Rate constants of elementary steps of the reversible chain reaction of N-phenyl-1,4-benzoquinonemonoimine with 2,5-dichlorohydroquinone

Article abstract of DOI:10.1007/s11172-007-0133-x

The kinetics of reversible chain reactions in quinoneimine-hydroquinone systems has first been studied for the reaction of N-phenyl-1,4- benzoquinonemonoimine with 2,5-dichloro-hydroquinone used as an example. The dependences of the reaction rate on the concentration of the initial reactants, initiator, and each product were studied. The reliable estimates of the rate constants of 11 (of 12) elementary steps of this reaction were obtained from the experimental data using the earlier derived formulas and the method of equal concentrations developed in the present work.

Full text of DOI:10.1007/s11172-007-0133-x

Russian Chemical Bulletin, International Edition, Vol. 56, No. 5, pp. 883—889, May, 2007
883
Rate constants of elementary steps of the reversible chain reaction
of Nꢀphenylꢀ1,4ꢀbenzoquinonemonoimine with 2,5ꢀdichlorohydroquinone
A. V. Antonov and V. T. Varlamovꢀ
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 kinetics of reversible chain reactions in quinoneimine—hydroquinone systems has first
been studied for the reaction of Nꢀphenylꢀ1,4ꢀbenzoquinonemonoimine with 2,5ꢀdichloroꢀ
hydroquinone used as an example. The dependences of the reaction rate on the concentration
of the initial reactants, initiator, and each product were studied. The reliable estimates of the
rate constants of 11 (of 12) elementary steps of this reaction were obtained from the experimenꢀ
tal data using the earlier derived formulas and the method of equal concentrations developed in
the present work.
Key words: Nꢀphenylꢀ1,4ꢀbenzoquinonemonoimine, 2,5ꢀdichlorohydroquinone, semiꢀ
quinone radicals, reversible chain reactions, kinetics, mechanism, elementary steps, reaction
rate constants.
the final purification was carried out by liquid chromatography
on SiO2 (Chemapol) using ether—hexane mixtures as eluent.
NꢀPhenylꢀ1,4ꢀbenzoquinonemonoimine (1) was synthesized
by the oxidation of compound 2 using PbO2 in a glass column
(5×0.8 cm) packed with PbO2 through which an ethereal soluꢀ
tion of compound 2 was slowly passed. Sample 1 was purified by
preparative LC on SiO2 (ether—hexane mixture as eluent) and
recrystallized from methanol.
2,5ꢀDichloroquinone (4, Aldrich) was purified by double
sublimation in vacuo. A portion of purified sample 4 was used for
the synthesis of hydroquinone 3 by the reduction of dichloroꢀ
quinone 4 by Na2S2O4 using an earlier described procedure,7
and hydroquinone 3 was twice recrystallized from methanol.
The initiator tetraphenylhydrazine Ph2N—NPh2 (5) as the
source of diphenylaminyl radicals Ph2N• (5•) was synthesized
according to the Wieland method by the oxidation of diphenylꢀ
amine with KMnO4 in acetone.8 The initiation rate constant of
this initiator is ki = 2ekdecomp, where e = 0.95 is the probability of
radicals 5• escape into the bulk, and the rate constant of decomꢀ
Quinoneimines are nitrogen analogs of quinones and,
hence, the reactions of quinoneimines with hydroquinones
are model in investigation of the interaction of quinones
with hydroquinones. Therefore, the study of the kinetics
and mechanism of reversible chain reactions in quinoneꢀ
imine—hydroquinone systems is urgent for chemistry and
biology, because facilitates understanding of the mechaꢀ
nism of action of lipidꢀsoluble bioantioxidants of the
quinone type (ubiquinones, vitamins K).1
The chain mechanism of the reactions in quinoneꢀ
imines with hydroquinones was determined for the first
time for the reaction of Nꢀphenylꢀ1,4ꢀbenzoquinoneꢀ
monoimine (1) with 2,5ꢀdiꢀtertꢀbutylhydroquinone.2,3
The study of the kinetics of this reaction in the presence
of one of the products, viz., 4ꢀhydroxydiphenylamine (2),
gave evidence that the reactions in the quinoneꢀ
imine—hydroquinone systems is a reversible chain proꢀ
cess.4 This conclusion has recently5 been confirmed exꢀ
perimentally for the reaction of quinoneimine 1 with
2,5ꢀdichlorohydroquinone (3). The equation for the iniꢀ
tial rate was derived from a kinetic analysis of the mechaꢀ
nism of these reversible chain reactions,6 which enables
the purposeful systematic study of the kinetic regularities
of the reactions and determination of the rate constants of
elementary steps from the experimental data. In the
present work, such a study was carried out for the first
time for the reaction of quinoneimine 1 with hydroꢀ
quinone 3.
