High-pressure influence on the rate of diels-alder cycloaddition reactions of maleic anhydride with some dienes

Article abstract of DOI:10.1002/kin.20800

The rate constants for temperature and pressure range, enthalpy, entropy, and volume of activation and reaction were measured in toluene solution for the Diels-Alder cycloaddition reaction of maleic anhydride (1) with a very active diene, 9,10-dimethylanthracene (4), and with a very inactive diene, 9-phenylanthracene (6), which is less reactive in the reaction with 1 by five orders of magnitude. Reaction rates under pressure up to 2600 bar were measured by using a high-pressure optical cell, adjusted to a UV-spectrophotometer. The volume of reaction was determined by two independent methods: by the difference of the partial molar volumes of the reactants and by the dependence of a specific volume of solution on the adduct concentration during the reaction. All parameters of activation and reaction were discussed.

Full text of DOI:10.1002/kin.20800

High-Pressure Influence
on the Rate of Diels–Alder
Cycloaddition Reactions
of Maleic Anhydride with
Some Dienes
VLADIMIR D. KISELEV
Department of Physical Chemistry, Butlerov Institute of Chemistry, Kazan Federal University, 18, Kazan 420008,
Russian Federation
Received 13 March 2013; revised 25 April 2013; accepted 25 April 2013
DOI 10.1002/kin.20800
Published online 23 July 2013 in Wiley Online Library (wileyonlinelibrary.com).
ABSTRACT: The rate constants for temperature and pressure range, enthalpy, entropy, and
volume of activation and reaction were measured in toluene solution for the Diels–Alder cy-
cloaddition reaction of maleic anhydride (1) with a very active diene, 9,10-dimethylanthracene
(4), and with a very inactive diene, 9-phenylanthracene (6), which is less reactive in the reac-
tion with 1 by five orders of magnitude. Reaction rates under pressure up to 2600 bar were
measured by using a high-pressure optical cell, adjusted to a UV-spectrophotometer. The vol-
ume of reaction was determined by two independent methods: by the difference of the partial
molar volumes of the reactants and by the dependence of a specific volume of solution on
the adduct concentration during the reaction. All parameters of activation and reaction were
discussed. ꢀC 2013 Wiley Periodicals, Inc. Int J Chem Kinet 45: 613–622, 2013
INTRODUCTION
Correspondence to: Vladimir D. Kiselev; e-mail: vkiselev.ksu@
gmail.com.
The fact that values of the activation volume (ꢀV=)
can get more negative than values of the reaction vol-
Contract grant sponsor: U.S. Civilian Research and Development
Foundation (CRDF).
Contract grant sponsor: Ministry of Science and Education of
the Russian Federation (Joint Program “Fundamental Research and
High Education”).
ume (ꢀVr-n) for the Diels–Alder cycloaddition reaction
of maleic anhydride (1) with isoprene (2) (Scheme 1)
was described in [1] for the first time, where the re-
action was studied in nine solvents of different po-
larity. Solvent electrostriction in this reaction can be
neglected due to the small effect of solvent polarity on
the enthalpy of activation (ꢀH=av = 52 2 kJ mol−1),
Contract grant number: REC-007.
Contract grant sponsor: Russian Foundation for Basic Research.
Contract grant number: 12-03-00029.
Contract grant sponsor: Russian Federal Agency of Education.
Contract grant numbers: P-2345, GK No 14.740.11.0377, GK
No OK-1/2010.
C
ꢀ
2013 Wiley Periodicals, Inc.

614
KISELEV
I
III
II
Scheme 1 Diels–Alder cycloaddition reaction of maleic anhydride 1 with isoprene 2 (reaction (I)), 9,10-dimethylanthrcene 4
(reaction (II)), and 9-phenylanthracene 6 (reaction (III)).
the volume of activation (ꢀV= = –38.5 1.0 cm3
have compared the values of activation volumes for the
rapid and slow-rate reactions.
av.
mol−1), and the reaction volume (ꢀVr-n, av = –35.5
1.0 cm3 mol−1) [1]. The “abnormal” ratio of ꢀV=/
ꢀVr-n > 1 corresponds to the higher volume compact-
ness of the activated complex with incomplete bond
EXPERIMENTAL
formation as compared to the adduct where bond for-
mation is entirely completed.
Materials
This means that elevated pressure should promote
the retro-Diels–Alder reaction corresponding to an
adduct decomposition. Currently, there are some ex-
perimental proofs of the fact that the adduct de-
composition is accelerated by a pressure elevation
[2–5].
In this work, the temperature and pressure influ-
ence on the rate constants of the Diels–Alder cycload-
dition reaction of maleic anhydride (1) with 9,10-
dimethylanthracene (4) and 9-phenylanthracene (6)
have been studied in toluene solution (Scheme 1).
