Activation and reaction volumes for [4 + 2] and [3 + 2] additions involving maleic anhydride

Article abstract of DOI:10.1023/B:RUGC.0000025148.16991.3a

The partial molar volumes of reactants and products of the [3 + 2] addition of C-(p-nitrophenyl)-N-phenylnitrone to maleic anhydride and of the [4 + 2] addition of 9,10-dimethylanthracene to the same dienophile were determined, and the reaction volumes were calculated. A new method was suggested for determining the reaction volume. The activation volumes of both reactions were calculated from the dependences of the reaction rates on the external pressure. The volume parameters of the reactions involving the reagents of close size are close. The ratios of the activation volumes to the reaction volumes are unity, which suggests a common concerted mechanism of the reactions. Factors that could be responsible for significant changes in the absolute values of the reaction volume parameters are discussed.

Full text of DOI:10.1023/B:RUGC.0000025148.16991.3a

Russian Journal of General Chemistry, Vol. 73, No. 12, 2003, pp. 1884 1892. Translated from Zhurnal Obshchei Khimii, Vol. 73, No. 12, 2003,
pp. 1992 2001.
Original Russian Text Copyright
2003 by Kiselev, Iskhakova, Kashaeva, Shikhab, Medvedeva, Konovalov.
Activation and Reaction Volumes
for [4+2] and [3+2] Additions Involving Maleic Anhydride
V. D. Kiselev, G. G. Iskhakova, E. A. Kashaeva, M. S. Shikhab,
M. D. Medvedeva, and A. I. Konovalov
Butlerov Research Chemical Institute, Kazan State University, Kazan, Tatarstan, Russia
Received December 20, 2003
Abstract The partial molar volumes of reactants and products of the [3+2] addition
of C-(p-nitrophenyl)-N-phenylnitrone to maleic anhydride and of the [4+2] addition of 9,10-dimethylanthra-
cene to the same dienophile were determined, and the reaction volumes were calculated. A new method was
suggested for determining the reaction volume. The activation volumes of both reactions were calculated from
the dependences of the reaction rates on the external pressure. The volume parameters of the reactions involv-
ing the reagents of close size are close. The ratios of the activation volumes to the reaction volumes are unity,
which suggests a common concerted mechanism of the reactions. Factors that could be responsible for signi-
ficant changes in the absolute values of the reaction volume parameters are discussed.
Addition of Lewis acids as catalysts accelerates
and (2) are strictly valid for systems in which varia-
tion of the free energy with increasing pressure is due
to the p V contribution only. The isothermal condi-
tions in the course of elevating pressure can be readily
ensured, but it is impossible to keep constant the
dielectric permittivity, density, viscosity, and other
properties of solvent. In this connection, questions
arise: To what extent do the experimentally deter-
mined volume parameters of a process [Eqs. (1), (2)]
correspond to the true values [7 9]? If elevated pres-
sure induces additional changes in the reaction rate
and position of the equilibrium, due to changes in the
properties of the medium, all the effects of the exter-
nal pressure on the rate and position of the equilibri-
um of the reaction should be summed up. Each pro-
cess, even at atmospheric pressure, is characterized by
its specific activation and reaction volumes. These
parameters include structural (van der Waals volumes)
and solvation (contraction of the solvation shell and
change in the volume of cavities) constituents. With
increasing pressure, the dielectric permittivity of the
medium always increases [2, 3], and this factor causes
the rates of reactions with an ionic or a polar transition
state to additionally increase (apart from the effect of
the p V factor). This may result in overestimated (in
the absolute value) activation and reaction volumes.
Such an analysis was made for the Menshutkin reac-
tion and for [2+2] cycloaddition [7, 8]. It should be
noted that the calculated additional contributions
[7, 8] are not associated with electrostriction of the
medium; this factor makes its contribution even when
the reaction is performed under normal conditions.
cycloadditions by a factor of up to 106 without affect-
ing the position of the equilibrium [1]. For exothermic
reactions, the rate constants usually grow with increas-
ing temperature, but the equilibrium constants, on the
contrary, decrease. With conjugated reagents, the reac-
tions are often slow and reversible. Apparently, nei-
ther variation of catalyst nor heating can ensure
complete conversion.
For reactions accompanied by a decrease in the
volume of the system, application of elevated external
pressure, firstly, accelerates the process and, secondly,
shifts the equilibrium toward reaction products [2 6].
From the pressure (p) dependences of the rate (k) and
equilibrium (K) constants [Eqs. (1), (2)], one can
calculate the activation volume ( V ) and reaction
volume ( V0):
(dln k/dp)T, ,d,
(dln K/dp)T, ,d,
=
1/RT(d G /dp)T, ,d,
1/RT(d G/dp)T, ,d,
=
V /RT, (1)
V0/RT. (2)
=
=
Here, R is the gas constant; T, temperature;
G
and G, activation and reaction free energies, respec-
tively; , dielectric constant; d, density; and , viscos-
ity of the medium.