position of initiator 5 in chlorobenzene at 298.2 K is kdecomp
2.06•10–7 s–1 3
=
.
The criterion of purity of all reagents used was the abꢀ
sence or a negligible intensity of peaks of admixtures on the
liquid chromatograms of the samples with UV detection at
λ = 290 nm.
Chlorobenzene (Fluka) thoroughly purified from admixtures
according to an earlier described procedure9 was used as a solvent.
The reaction kinetics was studied at 298.2 0.1 K in a temꢀ
peratureꢀcontrolled quartz cell (reactor) of the bubbling type
(volume 8.5 mL, optical path length l = 2.0 cm, argon bubbling)
embedded in a Specord UV—Vis spectrophotometer. The absorꢀ
bance at λ = const = 449.2, 500, or 526.3 nm (ν = 22260, 20000,
or 19000 cm–1), depending on the initial concentration of 1 was
continuously detected during experiment. Dichloroquinone 4
also absorbed weakly in this region, which was taken into acꢀ
count by introduction of the corresponding corrections.
Experimental
Compound 2 (analytically pure grade) was recrystallized
from methanol and then from a heptane—toluene mixture, and
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 5, pp. 849—855, May, 2007.
1066ꢀ5285/07/5605ꢀ0883 © 2007 Springer Science+Business Media, Inc.

884
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
Antonov and Varlamov
The quantitative regularities of the reaction of compound 1
tion of 1 in the backward reaction of compounds 2 and 4
in experiments with equimolar concentrations of the reꢀ
actants are shown in Fig. 1. The data show the acceleratꢀ
ing effect of additives of initiator 5 on the forward and
backward reactions, indicating the chain mechanism of
the both reactions.
with 3 were studied by the initial rates of consumption of
quinoneimine 1 (w1). To determine the numerical w1 values, the
initial regions of the experimental curves were processed by the
empirical equation
[1] = a[1 – bexp(–ct)],
The mechanism of the reaction of compounds 1 and 3
is presented as kinetic Scheme 2.2,6
where a, b, and c are the parameters chosen by an iteration
method. In this case, w1 = abc.
Scheme 2
Results and Discussion
5
5•
5
H + 6• [7•]
(i)
(1), (–1)
(2), (–2)
(3), (–3)
(4), (–4)
(5), (–5)
(6), (–6)
The stoichiometric equation for the reaction of comꢀ
pounds 1 and 3 are presented in Scheme 1.
1 + 3
7• + 6•
7• + 4
2 + 6•
1 + 2
1 + 6•
7• + 3
7• + 7•
7• + 6•
6• + 6•
Scheme 1
2 + 4
3 + 4
In this scheme, 5H designates diphenylamine Ph2NH,
6• are 2,5ꢀdichloroꢀ4ꢀhydroxyphenoxyl semiquinone
radicals, and 7• are radicals formed from quinoneimine 1
(or from 4ꢀhydroxydiphenylamine 2) by H atom addition
to molecule 1 (or by H atom abstraction from molecule 2).