The rate constant at 25◦C of reaction (II) exceeds the
rate of reaction (I) by three orders of magnitude, and
the rate of reaction (III) by five orders of magnitude.
One normally expects that for the rapid reactions the
coordinate of the activated complex is placed closer to
the initial state of the reaction. In the present work, we
Maleic anhydride 1 was distilled and then recrystal-
lized from benzene (where maleic acid can be separated
quantitatively as an insoluble impurity) and dried under
vacuum, melting point (m.p.) 52.5–53◦C, lit. 52.85◦C
[6]. Spectroscopically, pure dienes 4 (Alfa Aesar,
Heysham, UK), m.p. 182–183◦C, lit. 183–184◦C [7]),
and 6 (Sigma-Aldrich Chemie, Steinheim am Albuch,
Germany), m.p. 156–157◦C, lit. 156.5–157.5◦C [8],
were obtained after column chromatography with neu-
tral alumina (eluent benzene/n-hexane, 1:5 v/v), and
their reaction with 1 was confirmed by the complete
disappearance of the initial UV-absorption of the di-
enes (390–405 nm) in solution with an excess of maleic
anhydride. Adduct 7 was obtained by boiling a benzene
solution of 1 and 6 with a large excess of maleic anhy-
dride (∼2 mol L−1) for 20 h. The crystals were washed
with hexane and recrystallized from benzene, m.p.
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

HIGH-PRESSURE INFLUENCE ON THE RATE OF DIELS–ALDER CYCLOADDITION REACTIONS
615
251.0–251.5◦C with decomposition, lit. 249–251◦C,
lished value [13] of 17.514
0.008 kJ mol−1. The
dec. [8]. All solvents were purified and dried by known
methods [9].
calibration was made by the introduction of a certain
amount of heat. For all solutions, three to five mea-
surements of sequentially dissolving samples of 1 and
4 were carried out. In cyclohexane, after determination
of the finite base line of the thermal effect of solution
of reactants 1 and 4, an aliquot of solution was taken
out and the concentration of reactants 1 and 4 was de-
termined by UV spectrophotometric titration. The total
uncertainty of the measurements did not exceed 2%.
No concentration dependencies of the heat of solution
were observed.
Apparatus and Procedures
Kinetic Measurements. The rate of reactions (II) and
(III) was determined by measuring the UV absorp-
tion of dienes 4 and 6 at 390–405 nm. For reaction
(II), the initial concentration of diene 4 was about (2–
4) × 10−4 mol L−1 and that of dienophile 1 about
(1–4) × 10−2 mol L−1. The rate constants of reaction
(II) in trichloromethane–cyclohexane mixtures were
measured at 40◦C to ensure solubility in the full range
of this mixture. For reaction (III), the initial concen-
tration of 1 was about 2 mol L−1 due to the very low
reaction rate even at 60, 70, and 80◦C. The water-
circulated cell-holder adapter (210–2111) of the UV-
spectrophotometer (Hitachi-2900) with only one-sided
T-control was replaced by the homemade five-sided T-
control in a water-circulated box, which allowed trac-
ing with accuracy of 0.1◦C. The values of the rate
constants were determined with errors of 3%, en-
thalpy of activation of 1 kJ mol−1, and entropy of
Density Measurements. All methods of calculation of
the apparent molar volume (φА) of a solute (A) are
based on the assumption that the volume of solution
equals the sum of the solute volume and the unchanged
volume of the solvent. In terms of molar concentration
(cA), molal concentration (mA), moles per kilogram of
solution (wA), or grams per milliliter of solution (ТA),
the following equations can be obtained:
1000 − (1000d − cAMr )/d0 = cAϕA
(1000 + mAMr )/d = 1000/d0 + mAϕA
1000/d = 1000/d0 + WA (ϕA − Mr /d0)
d = d0 + TA(1 − ϕAd0/Mr )
(1)
(2)
(3)
(4)
activation of 4 J mol−1 K−1
.
The reaction rates under elevated pressure were
measured with a high-pressure system using the high-
pressure pump “HP-500” and high-pressure optical cell
“PCI-500” from Syn. Co. (Kyotanabe City, Japan),
adjusted to a UV-spectrophotometer from SCINCO
Co. (Seoul, Korea). The photodiode array of the
“SCINCO” UV-spectrophotometer performs all new
spectra in the selected time interval, and only a small
fluctuation in the curve of the optical density was ob-
served while monitoring the absorption on the sharp
slope of the spectra of dienes 4 and 6. Reaction (II) was
measured under pressure at 25◦C and reaction (III) at
60◦C, both in toluene.
