Interconversion equilibrium of para-meta isomerization of alkylbenzenes

Article abstract of DOI:10.1134/S0965544108060078

The equilibrium of the reaction of para-meta isomerization of alkylbenzenes in the liquid phase was studied. The thermodynamic characteristics of the reaction were determined and interpreted. It was shown that the enthalpic term of the interaction between substituents in the case of their meta arrangement in the molecule depends on the effective size of the substituents. An approach to the prediction of the equilibrium constants of para-meta isomerization is proposed.

Full text of DOI:10.1134/S0965544108060078

ISSN 0965-5441, Petroleum Chemistry, 2008, Vol. 48, No. 6, pp. 444–453. © Pleiades Publishing, Ltd., 2008.
Original Russian Text © N.A. Nesterov, T.N. Nesterova, I.Yu. Roshchupkina, 2008, published in Neftekhimiya, 2008, Vol. 48, No. 6, pp. 441–449.
Interconversion Equilibrium of Para–Meta Isomerization
of Alkylbenzenes
a
a
b
N. A. Nesterov , T. N. Nesterova , and I. Yu. Roshchupkina
a
Samara State Technical University, ul. Molodogvardeiskaya 244, Samara, 443100 Russia
b Samara State Aerospace University, Moskovskoe sh. 34, Samara, 443086 Russia
e-mail: xiao3xiong@gmail.com
Received March 21, 2007
Abstract—The equilibrium of the reaction of para–meta isomerization of alkylbenzenes in the liquid phase was
studied. The thermodynamic characteristics of the reaction were determined and interpreted. It was shown that
the enthalpic term of the interaction between substituents in the case of their meta arrangement in the molecule
depends on the effective size of the substituents. An approach to the prediction of the equilibrium constants of
para–meta isomerization is proposed.
DOI: 10.1134/S0965544108060078
The type of conversion considered in this communi-
cation is prevalent when alkylation processes are run
under the thermodynamic control conditions. Attaining
the equilibrium of the para–meta transformation is a
criterion for the establishment of equilibrium in the sys-
tem as a whole. The reliability of information about the
equilibrium of these reactions is a prerequisite for the
rigorous thermodynamic analysis of the processes for
the manufacture of sterically hindered alkylbenzenes
via alkylation. The material presented in this paper
shows the unique character of data on chemical equilib-
rium and makes it possible to speculate about the effect
of the interaction of substituents in alkylbenzene mole-
cules that is beyond the capabilities of calorimetry, a
basic source of such information.
RESULTS AND DISCUSSION
The experimental results and published data are
summarized in Table 1. The average values of the equi-
librium constants K were calculated as the mole frac-
x
tion ratios between the components of the reactions of
interest.
The gas-phase equilibrium constants K (Table 1) were
p
calculated on the assumption that the Raoult’s law holds
for the liquid–gas system of related components, namely
p
p
B
K = K -----, where  and  are the saturated vapor pres-
p
x
Ä
Ç
A
sures of the components in the reaction A
The saturated vapor pressures of most compounds
Table 1) were calculated according to the equation
B.
(
lnp(bar) = A + B · (ä/T) + C · ln(T/ä) + D · (T/ä),
EXPERIMENTAL
where T is in kelvin and the coefficients are as calcu-
lated by the least squares technique using orthogonal
functions and recommendations [12, 13] based on the
following array of experimental data (Table 2): for
,3-dimethylbenzene, intervals 6399–104001 Pa [14],
52160–3541200 Pa [15], and 143.6–3496000 Pa [16];
for 1,4-dimethylbenzene, interval 642–3501000 Pa [16];
for 3-isopropyltoluene, interval 4117–104884 Pa [17];
for 4-isopropyltoluene, interval 12026–104552 Pa [17];
for 1,3-diethylbenzene, interval 6425–104018 Pa [14];
for 1,4-diethylbenzene, interval 6422–104018 Pa [14];
for 1,3-diisopropylbenzene, intervals 14–184 Pa [18]
and 6666–101325 Pa [19]; and for 1,4-diisopropylben-
zene, intervals 11–143 Pa [18], 6666–101325 Pa [19],
and 6753–104626 Pa [20]. The –í data for tert-butyl-
benzenes and tert-butyltoluenes are reported in [1].
The equilibrium of transformations of alkylbenzenes
was studied in the liquid phase in the presence of a cata-
lytic complex based on aluminum chloride (2–10 wt %).
At a temperature of 363 K or below, a stirred reactor was
used, a constant temperature (±1 K) was maintained with
a heat transfer agent circulating in the reactor jacket. At
temperatures above 363 K, the experiment was run in a
thermostated (±0.5 K) ampule with the periodic agitation
of their contents. The composition of equilibrium mix-
tures in each system was varied over a wide range by
changing the composition of the reactant mixtures, in
which only immediate products of benzene alkylation
with a corresponding alkene were used as components in
all cases. That is, the reaction mixture did not contain com-
ponents other than alkylbenzenes in a chemical nature.
The procedure of the sampling and processing of the reac-
1
1
The experimental values of K and calculated equi-
x
tion mixture and its analysis on a Kristall 2000 M chro- librium constants K for the test reactions were approx-
p
matograph is described in [1].
imated by linear equations with the coefficients given in
4
44

