The kinetics of the reversible chain reaction between 2,5-dichloroquinone and 4-hydroxydiphenylamine

Article abstract of DOI:10.1134/S0036024407120114

The paper presents the results obtained in a study of the kinetics of the reversible chain reaction between 2,5-dichloroquinone and 4-hydroxydiphenylamine (K _eq = 3.2). We studied the dependence of the reaction rate on the concentrations of the initiator, initial reagents, and all products. The equations obtained earlier for the rate of reversible chain reactions and the method of equal concentrations suggested in this work were used to estimate the rate constants of most of the reaction mechanism elementary steps from the experimental data. The results obtained were shown to closely agree with and agument the data obtained earlier for the kinetics of the chain reaction between N-phenyl-1,4-benzoquinonemonoimine and 2,5-dichlorohydroquinone. On the whole, all the elementary steps of these two (forward and back) reversible chain reactions were characterized by rate constant values.

Full text of DOI:10.1134/S0036024407120114

ISSN 0036-0244, Russian Journal of Physical Chemistry A, 2007, Vol. 81, No. 12, pp. 1968–1975. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © A.V. Antonov, V.T. Varlamov, 2007, published in Zhurnal Fizicheskoi Khimii, 2007, Vol. 81, No. 12, pp. 2186–2193.
CHEMICAL KINETICS
AND CATALYSIS
The Kinetics of the Reversible Chain Reaction
between 2,5-Dichloroquinone and 4-Hydroxydiphenylamine
A. V. Antonov and V. T. Varlamov
Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow oblast, 142432 Russia
e-mail: varlamov@icp.ac.ru
Received February 9, 2007
Abstract—The paper presents the results obtained in a study of the kinetics of the reversible chain reaction
between 2,5-dichloroquinone and 4-hydroxydiphenylamine (Keq = 3.2). We studied the dependence of the reac-
tion rate on the concentrations of the initiator, initial reagents, and all products. The equations obtained earlier
for the rate of reversible chain reactions and the method of equal concentrations suggested in this work were
used to estimate the rate constants of most of the reaction mechanism elementary steps from the experimental
data. The results obtained were shown to closely agree with and augment the data obtained earlier for the kinet-
ics of the chain reaction between N-phenyl-1,4-benzoquinonemonoimine and 2,5-dichlorohydroquinone. On
the whole, all the elementary steps of these two (forward and back) reversible chain reactions were character-
ized by rate constant values.
DOI: 10.1134/S0036024407120114
INTRODUCTION
monoimine (QMI) and 2,5-dichlorohydroquinone
Ar(OH)2 were reported in [5]. The purpose of this work
was to study the kinetics of the reverse chain reaction
between 2,5-dichloroquinone (Q) and 4-hydroxydiphe-
nylamine (H2QMI), find a new independent set of ele-
mentary step rate constants, including those that we
were unable to determine earlier, and compare the new
data with those obtained earlier.
In [1], we experimentally substantiated the sugges-
tion [2, 3] that reactions in the quinoneimine + hydro-
quinone systems should be treated as a new class of liq-
uid-phase reactions, as reversible chain processes. This
was done for the example of the reaction between
N-phenyl-1,4-benzoquinonemonoimine (QMI) and
2,5-dichlorohydroquinone Ar(OH)2. The initial sub-
stances are not spent completely in such reactions but
only up to the attainment of equilibrium with the
reverse reaction between the products (4-hydroxy-
diphenylamine (H2QMI) and 2,5-dichloroquinone (Q)).
As for one-stage reversible reactions, the position of
equilibrium in reversible chain reactions is independent
of whether it is attained from the side of initial com-
pounds or products. The equilibrium constant is also
independent of the initial reagent concentrations and
the presence of product admixtures but is only deter-
mined by the temperature. The fundamental special
feature of reversible chain reactions is, however, the
chain mechanism of both the forward and back reac-
tions. The equilibrium state can therefore be attained as
chain propagation from the side of either initial sub-
stances or products.
EXPERIMENTAL
2,5-Dichloroquinone Q from Aldrich was purified
by double sublimation in a vacuum. 4-Hydroxydiphe-
nylamine H2QMI was recrystallized first from metha-
nol and then from a heptane–toluene mixture. Finally,
it was purified by preparative liquid chromatography on
SiO2 (Chemapol) with a mixture of ether and hexane as
an eluent. 2,5-Dichlorohydroquinone Ar(OH)2 was
synthesized from Q by the reduction of the latter with
sodium dithionite Na2S2O4 following the procedure
described in [6]. The product was purified by two-fold
recrystalliziation from a methanol–benzene mixture.