Here d0 and d are the densities of the solvent and solu-
tion, respectively, and Mr is the relative molar mass of
the solute. Equations (1)–(4) can be transformed to a
direct calculation of the value φА for each concentra-
tion. In this way, Eqs. (1) and (2) can be converted to
Eqs. (5) and (6) to calculate φA:
Calorimetric Experiment. The enthalpies of solution
of reactants 1 and 4 were measured at 25◦C with a dif-
ferential calorimeter, as previously reported [10–12].
Samples were weighed into a small stainless steel
cylinder, both polished sides of which were covered
by thin (0.1 mm) rings of Teflon seals. The mass of the
cylinders filled with diethyl ether proved to be constant
after 24 h, ensuring the tightness of the container. Af-
ter equalization of temperature of the inserted closed
cylinder with the sample in the calorimetric cell with
solution (150 cm3), these Teflon seals were cut out with
a razor. The accuracy of the calorimetric measurements
was verified by determining the enthalpy of dissolution
of dry potassium chloride in water at 25◦C. The result
(17.4 0.2 kJ mol−1) was in agreement with the pub-
ϕA = 1000(d0 − d)/cA d0 + Mr /d0
(5)
(6)
ϕA = 1000(d0 − d)/mA d0d + Mr /d
The vibration densimeter manufactured by Anton
Paar GmbH (Graz, Austria; model DSA 5000M) was
used for the measurements at 25 0.002◦C. The den-
simeter was calibrated with water and air following the
instructions. Very small differences (only a few ppm)
in the densities between the freshly prepared solutions
and those after a few hours exclude by-processes. The
apparent molar volume of 1, 6, and 7 in toluene solu-
tion was calculated from data on the density of their
solutions using Eq. (6).
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

616
KISELEV
Table I Rate Constants (k2) of the Diels–Alder Cycloaddition Reaction of 9,10-Dimethylanthracene (4) with Maleic
Anhydride (1), Heats of Solution of the Reactants (ꢀsolH4 and ꢀsolH1) in Pure Solvents with a Different Relative
Permittivity (εr) and in Binary Trichloromethane/Cyclohexane Solvent Mixtures
Data in Solvents No 1–16
Data in TCM/Cyclohexane Mixtures
k2 (× 104 L
ꢀsolH4
ꢀsolH1
ꢀsolH4
(kJ mol−1
ꢀsolH1
(kJ mol−1
k2 (× 103
a
a
a
b
b
b, c
No.
Solvent
Acetone
ε
mol−1 s−1
)
(kJ mol−1
)
(kJ mol−1
)
)
)
L mol−1 s−1
)
r
1
20.7
92
111
285
120
192
216
250
244
302
452
467
700
–
25.2
21.4
23.7
23.1
21.8
23.4
21.3
28.9
30.4
21.4
23.6
20.0
22.7
20.9
23.1
29.8
11.3
8.1
20.0 (100) 16.1 (100) 140 (100)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
N,N-Dimethyl formamide 36.7
21.3 (90)
21.3 (80)
21.5 (70)
22.3 (60)
22.7 (50)
24.1 (40)
24.5 (30)
25.9 (20)
26.3 (15)
27.1 (10)
29.8 (0)
–
17.4 (90)
17.7 (80)
19.8 (70)
20.3 (60)
21.3 (50)
22.5 (40)
24.0 (30)
24.5 (20)
34.3 (15)
43.4 (10)
46.5 (0)
–
146 (90)
176 (50)
178 (30)
180 (20)
163 (5)
157 (3)
152 (2)
147 (1)
120 (0)
–
Acetic acid
1,4-Dioxane
Toluene
6.1
2.2
2.4
15.0
10.4
16.4
16.9
14.2
13.1
12.6
18.3
24.9
16.1
11.4
13.8
15.9
46.4
Benzene
2.3
Nitrobenzene
Acetonitrile
34.8
37.5
34.9
5.6
2.2
4.8
Nitromethane
Chlorobenzene
Tetrachloromethane
Trichloromethane
Ethyl acetate
Anisole
–
–
6.0
4.3
–
–
636
–
–
–
Dichloromethane
Cyclohexane
9.1
2.0
–
–
–
–
–
–
аData for solvents No 1–16 at 25 ◦C.
bIn parenthesis are given the volume percentage of trichloromethane in the mixture with cyclohexane.
cAt 40◦C.
to the transition state in tetrachloromethane and cyclo-
hexane (entries 11 and 16), compared with acetone and
N,N-dimethyl formamide (entries 1 and 2 in Table I),
is a key possible reason for the rate constant changes.
It is interesting to consider the balance of ac-
celeration and retardation effects of reaction (II)
in trichloromethane/cyclohexane solvent mixtures.
