Volume parameters of some Diels - Alder reactions involving C=C, C=S, and N=N bonds

Article abstract of DOI:10.1007/s11172-006-0075-8

The effect of a hydrostatic pressure of up to 1000 kg cm^-2 on the rate constants of the Diels - Alder reactions of maleic anhydride with 1,2,3,4-tetraphenylcyclopentadiene and with 6,13-dichloropentacene, of 4-phenyl-1,2,4-triazoline-3,5-dione with hexachlorocyclopentadiene, and of thiobenzophenone with isoprene was studied at 25°C. The volume parameters and ratios of the activation to reaction volumes make it possible to exclude electrostriction of the solvent during transition state solvation in all the reactions studied, which corresponds to the nonpolar nature of the transition state.

Full text of DOI:10.1007/s11172-006-0075-8

2034
Russian Chemical Bulletin, International Edition, Vol. 54, No. 9, pp. 2034—2041, September, 2005
Volume parameters of some Diels—Alder reactions
involving С=С, C=S, and N=N bonds*
V. D. Kiselev,ꢀ E. A. Kashaeva, L. N. Potapova, G. G. Iskhakova, and A. I. Konovalov
A. M. Butlerov Chemical Institute, Kazan State University,
18 ul. Kremlevskaya, 420008 Kazan, Russian Federation.
Fax: +7 (843 2) 92 7278. Eꢀmail: vladimir.kiselev@ksu.ru
The effect of a hydrostatic pressure of up to 1000 kg cm–2 on the rate constants of the
Diels—Alder reactions of maleic anhydride with 1,2,3,4ꢀtetraphenylcyclopentadiene and with
6,13ꢀdichloropentacene, of 4ꢀphenylꢀ1,2,4ꢀtriazolineꢀ3,5ꢀdione with hexachlorocycloꢀ
pentadiene, and of thiobenzophenone with isoprene was studied at 25 °С. The volume paramꢀ
eters and ratios of the activation to reaction volumes make it possible to exclude electrostriction
of the solvent during transition state solvation in all the reactions studied, which corresponds to
the nonpolar nature of the transition state.
Key words: Diels—Alder reactions, activation volumes, reaction volumes.
Elevated pressure facilitates substantially chemical proꢀ
affects the free activation or reaction energy, then the
volume parameter values including the imaginary contriꢀ
butions can be obtained from Eqs (1) and (2). With a
pressure increase, the rate (k) or equilibrium (K ) conꢀ
stants can change due to the energy р•∆V≠ or р•∆V and
pressureꢀinduced changes: in the dielectric constant of
the medium,3 concentration of active species in the cataꢀ
lytic process,5 and viscosity of the medium to a level of
the diffusionally controlled rate of the process.4,6
cesses if the volume of the system decreases during the
reaction. The origin of a volume change is not the main
problem for practical purpose. However, the use of volꢀ
ume parameters of the reaction to refine the reaction
mechanism requires information on the contributions that
form these volume parameters. The factors that affect the
activation volume (∆V≠) and Diels—Alder reaction volꢀ
ume (∆V ) have been considered earlier.1—4 These volume
parameters can be determined from the dependence of
the rate (k) or equilibrium (K ) constant on the presꢀ
sure (p).
Two new C—C bonds are consistently formed in a
nonpolar Diels—Alder reaction. However, the values of
the activation and reaction volumes can strongly differ
(from –15 to –40 cm3 mol–1), depending on the size and
structure of the reactants.7 The formation of the products
from the reactants with elevated packing coefficients
(η = VW/V ) was found8 to be usually accompanied by a
weak increase in this parameter, while an increase in the
packing coefficients on going to the adducts is much higher
in the reactions involving "loose" reactants. The observed
reaction volume (∆V) by more than a factor of 2 exceeds
the van der Waals reaction volume ∆VW due to an addiꢀ
tional contribution caused by a change in the volume of
intermolecular cavities.1,2,7,8 This has recently been conꢀ
firmed experimentally by a comparison of the volumes of
several Diels—Alder reactions in the solid phase and in
solutions.9 The intrinsic volume of the Diels—Alder reacꢀ
tion determined by the difference in the van der Waals
volumes VW of the products and reactants is rather conꢀ
stant (–8 2 cm mol–1) for all types of reactants. The
contribution of a change in the volume of intermolecular
cavities to the observed reaction volume ranges from –10
to –30 cm3 mol–1, i.e., up to 50—75% of the total volume
effect.1,2,8—10 It is clear that this tendency in changing the
(∂lnk/∂p)T = –1/RT(∂G≠/∂p)T = –∆V≠/RT
(∂lnK/∂p)T = –1/RT(∂G/∂p)T = –∆V/RT
(1)
(2)
Real and imaginary changes in the volume parameters
should be distinguished. Real values of the volume paꢀ
rameters are caused by the general volume changes in the
system (addends, transition state, and solvents) and inꢀ
clude changes of the intrinsic (van der Waals, ∆VW) volꢀ
umes due to the bond redistribution and changes in interꢀ
molecular volumes (∆Vsolv) in the solvate shell of the corꢀ
responding states (reactants, transition state, products).