Knowledge of the activation volume can furnish
additional information on the volume of the activated
complex, and the ratio
=
V / V0 can be consid-
ered as a criterion of the position of the transition state
on the reaction coordinate [2 6]. Relationships (1)
1070-3632/03/7312-1884$25.00 2003 MAIK Nauka/Interperiodica

ACTIVATION AND REACTION VOLUMES FOR [4+ 2] AND [3+ 2] ADDITIONS
1885
In solvation of ionic species, the solvent undergoes
electrostriction as a result of a significant energy of
electrostatic interaction of charges with the medium.
This is experimentally confirmed by unexpectedly low
and even negative partial molar volumes of a number
of salts in aqueous solutions [10]. In dissociation of
an ion pair in weakly polar media to solvated ions,
the observed negative activation volume is virtually
exclusively due to the change in the dielectric permittiv-
ity of the medium, induced by elevated pressure [11].
The positive activation volume of a fast diffusion-
controlled reverse reaction of recombination of sol-
vated ions to an ion pair is due to an increase in the
viscosity with increasing hydrostatic pressure [11].
We have shown recently that the effect of the medium
on the reaction and activation volume parameters can
be strong for nonpolar processes also, if the solvent
interacts with one of the states [12 15].
free energy due to changes in the state of the activated
complex (but not reactants and products), then, ac-
cording to the microscopic reversibility principle,
these contributions should be equal for the forward
and reverse processes. Therefore, when calculating the
reaction volume as the difference between the activa-
tion volumes of the forward and reverse processes,
the possible additional contributions are canceled.
Additional effects can also contribute to the tem-
perature dependences of the activation and reaction
free energies [20, 21]. Since solvent properties
usually vary in opposite directions with increasing
pressure and temperature, the sums of contributions
can differ in sign. The necessity of considering possi-
ble additional contributions is dictated by experimen-
tal data that the activation volume of the nonpolar
Diels Alder reaction can be more negative than the
reaction volume [2 7, 12]. No convincing arguments
The reaction volume can be determined from the
difference between the partial molar volumes of the
products and reactants at normal pressure and can
be compared with a value calculated from the pres-
sure dependence of the position of the equilibrium
[Eq. (2)], whereas the only way to determine the acti-
vation volume is to calculate it from the pressure
dependence of the reaction rate [Eq. (1)]. The contri-
bution of electrostriction can be evaluated more
reliably from the variation of the partial molar vol-
umes of ionic compounds in a series of solvents.
Unfortunately, for salts in nonpolar and low-polarity
media such data are lacking, because the solubility in
these systems is insufficient for measurements [11].
have been suggested to explain the relationship
V / V > 1.
=
For concerted Diels Alder reactions involving such
dienes as cyclopentadiene and substituted butadienes,
the activation volumes usually range from 35 to
45 cm3 mol 1 [4 6]. For [3+2] cycloadditions, these
parameters are approximately two times smaller in the
absolute value [22 24], which could suggest a two-
step mechanism of this process [25, 26]. However,
this fact is insufficient for such conclusions. The ster-
eospecificity of [3+2] additions, weak solvent effect,
and large negative activation entropy all these facts
suggest a single-step concerted mechanism [27].
In our recent papers [7, 12, 15], we discussed the
causes of significant differences in the activation and
reaction volumes for a nonpolar Diels Alder reaction.
In reactions of tetracyanoethylene with dienes, in
going from cyclopentadiene or substituted butadienes
to substituted anthracenes, the activation and reaction
If with increasing pressure the solvent viscosity
grows to such an extent that the reaction becomes
diffusion-controlled, the experimental dependence of
lnk on p can pass through a maximum [16]. On the
contrary, there are indications that the reaction rate
in n-alkanes slightly grows with increasing viscosity,
i.e., under conditions far from diffusion control
[17]. The latter effect is assigned to processes that
occur faster in a solvent cage. Since the viscosity of
a medium always grows with increasing pressure, it
was suggested that this effect additionally contributes
to the experimental dependence of lnk on p for a
series of [4+2] and [3+2] cycloadditions [9]. However,
the validity of this generalization is subject to active
discussions [18, 19], because the influence of viscosi-
ty on reaction rate is weak and irregular.
1
volumes decrease in absolute value by 20 cm3 mol ,
i.e., almost by half [12, 15]. There are no experimen-
tal grounds to suggest a two-step mechanism of the
Diels Alder reaction with substituted anthracenes [1].
Such a difference in the volume parameters may be
due either to larger changes in the packing coefficients
of the pertinent states in reactions involving small
reactant molecules, as compared to the reactions with
large molecules [22, 23], or to a relative increase in
the partial molar volume of the activated complex and
adduct with anthracene [12, 15]. In the latter case, the
structure is sterically branched and may contain inter-
nal cavities inaccessible for solvating molecules [12,
15]. An additional contribution can be made by the
difference in the size of the forming ring. With equal
other effects, the volume parameters of [3+2] addi-
Comparison of the reaction volumes determined
from relationship (2) and from the difference between
the partial molar volumes revealed their good agree-
ment [2, 7]. It should be noted that, if the elevated
pressure induces additional changes in the activation
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

1886
KISELEV et al.