•
These can be both 4ꢀhydroxydiphenylaminyl 7N and
4ꢀanilinophenoxy radicals 7O•, the difference between
which is not considered for simplicity.*
The kinetic curves of quinoneimine 1 consumption in
the forward reaction with hydroquinone 3 and accumulaꢀ
[1]•104/mol L–1
2
1´
1″
1
2
1
2″
2´
The equation for the initial reaction rate has the folꢀ
lowing form6:
w1 = [1/(1 + λ)][λ(w1 + w–4) – (w–5 + w–6 + 0.5wi)] +
0
0.5
1.0
1.5
t•10–4/s
+
,
(I)
Fig. 1. Kinetic curves of consumption of quinoneimine 1 (2•10–4
mol L–1) in the forward reaction with hydroquinone 3 (2•10–4
mol L–1) (1, 1´, 1″) and accumulation of quinoneimine 1 in
the backward reaction of 2 (2•10–4 mol L–1) and 4 (2•10–4
mol L–1) (2, 2´, 2″). Acceleration of the forward and backward
reactions in the presence of initiator 5 with wi•1010 = 0 (1, 2);
1.17 (1´, 2´); 7.05 mol L–1 s–1 (1″, 2″). Chlorobenzene, 298.2 K,
Ar bubbling.
where λ = (k–2[4] + k3[3])/(k2[1] + (k–3[2]), and wj are
the rates of the corresponding steps in Scheme 2. Equaꢀ
* In chlorobenzene at T =298.2 K the molar fraction of radiꢀ
cals 7O x = 0.967, and the molar fraction of radicals 7N is
1 – x = 0.033.10
•
•

Kinetics of reversible chain reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
885
2
w1 •1016/mol2 L–2 s–2
tion (I) was obtained under assumption that the disproꢀ
portionation rate constants of the radicals differ slightly,
i.e., k4 ≈ k–1 ≈ k5 ≈ k6 ≈ kt.
2
8
Equation (I) contains two terms. The first of them
takes into account the consumption of quinoneimine 1 in
the steps of chain initiation and free radical formation,
and the second term is equal to the rate of its consumpꢀ
tion in the chain reaction. If the chains are rather long,
the first term can be neglected. In this case, the expresꢀ
sion for the initial reaction rate has the form
6
4
2
1
w1 =
•
0
1
2
w•109/mol L–1 s–1
2
Fig. 2. Plots of w1 vs. wi at low concentrations of comꢀ
pounds 1 (•104) and 3 (•104), mol L–1: 2.0 and 2.0 (1); 2.0 and
4.0 (2), respectively. Chlorobenzene, 298.2 K, Ar bubbling.
•
.
(II)
Effect of the initiator on the initial reaction rate. Acꢀ
cording to formula (II), in the presence of the initiator
2
w1 •1014/mol2 L–2 s–2
8
w1 =
3
or in the form more suitable for experimental verification,
4
2
w1
=
+
2
1
0
2
4
wi•109/mol L–1 s–1
+
.
(III)
Fig. 3. Dependence of the squared initial reaction rate on
the initiator concentration. Initial concentrations of comꢀ
pounds 1 (•104) and 3 (•103), mol L–1: 2.0 and 1.0 (1); 2.0 and
1.2 (2); 10.0 and 1.2 (3), respectively.
According to Eq. (III), linear plots should be observed
in the coordinates w1 —wi. The ratio of the sections cut in
2
the ordinate to the slope ratio is 2k1[1][3], from which k1
can be determined at the known [1] and [3] values.
The results of studying the reaction in the presence of
initiator 5 are presented in Figs 2 and 3. At low concenꢀ
concentration of another reactant are shown in Figs 4
and 5. They are nonlinear, and the humps of the curves
w1 = f [1] at [3]0 = const look up (see Fig. 4), while those
of the curves w1 = f [3] at [1]0 = const look down (see
2
trations of compounds 1 and 3, linear dependences of w1
on wi are not fulfilled (see Fig. 2). With increasing [3]0,
i.e., when the equilibrium state shifts toward the prodꢀ
ucts, the plots of w1 vs. wi become closer to linear (see
2
Table 1. Results of approximation of the dependence of w1
on wi by the empirical dependence w12 = a + b[1 – exp(–cwi)]
2
k1***•103
Fig. 2). To obtain quantitative results, the data in Figs 2
and 3 were approximated by the empirical function
w1 = a + b[1 – exp(–cwi)], according to which the
[1]
[3]
Cut section*
Slope**
104 mol L–1
2
intersept in the ordinate equals a and the slope ratio at
wi → 0 is bc. The results obtained are given in Table 1.