The reaction volume values can be obtained both by
Eq. (2) and directly from the difference between partial
molar volumes (PMVs) of the products and reactants.
The activation volumes can be calculated only using the
dependence (1). If an elevated pressure can induce a
change in the properties of the system, which, in turn,
* Dedicated to Academician A. L. Buchachenko on the occaꢀ
sion of his 70th birthday.
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 9, pp. 1973—1980, September, 2005.
1066ꢀ5285/05/5409ꢀ2034 © 2005 Springer Science+Business Media, Inc.

Volume parameters of Diels—Alder reactions
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
2035
packing coefficients and volume parameters should also
be observed in reactions with the polar transition state.
However, the superimposition of the electrostriction of
the solvent and a high sensitivity of the rate of polar and
ionic processes to a pressureꢀinduced change in the diꢀ
electric constant of the medium considerably impedes
this analysis.
4ꢀphenylꢀ1,2,4ꢀtriazolineꢀ3,5ꢀdione (7); and isoprene (9)
with thiobenzophenone (10). The data obtained make it
possible to monitor changes in the packing coefficients of
the addends and their effect on the activation and reacꢀ
tion volumes and the influence of dienophiles with the
С=С, N=N, and C=S bonds on the volume parameters
in the Diels—Alder reaction.
Reaction of 1,2,3,4ꢀtetraphenylcyclopentadiene (1) with
maleic anhydride (2). Tetraalkylcyclopentadienes usually
exist as a mixture of isomers of the C=C bond position
due to the easy 1,5ꢀhydrogen shift.11 Substituents increasꢀ
ing the conjugation energy facilitate an increase in the
fraction of more stable 1,2,3,4ꢀsubstituted cyclopentaꢀ
diene. Although the phenyl fragments in diene 1 are shifted
from the plane of the cyclopentadiene ring, it can be
assumed that its conjugation energy is much higher than
that in the unsubstituted cyclopentadiene. The equilibꢀ
rium constant in the reaction of diene 1 with maleic anꢀ
hydride is higher and, hence, more difficult for determiꢀ
nation. The reaction with the more conjugated dienophile,
viz., tetracyanoethylene, in 1,2ꢀdichloroethane at 25 °С
is rather fast (k2 = 96 5 L mol–1 s–1) and equilibrium
(Keq = 2140 100 L mol–1). The enthalpy of the reaction
of tetracyanoethylene with diene 1 in 1,2ꢀdichloroethane
was determined by calorimetric measurements and equals
–57.8 0.7 kJ mol–1. The calculated entropy of the reacꢀ
tion (–130 J mol–1 K–1) is typical of the Diels—Alder
reaction. It seems useful to compare the rate constants
(k2/L mol–1 s–1), equilibrium constants (Keq/L mol–1),
and enthalpies (∆H/kJ mol–1) in the Diels—Alder reacꢀ
tions of tetracyanoethylene with several dienes under these
conditions (25 °С, 1,2ꢀdichloroethane).
Results and Discussion
In this work, we determined the volume parameters of
four Diels—Alder reactions involving dienes and dienoꢀ
philes of different nature (Scheme 1): πꢀdonor dienes,
viz., 1,2,3,4ꢀtetraphenylcyclopentadiene (1) and 6,13ꢀdiꢀ
chloropentacene (4), with maleic anhydride (2); πꢀacꢀ
ceptor diene, viz., hexachlorocyclopentadiene (6), with
Scheme 1
Diene
k2
Keq
∆H
Cyclopentadiene12
1,2,3,4ꢀTetraphenylcyclopentadiene
Hexachlorocyclopentadiene12
Isoprene12
5•103
96
—
≥1012 –113
2.1•103 –58
~4
–42
0.074
≥1020 –166
For the reaction of 1,2,3,4ꢀtetraphenylcyclopentaꢀ
diene with maleic anhydride, the equilibrium constant
can be estimated as 3•106 L mol–1, based on the reaction
enthalpy12 –76 kJ mol–1 and with allowance for the reacꢀ
tion entropy –130 J mol–1 K–1. The resulting data on the
pressure effect on the rate of the reaction of diene 1 with
maleic anhydride are given in Table 1.
