Solvent effect on the equilibrium constant of the chain reversible reaction of N,N'-diphenyl-1,4-benzoquinonediimine with 2,5-dichlorohydroquinone

Article abstract of DOI:10.1007/s11172-007-0378-4

The temperature dependences of the equilibrium constant K of the reversible chain reaction of N,N'-diphenyl-1,4-benzoquinonediimine with 2,5-dichlorohydroquinone in benzene, chlorobenzene, anisole, benzonitrile, and CCl₄ were studied. The enthalpies and entropies of the reaction in these solvents were determined, and a linear dependence between them in aromatic solvents was found. The equilibrium constant depends on the solvent nature: the replacement of CCl₄ by benzene at T = 298 K increases K from 13.6 to 140. The solvation effects are caused by several types of intermolecular interactions of participants of equilibrium with the medium. The decrease in K in the benzene-anisole-benzonitrile series is related, to a great extent, to complex formation with hydrogen bonding between 2,5-dichlorohydroquinone and the solvents. In anisole a charge-transfer complex is formed between the solvent and reaction product (2,5-dichloroquinone). The constant and enthalpy of the complexation were estimated.

Full text of DOI:10.1007/s11172-007-0378-4

Russian Chemical Bulletin, International Edition, Vol. 56, No. 12, pp. 2376—2383, December, 2007
2376
Solvent effect on the equilibrium constant of the chain reversible reaction
of N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinonediimine with 2,5ꢀdichlorohydroquinone

S. Ya. Gadomsky and V. T. Varlamov
Institute of Problems of Chemical Physics, Russian Academy of Sciences,
1 prosp. Akad. Semenova, 142432 Chernogolovka, Moscow Region, Russian Federation.
Fax: +7 (496) 515 5420. Eꢀmail: varlamov@icp.ac.ru
The temperature dependences of the equilibrium constant K of the reversible chain reacꢀ
tion of N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinonediimine with 2,5ꢀdichlorohydroquinone in benzene,
chlorobenzene, anisole, benzonitrile, and CCl4 were studied. The enthalpies and entropies of
the reaction in these solvents were determined, and a linear dependence between them in
aromatic solvents was found. The equilibrium constant depends on the solvent nature: the
replacement of CCl4 by benzene at Т = 298 K increases K from 13.6 to 140. The solvation
effects are caused by several types of intermolecular interactions of participants of equilibrium
with the medium. The decrease in K in the benzene—anisole—benzonitrile series is related,
to a great extent, to complex formation with hydrogen bonding between 2,5ꢀdichlorohydroꢀ
quinone and the solvents. In anisole a chargeꢀtransfer complex is formed between the solvent
and reaction product (2,5ꢀdichloroquinone). The constant and enthalpy of the complexation
were estimated.
Key words: N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine, 2,5ꢀdichlorohydroquinone,
N,N´ꢀdiphenylꢀ1,4ꢀbenzoquinonediimine, 2,5ꢀdichloroquinone, reversible chain reactions,
equilibrium constant, reaction enthalpy and entropy, hydrogen bonding, complexation.
Quinoneimines are nitrogen anologs of quinones and,
hence, reactions of quinoneimines with hydroquinones
proceed analogously to the reactions of quinones with
hydroquinones. In this case, one of the components
(quinoneimine or quinone) is reduced due to the oxidaꢀ
tion of the second component (hydroquinone). In aprotic
organic solvents (chlorobenzene) quinoneimines react
with hydroquinones via the chain mechanism.1,2 It has
recently3,4 been confirmed experimentally that in the genꢀ
eral case these reactions are chain reversible processes.5
This implies that the equilibrium can be achieved via the
chain route from the side of both the reactants and proꢀ
ducts and in equilibrium the forward and backward chain
reactions have equal rates.
