The effect of solvents on the rate of catalytic hydrogenation of 6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione

Article abstract of DOI:10.1002/kin.20309

The rate of hydrogenation of 6-ethyl-1,2,3,4-tetrahydroanthracene-9,10- dione was investigated at 313 K and 0.1 MPa in 20 solvents. A multiple linear regression was used to describe the solvent effect. The regression of the reaction rates was carried out using two five-parameter linear regression models: the Abraham-Kamlet-Taft (AKT) and the Koppel-Palm (KP) model. After the elimination of the insignificant terms from the regression models, it was found that the basic character of the solvent and its Hildebrand cohesion energy density were the most important attributes influencing the hydrogenation rate. The analysis of both models led to the same conclusion. The resultant simplified AKT model gave closer fitting in comparison to the KP model. The results could facilitate the solvent selection for the industrial process of hydrogen peroxide production by the anthraquinone method with respect to the kinetics of anthraquinone hydrogenation.

Full text of DOI:10.1002/kin.20309

The Effect of Solvents on
the Rate of Catalytic
Hydrogenation of
6-Ethyl-1,2,3,4-tetrahydro-
anthracene-9,10-dione
ˇ
ˇ
´
VOJTECH FAJT, LADISLAV KURC, LIBOR CERVENY
Department of Organic Technology, Institute of Chemical Technology, Technicka´ 5, 166 28 Prague, Czech Republic
Received 29 January 2007; revised 28 June 2007, 20 November 2007; accepted 20 November 2007
DOI 10.1002/kin.20309
Published online in Wiley InterScience (www.interscience.wiley.com).
ABSTRACT: The rate of hydrogenation of 6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione was
investigated at 313 K and 0.1 MPa in 20 solvents. A multiple linear regression was used to
describe the solvent effect. The regression of the reaction rates was carried out using two five-
parameter linear regression models: the Abraham–Kamlet–Taft (AKT) and the Koppel–Palm
(KP) model. After the elimination of the insignificant terms from the regression models, it
was found that the basic character of the solvent and its Hildebrand cohesion energy density
were the most important attributes influencing the hydrogenation rate. The analysis of both
models led to the same conclusion. The resultant simplified AKT model gave closer fitting in
comparison to the KP model. The results could facilitate the solvent selection for the industrial
process of hydrogen peroxide production ꢀby the anthraquinone method with respect to the
C
kinetics of anthraquinone hydrogenation. 2008 Wiley Periodicals, Inc. Int J Chem Kinet 40:
240–252, 2008
complexity of the system is evident from the fact that
the solvent effect on the hydrogenation has been so far
evaluated stochastically. In the following text, some
conclusions of several publications dealing with this
problem are cited.
Specific attributes, which must be named in con-
nection with the mechanism of the influence of the
solvent on the kinetics of a heterogeneously catalyzed
hydrogenation, were summed up by Rajadhyaksha and
Karwa [1] into four points:
INTRODUCTION
Solvent Effects in Catalytic Hydrogenations
One of the important factors that influence the reaction
kinetics in the liquid phase is the solvent used. The
heterogeneously catalyzed hydrogenation is a typical
example of a complicated three- or four-phase reaction
system strongly influenced by the chosen solvent. The
ˇ
Correspondence to: Libor Cerveny´; e-mail: Libor.Cerveny@
vscht.cz.
1. different solubility of hydrogen in the reaction
mixture,
2. competitive adsorption of solvent molecules on
the active sites of the catalyst,
Contract grant sponsor: Grant Agency of the Czech Republic.
Contract grants numbers: 203/03/H140 and 104/06/0684.
2008 Wiley Periodicals, Inc.
c
ꢀ

EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
241
3. agglomeration of catalyst particles, and
4. nonbonding interactions between reactant or
product molecules with the solvent.
lyst. Because of the structurally similar solvents, the
authors attributed the different reaction rates only to
the different solubilities of hydrogen in the reaction
mixture.
By using an example of 2-nitrotoluene hydrogena-
tion in the presence of a 2 wt% Pd/C catalyst, the
authors proved that the predominant effect on the rate
of hydrogenation is precisely the interaction between
the substrate and the solvent. They used four alcohols,
benzene, n-hexane, and cyclohexane as solvents. In the
case of a positive interaction, the adsorption ability of
the reactant on the catalyst active site decreased; mean-
while, in the case of a negative interaction the adsorp-
tion was favored. They chose the activity coefficient of
the hydrogenated substrate as a suitable parameter to
describe the solvent effect.
Lo and Paulaitis [2] used the activity coefficient esti-
mated by the UNIFAC contribution method [3] for the
quantification of the solvation effect. They relatively
succeeded in finding the correlation between the pre-
viously published hydrogenation rates of acetone and
cyclohexene in the presence of nickel catalysts and the
activity coefficients.
Accessible information on the influence of solvents
on the kinetics of heterogeneously catalyzed hydro-
genation shows that the rate of hydrogenation clearly
depends on the combination of the solvent used, the
structure of the hydrogenated substrate, and the type of
catalyst [9]. The solubility of hydrogen in the reaction
mixture plays an important role, but in structurally dif-
ferent solvents other effects may occur, especially the
different substrate–solvent interaction. Furthermore, a
more complex situation occurs in the competitive hy-
drogenations when the solvent aids the adsorption of
one of the substrates on the catalyst active sites and
thus speeding up its hydrogenation. Different solvents
can then aid different substrates [10].
Solvent Effect Interpretation Using Linear
Free Energy Relationships
Certain potential for the quantification of the solvent
effect on the kinetics of hydrogenation can be explored
through the methods commonly used for the descrip-
tion of the solvent effect on the kinetics of homoge-
neous reactions in the liquid phase. The technique of
multiple linear regression derived on the basis of the
principle of linear free energy relationships (LFER)
reliably enables the evaluation of the solvent effect of
different physicochemical phenomena. The principle
is based on the distribution of the physicochemical
properties of the solvent into individual, mutually in-
dependent contributions. The number of contributions
is given by the number of independent variables of the
model.