The dependence of the reaction rate on the external
pressure is described (Fig. 1) by the linear equation (3)
(r = 0.9981; n = 6).
lnk2 = (–8.27 0.02) + (1.02 0.01)•10–3
р
(3)
An additional increase in the reaction rate under an
elevated pressure due to an increase in the concentrations
in the compressed solvent results in an overestimation (by

2036
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
Kiselev et al.
Table 1. Effect of the pressure (р) on the rate constant (k2) of the
Diels—Alder reaction of 1,2,3,4ꢀtetraphenylcyclopentadiene (1)
with maleic anhydride (2) in 1,2ꢀdichloroethane at 25 °С
Vt = [VS + (CA0VA + CB0VB)] +
+ CP(VP – VA – VB) = Vt=0 + CP∆V,
(6)
where Vt=0 and Vt are the initial and current volumes of
the solution of the reactants at the moment t; VS is the
р/kg cm–2
k2•104/L mol–1 s–1
–lnk2
solvent volume; VA, VB, and VP are the partial molar
0
1
2.61
3.39
3.56
4.35
6.17
7.24
8.25
7.99
7.94
7.74
7.39
7.23
volumes of the reactants (А and В) and product (P); CA
,
300
350
490
850
1005
0
CB , and CP are the initial molar concentrations of the
reactants and the concentration of the reaction product at
the moment t; ∆V is the reaction volume.
Dilatometric measurements of volume changes in time
(Eq. (6)) usually need comparatively large volumes of
concentrated solutions. To analyze the density data for
the reaction in the resonating tube of a precision densimꢀ
eter, it seems more convenient to transform Eq. (6)
into (7).
lnk
–7.2
1/dt = 1/dt=0 + CP∆V/1000dt=0
(7)
–7.4
–7.6
–7.8
–8.0
–8.2
The reaction volume determined from the difference
of the PMVs of adduct 3 (372.2 1.0 cm3 mol–1), diene 1
(334.8 0.8 cm3 mol–1), and dienophile 2 (72.0 0.1
cm3 mol–1) is –34.6 1.9 cm3 mol–1. Well reproducible
results of the reaction volume with an average value of
–32.9 0.3 cm3 mol–1 were obtained in three series of
measurements of the density of solutions of the reactants
in time (Fig. 2).
The coefficient θ (θ = ∆V≠corr/∆V = –23.8/–32.9 =
0.72) allows one to believe that the transition state volꢀ
0
200
400
600
800
p/kg cm–1
Fig. 1. Plot of lnk vs. external pressure (р) for the Diels—Alder
reaction of 1,2,3,4ꢀtetraphenylcyclopentadiene (1) with maleic
anhydride (2) in 1,2ꢀdichloroethane at 25 °C.
1/dt
0.80175
modulus) of the experimental value of the activation volꢀ
ume (–25.8 0.3 cm3 mol–1) by a value of ∆n•βRT
0.80165
∆V≠corr = ∆V≠exp + ∆n•βRT,
(4)
0.80155
where ∆n = –1 is the change in the number of moles
during the reaction; β = –7.9•10–5 bar–1 is the comꢀ
pressibility coefficient of 1,2ꢀdichloroethane;13 R =
84.78 cm3 kg cm–2 K–1 mol–1; T/K is temperature. The
corrected activation volume in the reaction between reacꢀ
tants 1 and 2 is –23.8 0.3 cm3 mol–1. In the calculation
of the reaction volume from the difference between
the PMVs of the products and reactants, all errors
are summated, which can result in an uncertainty of
(2—3) cm3 mol–1 for the reactions involving largeꢀvolꢀ
ume molecules. The kinetic method for determination of
the reaction volume by a change in the density of the
solution of the reactants needs no data on the PMVs and,
therefore, is more exact. The volume of the solution of
the reactants can be presented by Eqs (5) and (6)
1
2
0.80145
3
0.002
0.006
C/mol L–1
Fig. 2. Anamorphoses of the density of a solution of reactants 1
and 2 during the formation of adduct 3 in 1,2ꢀdichloroethane at
25 °С in measurement series 1—3:
0
0
Seꢀ
ries
C1
C2
r
sd•106
n
∆V
/cm3 mol–1
mol L–1
1
2
3
0.01867 0.2116 0.9994
0.01826 0.2128 0.9980
0.01846 0.2198 0.9993
2.6
4.4
2.9
42 –32.8 0.2
27 –32.9 0.4
44 –33.1 0.2
Vt = VS + (CA0 – CP)VA +
+ (CB0 – CP)VB + CPVP,
(5)

Volume parameters of Diels—Alder reactions
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
2037
ume (383 cm3 mol–1) is closer to the volume of the reacꢀ
tion product 3 (372 cm3 mol–1) than to that of the reacꢀ
tants (407 cm3 mol–1). It should be mentioned that the
further decrease in the volume of the system, when the
transition state moves to the reaction products, is mainly
caused by a decrease in the intermolecular cavities. Simiꢀ
lar volume parameters were obtained14 for the reaction of
1,2,3,4ꢀtetrachlorocyclopentadiene with methyl acrylate
in 1ꢀchlorobutane at 40 °С (θ = –24.6/–33.2 = 0.74).