Table 1. Solvent effect on the rate of [3+2] addition of
C,N-diphenylnitrone to N-(p-bromophenyl)maleimide
[reaction (d)] and on the rate of Diels Alder reaction (c) of
9,10-dimethylanthracene with maleic anhydride at 298.2 K
anhydride II (see scheme). These particular 1,3-dipole
and diene were chosen because of their close partial
molar volumes. Data on the solvent effect on the
reaction rates are given in Table 1.
These data show that there is no correlation be-
tween the rates of both reactions and the viscosity
or dielectric permittivity of the solvent. The solvent
effect is weak and irregular. A noticeable difference is
observed only in chloroform. Formation of a hydrogen
bond between chloroform and the lone electron pair of
the activating groups in dienophiles favors higher
stability of the transition state of [4+2] addition [1].
In [3+2] addition, a strong hydrogen bond with the
nitrone oxygen atom is additionally formed, decreas-
ing the energy levels of both the reactants and the
transition state. Data on the solvent effect on the
heat of solution of maleic anhydride and on its partial
molar volume are given in Table 2.
1
1000k, l mol 1 s
Viscosity,
Solvent
cP
reaction reaction
(d)
(c)
Acetone
0.306
0.794
20.7
38.2
2.41
2.12
9.2
11.1
Dimethyl-
formamide
Chloroform
Acetonitrile
1,4-Dioxane
Benzene
0.537
0.369
1.177
0.604
4.81
37.5
2.21
2.28
2.30
2.04
4.94
8.66
70.0
24.4
12.0
21.6
tions with formation of a five-membered ring should
be less negative than those of [4+2] additions with
formation of a six-membered ring [28].
Table 2 shows that, for tetracyanoethylene, the
partial molar volume and the rate of the Diels Alder
reaction appreciably decrease with increasing solva-
tion energy in the series of alkylbenzenes. Tetracyano-
ethylene exhibits a strong -acceptor power (electron
affinity EA 2.88 eV), which results in significant
changes in the volume and energy parameters depend-
ing on solvent [1, 12]. Strong intermolecular interac-
tion of the reactants is responsible for the negative
temperature coefficient in the reaction of 9,10-dimeth-
ylanthracene with tetracyanoethylene [20], in contrast
to the reactions with maleic anhydride (EA 0.97 eV)
and N-phenylmaleimide (EA 0.89 eV) [1]. In the reac-
tion of maleic anhydride with isoprene, the activation
In this work, we determined the volume parameters
of the [3+2] addition of nitrone I and of the [4+2]
addition of 9,10-dimethylanthracene VI to maleic
O
O2N
a
+
O
HC=N
N
H
O
O
C
O
II
O
O
1
volume ( 38.5 1 cm3 mol ) and reaction volume
NO2
O
1
( 35.5 1 cm3 mol ) in a series of solvents varied
I
III
in narrow ranges [29].
Reaction (a). Data on the influence of pressure on
the rate of reaction (a) in toluene are summarized in
Table 3.
O2N
O
O
N
H
b
O
C
I +
N
The function ln(kp/kp = 1) = f(p) (Fig. 1) is linear:
2
O
ln(kp/kp = 1
)
=
(2.384 1.218) 10
+
(7.220
O
N
4
0.059) 10 p, r 0.9963, n 11. The calculated activa-
IV
tion volume for reaction (a) in toluene is 18.2
1
0.2 cm3 mol .
V
The volume of reaction (a) in toluene at 298.2 K
was determined as the difference between the partial
O
O
1
molar volumes of adduct III (233.3 0.9 cm3 mol )
CH3
1
and reactants: nitrone I (179.6 0.5 cm3 mol ) and
CH3
O
1
maleic anhydride II (71.1 0.2 cm3 mol ); it is equal
c
+ II
1
to 17.4 1.6 cm3 mol . The relatively large error
(9%) in determination of the reaction volume is due
to the fact that this quantity is the difference of large
quantities. The low solubility of the adduct often
CH3
CH3
VI
VII
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

ACTIVATION AND REACTION VOLUMES FOR [4+ 2] AND [3+ 2] ADDITIONS
1887
1
1
1
Table 2. Heats of solution ( solH, kJ mol ), partial molar volumes (V, cm3 mol ), and rate constants (k, l mol 1 s )
of the Diels Alder reactions of maleic anhydride and tetracyanoethylene in a series of solvents at 25 C
Maleic anhydride
Tetracyanoethylenea
Solvent
solH
V
k 103 b
solH
V
k c
Benzene
Toluene
o-Xylene
Mesitylene
Acetonitrile
16.8 0.5
16.4 0.4
15.1 0.5
72.2 0.3
71.1 0.2
71.5 0.2
70.8 0.5
70.4 0.1,
69.8d, 70.0e
72.4d
21.6
19.2
14.9
9.7
1.4
2.7
15.2
108.4
104.6
102.1
98.1
0.38
0.13
0.061
0.010
2.18
13.1 0.4
25.8
30.2
9.2
108.7
Nitromethane
Dichloromethane
Acetone
12.6 0.5
15.9 0.5
11.3 0.4
71.1d
23.4
107.5
4.28
69.4d
a
b
c
Data for tetracyanoethylene were taken from [12]. Rate constants of reaction with 9,10-dimethylanthracene. Rate constants of
d
e
reaction with anthracene [12].