Iwamoto et al. [4] proved that the hydrogen adsorp-
tion enthalpy in C1–C4 alcohols is constant (11.3 kJ
mol−1) in their studies on the hydrogenation of toluene
using Raney nickel. However, the values of the acti-
vation energy varied in the range 30.5–44.0 kJ mol−1
.
They failed to clarify the trends in the variations of
the reaction rates. On the contrary, Beketaeva et al.
[5] proved that the solvent does not only influence
the mechanism but also the adsorption enthalpy of hy-
drogen on the catalysts‘ surface in the hydrogenation
of 2-methylbut-3-yne-2-ol. The consequence of this
was different reaction rates and selectivities of hy-
drogenation with respect to the chosen combination
of catalyst–solvent. The catalysts used were different
group VIIIB metal black. The chosen solvents were wa-
ter, 0.1 M NaOH solution, 1 M H2SO4, 96% ethanol,
and n-heptane. The different concentrations of water in
solvents used by Beketaeva et al. [5] could be the main
reason of different conclusions to those of Iwamoto
et al. [4].
The widely and elaborately used model is the
Abraham–Kamlet–Taft [11] (AKT) model in the form
shown in Eq. (1).
XYZ = XYZ0 + d · δ + s · π∗ + a · α
+ b · β + h · δH2
(1)
ˇ
Cerveny´ et al. [6] hydrogenated 2-methylbut-3-en-
2-ol in the presence of a 5-wt% Pt/SiO2 and 5-wt%
Pt/C. For the evaluation of the solvent effect, they
used the Drougard–Decroocq [7] model. The regres-
sion model, which was originally designed for reac-
tions in a homogeneous phase, was successful only
after the inclusion of structurally similar solvents (e.g.,
the homologous series of alcohols).
Rautanen et al. [8] investigated the hydrogena-
tion of toluene in cyclohexane, n-heptane, and 2,2,4-
trimethylpentane in the presence of a Ni/Al2O3 cata-
The terms d, s, a, b, and h represent solvent inde-
pendent parameters of the model. These parameters
characterize a given process, and they indicate its sen-
sitivity on the solvent properties. The quantity XYZ is a
dependent variable; XYZ0 is an intercept whose phys-
ical meaning is the standard state of the quantity XYZ.
The rest of the quantities are independent variables
characteristic of a given solvent: π∗ represents the sol-
vent polarity, α is the hydrogen bond donor ability, and
β is hydrogen bond acceptor ability of the solvent. The
International Journal of Chemical Kinetics DOI 10.1002/kin

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FAJT, KURC, AND CERVENY
242
quantity δH2 is the Hildebrand cohesion energy density,
and it is defined as the heat of evaporation of the sol-
vent at 298 K per unit volume (Eq. (2)). The term d · δ
in the AKT model is the correction on polarizability,
and parameter δ has a value of 0.5 for polyhalogenated
solvents, 1.0 for aromatic solvents, and zero for all
other solvents.
hydrogen peroxide by the anthraquinone method. Cho-
sen substrate 6-ethyl-1,2,3,4-tetrahydroanthracene-
9,10-dione is in comparison with commercially more
available structural analog 2-ethyl-9,10-anthraquinone
significantly more resistant against deep hydrogena-
tion and C O bonds hydrogenolysis [14]. According
to the patent literature, this process can be carried out
using a wide range of solvent systems [15]. The se-
lection criteria have so far been the physicochemical
properties of the solvents. However, the comparison of
the solvents in terms of their influence on the hydro-
genation kinetics was usually neglected. Furthermore,
the anthraquinone derivatives are particularly interest-
ing for the study of solvation mechanisms in different
solvents [16].
ꢀHv298 − RT
δH2 =
(2)
Vm298
The second important model is the Koppel–Palm
[12] (KP) model with a Makitra et al. [13] modification
in the form shown in Eq. (3).
XYZ = A0 + A1 · f (nD) + A2 · f (ε) + A3 · ET
The objective of this work was to determine the
reaction rate of the catalytic hydrogenation of 6-ethyl-
1,2,3,4-tetrahydroanthracene-9,10-dione (Eq. (6)) in
the presence of a palladium-supported catalyst in some
chosen solvents and the regression of experimental data
using the AKT and KP models.
+ A4 · B + A5 · δH2
(3)
In this model, A1–A5 are solvent independent param-
eters, A0 is an intercept with the similar meaning to
XYZ0, and XYZ is a dependent variable. In the KP
model, the independent variables are the refractive in-
dex function f (nD), dielectric constant function f (ε),
electrophilic solvation ability ET , nucleophilic solva-
tion ability B of the solvent, and its Hildebrand cohe-
sion energy density δH2 . The refractive index function
f (nD) and the dielectric constant function f (ε) are
usually expressed by the Kirwood functions (4) and
(5), respectively.
(6)
The main contribution of this work should be the
description of the solvent effect on the kinetics of 6-
ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione hydro-
genation in a three-phase reaction system using the
multiple linear regression models.
n2D − 1
f (nD) =
f (ε) =
(4)
(5)
n2D + 2
ε − 1
2 · ε + 1
EXPERIMENTAL
Chemicals Used
The given models have a wide application. In addi-
tion to the study of the solvent effect on the reaction
rate, they could also be applied in the studies of the
equilibrium constants in the liquid-phase reactions, the
distribution coefficients between two liquid phases, the
retention in gas chromatography, the solubilities of a
given substrate in a solvent, the chemical shifts in nu-
clear magnetic resonance experiments, wavelength or
wave number shifts in spectral characteristic measure-
ments, the Gibbs energy, and the enthalpy values of
equilibrium reactions.