Reaction of 6,13ꢀdichloropentacene (4) with maleic anꢀ
hydride (2). The solubility of diene 4 in chlorobenzene at
25 °С is higher (~5•10–4 mol L–1) than in 1,2ꢀdichloroꢀ
ethane and toluene and is sufficient for monitoring the
reaction rate by a change in the diene absorption. The
data on the pressure effect on this reaction rate are preꢀ
sented in Table 2.
lnk
–5.2
–5.4
–5.6
–5.8
–6.0
0
200
400
600
p/kg cm–1
Fig. 3. Plot of lnk vs. external pressure (р) for the Diels—Alder
reaction of 6,13ꢀdichloropentacene (4) with maleic anhydride (2)
in chlorobenzene at 25 °С.
The dependence of the reaction rate on the exterꢀ
nal pressure (Fig. 3) is described by Eq. (8)
(r = 0.9955; n = 13).
responds to the Diels—Alder reaction with the nonpolar
transition state.15 Note that the absolute values of the
volume parameters of the Diels—Alder reaction of dienoꢀ
phile 2 with "loose" alkylbutadienes are almost twofold
higher (–35—–45 cm3 mol–1).14
Reaction of hexachlorocyclopentadiene (6) with 4ꢀpheꢀ
nylꢀ1,2,4ꢀtriazolineꢀ3,5ꢀdione (7). It is known that hexaꢀ
chlorocyclopentadiene (6) is a πꢀacceptor diene and,
hence, is more reactive in the reactions with πꢀdonor
dienophiles.16 The rates of the most part of the earlier
studied Diels—Alder reactions of diene 6 with acyclic and
cyclic dienophiles are rather low. Therefore, the activaꢀ
tion volumes were calculated from the data obtained at
elevated temperatures (50—100 °С), whereas the reaction
volumes were determined14,17,18 at 25 °С. The rate conꢀ
lnk2 = (–5.993 0.013) + (8.872 0.067)•10–4
р
(8)
The experimental value of the activation volume
(–22.4 0.2 cm3 mol–1) with the correction for a conꢀ
centration increase with the pressure growth (βRT =
1.9 cm3 mol–1, for chlorobenzene13 β = –7.45•10–5 bar–1
)
results in the activation volume in the reaction between
reactants 4 and 2 equal to –20.5 0.2 cm3 mol–1. A similar
activation volume (–22.7 + 2.5 = –20.2 0.2 cm3 mol–1
)
has been obtained previously15 for the Diels—Alder reacꢀ
tion between maleic anhydride and 9,10ꢀdimethylanthraꢀ
cene in acetonitrile at 25 °С. The volume of the reaction
between reactants 4 and 2 was not determined because of
the low solubility of diene 4. The ratio of the activation
and reaction volumes for the reaction of dienophile 2 with
9,10ꢀdimethylanthracene (θ = –20.2/–23.6 = 0.856) corꢀ
stant and enthalpy for the reaction between reactants 6
12
and 2
at 25 °С are 1.1•10–8 L mol–1 s–1 and
–58 kJ mol–1, and for reactants 6 and 7 12,16 they are
1.84•10–3 L mol–1 s–1 and –77 kJ mol–1, respectively.
Table 2. Effect of the pressure (р) on the rate constant (k2) of the
Diels—Alder reaction of 6,13ꢀdichloropentacene (4) with maꢀ
leic anhydride (2) in chlorobenzene at 25 °С
For comparison, these parameters at 25 °С in the reaction
12
of cyclopentadiene with dienophile 2
are equal to
9.1•10–2 L mol–1 s–1 and –129 kJ mol–1, and those in
the reaction with dienophile 7 12,16 are 2.0•104 L mol–1 s–1
and –148 kJ mol–1, respectively. It follows12 from
the difference in the enthalpies of the reactions of sevꢀ
eral dienes with the common nucleophile that the conꢀ
jugation energy in hexachlorocyclopentadiene is by
71 kJ mol–1 higher than that in cyclopentadiene and by
14 kJ mol–1 higher than that in 1,2,3,4ꢀtetraphenylcycloꢀ
pentadiene.
The data obtained for the pressure effect on the reacꢀ
tion rate of reactants 6 and 7 are given in Table 3.