Data of [29] for 308.2 K.
Data of [24].
introduces an additional error. We suggest another
method for calculating the reaction volume without
using partial molar volumes of the reactants and prod-
ucts. The method is as follows. The volume of solu-
tion of reactants (A, B) and product (P) at time t is
given by
determining the reaction volume, and it can be taken
into account, if necessary, in a repeated calculation.
From the results of precision measurements of the
density of the reaction solution in time and from the
rate constant of the reaction at the same temperature,
it is possible to calculate the reaction volume ( V0)
from the dependence of 1/dt on cP [Eq. (6)]. The vol-
ume of reaction (a) in toluene at 298.2 K, calculated
Vt = VS + (c 0A
cP)VA + (c 0B
cP)VB + cPVP, (3)
VA VB)
1
by this method, is 18.2 0.3 cm3 mol . Thus, the ac-
Vt = [VS(c 0A VA + c B0 VB) + cP(VP
1
tivation volume ( 18.2 0.2 cm3 mol ) and the reac-
= Vt=0 + cP V0.
(4)
tion volumes determined as the difference of the partial
1
molar volumes ( 17.4 1.6 cm3 mol ) and by relation-
1
Here, Vt= 0 and Vt are the initial and current (at
time t) solution volumes, respectively; VS, solvent
volume; VA, VB, and VP, partial molar volumes of
reactants A and B and product P, respectively; c0A, cB0 ,
and cP, initial molar concentrations of reactants and
product concentration at time t, respectively; and V0,
reaction volume.
ship (6) ( 18.2 0.3 cm3 mol ) are virtually equal.
Table 3. Influence of external pressure on the rate of 1,3-
dipolar cycloaddition of C-(p-nitrophenyl)-N-phenyl-
nitrone I to maleic anhydride II in toluene at 298.2 K
p,
kg cm
kp 104,
lnkp/kp=1
ra
na
2
1
l mol 1 s
With a precision dilatometer, it is possible to cal-
culate the reaction volume from the dependence of
Vt Vt= 0 on cP using relationship (4). When measur-
ing the solution densities, it is more convenient to use
relationships (5) and (6) taking into account that the
solution weight M does not change in the reaction.
1
130
230
350
450
595
680
745
795
915
985
2.32
2.62
2.94
3.00
3.25
3.69
3.92
4.00
4.19
4.67
4.80
0
0.99988
0.99992
0.99987
0.99986
0.99997
0.99999
0.99990
0.99999
0.99990
0.99992
0.99995
15
14
14
26
27
23
17
23
19
22
21
0.122
0.237
0.257
0.337
0.464
0.525
0.545
0.591
0.699
0.727
M/dt = M/dt=0 + cP V0,
(5)
(6)
1/dt = 1/dt=0 + cP V0/(1000dt=0).
Here, as in the kinetic measurements, the only sim-
plification is the assumption that variation of the solu-
tion volume in the course of the reaction does not
affect the concentrations of components. However,
this factor introduces only a small error (<0.1%) in
a
(r) Correlation coefficient of the kinetic dependence and
(n) number of experimental points.
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

1888
KISELEV et al.
tion volumes of ionic reactions can include additional
0.8
0.6
contributions originating from variation of the solvent
properties with increasing pressure, whereas the par-
tial molar volumes of polar and some ionic com-
pounds can be determined under normal pressure.
However, the available direct experimental data on
variation of the partial molar volumes of polar com-
pounds in a series of solvents [31] do not confirm the
suggested decrease in the partial molar volumes in
low-polarity solvents. The low solubility of the major-
ity of salts in nonpolar media excludes direct measure-
ment of their partial molar volumes [11]. For lithium
perchlorate, the partial molar volume in a series of
solvents does not correlate with the enthalpy of its
solvation, cohesion energy, and compressibility coef-
ficient of the solvent [32]. Thus, the factors affecting
the partial molar volumes in solvents are numerous
and remain to be fully elucidated.
0.4
0.2
0
0
200 400 600 800 1000 1200
2
p, kg cm
Fig. 1. Rate constant [ln(k /k
of C-(p-nitrophenyl)-N-phenylnitrone to maleic anhyd-
ride in toluene at 298.2 K as a function of external pressure.