Propan-1-ol, propan-2-ol, butan-1-ol, butan-2-ol, 2-
methylpropan-1-ol, pentan-1-ol, cyclohexanol, ethyl
acetate, benzene, and 1,2-dichloroethane were sup-
plied by Lachema (Brno, Czech Republic); cyclo-
hexane, toluene and 1,4-dioxane were from Penta
(Chrudim, Czech Republic); 2,2,2-trifluoroethanol,
ethanol, cis-decaline, chlorobenzene, and triethy-
lamine were from Sigma Aldrich; m-xylene was from
Fluka Chemie GmbH; 2-methylpropan-2-ol was from
former Koch-Light Laboratories Ltd. (Colnbrook,
UK); 2-ethylanthracene-9,10-dione was delivered by
BASF Aktiengesellschaft (Ludwigshafen, Germany);
6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione was
synthesized via a Dawsey et al. [17] procedure.
Hydrogenation of 6-Ethyl-1,2,3,4-
tetrahydroanthracene-9,10-dione
The hydrogenation of anthraquinone derivatives is a
typical example of a solvent-sensitive reaction. This
reaction forms one step in the industrial production of
The chemicals were supplied with purity p.a. (ana-
lytical grade). The solvents were refined by distillation
International Journal of Chemical Kinetics DOI 10.1002/kin

EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
243
with sodium under nitrogen atmosphere and dried us-
ing a molecular sieve UOP type 3 A (Fluka) before
application.
The hydrogenation catalyst was an MGS5-type of
composition 2 wt% Pd/Al2O3-SiO2 in powder form,
supplied by Su¨d-Chemie MT S.r.l. Montecatini Tech-
nologie Catalysts (Novara, Italy).
terion did not surpass its critical value of 0.3 even in
the most viscous cyclohexanol.
The catalyst was activated in situ before the hydro-
genation. Amounts of 10 mg of catalyst and 1 cm3
of solvent were fed into the reactor, and the suspen-
sion was mixed in a hydrogen atmosphere for 30
min at reaction conditions. In this way, the catalyst
was brought to a standard state in which its activity
was constant during the course of hydrogenation. Af-
ter the catalyst activation, 19 cm3 of 6-ethyl-1,2,3,4-
tetrahydroanthracene-9,10-dione solution in a given
solvent was fed into the reactor. The initial substrate
concentration in the reaction mixture was 84 mmol
dm−3, and the total volume of the liquid phase was
20 cm3. After filling the reactor with hydrogen, the
reaction was initiated. The hydrogenation kinetics was
monitored by measuring the time dependency of hy-
drogen consumption using a gas volumetric burette.
Apparatus and Procedures
The hydrogenations were carried out in the presence
of a palladium catalyst at 313 K and 0.1 MPa in a
laboratory glass batch reactor (38 cm3) equipped with
a magnetic stirrer (4500 rpm). A combination of the
chosen substrate, mild reaction conditions, and a low
amount of the suitable catalyst enables to lead the hy-
drogenation with a 100% selectivity without respect to
the chosen solvent. In order for the hydrogenation to
take place in the kinetic regime even at high-reaction
rates, the reactor was equipped with horizontal baffles
that enabled higher mixing efficiency.
Computational Details
The kinetic region in terms of external mass diffu-
sion was achieved by specific reactor construction and
by intensive stirring of the reaction mixture. The reac-
tor was equipped with eight fixed baffles in sets of four
placed in two rows above each other. The baffles were
in the shape of the Lorentz curve and had a circular
cross section. The aerodynamic shape of the baffles
ensured the elimination of an axial vortex and the ad-
herence of the catalyst particles in inaccessible parts
of the reactor. The verification of the kinetic region
was carried out by the measurement of the hydrogena-
tion rates as a function of the rotational speed of the
impeller for cyclohexanol. The rate of hydrogenation
was constant in the range between 3800 and 4500 rpm.
Cyclohexanol was chosen because it had the lowest
value of Reynolds number ReM for mixing based on
the initial hydrogenation rate [18].
The kinetic region in terms of internal mass diffu-
sion using a catalyst with nonuniform palladium load-
ing (catalyst MGS5) is impossible to verify by a stan-
dard procedure of catalyst particle sieving. Therefore,
the internal mass-transfer limitations were considered
empirically. In the hydrogenation of anthraquinone
derivatives, the internal diffusion can only be limited
by the mass transfer of hydrogen and not by the mass
transfer of anthraquinone. This is caused by 105–106
times lower concentration of hydrogen compared to
anthraquinone. The differences in concentration can-
not be compensated by 101–102 times higher effec-
tive diffusion coefficient of hydrogen compared to an-
thraquinone. Thus, the kinetic region in terms of the
internal diffusion was verified using the Weisz–Prater
criterion ꢁs for hydrogen [19]. The Weisz–Prater cri-
The actual reaction rate rξ, i in the conversion range ξ
for the solvent i was evaluated from the dependence of
hydrogen moles consumed in time and per unit amount
of catalyst. If the range is narrow enough, the experi-
mental points in this interval can be described by linear
regression with high-close fitting. The slope of the re-
sultant line divided by the catalyst amount gives the
actual hydrogenation rate for the corresponding con-
version interval. The evaluation carried out using lin-
ear regression of the experimental points by the least-
squares method. The so-called initial reaction rate r0, i
was determined in the conversion range ξ ≡ 3%–15%,
the other actual rates were determined in the conver-
sion ranges 20%–25% (r20, i), 50%–55% (r50, i), and
70%–75% (r70, i).
The difference in hydrogen solubility in the reac-
tion mixture with respect to various solvents used was
eliminated by the introduction of the corrected actual
reaction rate rξc, i according to Eq. (7), where xH , i
2
is the hydrogen mole fraction dissolved in the liquid
phase.
rξ, i
rξc, i
=
(7)
x
H2, i
The introduction of the corrected hydrogenation rate
(Eq. (7)) assumes a first reaction order with respect
to hydrogen in all chosen solvents. This assumption
could experimentally be verified by the measurement
of the hydrogenation rates at various pressures with si-
multaneous knowledge of the pressure dependence of
hydrogen solubility. Such a dependence is not known
for each solvent used. Hence, the first reaction order
International Journal of Chemical Kinetics DOI 10.1002/kin

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FAJT, KURC, AND CERVENY
244
Bi
with respect to hydrogen was not experimentally ver-
ified but it was assumed in agreement with the results
of Santacesaria et al. [20].