It is seen that only a rough estimate of k1 can be
obtained from experiments in the presence of the iniꢀ
tiator.
Dependence of the initial reaction rate on the reactant
concentrations. Ratio between the reaction rate constants k2
and k3. The results of studying the dependence of w1 on
the concentration of one of the reactants at a constant
2.0
2.0
2.0
2.0
2.0
10.0
2.0 (3.5 1.0)•10–17 (3.2 1.5)•10–7 1.4 1.0
4.0 (2.2 0.4)•10–16 (2.8 2.1)•10–7 4.9 4.5
10.0 (1.6 0.12)•10–15 (1.2 0.2)•10–6 3.3 0.8
12.0 (1.9 0.3)•10–15 (1.9 0.3)•10–6 2.1 0.7
36.0 (1.8 0.1)•10–14 (3.2 0.4)•10–6 4.0 1.5
12.0 (2.4 0.3)•10–14 (1.4 0.1)•10–5 0.7 0.14
* In mol2 L–2 s–2
** In mol L–1 s–1
*** In L mol–1 s–1
.
.
.

886
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
Antonov and Varlamov
w1•107/mol L–1 s–1
k2[1] + k3[3] ≈ k2[1], and then Eq. (IV) can be written in
the form
4
w1 ≈ (k11/2k3/kt1/2)[1]1/2[3]3/2
.
1.2
0.8
0.4
It is seen that at [3]0 = const the reaction rate w1
≈
const1•[1]1/2, and at [1]0 = const the reaction rate w1 ≈
const2•[3]3/2. This agrees qualitatively with Figs 4 and 5.
Processing of the data (see Figs 4 and 5) by the iteraꢀ
tion methods using Eq. (IV) makes it possible to deterꢀ
mine simultaneously three reaction rate constants: k1, k2,
and k3. However, this problem has no unambiguous soluꢀ
tion, and differences in the determined values of the same
rate constant are several orders of magnitude. To obtain
additional independent data on the k1, k2, and k3 values
and ratios between them, we used the results of experiꢀ
ments carried out at equal concentrations of the reacꢀ
tants.
3
2
1
0
4
8
[1]•104/mol L–1
Fig. 4. Plots of w1 vs. concentration of quinoneimine 1 at
[3]0 = const (•10–4, mol L–1): 2.0 (1); 4.0 (2); 6.0 (3); 10.0 (4).
Points are experiment, and lines are calculation by formula (IV)
at k1 = 3.5•10–4 L mol–1 s–1 and the following k2•10–6 and
k3•10–5 values, L mol–1 s–1: 2.34 and 4.55 (1); 1.63 and 2.84 (2);
1.75 and 2.85 (3); 5.56 and 2.32 (4), respectively. Chlorobenꢀ
zene, 298.2 K.
Reaction rate at equimolar concentrations of reactants
and products (equal concentrations method). According to
Eq. (II), the reaction rate in experiments with equimolar
reactant concentrations [1]0 = [3]0 = c is the following:
w1 = (k1/kt)1/2[k2k3/(k2 + k3)]c2.
(V)
w1•107/mol L–1 s–1
4
In the experimental series with additives of reaction
product 2 but at equal concentrations of all the three
substances [1]0 = [3]0 = [2]0 = c, the following depenꢀ
dence should obey:
3
1.2
w1 = [(k1 + k–4)/kt]1/2[k2k3/(k2 + k3 + k–3)]c2.
(VI)
2
0.8
In experiments with additives of quinone 4 at equal
concentrations [1]0 = [3]0 = [4]0 = c, a similar depenꢀ
dence is obtained from Eq. (II)
1
0.4
w1 = [(k1 + k–6)/kt]1/2[k2k3/(k2 + k3 + k–2)]c2.
(VII)
The results of the experiments performed at equal conꢀ
centrations are shown in Fig. 6. It can be seen that linear
dependences (V)—(VII) obey well in all the cases. The
data processing (see Fig. 6) gave the parameter values
presented below.