Smooth changes of the heat of solvation (δsolvH,
with 100% trichloromethane taken as a blank) of di-
ene 4 can be observed in all concentration ranges
(Fig. 1).
The heat values in solvation of 1 and 1 + 4 change
dramatically when the trichloromethane volume is less
than 20% (Fig. 1). At this mixture composition, the
rate constant has the maximum value, with an optimal
balance of the low energy of reactant solvation and
sufficient activation of maleic anhydride by H-bond
formation with trichloromethane (Fig. 2).
It should be noted that the determination of the
heat of solution in cyclohexane is complicated by its
characteristically low and slow solubility. The experi-
mental value of the heat of solution 1 in cyclohexane
(46.5 kJ mol−1) is proximate to the calculated value
(45.7 kJ mol−1) derived from the heat of sublimation
of 1 (68.5 kJ mol−1 [6]) and the heat of solvation
(ꢀsolvH1/c-hexane) of 1 in cyclohexane (–22.8 kJ mol−1),
RESULTS AND DISCUSSION
Kinetic Measurements at Ambient Pressure
An analysis of the solvent influence on the enthalpy of
activation of the Diels–Alder reaction and the enthalpy
of solution of the reactants corroborates the conclu-
sion that the higher energy of intermolecular inter-
action of reactants with the solvent molecules makes
it more difficult to achieve the activated complex, as
it requires desolvation, i.e., removing a part of sol-
vent molecules from the reactants during their mutual
approach [12,14]. That can explain the elevated rate
constants of the Diels–Alder reaction observed in cy-
clohexane solution with weaker intermolecular solute–
solvent interactions as compared with other solvents,
including trichloromethane. But the rate of the Diels–
Alder reactions is usually elevated in trichloromethane
solution by the dienophile activation due to H-bond
formation between the solvent and the n-donor groups
of the dienophile [14]. Rate data in various solvents
and binary trichloromethane/cyclohexane mixtures at
ambient pressure are summarized in Table I, together
with heats of solution of 1 and 4.
It is clear that the influence of the solvent polarity
on the rate constant of this reaction is very small. Less
energy of a desolvation of reactants 1 and 4 on the way
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

HIGH-PRESSURE INFLUENCE ON THE RATE OF DIELS–ALDER CYCLOADDITION REACTIONS
617
A comparison of the kinetic parameters of reactions
(I)–(III) at ambient pressure (Table II) indicates that the
difference in the rate constants is caused by the variety
in the enthalpy of activation. As for the entropy of
activation, it is nearly the same for all these reactions.
Possible reasons for the substantial difference in
the reactivity of dienes 4 and 6 in a reaction with 1
(five orders of magnitude) are worth considering. The
reactivity of Diels–Alder reactions with the usual elec-
tronic demand (diene–donor, dienophile–acceptor) de-
pends on the π-donor and π-acceptor properties of the
diene–dienophile system and on the difference in the
conjugation energy of C=C bonds [14]. The ionization
potential of diene 6 (7.25 eV) is higher than that of 4
(7.11 eV) (IP) [16]. The predicted difference in the rate
constants due to the variety in the values of IP [14] is
only about one order of magnitude, whereas the rate
constant of reaction (III) is five orders of magnitude
less than that of reaction (II) (Table II). From these
data, it follows that the suppression of reaction (III) is
determined not only by the difference in the ionization
potential and electron affinity (IP-EA). The activation
energy of a concerted Diels–Alder reaction depends on
the energy balance of breaking C=C and forming new
C–C bonds, and the heat of reaction is a good measure
of this balance [14]. The value of the heat for reaction
(II) is –104 [14], and for reaction (III) this is only –81
kJ mol−1 [8]. Additional rate retardation can be caused
by shielding of the reaction center of diene 6, where
the phenyl group is nearly orthogonal to the anthracene
plane [17].
Figure
1
Influence
of
the
composition
of
trichloromethane/cyclohexane solvent mixtures on the
change in solvation enthalpy of 9,10-dimethylanthracene
(ꢀsolvH4; ꢀ), maleic anhydride (ꢀsolvH1; ꢁ), and of both
reactants (ꢀsolvH1+4; ꢂ).
predicted from the highly reliable equation (7) [15]:
− ꢀsolv H1/c−hexane = 5.09 + 1.03 R1
(7)
Here R1 is the molar refraction of the solute. A
similar calculation for the heat of solution of diene 4
in cyclohexane gives a value of 110.6 – 82.2 = 28.4
kJ mol−1, close to the measured one (29.8 kJ mol−1
Table I).