)] of the the [3+2] addition
p = 1
p
Since the extent of charge separation in a 1,3-di-
pole decreases upon adduct formation, the reaction
volume could be expected to regularly change in
going from less polar to more polar solvents [2 6].
It is commonly believed [2, 3] that the electrostriction
of low-polarity solvents with a lower cohesion energy
density and usually with a higher isothermal compres-
sibility coefficient causes a stronger decrease in the
partial molar volumes, compared to polar media. This
assumption was put forward to explain the more nega-
tive activation volume in low-polarity solvents for a
series of reactions with a highly polar transition state
[30]. Here, at least two effects are superimposed. First,
more polar solvents certainly interact with a charge
more strongly, forming a stronger and more compact
solvation packing. On the other hand, polar solvents
containing heteroatoms are usually packed them-
selves more tightly than nonpolar solvents [23]. As
already noted, the experimental values of the activa-
The volume of reaction (a) in acetonitrile at 298.2 K
was determined as the difference between the partial
1
molar volume of the adduct (224.8 0.6 cm3 mol )
1
and those of the nitrone (175. 0.7 cm3 mol ) plus
1
maleic anhydride (70.4 0.4 cm3 mol ). It should be
noted that, in acetonitrile, the partial molar volumes
of all the reaction participants are noticeably smaller
than in toluene (233.3, 179.6, and 71.1, respectively),
but the reaction volume in acetonitrile ( 20.9
1
1.3 cm3 mol ) differs from that in toluene insignif-
icantly. The volume of reaction (a) in DMSO was
determined from the results of kinetic and densimetric
measurements at 298.2 K [Eq. (6)] to be 19.2
1
0.1 cm3 mol . The molar volume of 1,3-dipole I in
1
DMSo is 186.8 0.1 cm3 mol .
Reaction (b). Adduct V is poorly soluble in tolu-
ene, which prevented kinetic measurements at
elevated pressure and determination of the reaction
volume as the difference between the partial molar
volumes of the product and reactants. On the other
hand, at normal pressure adduct V does not precipitate
from solution containing I and IV until its concentra-
Table 4. Kinetic data for Diels Alder reaction (c) of
9,10-dimethylanthracene VI with maleic anhydride II in
acetonitrile at 298.2 K and various pressures
p,
kg/cm2 l mol 1 s
kp 102,
lnkp/kp=1
r
n
3
1
tion of 5 10 M is attained. From relationship (6),
we calculated the reaction volume in toluene ( 17.4
1
1
0.5 cm3 mol ) and DMSO ( 19.9 0.1 cm3 mol ).
1
300
400
495
525
650
700
730
885
900
980
2.58
3.32
3.54
4.09
3.96
4.41
4.87
4.89
5.60
6.00
6.00
0
0.99983
0.99962
0.99986
0.99981
0.99990
0.99993
0.99988
0.99994
0.99980
0.99981
0.99998
24
18
22
17
20
21
18
30
22
21
30
0.252
0.316
0.461
0.428
0.536
0.635
0.639
0.775
0.844
0.844
Reaction (c). To compare the volume parameters
of [3+2] and [4+2] cycloadditions, we studied reac-
tion (c) (see scheme) of maleic anhydride with 9,10-
dimethylanthracene VI.
The effect of pressure on the reaction rate (Table 4)
is described by a linear dependence ln(kp/kp = 1) =
( 1.717 1.938) 10
r 0.9947, n 11 (Fig. 2). From this dependence, the
2
4
+
(9.015 0.088) 10 p,
activation volume of reaction (c) can be determined
as 22.7 0.2 cm3 mol .
1
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

ACTIVATION AND REACTION VOLUMES FOR [4+ 2] AND [3+ 2] ADDITIONS
1889
1
Table 5. Volume characteristics (cm3 mol ) of reaction (a) of nitrone I with maleic anhydride II, reaction (b) of nitrone I
with N-phenylmaleimide IV, and reaction (c) of 9,10-dimethylanthracene VI with maleic anhydride II in solvents at
298.2 K
Reaction
(a)
Solvent
Partial molar volumes of compounds
V0
V
Toluene
CH3CN
DMSO
CH3CN
179.6 0.5 (I)
71.1 0.2 (II)
70.4 0.4 (II)
233.3 0.9 (III)
224.8 0.6 (III)
19.4 1.6a
20.9 1.3a
19.2 0.1b
25.4 2.5a
18.2 0.2
175.3 0.7 (I)
186.8 0.5 (I)
187.2 1.1 (VI)
(c)
70.4 0.4 (II)
232.2 1.3 (VII)
22.7 0.2
a
b
Calculated as the difference between the partial molar volumes of the product and reactants. Calculated by Eq. (6). For reac-
3
1
3
1
tion (a) in toluene, this calculation gives
V
18.2 0.3 cm mol ; for reaction (b) in toluene, 17.4 0.7 cm mol , and in
0
3
1
3
1
DMSO, 19.9 0.1 cm mol ; and for reaction (c) in acetonitrile, 23.6 0.16 cm mol
1
.
