopy: JEOL 2000 TEM
microscope operated at an accelerating voltage of 200 kV. The
catalyst samples were dispersed in 1-butanol by ultrasonic vibra-
tion, deposited on a lacey-carbon/Cu grid (300 mesh) and dried
at 383 K for 12 h. Selected area electron diffraction (SAED) con-
firmed that the Ni distributed over each support was present in
the metallic form and not as an oxide. At least 650 individual Ni
particles were counted for each catalyst and the mean Ni particle
relative to stoichiometric quantities. From a consideration of
gas phase reaction equilibrium constants [24,25], HDC under
the stated reaction conditions can be taken to be irreversible.
Adherence to pseudo-first order kinetics has been demonstrated
elsewhere [14,26] and the specific rate constants extracted from
a pseudo-first order treatment are given in Table 1. In a series
of blank tests, passage of each halogenated feed in a stream of
H2 through the empty reactor, i.e. in the absence of catalyst,
did not result in any detectable conversion. Product analysis
by capillary GC has been described in some detail previously
[27]; the detection limit corresponded to a feedstock conver-
sion<0.1 mol%. A halogen (in the form of HCl product) mass
balance was performed by passing the effluent gas through an
aqueous NaOH (3.5–8.0 × 10−3 mol dm−3, kept under constant
agitation at ≥300 rpm) trap and monitoring continuously the
pH change by means of a Hanna HI Programmable Printing pH
Bench-Meter. TheconcentrationofHClgeneratedwasalsomea-
sured by titrimetric analysis of the NaOH trap solution using a
Metrohm (Model 728) Autotitrator (AgNO3, combined Ag elec-
trode); Cl mass balance was complete to better than 8%. All
the data presented here have been generated in the absence of
any significant catalyst deactivation where each catalytic run
was repeated (up to six times) using different samples from the
same batch of catalyst: the measured rates did not deviate by
more than 7%.
¯
sizes are quoted in this paper as the number average diameter (d):
ꢀ
inidi
¯
ꢀ
d =
(1)
ini
where ni is the number of particles of diameter di.
3. Results
2.2. Catalysis procedure
3.1. Catalyst(s) characteristics
Chlorobenzene (Sigma–Aldrich, 99.9%) HDC was con-
ducted with a co-current flow of the chloroarene feed in H2
under atmospheric pressure in a fixed-bed continuous flow glass
reactor over the temperature range 423 K ≤ T ≤ 593 K. Isother-
mal operation was maintained by diluting the catalyst bed with
ground glass (75–150 ␮m). Interparticle and intraparticle heat
transport effects can be disregarded when applying established
criteria [21]; the temperature differential between the catalyst
particle and bulk fluid phase was <1 K. Plug-flow conditions
were operable with reactor diameter/catalyst particle ratio = 90.
Mass transport contributions under reaction conditions were
The Ni loading, BET surface area and TEM derived mean
Ni particle diameters for the 10 activated catalysts considered in
this study are recorded in Table 2; representative TEM images
are provided in Fig. 1. The BET areas of the Ni/SiO2 sam-
ples were somewhat lower than that of the SiO2 support, a
response that can be attributed to a partial pore filling, which
is more pronounced at higher Ni loadings. Nickel supported
on silica exhibited an exclusively pseudo-spherical morphology
(see Fig. 1(a)), in keeping with earlier TEM characteriza-
tion reports [28,29]. Previous studies [19,30] have shown that
Ni/SiO2 prepared by impregnation realizes a relatively weak

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M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
Fig. 1. Representative TEM images of (a) Ni/SiO2-II, (b) Ni/Al2O3, (c) Ni/graphite and (d) Ni/AC.