;
Kinetic Measurements at High Pressure
In spite of the amount of data in this field [18–24],
there are two positions in the analysis of high-pressure
effects on the reaction rate to be mentioned. For small
molecules of reactants with low energies of inter-
molecular interaction and low boiling point (b.p.; ethy-
lene, 1,3-butadiene, isoprene, cyclopentadiene, furan,
etc.), the packing coefficients (η = VW/V), i.e., the
ratio of van-der-Waals volume (VW) to partial molar
volume (PMV) in solution (V), are significantly smaller
than those for large reactant molecules with high ener-
gies of intermolecular interaction and with high b.p.
(anthracene, maleic anhydride, maleimides, their
adducts, etc.) [14,25]. As follows from Table III, the
larger change of the packing coefficient is found for
reaction (I) than for reactions (II) and (III). As a re-
sult, the values of the activation and reaction volumes
should be more negative in reaction (I) than in reactions
(II) and (III).
Figure
2
Influence
of
the
composition
of
trichloromethane/cyclohexane solvent mixtures on the
rate constant of reaction (II).
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

618
KISELEV
Table II Rate Constants (k2), Enthalpy (ꢀH=), and Entropy of Activation (ꢀS= ) of the Diels–Alder Cycloaddition
Reactions (I)–(III), Measured in Toluene
Reaction
T (◦C)
k2 (L mol−1 s−1
)
ꢀH= (kJ mol−1
)
ꢀS= a (J mol−1 K−1
)
Ib
II
35
15
25
40
25
60
70
80
3.3 × 10−5
1.09 × 10−2
1.92 × 10−2
4.10 × 10−2
3.62 × 10−7c
7.11 × 10−6
1.50 × 10−5
3.00 × 10−5
59.0
40.2
−149
−150
III
68.0
−140
aCalculated for 25◦C.
bData in acetonitrile from [1].
cCalculated by extrapolation.
Table III Partial Molar Volumes (V), Van-der-Waals Volumes (VW), Volumes of Intermolecular Holes (VH) in Solution,
Packing Coefficients (η) of Compounds 1–7 and the Volume Changes (ꢀV, cm3 mol−1) in the Diels–Alder
Cycloaddition Reactions of Maleic Anhydride with Isoprene (I), 9,10-Dimethylanthracene (II), and 9-Phenylanthracene
(III), Measured in Acetonitrile at 25◦C
Reactants 1–7
Reaction Volume
Parameter
1
2
3
4
5
6
7
ꢀVI
ꢀVII
ꢀVIII
V
VW
VH
ηe
70a
43.9
26.1
100a
49.0
51.0
135a
88.4
46.6
187a
122.0
65.0
232a
162.1
69.9
219.5b
144.0
75.5
263.3b
184.2
79.1
–35
–4.5
–30.5
–
–25
–3.8
–21.2
–
–27.3b
–3.7
–22.5
–
c
d
0.63
0.49
0.65
0.65
0.70
0.66
0.70
aValues of V in acetonitrile of reactants 1–3 taken from [1] and 4, 5 from [25].
bIn toluene at 25◦C, this work.
cCalculated by Marvin Sketch software.
dCalculated by the difference of V and VW.
eCalculated from ratio η = VW/V.
It should be noted that in all Diels–Alder reactions,
the value of the van-der-Waals reaction volume is about
–(4–5) cm3 mol−1. It is appropriate to mention that the
volume of the Diels–Alder reaction of maleic anhy-
sure. It was suggested to use the pressure-independent
concentration scales (mole fraction, molality, etc.)
[26]. However, the increased pressure leads to the com-
pression and an increase in the number of molecules
per unit of volume in the liquid and the gas phase,
where the difference is only in the size of an effect.∗
Consequently, the rate of the second-order reaction
in solution under pressure should be increased even
when the value of ꢀV= is zero. This additional in-
crease in the reaction rate should be related with the
increased concentration of reagents for the correct de-
termination of the rate constants, because (∂ lnk2/∂P)T
= 0, when ꢀV= = 0. Using the initial values of the
concentration as prepared at ambient temperature and
pressure, the calculated value of the rate constant un-
der pressure is overestimated and the calculation of
dride with anthracene in the solid state (ꢀVr-n, solid
=
200.2 –141.6 – 65.4 = –6.8 cm3 mol−1) is nearly the
same as ꢀVW = (141.4 – 101.4 – 43.9 = –3.9 cm3
mol−1), and the large negative value of the reaction
volume in acetonitrile (ꢀV r-n = 201.8 – 158.2 – 70.4 =
–26.8 cm3 mol−1) is generated mainly by the change
of intermolecular holes in solution [25]. Since the total
compression of the intermolecular holes of 2 mol of
reagents in solution is higher than that of 1 mol of acti-
vated complex, the dependence ln(kP) versus P should
show a convex curve, and the limiting value of the vol-
ume of activation in solution under very high pressure
will approach to ꢀV=W. According to Table III, the
convex curvature for reaction (I) should be larger than
that for reactions (II) and (III).