The dependence of the reaction rate on the external
pressure (Fig. 4) is described by Eq. (9) (r = 0.9964; n = 9)
р/kg cm–2
k2•103/L mol–1 s–1
–lnk2
1
2.57
2.86
2.91
3.04
3.22
3.52
3.63
4.07
4.40
4.53
4.65
5.14
5.46
5.964
5.857
5.839
5.796
5.738
5.649
5.619
5.504
5.426
5.397
5.371
5.271
5.210
170
185
250
275
400
470
515
640
640
680
820
900
lnk2 = (–6.29 0.02) + (1.04 0.01)•10–3р.
(9)

2038
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
Kiselev et al.
Table 3. Effect of the pressure (р) on the rate constant (k2) of the
Diels—Alder reaction of hexachlorocyclopentadiene (6) with
4ꢀphenylꢀ1,2,4ꢀtriazolineꢀ3,5ꢀdione (7) in 1,2ꢀdichloroethane
at 25 °С
1/dt
0.7952
1
0.7951
0.7950
0.7949
0.7948
0.7947
р/kg cm–2
k2•103/L mol–1 s–1
–lnk2
1
1.84
2.55
2.74
3.09
3.51
4.02
4.35
4.58
4.87
6.30
5.97
5.90
5.78
5.65
5.52
5.44
5.39
5.32
320
410
490
590
705
810
910
950
2
0.004
0.008
0.012 C/mol L–1
Fig. 5. Anamorphoses of the density of a solution of reactants 6
and 7 during the formation of adduct 8 in 1,2ꢀdichloroethane at
25 °С in measurement series 1 and 2:
sd•106
n
∆V
0
0
Seꢀ
ries
C6
C7
r
lnk
/cm3 mol–1
mol L–1
–5.2
1
2
0.1633 0.01838 0.9997
0.1681 0.01360 0.9993
2.1
2.0
28 –25.0 0.1
32 –25.2 0.2
–5.4
–5.6
–5.8
–6.0
–6.2
hexamethylcyclopentadiene. This hindrance is absent in
1,2,3,4ꢀtetraphenylcyclopentadiene (1). The activation
volumes in the reactions between reactants 1 and 2
(–23.8 cm3 mol–1) and 6 and 7 (–24.2 cm3 mol–1) are
commensurable. However, the substantial difference
between the volumes of these reactions (–32.9 and
–25.1 cm3 mol–1), which considerably exceeds measureꢀ
ment errors, corresponds to a significantly loosened moꢀ
lar volume of adduct 8, probably, due to steric loads caused
by the geminal chlorine atoms at the C(5) atom.
Reaction of isoprene (9) with thiobenzophenone (10).
The reaction was studied in toluene at 25 °С. The reactivꢀ
ity of the C=S bond in dienophile 10 and the stability of
its adducts are much lower than those in the case of the
N=N bond in dienophile 7. Taking into account the asymꢀ
metry of the C=S bond, we can assume some asynchroꢀ
nous character for bond formation in the transition state
of the reaction. This asymmetry should be manifested in
the electrostriction of the solvent and an elevated (by
modulus) activation volume, which can be checked exꢀ
perimentally. The data on the pressure effect on the
Diels—Alder reaction rate between reactants 9 and 10 are
presented in Table 4.
0
200
400
600
800 p/kg cm–1
Fig. 4. Plot of lnk vs. external pressure (р) for the Diels—Alder
reaction of hexachlorocyclopentadiene (6) with 4ꢀphenylꢀ1,2,4ꢀ
triazolineꢀ3,5ꢀdione (7) in 1,2ꢀdichloroethane at 25 °С.
The activation volume corrected by the βRT value for
the reaction between reactants 6 and 7 is –24.2 0.3
cm3 mol–1
.
The reaction volume determined from the difference
between the PMVs of adduct 8 (271.5 1.5 cm3 mol–1),
diene 6 (162.1 0.5 cm3 mol–1), and dienophile 7
(131.5 0.5 cm3 mol–1), which is equal to –22.1 2.5
cm3 mol–1, is inferior in accuracy to the value determined
from the dependence of the density of a solution of the
reaction mixture on the concentration of the adduct that
formed (Eq. (7)). The reaction volumes were calculated
using these measurements (Fig. 5).
The dependence of the reaction rate on the external
pressure (Fig. 6) is described by the linear equation (10)
(r = 0.9921; n = 9)
Based on the obtained values of the reaction volume
∆V, we calculated the ratio of the volume parameters
lnk2 = (–9.289 0.027) + (1.050 0.051)•10–4р.
(10)
(θ = ∆V≠ /∆V ) as equal to 0.964.
.