N-Phenyl-1,4-benzoquinonemonoimine QMI was syn-
thesized by the oxidation of H2QMI with PbO2. It was
finally purified by preparative liquid chromatography
A kinetic analysis of reversible chain reactions in with an ether–hexane mixture as an eluent and recrys-
quinoneimine–hydroquinone systems was performed tallized from methanol. We used tetraphenylhydrazine
in [4]. An equation for the initial rate was obtained, Ph2N-NPh2 as an initiator synthesized according to
which allowed a systematic study of the kinetics of Wieland by the oxidation of diphenylamine in acetone
these reactions to be performed and the rate constants with potassium permanganate KMnO4 [7]. The rate
for elementary steps to be determined from the experi- constant for initiation with this initiator was ki = 2ekdec,
•
mental data. We undertook such a study for the chain where e = 0.95 is the probability of the escape of Ph2N
reaction specified above. The results obtained for the radicals into volume and kdec = 2.06 × 10–7 s–1 is the rate
forward reaction between N-phenyl-1,4-benzoquino- constant for the decomposition of Ph2N-NPh2 in chlo-
1968

THE KINETICS OF THE REVERSIBLE CHAIN REACTION
1969
[QMI] × 104, mol/l
2
robenzene at 298.2 K [3]. Chlorobenzene thoroughly
purified from impurities as described in [8] was used as
a solvent.
1'
The reaction was monitored spectrophotometrically
by tracking the accumulation of orange quinoneimine
QMI. The reaction kinetics was studied at 298.2 0.1 K
in a temperature-controlled quartz cell of the bubbling
reactor type (volume 8.5 ml, optical path l = 2.0 cm,
bubbling of argon) mounted in a Specord UV VIS spec-
trophotometer. During experiments, we continuously
recorded optical density changes for the QMI absorp-
tion band at ν = const = 22260, 20000, or 19000 cm–1
depending on the concentrations of the initial reagents
and the amount of QMI introduced. 2,5-Dichloro-
quinone Q also absorbed weakly in this spectral region;
the corresponding corrections were introduced.
1''
1
2
1
2''
2'
0
0.5
1.0
1.5
The quantitative characteristics of the reaction of Q
with H2QMI were studied on the basis of the initial
quinoneimine accumulation rates. The wQMI values
were determined by processing the initial experimental
curve portions according to the empirical equation
t × 10–4, s
Fig. 1. Kinetic curves of (1, 1', 1'') consumption of QMI in
the forward reaction between QMI and Ar(OH) ([QMI] =
2
0
–4
[Ar(OH) ] = 2 × 10 mol/l) and (2, 2', 2'') accumulation of
2 0
QMI in the back reaction between Q and H QMI ([Q] =
2
0
[QMI] = a(1 + bexp(–ct)),
–4
[H QMI] = 2 × 10 mol/l) and acceleration of the forward
2
0
and back reactions in the presence of tetraphenylhydrazine
where a, b, and c are the parameters selected iteratively.
According to this equation, wQMI = –abc.
10
(w × 10 , mol/(l s)): (1, 2) 0, (1', 2') 1.17, and (1'', 2'') 7.05.
i
Chlorobenzene, 298.2 K, Ar bubbling.
RESULTS AND DISCUSSION
Ar(OH)2 studied earlier [5]. The stoichiometric equa-
reaction with respect to the reaction between QMI and tion of both reactions can be written as
The reaction between Q and H2QMI is the reverse
Cl
Cl
+
+ O
O
O
N
HO
OH
HO
NH
Cl
Cl
QMI
Ar(OH)2
H2QMI
Q
•
•
The kinetic curves of the consumption of QMI in its
reaction with Ar(OH)2 and the accumulation of QMI in
the reverse reaction between Q and H2 QMI obtained in
experiments with equal concentrations of the reagents
are plotted in Fig. 1. The accelerating action of the ini-
tiator on the forward and back reactions, which is evi-
dence of their chain mechanism, is also shown in this
figure.