metal/support interaction resulting in Ni growth during acti-
vation, which accounts for the rather wide size distribution
(Table 2). An increase in Ni loading (Ni/SiO2-II versus Ni/SiO2-
I and Ni/SiO2-V versus Ni/SiO2-IV) and the introduction of a
calcination step prior to reduction (Ni/SiO2-III versus Ni/SiO2-
II) served to widen the Ni size distribution and increase the mean
Ni size as a result of increased particle agglomeration/sintering,
as is discussed elsewhere [19,27]. Ni/SiO2 preparation by
deposition-precipitation (Ni/SiO2-IV and Ni/SiO2-V) has been
shown previously [19,30–32] to generate smaller average Ni
particle diameters when compared with the less controlled
Ni(NO3)2 impregnation route. The deposition-precipitation syn-
thesis results in the formation of a nickel phyllosilicate phase
that is responsible for enhanced Ni dispersion [33]. Nickel sup-
ported on MgO and Ta2O5 yielded similar mean Ni size and size
distribution to Ni/SiO2-II which has a comparable Ni loading,
albeit the BET surface areas are quite different. The Ni phase
associated with Al2O3 is characterized by the narrowest Ni par-
ticle size distribution and smallest mean Ni size (Table 2) of
all the impregnated samples; the nature of the metal dispersion
is illustrated in Fig. 1(b). This response finds support in earlier
work by Hoang-Van et al. [34]. The suppression of Ni parti-
cle growth on alumina has been attributed to the ionic nature
of the Ni–Al2O3 interaction, leading to an enhanced dispersion
of electron-deficient Ni [35]. Graphite has a low (BET) sur-
face area with few edge positions available for depositing the
metal that, as a direct consequence, is present in the form of
large particles (up to 80 nm, see Table 2), as has been noted
elsewhere [36]. Indeed, Ni supported on either carbonaceous
(graphite or activated carbon) substrate exhibits a significantly
wider size distribution when compared with the oxide supports.
Nevertheless, Ni particles on the graphite substrate can be seen
in Fig. 1(c) to possess well-defined geometrical shapes, diag-
nostic of strong metal–support interaction [37]. Reduction of
the Ni-impregnated activated carbon (AC), an amorphous sub-
strate with a high BET area, yielded a metal phase of dimensions
comparable to that associated with Ni/graphite, albeit a narrower
size range and smaller average diameter (Table 2). Growth of Ni
particles in this case can be attributed to weaker metal/support
interaction, leading to increased Ni mobility and the subsequent
greater probability of agglomeration. The weaker Ni–AC inter-
action is manifested in the spherical/globular nature of the Ni

M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
91
Fig. 3. Arrhenius plots for the HDC of chlorobenzene over all the catalysts
studied: (ꢀ) Ni/SiO2-I; (ꢁ) Ni/SiO2-II; (×) Ni/SiO2-III; (ꢂ) Ni/SiO2-IV; (+)
Ni/SiO2-V; (ꢃ) Ni/Al2O3; (ꢀ) Ni/MgO; (ꢁ) Ni/AC; (᭹) Ni/graphite; (ꢄ)
Ni/Ta2O3.
Fig. 2. A “compensation plot” for the HDC of chlorobenzene over the 10 sup-
ported Ni catalysts (see Table 2).
particles, as shown in Fig. 1(d). The Ni catalysts considered
in this study exhibit some commonality albeit the Ni phase is
present in a range of sizes, morphologies and possible electronic
perturbations. The remit of this study is to establish some com-
monality in terms of HDC reaction kinetics and to provide a
coherent mechanistic argument to account for this.
Table 3
Formal description of the lines given in Figs. 4 and 5
Catalyst
y = kx + 1
R2 (correlation coefficient)
Ni/SiO2 (mean)
Ni/Al2O3
Ni/MgO
Ni/AC
Ni/graphite
Ni/Ta2O5
y = −6.9805x + 8.5173
y = −9.0844x + 11.359
y = −8.0708x + 10.167
y = −4.8569x + 5.3467
y = −14.325x + 19.125
y = −11.959x + 15.934
0.99717
0.99914
0.99783
0.99587
0.99862
0.99781
3.2. Analysis of experimental HDC data
ChlorobenzeneHDCproceededovereachcatalystwith100%
selectivity to yield benzene and HCl as the only products; there
was no evidence of Cl2 production or aromatic ring reduction.