0
4
8
[3]•104/mol L–1
Fig. 5. Plots of w1 vs. concentration of hydroquinone 3 at
[1]0 = const (•10–4, mol L–1): 2.0 (1); 4.0 (2); 6.0 (3); 10.0 (4).
Points are experiment, and lines are calculation by formula (IV)
at k1 = 3.5•10–4 L mol–1 s–1 and the following k2•10–6 and
k3•10–5 values, L mol–1 s–1: 2.71 and 2.81 (1); 2.15 and 2.44 (2);
1.03 and 3.22 (3); 1.39 and 2.55 (4). Chlorobenzene, 298.2 K,
Ar bubbling.
Straight line Equaꢀ
Parameter
Value
/L mol–1 s–1
in Fig. 6
tion
1
(V)
0.140 0.003
0.218 0.011
0.111 0.001
Fig. 5). Using Eq. (II), we have the formula to describe
these dependences
2
3
(VI)
w1 =
.
(IV)
(VII)
Analysis of the data presented in Figs 4 and 5 (in the
framework of Eq. (IV)) suggests that k2 > k3. Indeed,
assuming in the extreme case that k2 >> k3, we have
We used these results to estimate the rate constants of
some elementary steps and then applied them as the first

Kinetics of reversible chain reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
887
w1•107/mol L–1 s–1
Multiplication of Eqs (IX) and (X) and insertion of
the known3 value k–4 = 6.4•10–3 L mol–1 s–1 into the
result gives
2
k3/(1 + k–3/k2) ≈ 5.5•104 L mol–1 s–1
.
(XI)
1.6
The absolute k3 value can be estimated from relaꢀ
tion (XI), if the ratio of the reaction rate constants k–2
and k–3 is determined from the heat effects of reacꢀ
tions (–2) and (–3). In reaction (–2) dichloroquinone 4
is reduced to radical 6• in which the strength of the formꢀ
ing O—H bond is DOH = 253.6 kJ mol–1.9 Simultaneously
1
0.8
3
this reaction involves the cleavage of either the O—H
0
•
0.4
0.8
c2•106/mol2 L–2
bond in 4ꢀhydroxydiphenylaminyl radical 7N (DOH
=
259.5 kJ mol–1 11
or the N—H bond in isomeric
)
Fig. 6. Linear plots of the reaction rate w1 vs. squared equal
concentrations of the reactants and additives of the final
products: 1, [1]0 = [3]0 = c; 2, [1]0 = [3]0 = [2]0 = c; 3,
[1]0 = [3]0 = [4]0 = c. Chlorobenzene, 298.2 K, Ar bubbling.
•
4ꢀanilinophenoxy radical 7O (DNH = 273.6 kJ mol–1).11
In any case, reaction (–2) is endothermic. In reacꢀ
tion (–3) radical 6• is reduced to hydroquinone 3 in
which the strength of the forming O—H bond is DOH
=
=
=
362.4 kJ mol–1 9
339.3 kJ mol–1 11
353.4 kJ mol–1 11
.
)
The O—H bond (DOH
or the N—H bond (DNH
approximation in the search for their more exact values by
the iteration method from other experimental data.
Dividing the parameter of Eq. (VI) into the parameter
of Eq. (V), we have
)
in 4ꢀhydroxydiphenylamine 2 is simulꢀ
taneously broken. It is seen that reaction (–3) is exotherꢀ
mic anyway. The reactions of H atom abstraction by
quinones and phenoxy radicals in the intersecting paꢀ
rabolas method are attributed to the same class of elꢀ
ementary reactions and, therefore, the rate constants of
reactions (–2) and (–3) are determined from their heat
effects only.13 It follows from this that k–3 > k–2. As
mentioned above, k2 > k3. Since the equilibrium conꢀ
stant K of the reaction of compounds 1 and 3 equals to the
product K = K2K3 = (k2/k–2)(k3/k–3)6 and is close to
unity (K = 0.31)9 (see Fig. 1), we conclude that k2 ≈ k–3
and k–2 ≈ k3. Then using expression (XI) we can estimate
= 1.56 0.11.