nes and, therefore, the observed effect of the medium on
the equilibrium constant of the overall reaction evidences
for the dependence of the redox reactivity of the semiꢀ
quinone radicals on the solvation effects. These data are
important for understanding of the mechanism of action
of lipidꢀsoluble bioantioxidants of the quinone type
(ubiquinones, K group vitamins).7
In the present work, we studied the effect of the solꢀ
vent nature on the equilibrium constant of one of the
reversible chain reactions in a quinoneimine—hydroꢀ
quinone system, namely, the reaction of N,N´ꢀdiphenylꢀ
1,4ꢀbenzoquinonediimine (1) with 2,5ꢀdichlorohydroꢀ
quinone (2), whose chain mechanism has been estabꢀ
lished earlier.6
The reversible character of the chain reactions of
quinoneimines with hydroquinones is caused by a small
change in the free energy during these reactions. They are
characterized by equilibrium constants K low in absolute
values, which can reliably be measured experimentally.
The available data indicate that the K values are very
sensitive to the reactant structure.2,5,6 It could be assumed
that the K values also depend on the solvent nature. No
experimental research in this area was carried out, alꢀ
though these data are of doubtless interest. This is exꢀ
plained by the fact that the semiquinone radicals are inꢀ
volved in the reactions of quinoneimines with hydroquinoꢀ
Experimental
Compound 1 was synthesized by the oxidation of N,N´ꢀ
diphenylꢀ1,4ꢀphenylenediamine Ph—NH—C6H4—NH—Ph (3)
with PbO2.2 Compound 1 was purified by liquid chromatograꢀ
phy on SiO2 (benzene with additives of chloroform (5%) as
eluent) and recrystallization from methanol. Compound 3 (anaꢀ
lytically pure grade) was purified from mechanical and strongly
polar admixtures by passing a solution of compound 3 (in a
concentration close to saturation) in a benzene (95%) + chloroꢀ
form (5%) mixture through a column (10×2.5 cm) packed with
silica gel L (Chemapol, 40—100 µm). The eluate was evaporated
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 12, pp. 2296—2302, December, 2007.
1066ꢀ5285/07/5612ꢀ2376 © 2007 Springer Science+Business Media, Inc.

Solvent effect on chain reversible reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007 2377
at room temperature by ∼95%, the crystals were separated,
washed with benzene, and dried in vacuo. Sample 3 was recrysꢀ
tallized from a mixture of methanol with chloroform (3—5%)
and then from toluene.
Table 1. Corrections for the thermal expansion (β ) of solvents
at temperatures 298—383 K*
T
298
Solvent
β
T = VspT/Vsp
2,5ꢀDichloroquinone (4) (Aldrich) was purified by double
sublimation in vacuo. A portion of purified quinone 4 was used
for the synthesis of hydroquinone 2 by reduction with sodium
dithionite Na2S2O4 according to an earlier described proceꢀ
dure.8 After the synthesis hydroquinone 2 was purified by reꢀ
crystallization from methanol and then from toluene.
321
343
364
383
Benzene
СCl4
Benzonitrile**
Chlorobenzene
Anisole
1.029
1.030
1.023
1.023
1.022
1.059
1.060
1.043
1.045
1.045
—
—
1.064
1.068
1.067
—
—
1.085
1.090
1.088
Special attention was given to the purity of solvents because
of a prolong duration of experiments and small reactant concenꢀ
trations. At the initial stages, the solvents were purified accordꢀ
ing to commonly accepted procedures9,10 and then using the
treatment with tetraphenylhydrazine, distillation, and passing
through a column with a special packing.6 In the case of anisole
and benzonitrile, N,N´ꢀdiphenylꢀ1,4ꢀphenylenediamine (3)
(∼150 mg L–1) was added to the solvents purified according to
standard procedures, and the mixtures were heated to ∼370 K.
After 15—20 min Ar was bubbled through the hot solvent, disꢀ
placing air completely. During this procedure the solvents were
orangeꢀcolored due to quinonediimine 1, which was formed
from compound 3 in the reactions with oxidizing admixtures
and due to the oxidation of compound 3 with air oxygen. Then
the solvent was distilled in an Ar atmosphere in a vacuum of a
waterꢀjet pump in the presence of a 1 + 3 mixture. Owing to the
presence of the latter, residues of both oxidizing and reducing
admixtures were removed from the solvents during distillation.