BNi
=
(9)
BHMPA
The variable δH2 presented in both models was cal-
culated by the standard procedure according to (2) and
expressed in kJ cm−3. The enthalpies of vaporization
ꢀHv298 required to calculate δH2 for most of the sol-
vents were obtained from thermodynamic tables [27],
and for 2,2,2 trifluoroethanol the enthalpy of vaporiza-
tion was obtained from Rochester and Symonds [28].
The function of the refractive indices and the dielec-
tric constants were calculated according to Kirkwood
functions (4) and (5), respectively. Into the Kirkwood
expressions, the tabulated [29] refractive index of yel-
low sodium line at 293.15 K and the static dielectric
constant [30] of the solvent at either 298.15 K or at
reaction temperature were inserted.
By experimental verification, the hydrogenation
was carried out in the kinetic region with respect to ex-
ternal mass diffusion; hence, the equilibrium hydrogen
concentration in the reaction mixture was guaranteed.
The hydrogen concentration in the reaction mixture
was considered negligible in the reactant and product
solution; hence, it was taken as hydrogen solubility in
a pure solvent.
Regression calculations were computed using the
QC.Expert 2.7 software by the common least-squares
method. All the diagnostic tests were determined at
95% significance level. The quantities used for this
purpose were also computed using the QC.Expert soft-
ware, and their definitions can be found, for example,
in Meloun and Militky [21,22].
Hydrogen solubilities in various solvents were
taken from the Battino et al. [31] tables. However,
more contemporary data available for butan-1-ol [32],
butan-2-ol [33], 2-methylpropan-1-ol [34], and 2,2,2-
trifluoroethanol [35] were used. The inaccessible val-
ues for methylcyclohexane and triethylamine were
obtained by approximation. The dependence of the
hydrogen solubility for 11 other gases (He, Ne, Ar,
Kr, N2, O2, CO, CO2, CH4, CF4, SF6) in methylcyclo-
hexane on the hydrogen solubility of these gases in cy-
clohexane was found to be linear [36]. The dependence
had high-close fitting with a correlation coefficient of
0.999. Thus, the hydrogen solubility in methylcyclo-
hexane was computed by extrapolation from this de-
pendence. The solubility of hydrogen in triethylamine
was obtained from its pressure dependence [37].
Tabulated Data Collection
It was necessary to collect a lot of tabulated values
for successful regression calculations. The variables
in AKT and KP models and hydrogen solubilities in
pure solvents (see Table I) represent a series of physic-
ochemical quantities that are available from various
sources. The variables π∗, α, β, and ET (30) were taken
from Marcus [23]. The Dimroth–Reichardt character-
istic ET (30) was used to express the electrophilic sol-
vation ability of the solvent in the KP model instead
of the original ET quantity. The nucleophilic solvation
ability of solvent B for the interaction solvent–phenol
was accepted (in some works this quantity is assigned
Bꢁ to distinguish it from the original nucleophilic-
ity quantifying the interaction solvent–methan(2H)ol),
and it was taken from Aslam et al. [24] (alcohols) and
Abboud and Notario [25] (the rest of the solvents). The
unavailable value B for 2,2,2-trifluoroethanol was ob-
tained from the correlation between infrared stretching
frequency shifts of the OH group for solvated 2,2,2-
trifluoroethanol with corresponding shifts for solvated
phenol published by Purcell and Wilson [26]. The
variables ET (30) and B were normalized according
to the expressions (8) and (9), respectively. To com-
pute the normalized quantities for the ith solvent ETN, i
and BiN , the electrophilic solvation ability of water
RESULTS AND DISCUSSION
Preliminary Data Analysis
The hydrogenation of 6-ethyl-1,2,3,4-tetrahydroan-
thracene-9,10-dione was carried out in 20 solvents.
These included 10 alcohols (of which one was fluo-
rinated), 4 aromatics, 2 saturated hydrocarbons, ether,
ester, amine, and an alkylchloride. With a few sol-
vents, it was impossible to determine the hydrogena-
tion rate at some conversion intervals. This was due
to the low solubility of the hydrogenation product in
these solvents. The precipitation of 6-ethyl-1,2,3,4-
tetrahydroanthracene-9,10-diol was very fast and eas-
ily detectable by visual observation due to the trans-
parent glass reactor. The conversion intervals in which
the actual hydrogenation rates were determined were
selectively chosen to eliminate the precipitation effect
on the hydrogenation.
(ET (30)H O = 264 kJ mol−1), the electrophilic solva-
2
tion ability of trimethylsilane (ET (30)TMS = 129 kJ
mol−1), and the nucleophilic solvation ability of hex-
amethylphosphoric amide (BHMPA = 471 cm−1) had to
be known.