Two chlorine atoms at the C(5) atom in hexachloroꢀ
The experimental activation volume (–26.5 1.2
cm3 mol–1) with allowance for the solvent compresꢀ
sion (the β coefficient for toluene is equal13 to
–8.96•10–5 bar–1) gives a corrected activation volume in
cyclopentadiene (6) prevent a dienophile from approachꢀ
ing at the both sides of the diene. We have found19
a
similar effect in the Diels—Alder reaction involving

Volume parameters of Diels—Alder reactions
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
2039
Table 4. Effect of the pressure (р) on the rate constant (k2) of the
Diels—Alder reaction of isoprene (9) with thiobenzophenone
(10) in toluene at 25 °С
1/dt
1.229
1.228
1.227
1.226
1.225
р/kg cm–2
k2•104/L mol–1 s–1
–lnk2
1
0.932
1.10
1.24
1.22
1.49
1.73
1.78
2.11
2.51
9.28
9.11
8.99
9.01
8.81
8.66
8.63
8.46
8.29
160
285
320
510
535
605
770
980
0
0.04
0.08
C/mol L–1
Fig. 7. Anamorphosis of the density of a solution of reactants 9,
0
lnk
10 during the formation of adduct 11 in toluene at 25 °С, С10
0.1099 mol L–1, С90 = 2.4164 mol L–1, r = 0.9999, sd = 1.1•10–6
n = 38, ∆V = –33.2 0.1 cm3 mol–1
=
,
–8.2
.
–8.4
–8.6
–8.8
–9.0
–9.2
between changes in the reactivity of the studied series of
reactants and the stability of their adducts and, on the
other hand, changes in the activation volumes and the
reaction volumes. This corresponds to the fact that the
energy and volume profiles are formed under the influꢀ
ence of different factors. Even great differences in the
energy of orbital interaction of reacting atoms do not
Table 5. Intrinsic (VW) and partial molar volumes (V ) of comꢀ
pounds, their packing coefficients (η = VW/V ), and activation
(∆V≠) and reaction volumes (∆VW, ∆V) at 25 °С
0
200
400
600
800 p/kg cm–1
Fig. 6. Plot of lnk vs. external pressure (р) for the Diels—Alder
reaction of thiobenzophenone (10) with isoprene (9) in toluene
at 25 °С.
a
Comꢀ
pound
VW
V
η
∆VW
∆V≠/∆V
/cm3 mol–1
cm3 mol–1
1b
227.3 334.8 0.679
48.4 72.0 0.672
269.1 372.2 0.723
101.1 162.1 0.624
90.0 131.5 0.684
184.3 272.5 0.676
52.9 100.3 0.528
–6.6
–6.6
–6.6
–6.8
–6.8
–6.8
–6.8
–6.8
–6.8
–8.3
–8.3
–8.3
–23.8/–32.9 = 0.72
–24.2/–25.1 = 0.96
–24.3/–33.5 = 0.73
–20.2/–23.6 = 0.86
2b
the reaction between reactants 9 and 10 of –24.3 1.2
cm3 mol–1. The volume of this reaction determined from
3b
the kinetic dependence (Fig. 7) is –33.2 0.2 cm3 mol–1
.
6b
7b
The reaction volume was also calculated from the data on
the density of the reaction mixture obtained at the moꢀ
ment of mixing the reactants and after the reaction was
8b
9c
10c
11c
2d
116.9
163.0
—
—
—
—
completed, being –33.8 cm3 mol–1
.
48.4 70.4 0.687
129.6 187.2 0.692
169.7 232.2 0.731
12d
13d
*
*
*
It has previously been shown2,8 that the activation
volume for the Diels—Alder reaction with consistent bond
formation in the cyclic transition state should be by apꢀ
proximately 15 cm3 mol–1 more negative than that of the
radical process of successive bond formation (twoꢀstep
mechanism). The activation volumes obtained in this work
for all the four studied Diels—Alder reactions involving
С=С, N=N, and C=S bonds of dienophiles with πꢀdonor
(1, 4, 9) and πꢀacceptor (6) dienes are almost equal
(Table 5). No correlation is observed, on the one hand,
а The ∆VW value for the reaction 2 + 4 → 5: 223.8 – (48.4 +
183.8) = –8.4 cm3 mol–1
b In 1,2ꢀdichloroethane.
c In toluene.
.
d The data15 for the reaction of maleic anhydride (2) with 9,10ꢀdiꢀ
methylanthracene (12) with formation of cycloadduct 13 in acꢀ
etonitrile. The volume of this reaction calculated by the differꢀ
ence between the PMVs is –25.4 2.5 cm3 mol–1, and that calꢀ
culated from a change in the solution density in time is
–23.6 0.16 cm3 mol–1 15
.

2040
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
Kiselev et al.