∗Unsuitability of the mole fraction and weight concentration scales
is particularly clearly seen when trying to describe the rate of the
second-order reaction in the gas phase (r = k2xAxB) between the
same reagents located, e.g., in the volume of 1 cm3 and m3.
Another problem is related to the account for the
volume concentration change of solutions under pres-
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

HIGH-PRESSURE INFLUENCE ON THE RATE OF DIELS–ALDER CYCLOADDITION REACTIONS
619
Table IV Volumes of Activation for Reaction (I), Calculated Using the Mole Fraction Concentration Scale (ꢀV=exp),
Compressibility Coefficients (βT) for the Solvents, Correction Factors (βT·RT), Corrected Volumes of Activation
(ꢀV=corr), and Volumes of Reaction (I) (ꢀVr-n
)
a
b
d
a
ꢀV=
βT
βT·RTc
ꢀV=
ꢀVr-n
ꢀV=
ꢀVr-n
/
corr
exp
corr
No.
Solvent
(cm3 mol−1
)
(× 106 bar−1
)
(cm3 mol−1
)
(cm3 mol−1
)
(cm3 mol−1
)
1
2
3
4
5
6
7
8
9
Ethyl acetate
Dichloromethane
Nitromethane
Dimethyl carbonate
Acetonitrile
Diisopropyl ether
1-Chlorobutane
Acetone
–37.4
–39.8
–32.5
–39.3
–37.5
–38.5
–38.0
–39.0
–37.0
117
103
72.5
97
113
183
119
129
80
2.8
2.5
1.8
2.3
2.7
4.4
2.9
3.1
1.9
–34.6
–37.3
–30.7
–37.0
–34.8
–34.1
–35.1
–35.9
–35.1
–36.8
–33.4
–30.7
n.d.e
–34.5
–38.3
n.d.e
0.94
1.11
1.0
–
1.0
0.89
–
–35.9
–35.5
1.0
0.99
1,2-Dichloroethane
aExperimental values of activation volume at 35◦C [1].
bValues of compressibility coefficients at 25◦C [30].
cCorrection factor calculated for 25◦C. For 35◦C, it should be increased approximately on 10%.
dCalculated by Eq. (8).
eNo data because of very low solubility of adduct 3 [1].
the correct value of ꢀV=
(n – 1)·RT·βT (Eq. (8)).
requires the adjustment:
corr
ꢀVc=orr = −RT ∂ ln(kP)/∂ P + (n − 1) × RT × βT
(8)
Here kP is the rate constant under pressure, calcu-
lated without correction of the value of concentration
(molarity, molality, or mole fraction) under pressure P,
and (n – 1)·RT·βT is the correction term, where n is the
reaction order and βT = ∂ln(d)/∂P is the solvent com-
pressibility coefficient (positive value). Therefore, the
apparent value of the activation volume of the Diels–
Alder reaction will be more negative that corrected
by Eq. (8). It should be noted that an equation simi-
lar to (8) was proposed more than 90 years before by
Williams [27] and repeatedly mentioned by Eyring in
1938 [28].
Scheme 2
the apparent volume of activation and should be about
–(1–2) cm3 mol−1. Very large variations of the ratio
ꢀV=/ꢀVr-n (from 1.0 to 1.69) were observed in the re-
action of 1 with trans-1-methoxybutadiene in different
solvents [29]. There is a direct experimental validation
of the acceleration of some retro-Diels–Alder reactions
under elevated pressure [2–5].
The experimental and corrected values of activation
volume for reaction (I) are collected in Table IV.
With the correctedvalues of thevolume of activation
of reaction (I), the “normal” ratio, ꢀV=corr/ꢀVr-n ≤ 1,
can be obtained, except for the data in dichloromethane
(Table IV). All substituted butadienes are in equilib-
rium between the s-trans and the s-cis-isomer (see
Scheme 2) [1,29].
Because this equilibrium shifts to the s-trans-
isomer, and it is the s-cis-isomer that can react only
in Diels–Alder reactions, the apparent rate constant
(kapp) of reaction (I) is equal to Keq·ks-cis. Commonly,
the cis-isomer is 1–2% more compact as compared
with the trans-isomer [18,19]. Therefore, the addi-
tional pressure effect on Keq is included in the value of
The response to the pressure effects on the rate
constants of reactions (II) and (III) is presented in
Table V.
All kinetic runs under pressure (Fig. 3) were ana-
lyzed as straight lines at a conversion of ≥50% with a
correlation coefficient of R ≥ 0.999.