ET (30)i − ET (30)TMS
ETN, i
=
(8)
ET (30)
− ET (30)TMS
H2O
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EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
245
Table I Variables of the AKT and KP Models Used in the Regression and the Hydrogen Solubility
δH2
x
Solvent
δ
π∗
α
β
f (nD) f (ε) f (ε’) ETN
BN
(kJ mol−1
)
(× H102 4)
1
2
3
4
5
6
7
8
9
2,2,2-Trifluoroethanol 0.0 0.73 1.51 0.00
0.19
0.22
0.23
0.23
0.24
0.24
0.24
0.24
0.25
0.28
0.25
0.23
0.25
0.28
0.29
0.29
0.29
0.31
0.27
0.24
0.47
0.47
0.46
0.46
0.46
0.45
0.46
0.44
0.45
0.45
0.22
0.38
0.20
0.22
0.23
0.24
0.24
0.38
0.43
0.24
0.47
0.47
0.46
0.46
0.45
0.43
0.45
0.43
0.44
0.45
0.22
0.38
0.20
0.22
0.23
0.24
0.23
0.37
0.42
0.24
0.90
0.65
0.62
0.57
0.60
0.51
0.55
0.40
0.57
0.50
0.16
0.23
0.01
0.02
0.11
0.10
0.08
0.19
0.33
0.04
0.23a
0.49
0.49
0.51
0.50
0.51
0.49
0.53
0.50
0.52
0.50
0.38
0.00
0.00
0.10
0.12
0.14
0.08
0.08
1.38
0.56
0.68
0.60
0.56
0.54
0.51
0.52
0.47
0.50
0.56
0.42
0.33
0.26
0.31
0.35
0.33
0.32
0.38
0.41
0.23
2.77b
2.06
2.31
2.66
2.69c
2.73d
2.88e
3.00
3.29
1.68
1.76
3.46
5.39f
3.61
2.59
3.15
4.15
2.65
1.78
8.96g
Ethanol
0.0 0.54 0.86 0.75
0.0 0.52 0.84 0.90
0.0 0.48 0.76 0.84
0.0 0.47 0.84 0.84
0.0 0.40 0.69 0.80
0.0 0.40 0.79 0.84
0.0 0.41 0.42 0.93
0.0 0.40 0.84 0.86
0.0 0.45 0.66 0.84
0.0 0.55 0.00 0.37
0.0 0.55 0.00 0.45
0.0 0.00 0.00 0.00
0.0 0.11 0.00 0.08
1.0 0.59 0.00 0.10
1.0 0.54 0.00 0.11
1.0 0.47 0.00 0.12
1.0 0.71 0.00 0.07
0.5 0.81 0.00 0.10
0.0 0.14 0.00 0.71
Propan-1-ol
Propan-2-ol
Butan-1-ol
Butan-2-ol
2-Methylpropan-1-ol
2-Methylpropan-2-ol
Pentan-1-ol
10 Cyclohexanol
11 1,4-Dioxane
12 Ethyl acetate
13 Methylcyclohexane
14 cis-Decaline
15 Benzene
16 Toluene
17 m-Xylene
18 Chlorobenzene
19 1,2-Dichloroethane
20 Triethylamine
ε: Static dielectric constant at 298 K.
εꢁ: Static dielectric constant at a reaction temperature 313 K.
a Obtained by linear regression of the data published by Purcell and Wilson [26].
b Taken from the work of Mainar et al. [35].
c,d,e Taken from the works of Pardo et al. [32–34].
f
Calculated as described in the text.
g Obtained from the dependence of hydrogen solubility on pressure published by Brunner [37].
The highest reaction rates were detected in most
alcohols and in triethylamine. On the other hand, the
lowest reaction rates wereobserved in methylcyclohex-
ane, chlorobenzene, and 1,2-dichloroethane. In ethyl
acetate, the hydrogenation rate was approximately one-
third lower than the average rate in alcohols. In 2,2,2-
trifluoroethanol, 1,4-dioxane, benzene, toluene, and m-
xylene, the reaction rate was comparable (Table II).
The trends in the reaction rates cannot be described
by any individual physical properties of the solvent.
Therefore, to quantify the solvent effect on the hy-
drogenation, empirical linear expressions of solvation
energy with the use of AKT and KP models were
considered. To examine whether the variables of both
models satisfy the condition of mutually independence,
their partial correlation coefficients were investigated
(Table III).
relation coefficient slightly exceeds its critical limit in
several other combinations (Table III). A higher num-
ber of supercritical partial correlation coefficients and
its larger values in most of the combinations signal-
ized that the AKT model is designed better than the
KP model.
To examine the extent of one-dimensional linear
dependence of the measured reaction rates on individ-
ual variables of the AKT and KP models, the Pearson
partial correlation coefficient is evaluated.
In Table IV, it is apparent that the strongest linear
relationship exists between uncorrected initial hydro-
genation rates and the hydrogen bond acceptor ability
of solvent β. By correcting the concentration of hy-
drogen in the reaction mixture, the strength of this
relationship decreased by 6% but at the same time the
correlation with the Hildebrand cohesion energy den-
sity of the solvent increased by 28%. The dependence
between the hydrogenation rate and the nucleophilic
solvation ability of the solvent BN of model KP is
markedly weaker compared to the variable β, which
has a similar meaning in the AKT model.
From Table III, the partial correlation coefficients
explaining the variables showed strong mutual depen-
dence in the α versus δH2 pair of the AKT model and
between the variables f (ε) versus ETN , f (ε), versus δH2
and ETN versus δH2 of the KP model. The partial cor-
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246
Table II Corrected Hydrogenation Rates of 6-Ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione with Respect to the
Solvent Used at Four Different Conversions
r0c,i
r2c0,i
(mol min−1 gcat
r5c0,i
(mol min−1 gcat
r7c0,i
−1
−1
−1
−1
(mol min−1 gcat
)
Solvent
(mol min−1 gcat
)
)
)
1
2
3
4
5
6
7
8
2,2,2-Trifluoroethanol
Ethanol
Propan-1-ol
Propan-2-ol
Butan-1-ol
17.4
191.8
153.7
137.2
131.4
161.4
123.7
80.6
103.3
146.0
24.5
33.6
0.3
13.8
177.1
143.6
123.5
115.4
135.9
108.4
65.0
100.1
129.1
19.9
25.9
Ins
3.8
5.4
7.3
6.3
6.4
3.0
38.6
Insa
144.6
126.9
95.9
99.5
102.7
83.7
47.7
71.3
96.7
13.5
25.1
Ins
Ins
Ins
Ins
4.3
3.2
<1.0
35.9
Ins
118.3
111.2
73.3
87.4
80.6
67.2
36.6
52.0
74.2
<1.0
16.3
Ins
Ins
Ins
Ins
Ins
2.8
<1.0
29.2
Butan-2-ol
2-Methylpropan-1-ol
2-Methylpropan-2-ol
Pentan-1-ol
Cyclohexanol
1,4-Dioxane
Ethyl acetate
Methylcyclohexane
cis-Decaline
Benzene
Toluene
m-Xylene
Chlorobenzene
1,2-Dichloroethane
Triethylamine
9
10
11
12
13
14
15
16
17
18
19
20
9.5
13.5
16.1
10.2
7.2
4.6
37.6
a Ins means that at a given conversion the hydrogenation product was insoluble in the reaction mixture; hence, it was impossible to determine
the reaction rate.