Q + H2QåI
Ar(OH)O + HQåI , (–5, 5)
•
•
Q + HQåI
Ar(OH)O + QåI, (–2, 2)
•
•
Ar(OH)O + H2QåI
Ar(OH)2 + HQåI , (–3, 3)
•
•
HQåI + HQåI
QåI + H2QåI, (4, –4)
The forward and back reactions have the same
mechanism. To unify the numbering of elementary
steps, we here use the numbering introduced in [5]. The
mechanism of the reaction of Q with H2QMI can be
written in the form of the kinetic scheme
•
•
HQåI + Ar(OH)O
QåI + Ar(OH)2, (–1, 1)
H2QåI + Q, (5, –5)
•
•
Ar(OH)O + Ar(OH)O
Ar(OH)2 + Q. (6, –6)
Scheme
•
In this scheme, Ar(OH)O denotes 2,5-dichloro-4-
•
Ar(OH)2, [H2QMI]
hydroxyphenoxyl semiquinone radicals and HQMI ,
•
Ph2N-NPh2
Ph2N
radicals formed from quinoneimine QMI (or 4-hydroxy-
•
•
Ar(OH)O [HQåI ], (i)
diphenylamine H2QMI) by the addition of the H atom
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

1970
ANTONOV, VARLAMOV
to QMI (or by the detachment of the H atom from
1
------------
1 + µ
wQMI
=
{(w–5 + w–6 + 0.5wi)µ – (w1 + w–4)}
H2QMI). These can be both 4-hydoxydiphenylaminyl
•
•
HO–C6H4–N –C6H6 and 4-anilinophenoxyl O–C6H4–
NH–C6H6 radicals. For simplicity, we make no distinc-
(1)
µk–2[Q] – k2[QMI]
1/2
-----------------------------------------------
+
(w1 +w–4 +w–5 +w–6 +0.5wi) ,
•
(1 + µ)k1t /2
tion between HQMI radicals, although it is known
that, at 298.2 K in chlorobenzene, the mole fraction of
•
O–C6H4–NH–C6H6 radicals during the reaction is where µ = (k2[QMI] + k–3[H2QMI])/k–2[Q] +
•
0.967, and the mole fraction of HO–C6H4–N –C6H6 k3[Ar(OH)2]) and wj are the rates of the corresponding
radicals is 0.033 [9].
reactions in the Scheme. Equation (1) was obtained on
the assumption that the rate constants for the radical
disproportionation reactions were approximately equal
(k–1 ≈ k4 ≈ k5 ≈ k6 ≈ kt).
Equation (1) contains two terms. The first term
describes the accumulation of QMI at the chain initia-
tion stage, and the second term is the rate of the accu-
mulation of QMI in the chain reaction. If chains are
In the absence of an initiator and products, chains at
the initial stages are initiated in reaction (–5). The role
of chain propagation reactions is played by reac-
tions (–2) and (–3), and chain termination occurs in the
disproportionation of semiquinone radicals, reactions
(–1) and (4)–(6).
The equation for the initial reaction rate has the fairly long, the first term can be ignored. The equation
form [4] for the initial reaction rate then takes the form
k2k3[Q][H2QMI]
-------------------------------------------------------------------------------------------------------------------------------------
=
wQMI
k1t /2(k2[QMI] + k–3[H2QMI] + k–2[Q] + k3[Ar(OH)2])
(2)
k–2k–3 [QMI][Ar(OH)2]
k2k3
1/2
⎛
⎞
× ------------- – ------------------------------------------- (w1 + w–4 + w–5 + w–6 + 0.5wi) .
⎝
⎠
[Q][H2QMI]
Initiator Effects on the Initial Reaction Rate
The ratio between the y-intercepts of these straight lines
(A) and their slopes (B) is 2k–5[Q][H2QMI], which can
be used to determine k–5 if [Q]0 and [H2QMI]0 are
known. The results obtained for the reaction in the pres-
ence of an initiator are shown in Fig. 2, and the A and B
parameter values and the k–5 values found from their
ratios are listed in Table 1.
We see that experiments in the presence of an initi-
ator only allow us to obtain a crude estimate of k–5 ~
(3.1 – 13.5) × 10–3 l/(mol s). Note that attempts at deter-
mining k1 from the initiator effects on the rate of the
forward reaction between QMI and Ar(OH)2 also give
crude estimates of k1 only [4].