565—585 nm, C0 (1—2)•10–2 mol L–1; and adduct 11, from a
change in the absorption of dienophile 10 at 620—660 nm,
C0 (1.0—1.5)•10–2 mol L–1. The other components of the reacꢀ
tions were transparent in these spectral regions.
Kinetic measurements under an elevated pressure were carꢀ
ried out in a highꢀpressure temperatureꢀcontrolled optical cell
placed in the cell compartment of a Specord UV—VIS spectroꢀ
photometer. In all measurements, more than a 20ꢀfold excess of
an optically transparent reactant was used. Isooctane was used
as the pressureꢀtransmitting medium. The apparatus and proceꢀ
dure for measuring reaction rates at an elevated pressure have
been described earlier.3
determine volume changes in the reaction. This agrees
completely with the conclusion2 that the increase in the
absolute value of the activation volume over the reaction
volume (θ = ∆V≠/∆V > 1) cannot be explained by the
energy of interaction of secondary orbitals. The van der
Waals reaction volumes reflecting the change in the sysꢀ
tem volume upon the formation of new bonds are almost
the same for all reactions (see Table 5) and do not exceed
27% of the reaction volume. A great difference in the
volume parameters is caused by different changes in the
packing coefficients (η = VW/V ) during the reaction. It
should be assumed that the molar volume of the transition
state can be smaller than the molar volume of the adduct
(θ = ∆V≠/∆V > 1) despite partial bond formation only
because of a more compact parallel arrangement of the
molecules. This is confirmed by examples of negative acꢀ
tivation volumes for the reactions of adduct decomposiꢀ
tion.3,18 Note that a more exact determination of the
volume parameters (the same temperature, solvent, inꢀ
troduction of corrections for compressibility, kinetic
method of determination of the reaction volume) deꢀ
creases considerably the number of these examples (θ > 1)
but does not exclude them completely.
Apparent molar volumes (ϕ ) of the compounds in a soluꢀ
A
tion were calculated using the equation (11)
ϕ = 1000(d0 – d)/mA•d•d0 + MA/d,
(11)
A
where mA is the molality of the solution, d and d0 are the densiꢀ
ties of the solution and solvent, and MA is the molar weight of
the solute.
It is more reliable to determine the partial molar volume
(VA) from the concentration dependence. For this purpose,
Eq. (11) was transformed into (12).
(1000 + mAMA)/d = VAmA + 1000/d0
(12)
The angular coefficient of the dependence of (1000 + mAMA)/d
on mA is equal to VA.
Based on the obtained values of the volume paramꢀ
eters, we cannot assume that the mechanism of the Diels—
Alder reaction involving the N=N and C=S bonds differs
from the concert mechanism in the Diels—Alder reaction
involving the С=С bonds.
The order of operation of a DMAꢀ602 precision densimeter
has been described previously.3 The temperature of the resonatꢀ
ing tube was maintained with deviations of 2•10–3 °С.
The data on the change in the density of solutions of the
reactants with the conversion at least 50% were used for the
kinetic method of calculation of the reaction volumes (Eq. (7)).
The experimental plots are presented in Figs 2, 5, and 7. In
several cases, it was more convenient to determine the reaction
volumes from the data on a change in the density of the reaction
mixture at the completion of the process. Here only the data on
the concentration of the reactant taken in deficiency are addiꢀ
tionally needed. The change in the density of a solution of the
reactants was determined in an interval of 20—30 min and exꢀ
trapolated to the moment of preparation of the solution. Then
this solution of the reactants was left in the tube of a densimeter
until the reaction was completely ceased. In parallel, the initial
solution of the reactants in a sealed vessel was stored to the
completion of the reaction (≥99%, UV monitoring), and then its
density was determined. A good correspondence of the reaction
volumes indicates the absence of side processes. The kinetic
method (Eq. (7)) makes it possible to determine the reaction
volume with a considerably smaller error.