Table III Partial Correlation of the Parameters in the Models AKT and KP
Paired
variables
Partial
correlation
coefficient
Paired
variables
Partial
δ–π∗
δ–α
δ–β
δ–δH2
π∗–α
π∗–β
π∗–δH2
α–β
α–δH2
β–δH2
0.402
−0.510
−0.595
−0.411
0.202
−0.146
0.397
0.503
0.856 0.602
f (nD)–f (ε) f (nD)–ETN f (nD)–BN f (nD)–δH2 f (ε)–ETN f (ε)–BN f (ε)–δH2 ETN –BN ETN –δH2
B
N –δH2
−0.576 −0.709 −0.431 −0.538 0.909 0.209 0.856 0.204 0.921 0.156
correlation
coefficient
Partial correlation coefficients exceeding their critical limit at a significance level 95% are shown in bold.
Table IV Correlation of the Initial Hydrogenation Rates and the Individual Variables of the AKT and KP models
Expression of the Reaction Rate
r
0,i
r0c,i
Variable of the AKT model
Pearson correlation coefficient
Variable of the KP model
δ
π∗
α
β
δH2
δ
π∗
α
β
δH2
−0.558 −0.177 0.595 0.926 0.623
f (nD)
−0.517 −0.016 0.667 0.868 0.823
f (nD)
f (ε)
ETN
BN
δH2
f (ε)
ETN
BN
δH2
Pearson correlation coefficient
−0.496
0.620
0.589 0.694 0.623
−0.438
0.715
0.694 0.447 0.823
The Pearson correlation coefficients exceeding their critical limit at a significance level 95% are shown in bold.
The Kirkwood function of dielectric constants and
the reaction rate were strongly bound by a linear rela-
tionship, but a linear dependence of the polarity charac-
teristic π∗ and the reaction rate should not be expected.
The rest of the values of the Pearson correlation coeffi-
cients ranged from 0.5 to 0.7. An entirely different
result of the pairs correlation reaction rate versus f (ε)
and reaction rate versus π∗ shows that the AKT and
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EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
247
KP models significantly differ to their approach of the
effect of solvent polarity.
and 19%, respectively, for the α, f (ε), and f (nD)
variables. However, these variables at the same time
significantly correlate with the rest of the variables.
Hence, the terms with the α, f (ε), and f (nD) vari-
ables were found as statistically insignificant and they
were eliminated from the models. After the elimina-
tion, simplified AKT and KP models with new regres-
sion parameters were obtained. The new p-levels did
not exceed its critical limit. Even the significance of the
regression parameters with delta and ETN decreased be-
low its critical limit. The basic character of the solvent
expressed by beta or BN and the Hildebrand cohesive
energy density δH2 can be considered as the most signifi-
cant properties influencing the hydrogenation kinetics.
The Taft polarity/polarizability characteristics δ, π∗,
and the Dimroth–Reichardt electrophilic ability ETN
are also significant. Another way for the evaluation of
statistical significance is the calculation of Mallows Cp
values [38]. These are calculated for all of the poten-
tial models obtained by the elimination of a random
number of random terms. In this way, the same results
were obtained.
Precise Models Construction
The initial hydrogenation rate, which represents the
dependent variable in the regression models, was ex-
pressed in two ways: the initial rate (uncorrected) and
the initial rate corrected on the hydrogen solubility.
The correlation coefficient increased from 0.949 to
0.972 for the AKT model and from 0.880 to 0.919 for
the KP model after the correction. The closer fitting
of the corrected rates called for a detailed discussion
in the regression of these rates. The evaluation of the
parameters XYZ0, d, s, a, b, h, and A0–A5 is presented
in Table V.
The determination of the statistical significance of
the individual variables is possible using the calculated
probability (p-level) that at 95% should not exceed
a critical limit 0.05. In Table V, the critical limit of
p-level was exceeded in the terms with the variables
δ and α in the model AKT and in the terms with the
variables f (nD), f (ε), and ETN in the KP model. The
α, f (nD), and f (ε) variables were insignificant, and
the terms in which they occurred were eliminated.
The substitution of dielectric constant at hydrogena-
tion temperature instead of the dielectric constant at
298 K caused the increase of the correlation coeffi-
cient by about 2% but had no effect on the significance
of the term.
Models Comparison
The number of different tests and criteria have been
used are standard in multiple linear regression fitting.
They all are recommended and further explained in the
works of Meloun and Militky [21,22].
Since the simplified models were now void of the
insignificant terms, it was possible to compare the mod-
els in terms of their ability to describe the experimental
data. In this respect, the mean square error of predic-
tion (MEP) and the Akaike information criterion (AIC)
were evaluated. By comparing the basic statistic quan-
tities in the AKT model (10) and the KP model (11),
it can be seen that the MEP value of the AKT model
It is necessary to view the statistical significance
of the variables in Table V with respect to partial
Pearson correlation coefficients in Table IV. Although
the p-level surpassed its critical limit by 3%–4% for
the delta and ETN variables, these variables at the same
time do not significantly correlate with the rest of the
variables. The p-level was exceeded by 13%, 83%,
Table V The Enumeration of the Regression Parameters in the Description of the Corrected Rates Using the AKT and
the KP Models
Model AKT
Intercept
d
s
a
b
h
Value of the regression parameter
Standard deviation
p-level
−125.3
24.0
0.000
28.6
15.6
0.088
−112.9
32.6
0.004
−26.7
19.1
0.183
83.3
17.2
0.000
479.6
89.2
0.000
Model KP
Intercept
A
1
A
2
A
3
A
4
A5
Value of the regression parameter
Standard deviation
p-level
−231.4
105.1
0.045
62.0
407.8
0.881
191.8
161.0
0.235
−213.9
112.3
0.078
72.8
25.4
0.012
670.7
158.0
0.000
Parameters h and A5 are in cm3 kJ−1, and other parameters are dimensionless.