According to (2), we have
k–2k–3[Q][H2QMI]
------------------------------------------------------------------
=
wQMI
k1t /2(k–2[Q] + k–3[H2QMI])
× (k–5[Q][H2QMI] + 0.5wi)1/2
in the presence of an initiator. The equation can more
conveniently be verified experimentally in the form
2
k–2k–3[Q][H2QMI]
⎧
⎨
⎩
⎫
⎬
⎭
w2QMI
=
------------------------------------------------------------------
t
k1/2(k [Q] + k [H QMI])
The Dependence of the Initial Reaction Rate
on Reagent Concentrations
–2
–3
2
× k–5[Q][H2QMI]
(3)
The results obtained in studying the dependence of
wQMI on the concentration of one of the reagents at a
constant concentration of the other component are
shown in Figs. 3 and 4. These dependences are nonlin-
ear. Using (2), we obtain an equation that describes
them. This equation has the form
2
k–2k–3[Q][H2QMI]
⎧
⎨
⎩
⎫
⎬
⎭
------------------------------------------------------------------
t
+ 0.5
w .
i
k1/2(k [Q] + k [H QMI])
–2
–3
2
According to (3), linear dependences should be
observed in the w2QMI – wi coordinates,
k1/2k–2k–3[Q]3/2[H2QMI]3/2
–5
------------------------------------------------------------------
wQMI
=
.
(4)
k1t /2(k–2[Q] + k–3[H2QMI])
w2QMI = A + Bwi.
(3‡)
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

THE KINETICS OF THE REVERSIBLE CHAIN REACTION
1971
w2
× 1014, (mol/(l s))2
wQMI × 107, mol/(l s)
QMI
6
4
3
8
6
4
2
4
3
2
1
2
2
1
0
1
2
3
0
4
8
wi × 109, mol/(l s)
[H2QMI] × 104, mol/l
Fig. 3. Dependences of w
on the concentration of
QMI
4
H QMI at [Q] = const (×10 , mol/l) = (1) 2.0, (2) 4.0, (3) 6.0,
2
0
Fig. 2. Dependences of the square of the initial reaction
and (4) 10.0. The experimental data are shown by symbols.
Lines correspond to calculations according to (4) with k
rate on the rate of initiation. Initial concentrations of Q
=
–5
4
4
–3
–5
–6
(×10 ) and H QMI (×10 ), mol/l: (1) 2.0 and 2.0, (2) 4.0
1.5 × 10 l/(mol s) and k × 10 and k × 10 , l/(mol s),
2
–2 –3
and 2.0, and (3) 10.0 and 2.0, respectively. Chloroben-
zene, 298.2 K.
of (1) 6.1 and 3.2, (2) 6.4 and 3.5, (3) 5.2 and 5.4, and
(4) 4.3 and 6.6, respectively. Chlorobenzene, 298.2 K.
The data presented in Figs. 3 and 4 lead us to conclude that their relative values were obtained in experiments with
k–3 > k–2. Indeed, if we assume that, in the limiting case, equal reagent concentrations.
k–3 ꢀ k–2, we obtain k–2[Q] + k–3[H2QMI] ≈ k–3[H2QMI].
Equation (4) can then be written as
The Reaction Rate at Equimolar Reagent
and Product Concentrations
1/2
k k–2
(the Method of Equal Concentrations)
3/2
1/2
–5
---------------
wQMI
≈
[Q] [H2QMI] .
k1t /2
According to (2), the reaction rate in experiments
with equimolar reagent concentrations [Q]0
[H2QMI]0 = c is
=
It follows from this approximate equality that, at
1/2
[H2QMI]0 = const, the rate of the reaction is wQMI
≈
k–5
k–2k–3
k–2 + k–3
2
2
⎛
⎝
⎞
const1[Q]3/2, and, at [Q]0 = const, it is wQMI
≈
------ -------------------
wQMI
=
c = αc .
(5)
⎠
kt
const2[H2QMI]1/2. This is in qualitative agreement with
the data shown in Figs. 3 and 4.
The dependence
These data can be processed iteratively according to
(4), which makes it possible in principle to determine
three rate constants k–5, k–2, and k–3 simultaneously. This
problem, however, does not have a unique solution, and
1/2
k–5 + k–4
k–2k–3
k–2 + k–3 + k2
2
2
⎛
⎝
⎞
------------------- ------------------------------
wQMI
=
c = βc
(6)
⎠
kt
the difference between the values of the same rate con- should hold in a series of experiments with the addition
stant can be as large as several orders of magnitude. of the QMI product but equal concentrations of three
Additional independent data on k–5, k–2, and k–3 and substances, [Q]0 = [H2QMI]0 = [QMI]0 = c. For experi-
Table 1. Reaction characteristics in the presence of the initiator
[H2QMI] × 104,
[Q] × 104,
A,
B,
mol/(l s)
k–5 × 103,
mol/l
mol/l
(mol/(l s))2
l/(mol s)
2.0
2.0
2.0
2.0
4.0
(6.3 1.1) × 10–16
(5.0 1.7) × 10–15
(4.3 0.5) × 10–14
(1.7 0.25) × 10–6
(3.6 1.0) × 10–6
(1.6 0.4) × 10–5
4.6 1.5
8.5 5.0
6.6 2.5
10.0
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

1972
wQMI × 107, mol/(l s)
ANTONOV, VARLAMOV
wQMI × 107, mol/(l s)
3
6
4
2
4
1
2
2
1
3
2
1
0
4
8
0
0.1
0.2
0.3
[H2QMI] × 104, mol/l
c2 × 106, (mol/l)2
Fig. 4. Dependences of w
on the concentration of Q at
QMI
4
[H QMI] = const (×10 , mol/l) = (1) 2.0, (2) 4.0, (3) 6.0,
2
0
and (4) 10.0. The experimental data are shown by symbols.