Compounds 3 (∼2 mg L–1) were added again to the obtained
solvents, the mixtures were heated, air was replaced by argon,
and the mixtures were heated and again distilled in an Ar atmoꢀ
sphere under reduced pressure. The bottom residues had only a
slight orange shade, indicating a very low content of compound 1.
The spectrophotometric method was used to determine the
equilibrium constants. The experiments were carried out in a
temperatureꢀcontrolled quartz cell, being a bubblingꢀtype reacꢀ
tor (volume 6.0 mL, optical path length 2.0 cm), builtꢀin into a
Specord UV—Vis spectrophotometer. The consumption or acꢀ
cumulation of quinonediimine was continuously monitored by
its absorption in the visible region at one of the following waveꢀ
lengths: λ/nm: 449 (band maximum), 500, or 526 (ν = 22260,
20000, or 19000 cm–1, respectively), depending on the concenꢀ
tration. Usually the experiments were started at T = 298 K, and
we waited for the equilibration of the system. Then the temperaꢀ
ture was increased to a new specified value, the experiment was
continued to equilibration at the new temperature, etc. Since
the experiments were prolong, the intensity of Ar bubbling was
sharply decreased ∼15 min after the beginning of the experiment
at T = 298 K to decrease the error due to solvent evaporation.
When calculating the K equilibrium constant, the correction
* At T = 298 K βT = 1 for all solvents.
** Calculated by the formula βT = 1 + 0.001(T – 298).
Table 2. Molar absorptivities (ελT) of quinonediimine 1 at temꢀ
peratures 298—383 K
Solvent
λ/nm
ε
λ(1)/L mol–1 cm–1
T
298
321
343
364
383
Benzene
449
500
526
449
449
500
526
7133 6993 6928
3842 3714 3630
1567 1531 1517
7096 6953 6833
6831 6677 6542 6401 6280
3767 3688 3634 3591 3533
1617 1633 1652 1635 1654
—
—
—
—
—
—
—
—
ССl4
Benzonitrile
Chlorobenzene 449
7025 6881 6726 6598
3919 3845 3755 3686
1763 1708 1690 1710
—
—
—
500
526
Anisole
449
500
526
6792 6634 6534 6422 6312
3692 3602 3554 3487 3428
1517 1363 1389 1383
Results and Discussion
The reaction of quinonediimine 1 with hydroquinone
2 is presented in Scheme 1.
Scheme 1
for thermal expansion (β ) of the solvent was taken into account
T
(Table 1). The temperature dependences of specific volumes
(Vsp) of the solvents were determined from the data11 on their
densities.
The experimental molar absorptivities of quinonediimine 1
at the experimental temperature were calculated using the formula
ε
λ(1) = DTλ(1)expβ /([1]0298l),
(1)
T
T
where l is the cell thickness. The results obtained are given in
Table 2.

2378
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007
Gadomsky and Varlamov
D449
1.2
Table 3. Effective molar absorptivities of
the complex of quinone 4 with anisole
based in the analytical concentration of
quinone 4 at λ = 449 (I) and 500 nm (II)
4
3
2
T/K
(ελT eff/L mol–1 cm–1
)
0.8
0.4
1
1
b
a
I
II
4
3
298
321
343
364
383
438
392
352
317
280
90
74
65
61
50
2
0
50
100
t/min
If the equilibrium is achieved from the side of the
backward reaction 3 + 4, then
Fig. 1. Changes in absorbance at λ = 449 nm during equilibraꢀ
298
tion in chlorobenzene: from the forward reaction 1 + 2 ([1]0
=
= 9.12•10–5 mol L–1, [2]0298 = 2.70•10–4 mol L–1) in the presꢀ
ence of the initial additive of 3 ([3]0298 = 7.20•10–3 mol L–1) (a)
[3]Te [4]Te ([3]2098 − β [1]Te )([4]2098 − β [1]Te )
T
T
.