(VIII)
According to Scheme 2, reactions (1) and (–4) are of
the same type and represent H atom transfer to a molꢀ
ecule of 1 either from hydroquinone 3 (see reaction (1),
two equal OH groups), or from compound 2 (see reacꢀ
tion (–4)). It follows from this that the reaction rate conꢀ
stants k1 and k–4 are first determined by the strengths of
the broken bonds in molecules 3 and 2. The O—H bond
k3 ≈ 1.1•105 L mol–1 s–1
,
(XII)
dissociation energy in molecule 3 is known: DOH
=
362.4 0.9 kJ mol–1.9 In molecule 2 the O—H bond dissoꢀ
and using formula (X)
ciation energy is much lower than that of the N—H bond:
DNH = 353.4 kJ mol–1, DOH = 339.3 kJ mol–1 11
.
It folꢀ
k1 ≈ 6.5•10–4 L mol–1 s–1
.
(XIII)
lows from the latter data that predominantly the phenoxy
HO group of molecule 2 reacts with hydroquinone 1 in
reaction (–4). Then, taking into account that DOH in
molecule 3 is considerably (by 23.1 kJ mol–1) higher than
DOH в in molecule 2, we conclude that k–4 >> k1.
Under an additional assumption that k2 >> k3 (see
above), it follows from Eq. (VIII)
Finally, dividing the parameter in Eq. (VII) into the
parameter of Eq. (V) and assuming that k2 >> k3 ≈ k–2
,
we get
[(k1 + k–6)/k1]1/2 = 0.8,
from where
k–6 ≈ 0.27k1 ≈ 1.7•10–4 L mol–1 s–1
.
(XIV)
(k–4/k1)1/2[k2/(k2 + k–3)] ≈ 1.6.
(IX)
Calculation of the reaction rate constants k1, k2, and k3
from the dependence of the initial reaction rate on the conꢀ
centration of the starting substances. We processed the exꢀ
perimental data presented in Figs 4 and 5 using forꢀ
mula (IV) and taking into account the above presented
estimates (V)—(XIV). The following procedure was used.
We specified (held stationary) k1 = 1•10–4 L mol–1 s–1
Using the accepted assumption that k2 >> k3 and asꢀ
suming that 2kt = 8•108 L mol–1 s–1 (average rate conꢀ
stant of disproportionation of semiquinone radicals12),
we obtain the following inequality from the parameter
of Eq. (V)
k11/2k3 ≈ 2.8•103 L3/2 mol–3/2 s–3/2
.
(X)

888
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
Antonov and Varlamov
w1•108/mol L–1 s–1
and using the iteration method determined the k2 and k3
values for which formula (IV) describes most precisely
each experimental curve (see Figs 4 and 5). After this we
specified k1 = 2•10–4 L mol–1 s–1 and determined a new
set of k2 and k3. The procedure was repeated with the
increment k1 = 1•10–4 in the interval k1 = (1—15)•10–4
L mol–1 s–1. Then we compared all obtained sets of k1,
k2, and k3 and found that the best agreement of the results
(and satisfactory agreement with estimates (V)—(XIV)) is
observed at the k1 values lying in the interval (2—5)•10–4
L mol–1 s–1. This k1 range was additionally studied with
the increment k1 = 5•10–5 L mol–1 s–1. As a result, k1 =
(3.5 1)•10–4 L mol–1 s–1 was found as the best value.
The k2 and k3 values obtained for each series of runs at
k1 = 3.5•10–4 L mol–1 s–1 are shown in Figs 4 and 5.
As a whole, when studying the dependences of the
initial reaction rate, we obtained the following results
(k, L mol–1 s–1): k1 = (3.5 1)•10–4, k2 = (2.1 0.7)•106,
and k3 = (2.9 0.6)•105.
Effect of the final products on the initial reaction rate.
Dependence of the initial reaction rate on the 4ꢀhydroxyꢀ
diphenylamine (2) concentration. The experiments show
that in the presence of final product 2 the initial reaction
rate w1 increases, although the equilibrium shifts toward
the initial substances. These data indicate unambiguously
that the mechanism of the reaction is complicated, beꢀ
cause if the forward reaction of compounds 1 and 3 and
the backward reaction of compounds 4 and 2 were oneꢀ
step, then additives of the final products would induce
only a decrease in w1.