Table 6. Influence of the packing coefficient = VW/V on the volume (cm3 mol ) of the Diels Alder reaction of maleic
anhydride II with isoprene VIII to form 2-methylcyclohexene-4,5-dicarboxylic anhydride IX and with 9,10-dimethyl-
anthracene VI to form adduct VII
Reaction of maleic anhydride with isoprene Reaction of maleic anhydride with 9,10-dimethylanthracene
Parameter
VII
VVIII
VIX
V
VII
VVI
VVII
V
0.69
70
21.6
48.4
0.53
100
47.1
52.9
0.68
135
47.0
92.3
0.69
70
21.6
48.4
0.69
187
57.2
0.73
232
62.3
V
35
26
9.0
25
VHa
16.5
8.5
VW
129.8
169.8
a
Calculated by the MOLVOL program.
The volume of reaction (c) in acetonitrile, calcu-
The known volume effects in 1,3-dipolar additions
involving diphenyldiazomethane [22 24] and C-ben-
zoyl-N-phenylnitrone [24] are close to the values
given in Table 5.
lated from the partial molar volumes of adduct VII
1
(232.2 1.3 cm3 mol ), maleic anhydride (70.4
1
1
0.1 cm3 mol ), and diene VI (187.2 1.1 cm3 mol ),
is 25.4 2.5 cm3 mol . Again, the large relative
1
The contributions of changes in the van der Waals
volumes to the total activation and reaction volumes
are considered in [22, 23, 28, 33]. According to differ-
ent estimates, these contributions are much less than
50%. The coefficient of molecular packing in solution
error (10%), as in reaction (a), is due to the fact that
the reaction volume is the difference of large quanti-
ties. From the dependence of the reaction mixture
density on the conversion [Eq. (6)], the volume of this
reaction in acetonitrile can be determined as 23.63
1
0.16 cm3 mol . The repeated measurement gave
1
23.50 0.15 cm3 mol .
1.0
The volume parameters obtained are listed in
Table 5. In [3+2] cycloaddition (a) in toluene, the
0.8
0.6
1
ratio of the activation volume ( 18.2 cm3 mol ) to
1
the reaction volume ( 18.2 cm3 mol ) is unity. For
0.4
0.2
Diels Alder reaction (c) in acetone, this ratio is also
1
1
close to unity: ( 22.7 cm3 mol )/( 23.6 cm3 mol ) =
0.96.
0
The volume parameter of reactions (a) and (c)
differ by only 4 5 cm3 mol . It should be noted that,
1
0
200 400 600 800 1000 1200
2
p, kg cm
although in the activated complex, as compared to the
product, the bonds are formed only partially, the par-
tial molar volumes of the activated complex and prod-
uct are virtually equal in both reactions.
Fig. 2. Rate constant [ln(k /k
of 9,10-dimethylanthracene to maleic anhydride in aceto-
nitrile at 298.2 K as a function of external pressure.
)] of the [4+2] addition
p = 1
p
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

1890
KISELEV et al.
is defined as the ratio of the own (van der Waals)
molecules like fullerene C60 can become more com-
pact in solution than in crystals [34].
volume (VW) to the total partial molar volume (V):
= VW/V. An important consequence following from
the dependence of on the molecular size is that a
sharp growth of (from 0 to 0.65) should be expected
only in the range of partial molar volumes of up to
EXPERIMENTAL
Substituted nitrones were prepared and purified as
described in [35]. 9,10-Dimethylanthracene (Aldrich)
was additionally purified by passing through a column
packed with alumina (eluent hexane benzene, 3 : 1).
The optical purity of diene VI was evaluated by the
1
150 200 cm3 mol [22, 23, 28]. The partial molar
volumes of 9,10-dimethylanthracene and C-(p-nitro-
phenyl)-N-phenylnitrone appeared to be fairly close
(Table 5) and considerably larger than the partial
1
1
molar volumes of cyclopentadiene (81 cm3 mol ) and
final absorption (24600 25300 cm ) of its solution
1
butadiene (82 cm3 mol ) [12]. Based on data from
in the presence of excess maleic anhydride. Maleic
anhydride after distillation was additionally purified
by crystallization from benzene in which maleic acid
is virtually insoluble. N-Phenylmaleimide (Aldrich)
was used without additional purification. Adducts III
and VII were prepared by published procedures [27,
36].
[22, 23, 28, 33], we can estimate the contribution to
the volume ( V0) of the Diels Alder reaction of male-
ic anhydride with isoprene and 9,10-dimethylanthra-
cene (Table 6), made by the change in the volume of
intermolecular cavities ( V0, H): V0
V0, W
=
V0, H +
.