(3)
K =
=
298
298
and from the the backward reaction 3 + 4 ([3]0 = [4]0
=
[1]Te [2]Te
β [1]Te ([2]2098 + β [1]Te )
T
T
= 3.60•10–4 mol L–1) (b). The limiting absorbance values at
equilibration at 298 (1), 321 (2), 343 (3), and 364 К (4). Argon
bubbling, cell thickness 2.0 cm.
The results obtained are given in Table 4. The solvent
nature strongly affects K: when CCl4 is substituted for
benzene, at T = 298 K the equilibrium constant increases
from 13.6 to 140, i.e., by an order of magnitude. On the
contrary, the temperature exerts a weak effect on K. This
could be expected on the basis of a complex chain reacꢀ
tion mechanism. The linear dependence of the averaged
equilibrium constants on the inverse temperature is preꢀ
sented in Fig. 2. Based on these data, the thermodynamic
parameters of the reaction were determined
The results of experiments on equilibration from the
sides of the forward and backward reactions in chlorobenꢀ
zene are presented in Fig. 1. When calculating the K
equilibrium constant, it was taken into account that the
initial concentrations of the substances were specified at
T0 = 298 K, and at higher T temperatures the concentraꢀ
tions decreased due to the thermal expansion of the solꢀ
vent, for instance, [2]T = [2]2980/βT. The equilibrium
lnK = ∆S/R – ∆H/(RT),
0
concentrations of quinonediimine [1]T were determined
e
and presented in Table 5. As can be seen from the data in
Fig. 3, in aromatic solvents ∆H and ∆S are related by a
experimentally from the absorbance and molar absorptivꢀ
ity calculated by Eq. (1).
In all chosen solvents, except for anisole, the absorꢀ
bance of quinone 4 could be neglected at all analytical
wavelengths (ε ≈ 20 L mol–1 cm–1 at λ = 449 nm).
A chargeꢀtransfer complex between quinoline 4 and the
solvent is formed in anisole. In this case, a rather intense
absorption band of the complex appears in the visible
region (λmax ∼400 nm). This band is overlapped with the
absorption band of quinonediimine 1. Therefore, necesꢀ
sary corrections were applied for the calculation of the
composition of equilibrium reaction mixture. The effecꢀ
tive molar absorptivity of the complex based on the anaꢀ
lytical concentration of quinone 4 is given in Table 3.
If the absorbance of quinone 4 could be neglected, the
K equilibrium constant was determined by the formula
lnK
4
5
4.8
3
4.0
2
3.2
1
2.4
0.0027
0.0030
0.0033
T
–1/K–1
[3]Te [4]Te
[1]Te [2]Te
K =
=
Fig. 2. Temperature dependence of the equilibrium constants of
the reversible reaction of quinonediimine 1 with hydroquinone 2
in the lnK—T–1 coordinates when using CCl4 (1), benzonitrile
(2), chlorobenzene (3), benzene (4), and anisole (5) as solvent.
.