The raw kinetic data given in Table 1 are presented as a con-
ventional compensation plot, i.e. ln A versus the experimentally
determined activation energy (Eexp), in Fig. 2. The linear rela-
tionship is consistent with compensation behaviour where the
Tiso can be extracted from the slope (0.17525 mol kJ−1) accord-
ing to [7]
reduced dataset are shown in Fig. 4 where it can be seen that
there is still no perfect point of coalescence. However, a still
closer examination allows us to identify two groups of catalysts,
i.e. Group I (Ni/SiO2 (mean), Ni/MgO, Ni/AC and Ni/Ta2O5)
and Group II (Ni/Al2O3 and Ni/graphite) that present clear cut
examples of an isokinetic relationship, as is illustrated in Fig. 5.
1
Tiso
=
(2)
R(slope)
and equals 686 K. This value is close to that (658 K) reported
in our earlier paper [1] for the hydrodehalogenation of a fam-
ily of haloarenes over a common Ni/SiO2 catalyst. Applying
the approach recommended by Linert and Jameson [38], i.e.
obtaining a Tiso from the intersection of the Arrhenius lines
associated with the raw experimental data, it can be seen from
the entries in Fig. 3 that there is no obvious common point
of intersection. However, a closer inspection reveals that the
kinetic data generated for the five Ni/SiO2 catalysts show lit-
tle variance where the slight differences in activation energy
(see Table 1) means that the crossing point cannot be very
well defined. We have therefore decided to use a mean value
for the Ni/SiO2 data which is included in Table 3 wherein the
equations of the Arrhenius fits (and associated correlation coef-
ficients) are given. A rationale for the use of a mean activation
energy is provided later in the text. The Arrhenius plots for the
Fig. 4. Arrhenius plots for the HDC of chlorobenzene where the five Ni/SiO2
catalysts are combined (ꢁ) to generate mean values: (ꢃ) Ni/Al2O3; (ꢀ) Ni/MgO;
(ꢁ), Ni/AC; (᭹), Ni/graphite; (ꢄ) Ni/Ta2O3.

92
M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
where N represents the Avogadro number, c the velocity of light,
h the Planck constant and R the gas constant. While we have
categorized the catalysts into two groups in Fig. 5, the abscissa
corresponding to the crossing point for the catalysts in Group
I (1000/Tiso = 1.495 K−1) is very close to that which character-
izesGroupII (1000/Tiso = 1.482 K−1). Suchaslightdifferencein
the isokinetic abscissa for groups of reaction systems is typically
accompanied by a corresponding difference in the ordinate posi-
tion [39]. In order to account for this, we can turn to Eq. (3) which
arises from a coupling of the phenomenological expression of
the Arrhenius rate law
ꢃ
ꢄ
Eexp
R
1
1
ln k = ln Z +
−
(4)
Tiso
T
and the expression derived [2] under conditions of resonance
ꢃ
ꢄ
π
νω
2(ν2 − ω2)
ln k = ln Z + ω(ν2 − ω2)ω−1
− arctg
Fig. 5. Arrhenius plots as given in Fig. 4 where the ln k values for Ni/Al2O3 (ꢃ)
and Ni/graphite (᭹) have been shifted by a common term to lower values as a
visual aid.
2
ꢅ
ꢀEi
hc
Eexp
RT
×
−
(5)
It should be noted that the kinetic data for the Group II cata-
lysts has been shifted downwards by 3 units as a visual aid (in
Fig. 5) to clearly illustrate the basis for our Group classifica-
tion. Taking the data for the Group I catalysts plotted in Fig. 5,
one can extract a value of 1000/Tiso = 1.495 0.004 K−1 which
results in a Tiso = 669 2 K. The intersection of the two lower
Here Z represents all contributions to the rate constant that are
not dependent on SET via resonance, i.e. “collision number”,
“form factors”, etc. It follows that if T = Tiso, then ln kiso = ln Z. It
is therefore possible for two reaction systems, one with a certain
“form factor” and the second system with a “form factor” of
(slightly different) magnitude, to generate two different values
lines in Fig. 5 (Group II catalysts) yields 1000/Tiso = 1.482 K−1
,
of ln kiso but still possess a common value of Tiso
.