3
8
6
4
2
2
1
0
0.5
1.0
[2]•103/mol L–1
Fig. 7. Plots of the initial rate of the reaction of compounds 1
and 3 vs. concentration of product 2. Initial concentrations of
compounds 1 and 3 (•104, mol L–1): 2.0 and 2.0 (1); 2.0 and
12.0 (2); 6.0 and 6.0 (3), respectively. Points are experiment,
and lines are calculation by formula (XV) at k1 = 3.5•10–4
L mol–1 s–1, k–4 = 6.4•10–3 L mol–1 s–1 and the following
k2•10–6, k3•10–5, and k–3•10–6 values, L mol–1 s–1: 1.65, 1.70,
and 2.30 (1); 2.72, 2.13, and 2.78 (2); 1.00, 2.51, and 1.80 (3),
respectively. Chlorobenzene, 298.2 K, Ar bubbling.
The k–4 value in chlorobenzene at 298 K was deterꢀ
mined3: k–4 = 6.4•10–3 L mol–1 s–1. The reliable estiꢀ
mates for k1, k2, and k3 were presented above. Thus, the
data in Fig. 7 can be used to determine k–3
.
We also used another, more general approach: the
experimental data (see Fig. 7) were processed by forꢀ
mula (XV) using the iteration methods according to the
procedure similar to that described above. Each curve in
Fig. 7 was processed at fixed k1 values in the interval
(2—5)•10–4 L mol–1 s–1 with an increment of 5•10–5
L mol–1 s–1, and every time we obtained a set of the rate
constant values k2, k3, and k–3. The value k–4 = 6.4•10–3
L mol–1 s–1 was not varied. A comparison of thus obꢀ
tained data showed that the best agreement of the results
is achieved again at k1 = 3.5•10–4 L mol–1 s–1. The sets
of the k2, k3, and k–3 values determined at this k1 value
are presented in Fig. 7.
Thus, the study of the dependence of w1 on the conꢀ
centration of compound 2 provided the following results
(k, L mol–1 s–1): k1 = 3.5•10–4, k2 = (1.8 0.5)•106,
k3 = (2.1 0.3)•105, and k–3 = (2.3 0.3)•106.
Dependence of the initial reaction rate on the concentraꢀ
tion of 2,5ꢀdichloroquinone. As can be seen from the
data in Fig. 8, additives of dichloroquinone 4 exert only
a weak inhibition effect on the reaction of comꢀ
pounds 1 and 3. We have earlier observed a similar effect
of 2,5ꢀdimethylquinone additives on the chain reaction
of quinonenimine 1 with 2,5ꢀdimethylhydroquinone (it is
virtually irreversible14). From Eq. (2) we obtain the forꢀ
As can be seen from the data in Fig. 7, the curves of
the plot of w1 vs. [2]0 have a maximum, whose position
depends on the ratio of concentrations of compounds 1
and 3. Similar dependences have been observed earlier
when the effect of additive 2 on the reaction rate of
quinoneimine 1 with 2,5ꢀdiꢀtertꢀbutylhydroquinone was
studied (however, this reaction, unlike that of comꢀ
pounds 1 and 3, is virtually irreversible, K298K >> 1).3,4
The dual accelerating and inhibiting effect of compound 2
is explained by its participation in elementary steps that
exert an opposite effect on the rate of the overall reaction.
In the presence of additive 2 in the system, additional
initial reaction (–4) occurs from the very beginning,
which accelerates the interaction of compounds 1 and 3.
Along with this, the rate of backward reaction (–3) inꢀ
creases more and more strongly with an increase in the
concentration of compound 2, due to which the chain
length of the forward chain reaction shortens to decrease
its rate.
From Eq. (II) we obtain the formula for the reaction
rate in the presence of additive 2
w1 =
.