(2)
([3]2098 + [1]2098 − β [1]Te )([4]2098 + [1]2098 − β [1]Te )
T
T
=
β [1]Te ([2]2098 − [1]2098 + β [1]Te )
T
T

Solvent effect on chain reversible reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007 2379
Table 4. Experimental data on the temperature dependence of the equilibrium rate constant in different
solvents
С*•105/mol L–1
K at various T/K
1
2
3
4
298
321
343
364
СCl4
9.00
9.00
—
9.02
—
27.0
9.00
—
27.1
—
180
113
45.0
359
31.7
45.0
127
—
—
45.0
—
31.7
45.0
—
11.8
15.7
14.5
13.9
13.8
10.9
13.9
13.5
13.4
13.5
10.1
12.0
12.7
13.0
13.2
—
—
—
—
—
—
—
—
9.02
36.0
27.0
12.8
12.4
11.9
11.9
11.0
11.5
Average
13.6 1.3
12.7 1.1
11.9 1.1
Benzonitrile
9.00
8.45
—
9.00
45.2
—
27.0
33.2
—
27.0
45.0
—
540
332
72.0
—
—
36.0
360
—
—
72.0
540
180
36.0
31.2
26.2
33.5
30.6
24.6
26.8
23.6
30.6
28.2
23.2
27.8
22.1
23.5
20.7
28.3
26.1
20.0
24.9
18.9
29.4
37.8
33.1
26.4
35.7
30.9
26.0
9.00
27.00
28.8
Average
31.9 4.4
29.0 3.4
26.0 3.1 23.2 3.5
Chlorobenzene
9.00
9.00
9.00
—
—
9.00
45.0
27.0
9.00
27.0
—
—
27.0
45.0
450
126
540
36.0
54.0
720
180
—
—
—
36.0
54.0
—
82.8
59.0
84.8
65.0
69.3
70.7
64.5
53.4
67 10
46.3
63.2
48.0
52.1
52.7
49.2
42.0
37.0
48.3
38.7
41.4
42.1
39.5
35.3
116
92.5
94.2
97.1
87.6
74.9
—
Average
92 13
50
7
40 4
Benzene
9.00
9.00
9.00
9.00
9.82
0.00
45.0
45.0
9.00
9.00
27.0
9.00
29.5
0.00
45.0
45.0
900
225
720
0.00
0.00
90.0
—
0.00
0.00
0.00
900
589
90.0
540
139
133
126
152
136
134
139
160
91.4
84.1
80.7
96.0
89.2
83.9
84.5
105
62.9
56.2
55.7
62.6
65.1
—
61.2
73.1
—
—
—
—
—
—
—
—
—
90.0
Average
140 11
89.4 8.0
62.4 5.9
Anisole**
9.00
9.00
9.00
9.00
—
9.00
18.0
27.0
9.00
—
—
—
—
—
—
73.8
—
139
115
117
133
—
91.7
83.5
85.4
95.5
74.2
65.9
63.2
64.9
65.0
59.9
50.6
45.5
48.9
50.1
48.8
50.2
43.8
180
540
450
73.8
540
14.4
28.8
—
70.0
Average
126 12
83.4 9.8
62.0 5.8 48.0 2.6
* Initial concentrations of the reactants at T = 298 K.
** At 383 K K = 40.7 and 34.7 at the initial concentration of compounds 3 and 4 equal to 73.8•10–5 and
compound 3 equal to 540•10–5 mol L–1, respectively (Kav = 37.7 4.3).

2380
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007
Gadomsky and Varlamov
Table 5. Thermodynamic parameters of the reaction of quinoꢀ
nediimine 1 with hydroquinone 2
To estimate the contribution of complexation to the
thermodynamics of the reaction, we considered the reacꢀ
tion in the simplest form
Solvent
∆S
–∆H –∆G = RTlnK298
av
4 + Solv
4...Solv (KSolv),
/J mol–1 K–1
kJ mol–1
where Solv is anisole. At [Solv] >> [4]0 the following
equations are valid:
СCl4
13.3 0.03
14.4 1.1
–0.2 0.05
–10.2 0.5
–5.3 1.0
2.5 0.1
4.3 0.1
11.3 0.1
15.3 0.2
13.6 0.3
6.5
8.6
11.2
12.2
12.0
Benzonitrile
Chlorobenzene
Benzene
KSolv [Solv][4]0
,
(4)
(5)
[4...Solv]e =
KSolv [Solv]+1
Anisole
KSolv [Solv][4]0
KSolv [Solv]+1
Dλ = (ελl)
,
distinct linear dependence. The data for CCl4 do not fall
on this plot and are much closer to the parameters of the
reaction in polar benzonitrile than in nonpolar benzene.
