Solvent effect on the activation volume of the diels-alder reaction between tetracyanoethylene and trans, trans-1,4-diphenyl-1,3-butadiene

Article abstract of DOI:10.1023/A:1015357731693

The effect of increased hydrostatic pressure on the rate of the Diels-Alder reaction of tetracyanoethylene with trans, trans-1,4-diphenyl-1,3-butadiene at 25°C was studied to estimate the reaction volume and to show that it considerably varies with π-donor properties of the medium.

Full text of DOI:10.1023/A:1015357731693

Russian Journal of General Chemistry, Vol. 72, No. 1, 2002, pp. 98 104. Translated from Zhurnal Obshchei Khimii, Vol. 72, No. 1, 2002,
pp. 106 112.
Original Russian Text Copyright
2002 by Kiselev, Shikhaab, Iskhakova, Konovalov.
Solvent Effect on the Activation Volume
of the Diels Alder Reaction Between Tetracyanoethylene
and trans,trans-1,4-Diphenyl-1,3-butadiene
V. D. Kiselev, M. S. Shikhaab, G. G. Iskhakova, and A. I. Konovalov
Butlerov Research Institute of Chemistry, Kazan State University, Kazan, Tatarstan, Russia
Received May 15, 2000
Abstract The effect of increased hydrostatic pressure on the rate of the Diels Alder reaction of tetracyano-
ethylene with trans,trans-1,4-diphenyl-1,3-butadiene at 25 C was studied to estimate the reaction volume and
to show that it considerably varies with -donor properties of the medium.
The intensive research into the effect of increased
hydrostatic pressure on chemical reactions is associa-
ted both with the considerable rate and equilibrium
effects of external pressure (which is especially im-
portant for practical purposes) and with a view to
determination of additional activation and reaction
parameters. Quantitative data on the activation volume
( V ) and the reaction volume ( V0) of a reaction,
together with its energetic characteristics, allow one to
gain a deeper insight into the reaction mechanism
[1 3]. The activation and reaction volumes can be
estimated from the dependences of the rate constant
(k) or the equilibrium constant (K) of the reaction on
external pressure (p) at constant temperature, using
Eqs. (1) and (2):
account that if the rate or equilibrium of a reaction
are highly medium-dependent then the volume cha-
racteristics estimated by Eqs. (1) and (2) may not be
very exact [6 9]. Thus, increasing pressure may
accelerate reactions in low-viscosity media (Fig. 1,
plot 1) and decelerate the same reactions in more
viscous media of the same polarity (Fig. 1, plot 4).
This fact can be explained by the imposition of dif-
fusion control (Fig. 1, plot 2) on the rates of such
reactions in viscous media [8, 9].
A more complicated pattern is observed in ionic or
highly polar processes. In terms of the transition state
theory which includes a thermodynamic treatment of
activation parameters, the rate constant of a reaction
and its pressure dependence are determined by
Eqs. (3) and (4) [10 12].
(dln k/dp)T
(dln K/dp)T
=
1/RT(d G /dp)T
1/RT(d G/dp)T
=
V /RT,
V 0/RT.
(1)
(2)
k = (RT/Nh)K (
/
),
(3)
A B
=
=
(dln k/dp)T
=
V /RT + [dln (
/
)/dp]T. (4)
A B
It is well known that the activation and reaction
volumes of ionic or highly polar reactions conside-
rably vary with solvent polarity. Experimental evi-
dence for the electrostriction of solvent molecules
near ions is provided by decreased molar volumes of
a series of salts, acids, and bases in solutions; more-
over, as found in [4, 5] from solution density data,
some salts have negative partial molar volumes. The
termodynamic equations (1) and (2) are based on the
Here K is the thermodynamic equilibrium con-
stant between reagents A and B and transition state
X in infinitely dilute solution and are the activity
coefficients of the corresponding stateis in the solution.