Lines correspond to calculations according to (4) with k
Fig. 5. Linear dependences of the rate of accumulation of
QMI w on the square of equal reagent and product con-
=
–5
QMI
–3
–5
–6
1.5 × 10 l/(mol s) and k × 10 and k × 10 , l/(mol s),
centrations; (1) [Q] = [H QMI] = c, (2) [Q] = [H QMI] =
−2
–3
0 2 0 0 2 0
of (1) 6.5 and 4.4, (2) 6.6 and 2.0, (3) 5.8 and 2.2, and
(4) 6.0 and 3.2, respectively. Chlorobenzene, 298.2 K.
[Ar(OH) ] = c, and (3) [Q] = [H QMI] = [QMI] = c.
2 0 0 2 0 0
Chlorobenzene, 298.2 K, Ar bubbling.
ments with the addition of Ar(OH)2 at [Q]0 = [H2QMI]0 = tive phenoxyl OH group of H2QMI is predominantly
[Ar(OH)2]0 = c, Eq. (2) yields a similar dependence,
involved in the reactions with QMI and Q. The QMI
molecule also contains two reaction centers, the O and N
atoms. If QMI attaches H at its O atom, the 4-hydroxy-
1/2
k–5 + k–6
k–2k–3
k–2 + k–3 + k3
2
2
⎛
⎝
⎞
------------------- ------------------------------
c = γc . (7)
wQMI
=
•
⎠
kt
diphenylaminyl radical HQMI with DOH = 259.5 kJ/mol
[10] is formed. The reaction of QMI at nitrogen yields
The results obtained at equal concentrations are
shown in Fig. 5. We see that dependences (5)–(7) are
close to linear in all cases. The data presented in Fig. 5
were processed to obtain the following parameters for
Eqs. (5)–(7) (l/(mol s)): α = 0.567 0.025 (curve 1, no
addition), β = 0.649 0.041 (curve 2, addition of QMI),
and γ = 0.526 0.011 (curve 3, addition of Ar(OH)2).
These values allow us to obtain initial rate constant
estimates for several elementary reactions. These esti-
mates can, in turn, be used as first approximations in the
search for more exact constant values by iteration meth-
ods on the basis of other experimental data.
•
the 4-anilinophenoxyl radical HQMI with DNH
=
273.6 kJ/mol [10]. It follows that we mainly observe
the second reaction, and the enthalpy of reaction (–4) is
∆H–4= 65.7 kJ/mol. The dissociation energy for the
•
H−O bond of the Ar(OH)O radical formed in reaction
(–5) between Q and H2QåI is DOH = 253.6 kJ/mol [8];
that is, ∆H–5 = 85.7 kJ/mol. It follows from the ∆H–4 and
∆H–5 values that k–4 > k–5, even though Q contains
two equivalent O atoms. Using this inequality and
the k–3 ꢀ k–2 inequality obtained above in (8) yields
1/2
k–4
k–3
⎛
⎝
⎞
------ -----------------
∼ 1.15.
(9)
In particular, dividing the parameter of Eq. (6) by
the parameter of Eq. (5) yields
⎠
k–5 k–3 + k2
The assumption that 2kt = 8 × 108 l/(mol s) (this is
the mean rate constant for the disproportionation of
semiquinone radicals [11, 12]) and the inequality k–3 ꢀ
k–2 allow us to obtain
1/2
k–5 + k–4
k–2 + k–3
k–2 + k–3 + k2
⎛
⎝
⎞
------------------- ------------------------------
= 1.15 0.12.