From the dependence ln(kP/kP = 1) = bP + cP2
(Fig. 4), the value b was determined for reaction (II) as
9.91 × 10−4, R = 0.9982, N = 8, and for reaction (III)
as 9.75 × 10−4, R = 0.9985; N = 7. The experimental
values of the volume of activation of reaction (II) at
25◦C are equal to –23.9
60◦C equals to –26.3 1.2 cm3 mol −1
1.0, and reaction (III) at
.
The value of the correction term (RTβT) was calcu-
lated, using the compressibility coefficient of toluene at
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

620
KISELEV
Table V Pressure (Pbar) Influence on the Rate Constants (k2) of the Diels–Alder Cycloaddition Reaction of Maleic
Anhydride (1) with 9,10-Dimethylanthracene (4) (Reaction (II)), Measured at 250С and with 9-Phenylanthracene (6),
(Reaction (III)), Measured at 60oС in Toluene
Reaction (II)
Reaction (III)
P (bar)
.k2 (×103 L mol−1 s−1
)
ln (kP/kP = 1
)
P (bar)
k2 (×106 L mol−1 s−1
)
ln(kP/kP = 1
)
1
19.2 0.4
25.6 0.2
31.6 0.4
34.1 0.15
57.0 0.3
81.1 1.1
145 0.2
199 1.2
0
1
661
975
1406
1673
2061
2342
–
6.6 0.2
11.2 0.1
16.0 0.2
23.3 0.1
29.2 0.2
36.6 0.7
46.4 0.4
–
0
273
503
645
1085
1592
2147
2602
0.292
0.500
0.578
1.091
1.443
2.023
2.340
0.529
0.885
1.261
1.487
1.713
1.950
–
written as Eqs. (9) and (10):
ꢀ
ꢁ
ꢀ
ꢁ
V(t) = Vs + cA0 − cAdd,t VA + cB0 − cAdd,t VB
+ cAdd,t VAdd
(9)
ꢂ
ꢀ
ꢁꢃ
V(t) = Vs + cA0 VA + cB0 VB
ꢀ
ꢁ
+ cAdd,t VAdd − VA − VB
= V(t=0) + cAdd,t ꢀVr−n
(10)
(11)
1/d(t) = 1/d(t = 0) + cAdd,t ꢀVr−n/1000 d(t = 0)
Equation (11), rewritten from Eq. (10), is more con-
venient for the density measurements of reaction mix-
tures. Here, V(t = 0) and V(t) are the solution volumes
at the start of and during the reaction, respectively; Vs
is the volume of solvent; VA, VB, and VAdd are PMVs
of compounds (А), (В) and (Add), respectively; c0
,
A
c0B, and cAdd,t are the initial molar concentrations of
[A] and [B] and the current concentration of [Add], re-
spectively; and ꢀVr-n is the reaction volume. A linear
dependence 1/d(t) versus cAdd,t [Fig. 5, Eq. (12)] has
been obtained for up to 80% of conversion, followed
by a sharp bend due to the beginning of the adduct
crystallization from the oversaturated solution in the
densimeter tube:
Figure 3 Kinetic runs of reaction (II), measured in toluene
at 25◦C under pressure: 1, – 1; 2, – 273; 3, –502; 4, –643; 5,
–1085; 6, –1591; 7, –2147; 8, –2602 bar.
25◦ С (92 × 10−6) and at 60◦C (116 × 10−6 bar−1) [30].
The corrected value of the volume of activation of re-
action (II) is –21.7 1.0 at 25◦C, and that of reaction
1/d(t) = (1.15836 2.8 × 10−7
)
(III) at 60◦C is –23.2 1.2 cm3 mol−1
.
− (2.188 × 10−2 7.1 × 10−5) cAdd,t
R = 0.9997; N = 43
;
The difference of PMVs is the commonly used
method for the determination of the value of ꢀVr-n
with an accuracy of about (1–2) cm3 mol−1 [18–23].
The solubility of adduct 5 of reaction (II) in toluene
was insufficient for PMV determination. Here we used
a more convenient method. The total volume of a so-
lution with reactants (A, B) and adduct (Add) can be
(12)
From relation (12), the volume of reaction (II),
ꢀVII, is –18.9 0.2 cm3 mol−1. Repeated measure-
ments (R = 0.9995; N = 55) gave –18.6 0.2 cm3
mol−1. When the same reaction mixture (c1 > c4) in
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

HIGH-PRESSURE INFLUENCE ON THE RATE OF DIELS–ALDER CYCLOADDITION REACTIONS
621
Figure 4 Pressure (P) influence on the rate constants [ln(kP/kP = 1)] of reaction (II) (ꢀ), measured at 25◦C and reaction (III)
(ꢁ), measured at 60◦C in toluene. For clarity, data points for reaction (III) have been shifted upward by unity on the ordinate
axis.