The activation volume ( V ) at usual pressure is
equal to a difference in the partial molar volumes of
the transition state and the reagents. This activation
assumption that at constant temperature the depen- volume includes structural and solvation contributions,
dences of the free energies of activation and reaction
at constant temperature on external pressure are
determined by the contribution p V at invariable
and it can experimentally be determined only from
the pressure dependence of the free activation energy
(Fig. 1, plot 1). For ideal solutions at fixed tempera-
effects on the free energies of other properties of the tures, Eqs. (1) and (2) provide reliable volume cha-
system. Increasing external pressure affects the racteristics. By contrast, for real solutions one should
density, viscosity, dielectric constant, and refractive
index of a real liquid. Therefore, one should take into
take account of the possible contribution in the pres-
sure-induced free energy change of changes in activity
1070-3632/02/7201-0098$27.00 2002 MAIK Nauka/Interperiodica

SOLVENT EFFECT ON THE ACTIVATION VOLUME
99
coefficients [Eq. (4)]. The rates of nonpolar reactions
ln (kp/k0)
5
are usually only slightly sensitive to properties of the
medium (for instance, to ), and, therefore, the second
term in Eq. (4) is small. The equation for the electro-
striction volume ( Vel) of a solvent with dielectric
constant around charge q has been proposed in [13]
[Eq. (5)]:
1
3
Vel = (Nq2/2b)[d(1/ )/dp]T.
(5)
0
p
The description of the free energy of charge trans-
fer from vacuum to a surrounding continuum with
dielectric constant has been theoretically substan-
tiated in [14] [Eq. (6)]:
4
2
Gel
=
[Nq2/2b][(
1)/ ].
(6)
Fig. 1. (1) Effect of external pressure (p) on reaction
rate [(ln(k /k )] at invariable solvent properties; (2) ef-
p
0
Here b is the radius of the sphere encompassed by
the surrounding continuum and N is the Avogadro
number. From Eq. (6) it follows that the energy of
electrostatic stabilization increases with increasing
dielectric constant of the medium. At the same time,
Eq. (5) expects increase in solvent electrostriction
with decreasing dielectric constant. This is ex-
plained by the fact that [d(1/ )/dp]T sharper decreases
with pressure in media with lower dielectric constants.
The transfer from the initial state to a polar transition
state at atmospheric pressure already has an activation
volume (Fig. 1, plot 1), no matter whether changes
with pressure or not. This activation volume can be
determined by Eq. (1) on condition that solvent pro-
perties are unchanged [(d G /dp)T, , , ] or estimated
with small errors on condition that the process in hand
is weakly sensitive to pressure-induced changes in the
properties of the medium [6 9]. The effect of the
medium on the rates of polar and ionic reactions is
frequently described in terms of Eq. (7):
fect on reaction rate of pressure-induced change in sol-
vent viscosity under diffusion control; (3) effect on reac-
tion rate of pressure-induced change in solvent dielectric
constant for polar reactions; and (4) and (5) total effects
for polar reactions: ( V
V ) = V .
+
V ) =
V
and ( V
+
1
1
2
4
3
5
measured free activation energy in reactions with
strong intermolecular interactions between the re-
agents [15, 16], where reaction rate decreases with
temperature, i.e. in such intricate processes in which
the parameter studied changes sign. The fact that this
problem in the determination of the volumes of polar
and ionic reactions [Eqs. (1) and (2)] is not so obvious
can be explained by that (d G /dp)T = c, [d(1/ )/dp]T
from Eq. (7) change in the same direction as the
partial molar volumes of ions in solutions of alkali
metals salts or zwitter ions (for instance, amino acids)
in a series of solvents with different dielectric con-
stants [4, 5]. The change in the volume of the dis-
sociation of a molecule into solvated ions in a series
of solvents fairly correlates with the compressibility
factors of the media [5], while the pressure-induced
changes in the density of solvents determine changes
in [17]. It should be noted the experimental forward
and backward activation volumes of an equilibrium
process with nonpolar initial and final states and a
polar activated complex may be overestimated in
absolute values, but their difference will be equal to
the reaction volume determined independently from
the partial molar volumes of the reagents and products
at normal pressure.
G
= a + b(1/ ).