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FAJT, KURC, AND CERVENY
248
is four times lower than MEP of the KP model and the
AIC value of AKT model is about 13% lower than AIC
of the KP model. Hence, both quantities indicate that
the simplified AKT model is more suitable in terms
of close fitting for the quantification of the solvent
effect on corrected hydrogenation rates than the sim-
plified KP model. On the other hand, according to the
Scott criterion value, the simplified AKT model in con-
trast to the KP model showed a slight multicollinearity,
which is caused by the stronger partial relationship of
variables β versus δH2 (Table II). The multicollinear-
ity in the AKT model could be eliminated by the
use of the generalized principal component regression
method (GCPR) instead of the common least-squares
method. However, this would decrease the accessibility
of such a model. According to Fisher–Snedecor test,
both simplified models were found to be significant. In
other words, the corrected initial rate of hydrogenation
is strongly dependent on the retained variables in the
simplified models AKT and KP.
indicate the outliers [22]. However, a set of influential
points is composed from a subset of outliers and a
subset of high-leverage points (extremes). Some points
could be incorporated in both subsets.
To detect the influential points, three types of di-
agnostic measures were used: diagnostics based on
residual plots, diagnostics based on scalar influence
measures, and diagnostics based on the diagonal ele-
ments of the hat matrix. Jackknife residuals are able
to indicate the outliers. The diagonal elements of hat
matrix are able to detect high-leverage points only.
The Williams and McCulloh–Meeter plots can indi-
cate both. The rest of the diagnostics used can detect
influential points in general. The Pregibon plot is able
to distinguish whether the point is strongly influential
or intermediately influential.
Practically all the diagnostic tests showed the influ-
ential point for 2,2,2-trifluoroethanol in both models
(see Table VI). The Williams plot and the jackknife
residuals in the KP model indicated this point as outlier.
r0c,i = −103( 18) + 34( 16) · δ − 105( 33) · π∗ + 90( 17) · β + 385( 60) · δH2
R = 0.968, Radj = 0.780, MEP = 479, AIC = 121, F = 56.3
(10)
(11)
r0c,i = −209( 43) − 144( 68) · ETN + 77( 22) · BN + 682( 141) · δH2
R = 0.911, Radj = 0.282, MEP = 1919, AIC = 139, F = 25.9
The other diagnostic tests were carried out for the
residuals. Besides the identification of the influential
points that are discussed below, no other important dif-
ferences between the diagnostic tests of the AKT and
the KP models were detected. From the Jarque–Berra
test of residuals normality, it was found that the residu-
als have a Gauss distribution. From the Wald test, it was
observed that the autocorrelation of the ordinary resid-
uals is insignificant. And from the Cook–Weisberg test,
the homoscedasticity was observed (constant residual
distribution).
Influential Points Detection
A skilled identification of the outlying experimental
points (outliers) for the multiple linear regression is
a sophisticated problem that has been advanced in the
last 20 years [22]. From Figs. 1 and 2, it cannot be easily
distinguished which points are high-leverage points
and which ones are the outliers. A number of diagnostic
tools, which have been developed for this purpose, are
able to indicate only the influential points and may not
Figure 1 Dependence of the experimental values of cor-
rected initial hydrogenation rates on the values predicted by
the simplified AKT model; red (solid) line represents y = x
function, blue (dashed) lines represent the confidence bands,
and green (dotted) lines represent prediction bands. [Color
figure can be viewed in the online issue, which is available
at www.interscience.wiley.com.]
International Journal of Chemical Kinetics DOI 10.1002/kin

EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
249
agreement for the KP model, and they indicated 2,2,2-
trifluoroethanol, 1,4-dioxane and triethylamine. For the
AKT model, in addition to 2,2,2-trifluoroethanol, they
indicated ethanol, 2-methylbutan-2-ol, ethyl acetate,
and methylcyclohexane as influential points.
The reason why the experimental values in the
above-mentioned solvents were found to be influential
is a matter of presumption. Owing to the similarity of
all the diagnostic measures for 2,2,2-trifluoroethanol
in both models, the lower stability of this solvent in
the hydrogenation could be the reason. The detection
of high-leverage points is relatively logical because,
for example, triethylamine exhibited the highest nu-
cleophilic solvation ability (BN = 1.38); meanwhile,
ethanol exhibited the highest Hildebrand cohesion en-
ergy density (δH2 = 0.677 kJ cm−3), and methylcyclo-
hexane had a zero Taft polarity characteristic π∗.
Figure 2 Dependence of the experimental values of cor-
rected initial hydrogenation rates on the values predicted by
the simplified KP model; red (solid) line represents y = x
function, blue (dashed) lines represent the confidence bands,
and green (dotted) lines represent prediction bands. [Color
figure can be viewed in the online issue, which is available
at www.interscience.wiley.com.]