(8)
⎠
k–5
Several points should be mentioned. Reactions (–4)
and (–5) (see Scheme) are the transfer of the H atom
from H2QMI to QMI and from H2QMI to Q, respec-
tively. The 4-hydroxydiphenylamine molecule H2QMI
contains two reaction centers, the OH and NH bonds,
and the dissociation energies of these bonds differ fairly
substantially, DOH = 339.3 and DNH = 353.4 kJ/mol
k1–5/2 k–2 ~ 1.2 × 104 (l/(mol s))3/2
from the parameter of Eq. (5).
(10)
Multiplying (9) by (10) and substituting the value
[10]. These data lead us to conclude that the more reac- k–4 = 6.4 × 10–3 l/(mol s) [3] into the result yields
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

THE KINETICS OF THE REVERSIBLE CHAIN REACTION
1973
k–2
wQMI × 107, mol/(l s)
5
----------------------
1 + k2/k–3
∼ 1.7 × 10 l/(mol s).
(11)
3.2
2.8
2.4
2.0
1.6
Equation (11) allows us to estimate k–2. For this pur-
pose, let us compare the k2 and k–3 rate constants using
the heat effects of these reactions. In reaction (2), QMI
•
3
attacks the Ar(OH)O semiquinone radical at the OH
bond (DOH = 253.6 kJ/mol [8]) with its N or O atom.
This results in the formation of the HN (DNH
=
2
273.6 kJ/mol [10]) or OH (DOH = 259.5 kJ/mol [10])
•
bond in the HQåI radical. The heat effects of the
first and second reactions are ∆H = –20 and –5.9 kJ/mol,
1
respectively. It follows that the first reaction should pre-
•
dominantly occur. In reaction (–3), the Ar(OH)O radi-
cal attacks the H2QåI molecule at its H−O or H–N
group. The dissociation energies of these groups are
DOH = 339.3 and DNH = 353.4 kJ/mol [10]. The strength
0
4
8
[QMI] × 104, mol/l
of the resulting HO bond in Ar(OH)2 is DOH
=
362.4 kJ/mol [8]. The enthalpies of the reactions with
the attack at the HO and NH groups are ∆H = –23.1 and
–9 kJ/mol; that is, the first reaction predominates. The
close heat effect values for reactions (2) and (–3) lead
us to suggest that k2 ≈ k–3. Equation (11) then gives the
estimate
Fig. 6. Dependences of the initial rate of the reaction
between Q and H QMI on the concentration of the reaction
2
4
product QMI. Initial concentrations of Q and H QMI (×10 ,
2
mol/l): (1) 6.0 and 6.0, (2) 12.0 and 4.0, and (3) 4.0 and
12.0, respectively. The experimental data are shown by
symbols. Lines correspond to calculations according to (15)
–3
–5
–3
with k = 1.5 × 10 l/(mol s) and k = 6.4 × 10 l/(mol s);
–5
–4
–6
–6
k–2 ~ 3.4 × 105 l/(mol s).
Accordingly, we find from (10) that
k–5 ~ 1.2 × 10–3 l/(mol s).
(12)
k
× 10 , k × 10 , and k × 10 values (l/(mol s)):
–2 –3
2
(1) 2.9, 8.1, and 2.1; (2) 3.0, 5.1, and 2.2; and (3) 3.3, 7.1,
and 1.2, respectively. Chlorobenzene, 298.2 K, Ar bubbling.
(13)
(1.5 0.5) × 10–3 l/(mol s). The k–2 and k–3 values
obtained in each series of experiments at this k–5 value
are given in the captions to Figs. 3 and 4.
On the whole, studies of the dependence of the initial
reaction rate on reagent concentrations gave (k, l/(mol s))
Lastly, let us estimate k–6. Let us divide the parame-
ter of (7) by the parameter of (5),
1/2
k–5 + k–6
k–2 + k–3
k–2 + k–3 + k3
⎛
⎝
⎞
------------------- ------------------------------
= 0.93.
⎠
k–5
k–5 = (1.5 0.5) × 10–3, k–2 = (5.9 0.3) × 105,
k–3 = (3.8 0.6) × 106.
The equilibrium constant K of the reaction between Q
and H2QMI equals the product K = K–2K–3 = (k–2/k2) ×
(k–3/k3) [4] and is close to one (K = 3.2) [1, 8] (see Fig. 1).
For this reason, if k2 ≈ k–3 and k–3 ꢀ k–2 (see above), we
have k–2 ≈ k3 ꢁ k–3. The last equation therefore gives
The Influence of Products on the Initial Reaction Rate
1/2 ≈ 0.93
k–5 + k–6
The Dependence of the Reaction Rate
on the Concentration of Quinonemonoimine QMI
⎛
⎝
⎞
⎠
-------------------
k–5
The addition of QMI in small amounts increases the
initial reaction rate wQMI, although, clearly, equilibrium
shifts to the initial substances in the presence of QMI,
and, seemingly, the rate of the reaction should decrease.