(7)
Here a and b are constants. Further decrease in the
free activation energy of a polar reaction, produced
by the pressure-induced increase in the dielectric
constant of the medium (Fig. 1, plot 3), gives rise to
increased slope of the pressure dependence of the free
energy of activation (Fig. 1, plot 5) [7]. In other
words, the activation volume of a polar reaction is
only partly contributed by the pressure-induced
change in the activation energy (d G /dp)T. More
illustrative examples of such superpositions of effects
one can find by following changes in the free activa-
tion energy of fast reactions under pressure in high-
viscosity media, where such changes are complicated
by diffusion control [8, 9], or of changes in the
Diels Alder reactions are commonly weakly sen-
sitive to solvent polarity and, consequently, to pres-
sure-induced changes in . Recently we showed that
the volumes of the nonpolar Diels Alder reactions of
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 72 No. 1 2002

100
KISELEV et al.
cyanoethylene, calculated from the Born cycle [22],
7
showed that the enthalpy level of the activated
compex in a series of -donor solvents is almost in-
variable. For this reason, one can expect considerable
changes in activation volumes for the reactions in-
volving tetracyanoethylene over a series of solvents
appreciably differing in -donor properties. The effect
of the medium on the activation and reaction volumes
of Diels Alder reactions has been studied in [23], but
the reagents used (isoprene and maleic anhydride) are
incapable of appreciable specific interactions with
solvents. The Diels Alder reactions of tetracyano-
ethylene with most dienes are very fast [24], which
complicates kinetic studies at elevated pressures. We
chose the reaction of trans,trans-1,4-diphenyl-1,3-
budadiene (I) with tetracyanoethylene (II) (see the
scheme below) because it gives a fairly stable adduct
III, and the rate of this reaction is much reduced by
the increased conjugation energy in the diene [24].
10
15
20
25
30
35
40
6
5
4
7
3
3
6
1
5
2
1
4
2
98
100
102 104
106 108
110
VII, cm3/mol
Fig. 2. (Circles) Activation volumes ( V ) of the Diels
Alder reaction of dienophile II with diene I and (squares;
the ordinates of the points are shifted upward by
10 cm /mol) the reaction volumes ( V ) of dienophile
II with cyclopentadiene against the partial molar
The resulting data are listed in Table 1.
Table 2 compares the solvent effects on the partial
molar volume of tetracyanoethylene, on the activation
volume of the reaction studied, and on the volume of
the Diels Alder reaction of tetracyanoethylene with
cyclopentadiene.
3
0
volumes of tetracyanoethylene (V ) in various solvents.
The numbering of solvents is the same as in Table 2.
II
NC
CN
tetracyanoethylene with cyclopentadiene [18] and
9-chloroanthracene [19] are strongly affected by
specific interactions of the reagents with solvents.
+
CN
NC
I
II
Strong interactions of a -donor solvent and the
-
acceptor tetracyanoethylene (Ea 2.88 eV [20]) pro-
portionally affect the solvation enthalpy and the
partial molar volume of tetracyanoethylene [21]. Since
the reaction adduct does not possess -acceptor pro-
perties, then its solvation enthalpy and partial molar
volume are already weakly dependent on -donor
properties of solvent, resulting in considerable
changes in the reaction volume over a series of sol-
vents. For the equilibrium reaction of tetracyano-
ethylene with 9-chloroanthracene in a series of sol-
vents the reaction volumes were calculated from the
pressure dependence of the equilibrium constant. The
volumes of the nonequilibrium reaction of tetracyano-
ethylene with cyclopentadiene were determined di-
rectly from the difference in the partial molar volumes
of the reagents and adduct. The sharp increase in the
volume of the latter reaction in going from benzene
( 32.0 cm3/mol) to mesitylene ( 21.8 cm3/mol) is
nicely consistent with the corresponding change in
the partial molar volume of tetracyanoethylene (108.4
and 98.1 cm3/mol in benzene and mesitylene, res-
pectively) [21].