(XV)

Kinetics of reversible chain reaction
Russ.Chem.Bull., Int.Ed., Vol. 56, No. 5, May, 2007
889
w1•108/mol L–1 s–1
Parameter
k/L mol–1 s–1
Parameter k/L mol–1 s–1
k1
k2
k3
2k4
2k5
2k6
(3.5 1)•10–4
(1.8 0.7)•106
(2.4 0.6)•105
8•108
2k–1
k–2
k–3
k–4
k–5
k–6
8•108
(6 2.5)•105
(2.3 0.3)•106
6.4•10–3 3
?
5
8•108
4
2
3
8•108
(0.8 0.4)•10–4
Thus, the rate constants of almost all elementary steps
of the chain reaction of compounds 1 and 3, which has a
pronounced reversible character, were reliably estimated
for the first time from the experimental data. We conꢀ
firmed thus the earlier proposed mechanism of interacꢀ
tion in quinoneimine—hydroquinone systems and showed
that the relations obtained by the kinetic analysis are valid.
1
3
2
1
2
[4]•103/mol L–1
Fig. 8. Plots of the initial rate of the reaction of compounds 1
and 3 vs. concentration of product 4. Initial concentrations of
compounds 1 and 3 (•104, mol L–1): 6.0 and 6.0 (1); 2.0 and
12.0 (2); 4.0 and 6.0 (3), respectively. Points are experiment,
This work was financially supported by the Division of
Chemistry and Materials Science of the Russian Acadꢀ
emy of Sciences (Program "Theoretical and Experimental
Investigation of the Chemical Bond Nature and Mechaꢀ
nisms of the Most Important Chemical Reactions and
Processes").
and lines are iteration calculation by formula (XVI) at k1
=
,
3.5•10–4 L mol–1 s–1 and the following k2•10–6, k3•10–5
k–2•10–5, and k–6•104 values, L mol–1 s–1: 1.95, 2.15, 9.37, and
1.51 (1); 1.43, 2.09, 3.15, and 0.41 (2); 1.31, 2.05, 5.03,
and 0.44 (3), respectively. Chlorobenzene, 298.2 K.
References
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mula for the reaction rate in the presence of dichloroꢀ
quinone 4
3. V. T. Varlamov, Kinet. Katal., 2001, 42, 836 [Kinet. Catal.,
2001, 42 (Engl. Transl.)].
w1 =
.
(XVI)
4. V. T. Varlamov, Dokl. Akad. Nauk, 1994, 337, 757 [Dokl.
Chem., 1994 (Engl. Transl.)].
Formula (XVI) is analogous to formula (XV) for the
dependence of w1 on the concentration of compound 2
and, therefore, the different shapes of the curves in Figs 7
and 8 indicate that at close concentrations of compounds
2 and 4 the value k–4[2] >> k–6[4] or that k–4 >> k–6. The
data in Fig. 8 were used to estimate the k–2 and k–6 values
by the iteration method. In this case, k1 had the fixed
value k1 = 3.5•10–4 L mol–1 s–1, and k2 and k3 were
varied in the ranges (1.3—2.8)•106 and (1.8—3.5)•105
L mol–1 s–1, respectively. Thus determined reaction rate
constant values are shown in Fig. 8. As a whole, in the
study of the dependence of w1 on the concentration of
dichloroquinone 4 we obtained the following results
(k, L mol–1 s–1): k2 = (1.6 0.3)•106, k3 = (2.1 0.1)•105,
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408, 63 [Dokl. Chem., 2006 (Engl. Transl.)].
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1972, 50, 3052.
k–2 = (6 2.5)•105, and k–6 = (0.8 0.4)•10–4
.
As can be seen, the rate constants of elementary steps
of the chain reaction determined by us using different
methods in the present work agree satisfactorily with each
other. The averaged rate constants of the elementary
steps (see Scheme 2) are given below (chlorobenzene,
T = 298.2 K).
13. E. T. Denisov and T. G. Denisova, Handbook of Antioxiꢀ
dants, CRC Press, Boca Raton, New York, 2000, 289 pp.
14. A. V. Antonov and V. T. Varlamov, Kinet. Katal., 2006, 47,
541 [Kinet. Catal., 2006, 47 (Engl. Transl.)].
Received December 28, 2006;
in revised form February 9, 2007