The Effect of Conversion on the
Parameters Significance
Another question is whether using the simplified AKT
and KP models the corrected rate of hydrogenation
could be described at a selected conversion in the
course of hydrogenation (see Table VII). By observa-
tion of the probabilities of the individual independent
variables of the AKT and KP models, it could be pos-
sible to discuss the main factors influencing the mech-
anism of hydrogenation. In Table II, in addition to the
corrected initial hydrogenation rates, the rates at dif-
ferent conversion levels are given. In some solvents, it
was impossible to determine the hydrogenation rate at
higher conversions due to the above-mentioned prob-
lems. Such solvents were not included in the selection
The Williams plot, which appeared to be the most
strictest of all diagnostics, indicated as outliers also
butan-2-ol, 2-methylpropan-2-ol and ethyl acetate for
the AKT model, and butan-2-ol and 1,4-dioxane for
the KP model. The diagonal elements of Tukey’s
hat matrix showed high-leverage points for 2,2,2-
trifluoroethanol and methylcyclohexane for the AKT
model, and 2,2,2-trifluoroethanol, 1,4-dioxane and tri-
ethylamine for the KP model. The diagnostics, which
are able to detect the high-leverage points only, were in
Table VI Indication of the Influential Points Using Different Diagnostic Tests
Model AKT
Model KP
Influential
Point
High-Leverage
Point
Influential
Point
High-Leverage
Point
Diagnostic Test
Outlier
Outlier
McCulloh–Meeter plot
Williams plot
Pregibon plot
Jackknife residuals
Cook’s distance
Atkinson’s measure
Belsey’s DFFITS
Anders–Pregibon
diagnostics
1, 12
1, 6, 8, 12, 13
1
Undetected
Undetected
1, 2, 8, 12
1, 2, 8, 12
1
1, 12
1, 13
Undetected
1, 6, 8, 12
1, 11, 20
1, 6, 11, 20
1(S), 11, 20(S)
1
1, 11, 20
1, 20
Undetected
1, 6, 11
–
–
–
–
–
–
–
–
–
–
–
–
–
–
1
–
–
–
–
Undetected
–
–
–
–
1, 20
1, 11, 20
1, 11, 20
1, 11, 20
Diagonal elements of
Tukey’s hat matrix
Diagonal elements of
extended hat matrix
1, 13
1
1, 13
1
–
–
1, 11, 20
1, 11, 20
1, 11, 20
1, 11, 20
–
–
(S) means a strongly influential point.
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FAJT, KURC, AND CERVENY
250
Table VII Statistical Significance of the Parameters in the AKT and KP Models with Respect to Hydrogenation
Conversion
Reaction Rate at Conversion
0%
15
20%
14
50%
9
70%
7
Model AKT
Degrees of freedom
p-level
Intercept
d
0.000
0.006
0.045
0.000
0.000
0.968
0.000
0.059
0.032
0.000
0.000
0.968
0.286
0.859
0.161
0.999
0.004
0.946
0.836
0.312
0.143
0.271
0.006
0.937
s
b
h
Correlation coefficient R
Model KP
Degrees of freedom
p-level
16
15
10
8
Intercept
0.000
0.044
0.004
0.000
0.910
0.000
0.027
0.001
0.000
0.926
0.015
0.245
0.010
0.060
0.953
0.009
0.938
0.011
0.037
0.944
A
3
A
4
A5
Correlation coefficient R
for the description of the corrected rates at higher con-
versions. Attention was devoted to the basic statisti-
cal characteristics and the p-levels of the regression
parameters.
of 6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-dione to
6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-diol. The
kinetics of hydrogenation was studied in 21 compo-
nent solvents comprising alcohols, aromatics, alkanes,
ether, ester, amine, and an alkylchloride. The hydro-
genation rates in the individual solvents significantly
differed, and the differences were not possible to
explain due to different hydrogen solubilities in the
reaction mixture.
It was pointed out that the hydrogenation rate can-
not be correlated with the individual physicochemical
solvent properties. Therefore, the approach to the de-
scription of the reaction rates was done using the two
chosen models that were originally proposed for the ho-
mogeneous liquid-phase reactions. Those models were
derived on basis of the LFER principle. Both models
satisfactorily described the experimental data though
each one had a certain disadvantage. The AKT model
gave closer fitting, but using the least-squares method
it showed slight multicollinearity.
The KP model had a rather lower correlation coef-
ficient but turned out to be universal in the evaluation
of the solvent effect at any conversion. Using selected
statistical diagnostic tests, it was possible to identify
the most important factors of the solvent that influence
the hydrogenation kinetics. In the AKT model the most
important parameter was the hydrogen bond acceptor
ability of the solvent, and in the KP model it was its nu-
cleophilic solvation ability. In addition, the Hildebrand
cohesion energy density contained in both models had
a significant influence.
Because of a similar interpretational meaning of the
h and A5 parameters, it can be claimed that in the
whole course of hydrogenation the Hildebrand cohe-
sion energy density of the solvent had a fundamental
influence on the reaction rate. The p-level of the terms
with this quantity slightly exceeded its critical limit
only for the KP model at 50% conversion. On the con-
trary, the p-level of the terms with the π∗, β, and ETN
variables decreased with conversion. Under its critical
limit of 0.05, the parameter A4 associated with the vari-
able BN was found to be significant at all conversions.
The KP model gave better correlation coefficients at
higher conversions (50% and 70%), whereas the AKT
model gave higher correlations coefficients at lower
conversions (0% and 20%). This statement must be
considered with respect to the differences in degrees
of freedom caused by the product precipitation in a
few solvents (Table II). With respect to the lower vari-
ability in close fitting and statistical significance of the
parameters, the KP model seems to be more universal.
CONCLUSIONS
For a deeper understanding of the phenomena that
occur in the liquid-phase catalytic hydrogenations, the
solvent effect on a model hydrogenation in the pres-
ence of a supported palladium catalyst was studied.
The model reaction was the selective hydrogenation
The results of this work should lead to the clar-
ification of the solvent characteristics influencing
International Journal of Chemical Kinetics DOI 10.1002/kin

EFFECT OF SOLVENTS ON THE RATE OF CATALYTIC HYDROGENATION
251
the rate of 6-ethyl-1,2,3,4-tetrahydroanthracene-9,10-
dione hydrogenation and hence help with the selection
of a proper solvent system for the industrial production
of hydrogen peroxide by the anthraquinone method.
ε
Relative static dielectric constant
ꢁs Weisz–Prater criterion
π∗ Taft polarity parameter of the solvent
Indexes
ABBREVIATIONS AND SYMBOLS
c
i
Corrected quantity
Component i
A0
A1–A5
Intercept in the Koppel–Palm model
Parameters in the Koppel–Palm model
HMPA Hexamethylphosphoric amide
N
Normalized quantity
Trimethylsilane
Conversion range
a, b, d, h, s Parameters in the Abraham–Kamlet–
TMS
ξ
Taft model
AIC
AKT
B
Akaike information criterion
Abraham–Kamlet–Taft model
Nucleophilic solvation ability of the
solvent
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Dimroth–Reichardt parameter
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Kirkwood function of refractive
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Generalized principal component
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