NC
NC
CN
CN
X
CN
CN
NC
NC
III
As seen from the data in Table 2, the enthalpies of
solution of tetracyanoethylene, its partial molar
volumes, as well as the activation and reaction
volumes in aromatic solvents vary in parallel. Corre-
lating the volume characteristics (Fig. 2) leads to
Eqs. (8) and (9):
V
= (64 3)
(0.895 0.029)VII; r 0.9974, n 7,
s 0.3076,
(8)
V0 = (79 11)
(1.029 0.053)VII; r 0.9846, n 4,
The changes in the enthalpies of solvation of the
transition state of the Diels Alder reaction with tetra-
s 0.7910.
(9)
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 72 No. 1 2002

SOLVENT EFFECT ON THE ACTIVATION VOLUME
101
Table 1. Effect of external pressure on the rate constant of the Diels Alder reaction between diene I and dienophile II
at 25 Ca
p,
kg/cm2 l mol 1 s
k2 103,
p,
k2 103,
p,
kg/cm2 l mol 1 s
k2 103,
p,
k2 103,
ln k2
ln k2
ln k2
ln k2
1
1
1
1
kg/cm2 l mol 1 s
kg/cm2 l mol 1 s
4
3
2
3
1,2-Dichloroethane; cI 3.01 10 , cII 4.50 10 M,
Benzene; cI 2.51 10 , cII 1.46 10 M,
1
1
27780 cm
22520 cm
0
160
230
330
445
95
111
132
147
176
2.35
2.20
2.25
1.92
1.74
620
705
770
805
975
209
232
260
268
319
1.56
1.46
1.35
1.32
1.14
0
0
220
330
6.97
7.27
9.88
4.97
4.92
4.62
4.51
390
460
550
620
11.7
13.4
14.7
15.7
4.45
4.31
4.22
4.15
11.0
3
3
ln k2 = ( 2.344 0.018) + (1.260 0.011) 10 p;
ln k2 = ( 4.940 0.015) + (1.298 0.014) 10 p;
r 0.9972, n 10, s 0.0303,
Acetonitrile; cI 4.70 10 , cII 7.64 10 M,
V
31.7 0.3 cm3/mol
r 0.9970, n 8, s 0.0237;
Toluene; cI 7.41 10 , cII 1.45 10 M,
V
32.7 0.4 cm3/mol
4
3
2
3
1
1
27900 cm
23000 cm
0
210
310
410
79
102
124
141
2.54
2.28
2.09
1.96
510
605
755
905
165
176
212
259
1.80
1.74
1.55
1.35
0
0
300
500
2.56
2.61
3.54
4.71
5.97
5.95
5.64
5.36
630
770
980
5.01
6.34
8.34
5.30
5.06
4.79
3
3
ln k2 ( 2.522 0.020) + (1.312 0.013) 10 p;
r 0.9971, n 8, s 0.0297;
33.1 0.3 cm3/mol
ln k2 = ( 5.972 0.021) + (1.175 0.014) 10 p;
V
r 0.9970, n 7, s 0.0345;
o-Xylene; cI 1.72 10 , cII 4.05 10 M,
V
29.6 0.4 cm3/mol
2
3
2
3
Cyclohexanone; cI 3.01 10 , cII 2.60 10
M
1
1
25130 cm
18530 cm
0
0
150
175
310
14.2
14.1
16.5
17.2
22.2
4.25
4.26
4.11
4.06
3.81
415
625
750
950
27.4
32.5
36.3
51.7
3.60
0
150
175
270
495
1.08
1.24
1.31
1.53
1.82
6.83
6.69
6.64
6.48
6.31
580
700
825
825
985
2.09
2.38
2.71
2.55
3.03
6.17
6.04
5.91
5.97
5.80
3.43
3.32
2.96
3
3
ln k2 = ( 4.260 0.026) + (1.346 0.018) 10 p;
r 0.9938, n 9, s 0.0510;
ln k2 = ( 6.818 0.018) + (1.067 0.010) 10 p;
r 0.9962, n 10, s 0.0314;
Mesitylene; cI 8.86 10 , cII 1.80 10 M,
V
34.1 0.5 cm3/mol
V
26.9 0.3 cm3/mol
2
3
1
18150 cm
0
320
500
0.217
0.284
0.356
8.44
8.17
7.94
705
800
970
0.395
0.440
0.485
7.84
7.73
7.63
4
ln k2 = ( 8.476 0.037) + (9.180 0.235) 10 p;
r 0.9903, n 6, s 0.0453;
V
23.2 0.6 cm3/mol
a
c
and c are the initial concentrations of the reagents and
is the working wavelength.