This indicates, most likely, that the nature of solvation
interactions in CCl4 and aromatic solvents differs subꢀ
stantially.
1
Dλ
1
1
=
+
.
(6)
(ελl)[4]0
(ελl)KSolv [4]0[Solv]
According to Eqs (5) and (6), two series of experiꢀ
ments were carried out at T = 298 K, and each series the
anisole concentration was measured at [4]0 = const. Deꢀ
cane was used as the inert solvent. The obtained depenꢀ
dences of the absorption intensity of the complex on the
anisole concentration are shown in Fig. 4, and their rectiꢀ
fication in the coordinates of Eq. (6) is shown in Fig. 5.
Based on these data, we calculated the KSolv(298) and ε500
values given below (average values (6.8 1.0)•102 L mol–1 and
246 39 L mol–1 cm–1, respectively).
As mentioned above, quinone 4 forms a complex with
anisole. The formation of donorꢀacceptor complexes with
electronꢀreleasing molecules is characteristic of quinoꢀ
nes, especially for quinones with electronꢀwithdrawing
substituents in the cyclohexadiene ring.12—14 The comꢀ
plex formation is visually manifested by the fact that soluꢀ
tions of quinone 4 in anisole are brightly yellow—orange
rather than weakly yellowish as in other solvents. Soluꢀ
tions of quinone 4 in decane are almost colorless:
λmax ∼330 nm, ε330 = 230 L mol–1 cm–1. The absorption
of quinone 4 in anisole has λmax ≈ 400 nm and the effective
molar absorptivity (based on the analytical concentration
of 4) ε400 ≈ 670 L mol–1 cm–1. The formation of a comꢀ
plex of 4 with anisole is an exothermic process decreasing
the apparent enthalpy and entropy values of the reaction
of quinonediimine with 2,5ꢀhydroquinone.
[4]•104
/mol L–1
4.5
KSolv(298)•102
/L mol–1
6.6 1.3
ε
500
/L mol–1 cm–1
252 36
16.8
7.0 0.6
241 16
Using the determined KSolv(298) value, we obtained the
ratio [4...Solv]e/[4]0 = 0.38 using Eq. (4), i.e., in anisole
at T = 298 K ∼40% quinone 4 exist as a complex with the
solvent.
∆D500
∆H/kJ mol–1
1
0.3
2
2
–4
–8
0.2
3
1
0.1
0
–12
–16
5
4
∆S/J mol–1 K–1
0
2
4
6
[Solv]/mol L–1
–10
0
Fig. 3. Plots of the enthalpy (∆H) vs entropy (∆S) of the reversꢀ
ible reaction of quinonediimine 1 with hydroquinone 2 in
CCl4 (1), benzonitrile (2), chlorobenzene (3), benzene (4), and
anisole (5).
Fig. 4. Influence of the anisole (Solv) concentration on the
absorbance of the complex at λ = 500 nm (∆D500); T = 298 K,
cell thickness 2.0 cm, and concentration of compound 4:
4.5•10–4 (1) and 16.8•10–4 mol L–1 (2).

Solvent effect on chain reversible reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007 2381
–1
(∆D500
)
effect of the reaction under study and, hence, the comꢀ
plexation of 4 with anisole contributes substantially to the
experimental enthalpy of the reaction of 1 with 2 in this
solvent.
1
60
The solvation effects (enthalpy of the reaction ∆Н) in
benzonitrile, anisole, and benzene are determined to a
great extent by the thermal effect of formation of hydroꢀ
genꢀbonded complexes of hydroquinone 2 with the solꢀ
vent molecules as proton acceptors. This follows from the
data in Fig. 6 showing the dependence of the experimenꢀ
tal ∆Н values of the reaction on the estimated values of
40
20
0
2
the enthalpy of formation of the Hꢀcomplex (∆Hbond
)
between the solvent and hydroquinone 2. The estimates
of ∆Hbond were obtained in the framework of the multipliꢀ
cative approach to the thermodynamics of hydrogen bondꢀ
ing.15,16 In this method, the following formula was used
0.4
0.8
1.2 [Solv]–1/L mol–1
Fig. 5. Processing of the experimental data (see Fig. 4) in the
coordinates of Eq. (6).