The contribution from the change in the van der
The progress of reaction (a) in toluene and of reac-
tion (c) in acetonitrile at 298.2 K under normal and
elevated pressures was monitored by the variation of
the absorption of nitrone I in the range 23820
1
Waals volume ( V0, W), 8 to 10 cm3 mol , agrees
with data of [22, 23]. The major contribution to the
experimental reaction volume ( V0) can be made by
the change in the volume of intermolecular cavities
( V0, H), which, within this concept, should approach
1
23900 cm and that of diene VI in the range 24600
1
24880 cm , respectively (Specord UV-Vis). The
1
the limiting value, from 15 to 20 cm3 mol , at
initial concentration of reactants in reaction (a) was
4
further increase in the partial molar volumes of the
reactants.
as follows: diene (5 7) 10 and maleic anhydride
0.13 0.15 M. The procedure of kinetic measurements
at elevated pressure is described in detail elsewhere
[7, 12].
Thus, replacement of low-polarity toluene ( 2.4)
by acetonitrile ( 36.6) and DMSO ( 47.2) results in
irregular changes in the partial molar volumes of the
1,3-dipole, dipolarophile, and their adduct. The activa-
tion and reaction volumes in the reactions of nitrone I
with maleic anhydride II and N-phenylmaleimide IV
vary in the above solvents insignificantly (from 17.4
The apparent molar volumes of the reactants and
adducts in solution were calculated from the densities
of solutions of known concentrations and solvent den-
sity, as described in [7, 12]. The high accuracy of
3
density measurements ( 2 10 6 g cm , 2 10 3 K,
1
to 20.9 cm3 mol ), in agreement with published
DMA-602 densimeter) allowed experiments with
dilute solutions. The apparent molar volumes did not
data [22 24]. Comparison of [3+2] and [4+2] cyclo-
additions in which the 4 -reagents have large and
comparable partial molar volumes shows that the acti-
vation and reaction volumes of these processes differ
insignificantly and their ratio is close to unity. This
fact additionally supports the single-step concerted
mechanism of these reactions.
1
change in the concentration range 0.005 0.10 mol kg
and were used as partial volumes. Calculations were
performed using relationship (7) obtained in [32]:
y = (1000 + Mm)/d = 1000/d0 + m ,
(7)
where M is the molar weight of the solute; m, molal
concentration; d0 and d, densities of the solvent and
solution, respectively; and , apparent molar volume.
The experimental data are listed in Table 7.
It should be noted in conclusion that the real vol-
ume parameters of activation and reaction, determin-
ing the effect of external pressure on the rate and
equilibrium of reactions in solution, are not governed
solely by the change in the structural volume ( V0, W).
The packing coefficient does not reach the limiting
value of unity even in solids. This follows from the
fact that an increase in the density and hence in the
packing coefficient of a substance in its passing from
a solution or liquid state to the solid state is relatively
low ( 10%). Furthermore, packing of large spherical
Determination of the reaction volume from kinetic
data. Using data on variation of the reaction mixture
density in time and knowing the reaction rate con-
stant, we can calculate the reaction volume without
using data on partial molar volumes. Relationship (6)
is deduced above. Although the relative error in deter-
mination of the partial molar volumes (<0.5%) is
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

ACTIVATION AND REACTION VOLUMES FOR [4+ 2] AND [3+ 2] ADDITIONS
1891
1
3
1
Table 7. Solute concentrations (m, mol kg ), solution densities (d, g cm ), functions y [cm3 g , Eq. (7)], and calculated
apparent molar volumes ( , cm3 mol ) at 298.2 K
1
1
3
1
1
3
1
m, mol kg
d, g cm
1000y, cm3 g
m, mol kg
d, g cm
1000y, cm3 g
Maleic anhydride in toluene
0.862294
C-(p-Nitrophenyl)-N-phenylnitrone in DMSO
0
1159.70
1163.96
1165.78
1169.01
0
0
1.095073
1.095080
1.096054
1.096464
1.096835
913.18
913.17
917.35
919.48
921.31
924.56
0.0599
0.0846
0.1172
0.864177
0.864911
0.865989
0.02261
0.03383
0.04348
0.06104
71.11 0.11, r 0.99994, n 4
Maleic anhydride in acetonitrile
0.777078
1.097558
1286.87
1286.88
1294.57
1301.51
186.83 0.14, r 0.99999, n 6
9,10-Dimethylanthracene in acetonitrile
0.777073