I
II
The slope of Eq. (9) is equal to one, which cor-
( 0.1) of the -acceptor capacity of tetracyanoethylene
is preserved in the activated complex. As seen from
Table 2, in nonaromatic solvents the reaction volume
does not change proportionally with the partial molar
volume of tetracyanoethylene. Since the partial molar
volume of cyclopentadiene in all the solvents
(Table 2) changes only slightly, the deviation ob-
served for nonaromatic solvents (Fig. 2, plot 2) should
be related to some specific medium effects on the
responds to a complete loss of -acceptor properties
in the adduct. This conclusion is consistent with the
data in [18], which point to a weak effect of aromatic
solvents on the heats of solution and the partial molar
volume of the adduct of the cyclopentadiene with
tetracyanoethylene.
The slope of Eq. (8) suggests that only a small part
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 72 No. 1 2002

102
KISELEV et al.
Table 2. Medium effects on the enthalpies of solution of tetracyanoethylene ( HII,sol), its partial molar volumes (VII),
the activation volume ( V ) of the Diels Alder reaction between dienophile II and diene I, and the reaction volume of
dienophile II with cyclopentadiene at 25 C
No.
Solvent
VIIa, cm3/mol
V , cm3/mol
V 0a,b, cm3/mol HII,sola, kJ/mol
1
2
3
4
5
6
7
1,2 Dichloroethane
Acetonitrile
Cyclohexanone
Benzene
Toluene
o-Xylene
107.7
108.7
110.4
108.4
104.6
102.1
98.1
31.7
33.1
34.1
32.7
29.6
26.9
23.2
36.8
40.7
34.3
32.0
28.6
24.3
21.8
21.3
15.2
7.6
14.9
9.7
1.4
2.7
Mesitylene
a
b
Data of [18]. The reaction volume was not estimated from the difference in the molar volumes of adduct III and reagents I and II
because of the poor solubility of adduct III in aromatic solvents.
partial molar volume of the adduct. According to
[7, 18], accessibility for interaction with solvents of
internal (two tertiary and two quaternary) carbon
the second case, the apparent activation volume
corresponds to transition from complexed tetracyano-
ethylene whose fraction is 0.97. Quantitative relation-
atoms in the branched adduct depends strongly on the ships for the two pathways have one and the same
volume and structure of the solvent, which determines starting point and, therefore, are identical to each
the volume of cavities in the adduct, inaccessible for other. This conclusion remains valid for the reaction
solvation. As a result, the partial molar volume of the
adduct undergoes considerable changes even in media
where no specific interactions are possible. On the
other hand, a high correlation coefficient [Eq. (8)] is
observed with all the solvents studied. Thus, the transi-
tion state has structure X , where approach of sol-
vents is not yet hindered, but the ability of the tetra-
cyanoethylene fragment to specific interactions with
-donor solvents is sharply weakened.
performed under pressure in a mixture of an inert and
-donor solvent.
a
EXPERIMENTAL
trans,trans-1,4-Diphenyl-1,3-butadiene (I) was
purified by recrystallization from ethanol, mp 150
151 C (149 150 C [25]). Tetracyanoethylene (II)
(Merck) was sublimed in a vacuum ( 50 Pa) at 110 C,
mp 200 201 C (201 202 C [26]. All solvents were
purified by known procedures [27]. Adduct III was
obtained from equimolar solutions of reagents I and II
in 1,2-dichloroethane, followed by recrystallization
from benzene, mp 211 212 C (211 212 C [28]).
The resulting data are the first example of a con-
siderable effect of the medium on the activation
volume of a nonpolar reaction. These results allow us
to expect appreciable medium effects on activation
and reaction volumes for ionic, polar, low-polarity,
and nonpolar reactions, where there is a strong inter-
action of the solvent with one of the two states of the
reaction.