i.e. Tiso = 675 K. Both values of Tiso differ slightly from that
obtained from the compensation plot in Fig. 2 (Tiso = 686 K). A
Tiso = 669 2 K is taken to be a more reliable value to charac-
terize catalytic HDC over supported Ni as it is based on more
data than the single point of intersection for the Group II cata-
lysts. Moreover, a higher confidence in the Tiso value obtained
from the intersection of Arrhenius lines has been established
[38] when compared with that which results from the slope of a
“compensation line”.
In our previous analysis [1], we assumed that Ni–H vibra-
tions served as the source of catalytic energy, operating on a
C–H out-of-plane vibration of the halogenated arene. In this
way a transformation from sp2 to sp3 hybridization is facili-
tated, which was deemed necessary for the reaction. From the
available literature [3], we chose ω = 940 cm−1 as the Ni–H
vibration (high hydrogen coverage on Raney Ni) that provides
the best match to our reaction conditions, i.e. hydrogen supply
maintained far in excess of reaction stoichiometry where non-
competitive adsorption of hydrogen and haloarene prevails [40].
From Eq. (3) we have calculated Tiso as a function of the vibra-
tional frequency (ν) of the reacting molecule and the results are
presented in Fig. 6. There are four classes of out-of-plane C–H
vibrations associated with chlorobenzene [41], which are given
in Table 4. In our earlier analysis [1], we adopted the “17b” out-
of-plane vibration, i.e. ν = 902 cm−1 which gives (from Eq. (3)) a
Tiso = 654 Kthat agreedwell withtheexperimentally determined
Tiso associated with the hydrodehalogenation of 12 different
3.3. On the origin of the isokinetic temperatures
In our previous paper [1], we demonstrated the pragmatic
value of the Selective Energy Transfer (SET) model to account
for the isokinetic response exhibited by a group of catalytic
hydrodehalogenation reactions. The model is based on the
premise that the energy necessary for a reaction to proceed is
supplied via vibrational resonance; the energy of a vibrator of
the catalyst system is transferred to that vibrational mode of the
reacting molecule which transforms the molecule towards the
“activated state” [2]. From this starting point, where ν represents
the wave number of the vibration mode of the reacting molecule
and ω is the wave number of the energy source (the catalyst
system), it is possible to calculate the isokinetic temperature
according to Eq. (3)
Table 4
Chlorobenzene C–H out-of-plane vibrations, taken from Varsanyi’s compilation
[41]
Mode notation
ν (cm−1
)
5
10a
10b
11
17a
17b
985
830
196
740
965
902
Tiso = NhcR−1(ν2 − ω2)ω−1
ꢁ
ꢂ−1
π
×
− arctg[0.5νω(ν2 − ω2)]−1
(3)
2

M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
93
Table 5
Analysis of consecutive differences (ꢀEexp) of the experimentally determined
activation energies
Catalyst
Eexp (kJ mol−1
)
ꢀEexp (kJ mol−1
)
nguess
n
Ni/SiO2 (mean)
58.0
17.5
8.4
2.08
1.00
3.18
9.38
2.33
4.94
2
1
3
9
2
5
Ni/Al2O3
Ni/MgO
Ni/AC
75.5
67.1
26.7
78.7
19.6
40.4
Ni/graphite
Ni/Ta2O5
119.1
99.5
41.5
Sum
192.4
22
ꢀ
ꢀ
Fig. 6. Calculated (from Eq. (3)) Tiso as a function of the frequency of the
vibration of the reacting molecule (ν) for an assumed value of the heat bath
ꢀEexp
/
n = 8.75 kJ mol−1 = 731 cm−1
.
frequency = 940 cm−1
.