for the calculation of ∆Hbond
:
The intensity of the absorption band of the 4...Solv
complex decreases strongly with the temperature rise. The
temperature effect on ελ is much stronger than that in the
case of quinonediimine 1 when the absorption intensity
decreases mainly because of dilution due to the thermal
expansion of the solvent. The decrease in the absorption
band intensity of the complex with the temperature rise is
mainly caused by a decrease in the concentration of the
complex because of its thermal instability.
Using the temperature dependences of D500 of quinoꢀ
ne 4 solutions in anisole under the assumption that ε500 is
temperatureꢀindependent being 246 L mol–1 cm–1, we
obtained a tentative estimate of the enthalpy of formation
∆Hbond (kJ mol–1) = 4.96EaEd,
where Ea and Ed are the enthalpy factors of the Hꢀaccepꢀ
tor (a) (solvent) and Hꢀdonor (d) (hydroquinone 2), reꢀ
spectively. The Ea and Ed factors characterize the relative
ability to Hꢀbonding formation with respect to the stanꢀ
dard substances, namely, unsubstituted phenol
(Ed = –2.50 kJ0.5 mol–0.5) and hexamethylphosphotriaꢀ
mide (Ea = 2.50 kJ0.5 mol–0.5). For other compounds the
Ea and Ed values determined from the experimental data
are tabulated.15,16 For CCl4 Ea = 0 (by definition), and
for benzene, chlorobenzene, anisole, and benzonitrile
Ea = 0.66, 0.30, 1.00, and 1.19 kJ0.5 mol–0.5, respectively;
the protonꢀdonating ability of hydroquinone 2 being Ed =
of a complex of quinone 4 with anisole. For this purpose
= 1.98•10–3
298
–2.60 kJ0.5 mol–0.5 16
.
we used the data for the solution: [4]0
mol L–1. The KSolv(T) value was calculated by the formula
∆H/kJ mol–1
β [4...Solv]e
T
,
KSolv(T)
=
[Solv]298(1.98 ⋅10−3 − [4...Solv]e )
1
–4
and [Solv]298 = 9.16 mol L–1. The results of calculations
are presented below.
2
5´
–8
T/K
[4...Solv]e•105
/mol L–1
7.54
KSolv(T)•102
/L mol–1
6.72
3
298.2
321.5
343.7
364
–12
6.50
5.52
4.86
5.45
4.41
3.79
b
a
5
4
–16
–16
Based on these data, we derive the dependence of
lnKSolv(T) on T–1
–12
–8
∆Hbond/kJ mol–1
3 + 4 vs enthalpy
Fig. 6. Plots of ∆Н of the reaction 1 + 2
lnKSolv(T) = –(5.89 0.08) + (954 27)T–1
from which
,
of hydrogen bonding of hydroquinone 2 with various solvents: 1,
CCl4; 2, benzonitrile; 3, chlorobenzene; 4, benzene; 5, anisole
(experimental value); 5´, with allowance for the enthalpy of
formation of a donorꢀacceptor complex of quinone 4 with aniꢀ
sole (–7.9 kJ mol–1); а is the parabolic curve y = 0.205x2 +3.37x
– 2.03 approximating all experimental points, and b is the paꢀ
rabola y = 0.198x2 +3.18x – 2.35 constructed ignoring the data
on ∆Н of the reaction in anisole.
∆H ≈ –7.9 0.2 kJ mol–1
.