Before kinetic measurements we chose an optimal
working spectral range, where one of the reagents
absorbs rather strongly and the second reagent and the
adduct absorb weakly (Table 1). The reaction progress
in nonaromatic solvents was followed by the absor-
bance of diene I, using a large excess of dienophile
II, while in aromatic solvents, by the absorbance of
the complex of dienophile II with the solvent, using a
large excess of diene I. It was found that the pressure
range studied the reagent absorbances fit the Beer law.
The concentration of a compound taken in excess was
always 10 times higher that the concentration of a
compound whose absorbance was used for rate measu-
rements. The second-order rate constants (k2) were
calculated by Eq. (10):
From the activation volumes of the reaction
studied in aromatic solvents we cannot decide
between two reaction pathways: involving free
tetracyanoethylene molecules or involving the com-
plex of tetracyanoethylene with the solvent. In the
first case, increased pressure should raise the apparent
rate constant to a lesser degree, because the fraction
of free tetracyanoethylene molecules is descreased by
increased equilibrium constant of the complex
between tetracyanoethylene and the -donor solvent.
In this case, the apparent activation volume is equal
to the difference in the activation volumes of the
reagents in an inert medium and the formation volume
of tetracyanoethylene with the aromatic solvent. In
k2 = 1/ciln (D0/D ).
(10)
RUSSIAN JOURNAL OF GENERAL CHEMISTRY Vol. 72 No. 1 2002

SOLVENT EFFECT ON THE ACTIVATION VOLUME
Here is time, ci is the concentration of a reagent
103
ACKNOWLEDGMENTS
taken in excess, and D0 and D are the initial and
current absorbances. The reaction completeness was
40 80%. The correlation coefficients for all the rate
constants were higher than 0.999.
The work was financially supported by the Russian
Foundation for Basic Research (project no. 98-03-
33053-a) and the Competitive Foundation of Kazan
State University.
The design and operation of the barostat and the
high-pressure unit with a variable-volume quartz cell
(Specord UV-Vis spectrophotometer) have been des-
cribed in [7, 29]. The new design of the cylinder,
which allows complete isolation of the oil fed under
pressure from a transparent liquid (octane) transferring
pressure to the instrument cell, makes possible spec-
tral measurements in the UV range without contamina-
tion of the octane even at multiple measurements. The
necessity in choosing conditions providing pseudo-
first-order reaction conditions stems from the fact that
at concentrations ensuring optimal reagent absor-
bances the reaction half-time was 0.5 to 4 h. The
initial reaction period (5 7 min) after raising the pres-
sure is required for relaxation of the temperature jump
produced by solution compression, and, therefore, this
period should not be taken into account in calculating
rate constants. The reaction was performed in a quartz
cell (l 1 cm), whose neck was thoroughly ground in
the base of a cylindrical glass tube. The base of this
tube had a thin capillary for communicating the cell
with the upper cylinder. The cell was charged with a
reaction mixture and tightly stopped with the cylindri-
cal tube which then filled with mercury for equalizing
the pressure in the operation mode. All solvents were
checked for constant absorbances of the components
in the presence and in the absence of mercury. The
initial transmittance of the temperature-controlled
(25 0.1 C) high-pressure unit with a solvent-filled
cell (T 100%) was set by smoothly aligning the dia-
phragm fixed in the cell compartment on the path of
the reference beam. After that the high-pressure unit
was taken out from the cell compartment, and one
more diaphragm was placed on the path of the
working beam, aligned to the initial transmittance
(T 100%), and taken away, after fixing its orifice
diameter, from the special holder. At prolonged
measurements (more than 1 2 h) the high-pressure
unit was temporarily taken out of the cell compart-
ment, the latter diaphragm was placed on the path of
the working beam, and testing for possible variations
in the dark current was performed. In most experi-
ments no corrections were required in optical density
calculations.
The authors are grateful to Yu.M. Kargin (Kazan
University) and T. Asano (University of Oita, Japan)
for valuable advices in discussion of this work, as
well as to E.A. Kashaeva and M.D. Medvedeva for
some measurements.
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