Figure 5 Dependence of the specific volume (d−1/(cm3
g
−1)) of the solution of diene 4 (c0 = 0.00806 mol L−1) and
4
dienophile 1 (c0 = 0.03092 mol L−1) on the adduct 5 concentration, according to Eq. (11).
1
toluene was placed in the cell of the densimeter (DSA
5000M) and in the quartz cell of the UV spectropho-
tometer (Hitachi 2900), the values of cAdd (t) were
calculated independently by relation (13):
The volume of the very slow reaction (III) in toluene
at 25◦C (kIII = 3.3 × 10−7 L mol−1
s
−1) was not de-
termined by this method. But because of the sufficient
solubility of adduct 7, the volume of reaction (III) was
calculated by the difference of PMVs (Eq. (6)). The
mean values of three measurements are as follows:
V1 = 71.1 0.3; V6 = 219.5 0.8; and V7 = 263.3
0.5 cm3 mol−1, whence the value ꢀVIII, is equal to
–27.3 1.6 cm3 mol−1. From these results, it follows
that the corrected values of activation volume of reac-
tion (II) at 25◦C (–21.7 1.0) and that of reaction (III)
at 60◦C (–23.2 1.2 cm3 mol−1) are very close in spite
of the huge difference in reactivity. For reactions (II)
ꢀ
ꢁ
cAdd (t) = c40 D40 − D4 /D40
(13)
Here, D04 and D4 are the UV absorptions of diene 4 at
the start of and during reaction (II). The same value of
ꢀVII was obtained from Eqs. (13) and (12), but with
Eq. (13) the calculation was performed without the data
for kII and c0 .
1
International Journal of Chemical Kinetics DOI 10.1002/kin.20800

622
KISELEV
and (III) in toluene solution, a diverse ratio ꢀV=
ꢀVr-n was obtained: 1.15 and 0.85, respectively. With
/
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corr
a solvent change for reaction (II) from acetonitrile to
toluene, the ratio ꢀV=
/ꢀVr-n transforms from a
corr
“normal” (–20.0/–23.6 = 0.85 [24]) to an “abnormal”
value (–21.7/–18.9 = 1.15).
SUMMARY
It was noted that the solvent influence on the changes
of PMV and the enthalpy of solution is usually very dif-
ferent, in contrast to the changes in entropy [12,18,19].
A comparison of the kinetic parameters of reactions
(II) and (III) makes it clear that the difference in
the rate constants is caused by the variety in the en-
thalpy of activation, with nearly the same values of
activation entropy and activation volume. It was con-
cluded that the apparent volume of activation, obtained
with the pressure-independent concentrations, should
be corrected for second-order reactions on the value
RTβT.
It is necessary to note that the solvent influence
on the values of PMVs for different planar structures
of dienes and dienophiles (except tetracyanoethylene
as a strong π-acceptor) with the surface accessible
for solvation is usually small [31]. On the contrary,
large differences of the partial molar volumes of the
branched molecular structure of adducts were observed
[12,21–23,32]. The results obtained in this work are in
agreement with the suggestion [12] that the abnormal
volume ratio ꢀV=corr /ꢀVr-n > 1 for the forward isopo-
lar Diels–Alder reactions can be caused by the differ-
ing abilities of solvent molecules to penetrate into the
large branched molecules of the activated complex and
adduct.
24. Kiselev V. D.; Iskhakova G. G.; Kashaeva E. A.; Shihab
M. S.; Medvedeva M. D.; Konovalov A. I. Russ J Gen
Chem, Int Ed 2003, 73, 1884–1892.
ACKNOWLEDGMENTS
25. Kiselev, V. D.; Iskhakova, G. G.; Kashaeva, E. A.;
Potapova, L. N.; Konovalov, A. I. Russ Chem Bull, Int
Ed 2004, 53, 2490–2495.
26. Hamann D.; le Noble W. G. J Chem Educ 1984, 61,
658–660
I am grateful to Ilzida Shakirova, Helen Kashaeva, and Lubov
Potapova for carrying out some measurements. I also appre-
ciate fruitful comments from the reviewers, which helped for
me in finalizing the manuscript.
27. Williams, A. M. Trans Faraday Soc 1920, 16, 458–463.
28. Eyring, H. Trans Faraday Soc 1938, 34, 41–48.
29. Grieger, R. A.; Eckert, C. A. Ind Eng Chem Fund 1971,
10, 369–374.
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International Journal of Chemical Kinetics DOI 10.1002/kin.20800