ν = 740 cm−1 generates the isokinetic temperature obtained in
this study. The basis for the derivation of Eq. (3) is the classi-
cal physics treatment of resonance where the reaction system
is treated as a coupled, damped oscillator [2,43]. The ques-
tion, whether this approach applies for any value of ν has been
addressed in an earlier study [44] wherein “good” resonances
were taken to be those where the ratio between the two wave
numbers could be expressed as the ratio between two small
integers. Only in such cases is it acceptable to speak about
resonance in a quantum physical sense. We note here that the
ratio ω/ν = 1.27 is very close to 5/4 and the implied interac-
tion between five quanta of ω with four quanta of ν is in good
agreement with tests for the proposed condition of resonance
[44].
haloarene reactants over a common catalyst. However, the Tiso
generated in this study (669 2 K) is higher than that predicted
by adopting the “17b” mode as the critical reactant vibration.
Better agreement is reached by applying the vibration mode
denoted “11” as that which is excited before reaction. This vibra-
tion mode absorbs infrared radiation at 740 cm−1 [41] and one
can see from the curve presented in Fig. 6 that the associated
Tiso ≈ 670 K. Indeed, taking ω = 940 cm−1 and ν = 740 cm−1
,
the calculated (from Eq. (3)) Tiso = 669.2 K, which represents
very good agreement between theory and experiment (Tiso
=
669 2 K).
The involvement of two different vibrational modes as a
composite vibration that “brings the molecule to reaction” is
allowed in Eq. (5) where the contribution of one vibrational
mode may be greater in terms of overall reaction rate. In our
earlier study [1] we demonstrated that, with the exception of
polysubstituted haloarenes (with fewer C–H bonds), it was pos-
sible to account for the experimentally determined Tiso by using
the “17b” vibration. The data for all the reactants fell into the
range of vibrations that is defined by the curve presented in
Fig. 6. The virtue of the “17b” vibration mode is that it exists
for even high degrees of benzene substitution [41]. The “11”
mode, on the other hand, corresponds to the “umbrella” vibra-
tion of benzene (lowest out-of-plane vibrational frequency at
740 cm−1) where all hydrogens (and all carbons) vibrate in-
phase. This vibrational mode works well for mono-substituted
or ortho di-substituted benzenes, where there is still a sufficient
number of hydrogens to mimic the umbrella type of motion.
In the case of para di-substituted species it changes character
and disappears [41]. Taking chlorobenzene as reactant, the “11”
mode should be effective and our results indicate that it actu-
ally supercedes the contribution of the “17b” mode. We must,
however, introduce the proviso that we are applying reference
values based on free molecule spectral data for chlorobenzene
and any catalyst/reactant interaction(s) must result in some devi-
ation of the vibrational frequencies relative to the free molecule.
Nevertheless, application of Eq. (3) where ω = 940 cm−1 and
3.4. Treatment of the Ni/SiO2 data
In order to justify our lumping together of the five kinetic
datasetsforNi/SiO2, aconsiderationoftheexperimentallydeter-
mined activation energies (Eexp) is required. These values are
included in Table 5 where the consecutive differences between
the Eexp values (ꢀEexp) are identified. It is a corollary to the
deduction of Eq. (3) that the activation energies in such a series
should change in a stepwise fashion with a least common term
that is dependent on the frequency (ν). The basis and application
ofthis“rule”hasreceivedafulltreatmentelsewhere [42,43]. The
differences in activation energy (ꢀEexp) in such a series can be
expressed as a multiple of the least common term [43]. In the
first instance, we must guess the least common term; let us take
the lowest tabulated value (Table 5), i.e. 8.4 kJ mol−1. From this
we obtain a “guessed” factor by dividing the differences by 8.4;
the resulting number is denoted by nguess. Thereafter we take
nguess to the nearest whole number (n) and sum the n values. A
more precise value of the common least term is then obtained
from
ꢀ
ꢀEexp
ꢀ
(6)
n

94
M.A. Keane, R. Larsson / Journal of Molecular Catalysis A: Chemical 268 (2007) 87–94
and we arrive at a common least term equal to 8.75 kJ mol−1
,
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