These data are evidence of a complex mechanism of the
reaction between Q and H2QMI.
and
k–6 ≈ 0.13k–5 ~ 1.6 × 10–4 l/(mol s).
(14)
Calculation of Reaction Rate Constants k–5, k–2, and k–3
from the Dependence of the Reaction Rate
Figure 6 shows that the dependences of wQMI on
[QMI]0 are curves with maxima, whose positions
on the Concentration of the Initial Substances
We iteratively processed the data shown in Figs. 3 depend on the ratio between the concentrations of Q
and 4 according to (4) taking into account estimates (5)– and H2QMI. We observed similar dependences in
(14). Two parameters, k–2 and k–3, were adjusted at a studying the influence of H2QMI on the rate of the for-
fixed k–5 value. The latter was varied over the range ward reaction between QMI and Ar(OH)2 [5]. The dual
(0.5–5) × 10–3 l/(mol s) in steps of 5 × 10–4 l/(mol s). A character of the action of QMI (accelerating and decel-
comparison of the data obtained showed that the results erating) is explained by its participation in reactions
were in the closest agreement with each other and in that have opposite effects on the rate of the overall pro-
satisfactory agreement with estimates (5)–(14) at k–5 = cess. In the presence of QMI, additional initiation reac-
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

1974
wQMI × 107, mol/(l s)
ANTONOV, VARLAMOV
Equation (2) can be used to determine the rate of the
reaction in the presence of QMI,
4
k–2k–3[Q][H2QMI]3/2
2.5
2.0
1.5
1.0
----------------------------------------------------------------------------------------------
=
wQMI
k1t /2(k–2[Q] + k–3[H2QMI] + k2[QMI])
(15)
× (k–5[Q] + k–4[QMI])1/2.
We used (15) and the k–4 = 6.4 × 10–3 l/(mol s) value
obtained in [3] to iteratively process the experimental
data shown in Fig. 6. For each curve, three parameters
(k2, k–2, and k–3) were determined at a fixed k–5 value; k–5
was varied over the range (0.5–5) × 10–3 l/(mol s) in
steps of 5 × 10–4 l/(mol s). A comparison of the results
obtained this way showed that k–5 = 1.5 × 10–3 l/(mol s)
again gave the closest agreement. The k2, k–2, and k–3
values obtained in each series of experiments at k–4 =
6.4 × 10–3 and k–5 = 1.5 × 10–3 l/(mol s) are given in the
caption to Fig. 6.
3
1
2
0
5
10
15
[Ar(OH)2]0 × 104, mol/l
Fig. 7. Dependences of the initial rate of the reaction
between Q and H QMI on the concentration of Ar(OH) .
2
2
4
Our study of the dependence of wQMI on the concen-
tration of QMI gave the following results (k, l/(mol s)):
Initial concentrations of Q and H QMI (×10 , mol/l): (1)
6.0 and 6.0, (2) 4.0 and 6.0, (3) 4.0 and 12.0, and (4) 12.0
and 4.0, respectively. The experimental data are shown by
symbols. Lines correspond to iterative calculations accord-
2
k–5 = 1.5 × 10–3, k2 = (3.1 0.2) × 106,
–3
–5
k–2 = (6.8 0.9) × 105, k–3 = (1.8 0.3) × 106.
ing to (16) with k = 1.5 × 10 l/(mol s); k × 10 , k ×
−2
–5
3
–5
–6
4
10 , k × 10 , and k × 10 values (l/(mol s)): (1) 3.3,
–3
–6
4.4, 2.7, and 1.6; (2) 5.6, 5.2, 4.0, and 5.0; (3) 3.3, 5.2, 1.9,
and 1.0; and (4) 1.6, 7.4, 1.1, and 1.5, respectively. Chlo-
robenzene, 298.2 K.
The Dependence of the Rate of the Reaction
on the Concentration
of 2,5-Dichlorohydroquinone Ar(OH)2
tion (–4) initially occurs in the system. This increases
the rate of the chain reaction between Q and H2QMI.
Simultaneously, the rate of reaction (2) becomes
increasingly higher as the concentration of QMI
increases, which decreases the chain length and the rate
of the reaction.