Although the obtained estimate of ∆H is only tentaꢀ
tive, it is rather high and comparable with the thermal

2382
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 12, December, 2007
Gadomsky and Varlamov
As can be seen from the data in Fig. 6, the experimenꢀ
tal data are described by a parabolic function, especially if
the results of measurements in anisole are omitted (cf.
parabolas a and b in Fig. 6). The vertex of the parabola
lies near the values for benzene. The left descending
branch contains the values for benzonitrile and anisole
(in these solvents the heteroatoms of the substituents are
proton acceptors16), and the right ascending branch inꢀ
cludes the values for chlorobenzene (in which, as in benꢀ
Note that the plots of lnK298 vs dielectric functions
(lnε, 1/ε, Kirkwood´s function (ε – 1)/(2ε + 1)) are also
nonlinear and qualitatively resemble the dependence of
lnK298 on DN. It is seen from the data in Fig. 7 that in a
rough approximation one can speak about a weak linear
dependence of lnK298 on AN for the aromatic solvents,
whereas no linear dependence of lnK298 on DN is obꢀ
served for these solvents. The data for CCl4 deviate strongꢀ
ly from the both dependences. This agrees with the asꢀ
sumption on a substantial difference in the mechanisms
of solvation of participants of equilibrium in CCl4 and
aromatic solvents (see Fig. 3).
Thus, this study revealed that the solvent nature exerts
rather strong effect on the equilibrium constant and therꢀ
modynamic parameters of the chain reversible reaction of
quinonediimine 1 with hydroquinone 2. The solvation
effects are caused by several types of intermolecular interꢀ
actions of participants of equilibrium with the medium.
The results obtained indicate that the reactivity of the
semiquinone radicals depends on the solvation interacꢀ
tions with the solvent and indicate a possibility of the
existence of a strong dependence of the rate constants of
elementary steps of chain reversible reactions in quinoneꢀ
imine—hydroquinone systems on the solvent nature.
zene, a system of πꢀelectrons is the proton acceptor16
)
and CCl4 (in the multiplicative approach, CCl4 was acꢀ
cepted as the standard "nonꢀsolvating" solvent). The deꢀ
pendence of ∆H on ∆Hbond for the series of solvents benꢀ
zonitrile—anisole—benzene agrees with the assumption
that in the case of relatively strong hydrogen bonding the
reaction enthalpy ∆Н depends mainly on the heat of forꢀ
mation of the Hꢀcomplex of hydroquinone 2 with the
solvents (∆Нbond).
The reaction of 1 with 2 proceeds via the mechanism
of chain reversible reactions. The K equilibrium constant
of these reactions is equal to the product of the equilibriꢀ
um constants of the both chain propagation steps,4 i.e.,
the K value is determined by the rate constants of four
elementary reactions. Therefore, it is not surprising that
no simple correlations are observed between lnK and paꢀ
rameters of the solvents. This is exemplified in Fig. 7 by
the plots of lnK298 vs donor (DN) and acceptor (AN)
numbers of the solvents. The DN values were borrowed
from Ref. 17, and AN were calculated* using the known18
ET parameters by the formula17
This work was financially supported by the Division of
Chemistry and Materials Science of the Russian Acadeꢀ
my of Sciences (Program No. 1 "Theoretical and Experiꢀ
mental Investigation of the Chemical Bond Nature and
Mechanisms of Most Important Chemical Reactions and
Processes") and the Project "Development of Mechanisms
of Integration of the Bashkir State University, the Instiꢀ
tute of Organic Chemistry (Ufa Research Center of the
Russian Academy of Sciences), and the Institute of
Problems of Chemical Physics (Russian Academy of
Sciences)."
AN = –40.52 + 1.29ET.
lnK298
4d
References
5
5d
4a
5a
3d
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Chem., 2006 (Engl. Transl.)].
3a
AN
4
3
2a
2d
DN
1a
1d
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0
4
8
12 AN, DN
Fig. 7. Plots of lnK298 vs donor (DN) and acceptor (AN) numbers
of the solvents: 1, CCl4; 2, benzonitrile; 3, chlorobenzene;
4, benzene; 5, anisole.
* No reliable data on the AN values are available for CCl4.

Solvent effect on chain reversible reaction
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Received April 18, 2007