Experimental
Reagents and solvents. Hexachlorocyclopentadiene (Aldrich)
was purified by distillation in vacuo(118 °С (2 kPa),
20
20
nD = 1.5660; cf. Ref. 20: nD = 1.5652). 1,2,3,4ꢀTetraꢀ
phenylcyclopentadiene (Aldrich) was recrystallized from a benꢀ
zene—ethanol (1 : 4) mixture, m.p. 178—179 °С (cf. Ref. 21:
m.p. 178 °С). 6,13ꢀDichloropentacene (m.p. 297—300 °С;
cf. Ref. 22: m.p. 300 °С) was used without additional purificaꢀ
tion. 4ꢀPhenylꢀ1,2,4ꢀtriazolineꢀ3,5ꢀdione (7) was synthesized
by a known method23 and purified by sublimation at 100 °С
(20 Pa), m.p. 180 °С (decomp.) (cf. Ref. 23: m.p. 180 °С). The
spectral purity of dienophile 7 was checked from the absence of
the final absorption of its solution after the end of the reaction
with excess trans,transꢀ1,4ꢀdiphenylbutadiene and from the abꢀ
sorption coefficient of sublimed dienophile 7 (186.2 at 527 nm,
dioxane, 25 °С). Thiobenzophenone (10) was synthesized by a
known method24 and purified by distillation in vacuo at 100 Pa,
m.p. 51—53 °С (cf. Ref. 24: m.p. 53 °С). Maleic anhydride was
distilled and additionally purified by recrystallization from a
benzene—hexane (1 : 6) mixture. Solvents were purified accordꢀ
ing to known procedures.25
The equilibrium constant of the reaction between diene 1
and tetracyanoethylene (К = 2140 L mol–1) was calculated from
the data on the absorption of diene 1 before the reaction and
after equilibration in 1,2ꢀdichloroethane at 25 °С. The initial
concentration of diene 1 was equal to (3.5—5.5)•10–4 mol L–1
,
and that of tetracyanoethylene was (2—10)•10–3 mol L–1. The
change in the absorption of diene 1 at 390—400 nm was 70—80%.
The enthalpy of the reaction between these reactants in 1,2ꢀdiꢀ
chloroethane at 25 °С was calculated from the data on the
thermal effect of the reaction (–27.2 0.7 kJ mol–1) for the mixꢀ
ing of a weighed sample of crystals of diene 1 with a solution of
tetracyanoethylene (0.021 mol L–1) in 1,2ꢀdichloroethane
Kinetic measurements. The reaction rates of formation of
adduct 3 were monitored by a change in the absorption (SFꢀ46
and Specord UV—VIS spectrometers) of diene 1 at 400—420 nm,
C0 (1—3)•10–3 mol L–1; adduct 5, from a change in the absorpꢀ
tion of diene 4 at 565—570 nm, C0 (1—2)•10–4 mol L–1; adꢀ
duct 8, from a change in the absorption of dienophile 7 at

Volume parameters of Diels—Alder reactions
Russ.Chem.Bull., Int.Ed., Vol. 54, No. 9, September, 2005
2041
(153 mL) in the calorimeter cell and the heat of dissolution
(30.6 0.5 kJ mol–1) of crystalline diene 1 in 1,2ꢀdichloroethane.
10. V. D. Kiselev, A. I. Konovalov, T. Asano, G. G. Iskhakova,
E. A. Kashaeva, M. S. Shihaab, and M. D. Medvedeva,
J. Phys. Org. Chem., 2001, 14, 636.
The authors thank A. A. Zharov (N. D. Zelinsky Instiꢀ
tute of Organic Chemistry, Russian Academy of Sciences)
for help in producing barostats.
This work was financially supported by the Russian
Foundation for Basic Research (Project Nos 02ꢀ03ꢀ32945
and 05ꢀ03ꢀ32583), the USA Civil Research and Developꢀ
ment Foundation (CRDF, Grant RECꢀ007), and the
Ministry of Education and Science of the Russian Fedꢀ
eration.
11. V. A. Mironov, E. V. Sobolev, and A. N. Elizarova, Tetraꢀ
hedron, 1963, 19, 1939.
12. V. D. Kiselev and A. I. Konovalov, Usp. Khim., 1989, 58, 383
[Russ. Chem. Rev., 1989, 58 (Engl. Transl.)].
13. N. S. Isaacs, Liquid Phase High Pressure Chemistry,
Wiley—Interscience, Chichester—New York—Brisbane—
Toronto, 1981, 414 pp.
14. T. Asano and W. J. le Noble, Chem. Rev., 1978, 78, 408.
15. V. D. Kiselev, G. G. Iskhakova, E. A. Kashaeva, M. S.
Shikhab, M. D. Medvedeva, and A. I. Konovalov,
Zh. Obshch. Khim., 2003, 73, 1992 [Russ. J. Gen. Chem.,
2003, 73 (Engl. Transl.)].
16. J. Sauer and H. M. Schuhbauer, Liebigs Ann. Chem. Recl,
1997, 1739.
17. R. Van Eldik, T. Asano, and W. J. le Noble, Chem. Rev.,
1989, 89, 549.
18. G. Jenner, in Organic High Pressure Chemistry,
Ed. W. le Noble, Elsevier, Amsterdam—Oxford—New
York—Tokyo, 1988, 143.
19. V. D. Kiselev, A. G. Sakhabutdinov, I. M. Shakirov, and
A. I. Konovalov, Zh. Org. Khim., 1991, 27, 1641 [J. Org.
Chem. USSR, 1991, 27 (Engl. Transl.)].
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Received February 15, 2005;
in revised form June 6, 2005