Figure 7 shows that the addition of Ar(OH)2 has a
weak inhibiting action on the reaction of Q with
H2QMI. Note that we observed a similar effect of the
addition of Q for the forward reaction between QMI
and Ar(OH)2 [5]. Equation (2) yields the rate of the
reaction in the presence of Ar(OH)2 in the form
k–2k–3[Q]3/2[H2QMI]
1/2
-------------------------------------------------------------------------------------------------------
wQMI
=
(k–5[Q] + k–6[Ar(OH)2]) .
(16)
k1t /2(k–2[Q] + k–3[H2QMI] + k3[Ar(OH)2])
Equation (16) is similar to (15) for the depen-
dence of wQMI on the concentration of QMI, but
the curves in Figs. 6 and 7 have different shapes,
which is evidence that k–4[QMI] ꢀ k–6[Ar(OH)2]
at close concentrations of QMI and Ar(OH)2; that is,
k–4 ꢀ k–6. The data presented in Fig. 7 were used to
estimate k3 and k–6 by the method of iterations. The
k–5 constant was set at a constant value, k–5 = 1.5 ×
10–3 l/(mol s), and k–3 and k–2 were varied over the
ranges (1–5) × 106 and (4–9) × 105 l/(mol s), respec-
tively. The k values obtained are given in the caption
to Fig. 7.
k–3 = (2.4 0.6) × 106, k–6 = (2.2 0.9) × 10–4.
A comparison of the sets of k values given above
leads us to conclude that the estimates obtained for the
rate constants of the same elementary steps satisfacto-
rily agree with each other irrespective of the method
used for their determination. Table 2 presents the aver-
aged values of the reaction rate constants for the ele-
mentary steps. For comparison, the results obtained in
[5] for the back chain reaction between QMI and
Ar(OH)2 are also included (Table 2).
A comparison of the data obtained in this work and
[5] shows that the results of these two independent
studies augment each other, and the estimates of the
rate constants of the same elementary reactions are
closely similar.
On the whole, our study of the dependence of wQMI
on the concentration of H2QMI gave the following
results (k, l/(mol s)):
k3 = (3.4 0.8) × 105, k–2 = (5.6 0.7) × 105,
RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007

THE KINETICS OF THE REVERSIBLE CHAIN REACTION
1975
Table 2. Rate constants (k298, l/(mol s)) of the elementary steps
ACKNOWLEDGMENTS
obtained in [5] and this work for the reversible chain reaction be-
tween QMI and Ar(OH)2
This work was financially supported by the Division
of Chemistry and Materials Sciences of the Russian
Academy of Sciences (a grant within the program
“Theoretical and Experimental Studies of the Nature of
Chemical Bonds and Mechanisms of the Most Impor-
tant Chemical Reactions and Processes”) and the “Inte-
gratsiya” program (project no. 2.2.1.1.7181).
Back reaction
Q + H2QMI
Forward reaction
QMI + Ar(OH)2 [5]
Stage
(1, –1) k1 = ?
k1 = (3.5 1) × 10–4
2k–1 = 8 × 108
(2, –2) k2 = (3.1 0.2) × 106 k2 = (1.8 0.7) × 106
k–2 = (6.3 1.3) × 105 k–2 = (6 2.5) × 105
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(3, –3) k3 = (3.4 0.8) × 105 k3 = (2.4 0.6) × 105
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k–3 = (2.7 1) × 106
k–3 = (2.3 0.3) × 106
(4, –4)
(5, –5)
(–1, 1)
(6, –6)
2k4 = 8 × 108
k–4 = 6.4 × 10–3 [3]
2k5 = 8 × 108
k–5 = (1.5 0.5) × 10–3 k–5 = ?
2k–1 = 8 × 108
k1 = (3.5 1) × 10–4
2k6 = 8 × 108
k–6 = (2.2 0.9) × 10–4 k–6 = (0.8 0.4) × 10–4
k1 = ?
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7. L. Gattermann and G. Wieland, Laboratory Methods of
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To summarize, our study of the kinetics of the for-
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characterize all the elementary reactions of the overall
reversible chain reaction in the quinoneimine + hydro-
quinone system for the first time and obtain reliable 10. V. T. Varlamov, Izv. Akad. Nauk, Ser. Khim., No. 2, 293
(2004).
estimates of their rate constants. The results substanti-
ated the mechanism of such reactions suggested earlier
and the validity of the equations obtained in a kinetic
analysis of this mechanism. We also suggested proce-
dures for experimental data processing.
11. S. K. Wong, W. Sytnyk, and J. K. S. Wan, Can. J. Chem.
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RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY A Vol. 81 No. 12 2007