0.780708
0.783978
0.1090
0.2077
0
0.777055
0.777654
0.777288
1286.91
1289.34
1288.74
0.01289
0.00999
70.37 0.07, r 0.99999, n 5
C-(p-Nitrophenyl)-N-phenylnitrone in toluene
187.21 1.13, r 0.99989, n 3
Adduct VII in acetonitrile
0.777056
0
0
0.861984
0.861988
0.862471
0.862602
0.862799
1160.11
1160.11
1161.22
1161.52
1162.04
1162.21
0
1286.91
1288.17
1288.50
1288.40
1287.97
0.00626
0.00797
0.01076
0.01160
0.00547
0.00686
0.00618
0.00438
0.777592
0.777722
0.777623
0.777456
0.862846
179.56 0.51, r 0.99988, n 6
C-(p-Nitrophenyl)-N-phenylnitrone in acetonitrile
232.2 1.30, r 0.9989, n 5
Adduct III in toluene
0.861987
0
0.776521
0.777731
0.778101
0.778396
0.778925
1287.79
1290.46
1291.06
1291.78
1292.99
0
1160.11
1161.59
1161.91
1162.11
1162.42
0.01501
0.01891
0.02282
0.02961
0.00638
0.00777
0.00853
0.00999
0.862764
0.862936
0.862990
0.863170
175.30 0.71, r 0.99986, n 5
233.32 0.90, r 0.99985, n 5
Adduct III in acetonitrile
0.776496
0
1287.84
1289.72
1290.19
1290.74
1291.60
0.00849
0.01059
0.01305
0.01669
0.777600
0.777873
0.778173
0.778631
224.81 0.61, r 0.99988, n 5
3
smaller than in calculation with Eq. (6) (1 3%), in the
former case we deal with the difference between large
quantities, which results in a large (reaching 10%)
deviations ( 3 10 K), the measured values of
density were corrected using the coefficient of thermal
expansion of the solvent. The experimental depen-
dence for reaction (a) in DMSO is shown as example
in Fig. 3. The rate constant of reaction (a) is 2.38
1
error in the reaction volume, (1.5 2.5) cm3 mol .
The direct method for calculating the reaction volume
[Eq. (6)] is considerably more accurate: the error is
10 l mol 1 s at 298.2 K and concentrations of
nitrone I and maleic anhydride of 0.02542 and
0.4350 M, respectively.
4
1
1
(0.15 0.5) cm3 mol . Another advantage of the
suggested calculation procedure is that Eq. (6)
is applicable in cases when a supersaturated solution
of a poorly soluble adduct is formed (which is ob-
served frequently); in such cases, the direct method
for determination of partial molar volumes [Eq. (7)] is
unsuitable. The optimal reaction half-time in a tube
of a precision densimeter is 0.5 3 h. At temperature
Simple transformations of experimental data (using,
e.g., Origin 4.0 software) allow us to obtain the de-
pendence of the specific volume (1/dt) on the concen-
tration of adduct III. The calculated volume of reac-
tion (a) in DMSO, determined at 25% conversion
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 73 No. 12 2003

1892
KISELEV et al.
12. Kiselev, V.D., Konovalov, A.I., Asano, T., Kashae-
1/dt
0.9063
va, E.A., Iskhakova, G.G., and Medvedeva, M.D.,
J. Phys. Org. Chem., 2001, vol. 14, no. 7, p. 636.
13. Kiselev, V.D., Medvedeva, M.D., Kashaeva, E.A.,
Shikhab, M.S., Iskhakova, G.G., and Konovalov, A.I.,
Zh. Obshch. Khim., 2002, vol. 72, no. 3, p. 465.
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Konovalov, A.I., Zh. Obshch. Khim., 2002, vol. 72,
no. 1, p. 106.
0.9062
0.9061
0.9060
15. Kiselev, V.D., Kashaeva, E.A., Shikhab, M.S., Med-
vedeva, M.D., and Konovalov, A.I., Izv. Ross. Akad.
Nauk, Ser. Khim., 2000, no. 6, p. 1046.
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no. 2, p. 301.
0.9059
0.9058
0 0.005 0.010 0.015 0.020 0.025 c, M
Fig. 3. Reciprocal density 1/d of solution of a mixture
t
of C-(p-nitrophenyl)-N-phenylnitrone (c 0.02542 M)
17. Swiss, K.A. and Firestone, R.A., J. Phys. Chem. A,
1999, vol. 103, no. 27, p. 5369.
0
with maleic anhydride (c 0.4350 M) in DMSO as a
0
function of concentration c of the forming product.
T 298.2 K.
18. Le Noble, W.J. and Asano, T., J. Phys. Chem. A,
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20. Kiselev, V.D. and Miller, J.G., J. Am. Chem. Soc.,
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1
(60 min), is 19.02 0.18 cm3 mol (r 0.9993, n 8);
at 50% conversion (112 min), 18.95 0.08 cm3 mol
1
(r 0.9997, n 32); and at 78% conversion (240 min),
19.21 0.05 cm3 mol (r 0.9998, n 58).
1
ACKNOWLEDGMENTS
The study was supported by the Joint Program of
CRDF and RF Ministry of Education (REC-007),
Academy of Sciences of the Tatarstan Republic (pro-
ject no. 07-7.1-74/01), and Competitive Research
Center of the Kazan University.
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