INTERCONVERSION EQUILIBRIUM OF PARA–META ISOMERIZATION
445
Table 3, which also presents values for the reaction Table 1. Results of the study of transformation equilibrium
of alkylbenzenes
T, K Kx
1,4-Dimethylbenzene
enthalpies and entropies calculated on the basis of these
coefficients.
n*
m
± ts
p /p
Kp
fin in
Data on the isomerization equilibrium of xylenes
(
Table 1) cover a wide range of temperatures (355–563 K)
1,3-Dimethylbenzene (1)
and refer to liquid-phase transformations in the presence
2.9a
3.1a
2.9a
2.9b
3.0b
2.7b
3
3
55
73
1
1
1
1
1
1
1
0.967
0.971
0.976
0.967
0.971
0.976
2.8
3.0
2.8
2.8
2.9
of 5–13 wt % BF · HF [2] and gas-phase heterogeneous
3
catalytic transformations at a pressure of 300–6000 atm
[
4]. We found it unreasonable to use the data obtained by
394
355
Allen and Yats [2] for 323 K on Al Br because of the
2
6
abnormal tendency of the equilibrium constant for reac-
3
73
tion (1) to vary (values of K are 4.4, 3.0, and 4.0 at 5, 25,
x
and 50 wt % Al Br , respectively) and the likely distortion
394
2.6
2.7c
2
6
of the results by catalyst complexes with xylenes at high
catalyst concentrations.
5
63
1
,4-Diethylbenzene
1,3-Diethylbenzene (2)
The experimental –í data for xylenes are reliable
2
90
2.31d
2.46e
2.25d
2.16d
2.22d
2.18d
2.16d
2.06k
27
15
11
8
2
4
1
1
1
2
1
1
0.04 1.086
0.07 1.084
0.02 1.081
0.03 1.077
0.01 1.075
0.01 1.074
0.03 1.073
1.069
2.508
and entirely cover the temperature range of the study of
chemical equilibrium. That is, the transition from K to
298
309
2.668
2.433
2.326
2.387
2.341
2.318
2.204
x
K is not complicated by extrapolation problems and

the information on K obtained on the basis of the

3
3
42
57
results of the liquid-phase and gas-phase experiments
agree well with each other.
12
27
9
o
373
The value of ∆ H (g, í ) of reaction (1) is –0.47 ±
r
m
av
3
4
84
43
0
.41 kJ/mol (Table 3) according to equilibrium data.
1
The value of –0.71 kJ/mol (Table 4) with errors of 0.75
and 1.0 kJ/mol for 1,3- and 1,4-dimethylbenzenes,
1
,4-Diisopropylbenzene
1,3-Diisopropylbenzene (3)
o
1.95h
1.89i
1.89i
1.89i
1.87i
1.88j
1.89j
1.92j
1.88j
14
25
31
35
19
21
28
35
68
3
5
6
6
3
4
5
6
7
0.06 1.33
0.03 1.32
0.03 1.30
0.03 1.28
0.01 1.25
0.02 1.32
0.01 1.30
0.03 1.28
0.03 1.25
3-Isopropyltoluene (5)
0.08 1.088
0.04 1.074
0.05 1.061
0.07 1.052
1.106
2.60
2.50
2.45
2.41
2.34
2.48
2.45
2.45
2.35
respectively, was obtained on the basis of ∆ H (g,
298
f
m
2
98 K) [21]. This value suggests either an equality or
3
13
33
53
73
13
33
53
73
the absence of significant effects of the interaction
between the substituents in isomer molecules. The esti-
mation of such an effect for 1,4-dimethylbenzene gives
a value of –0.59 kJ/mol (on the basis of the enthalpies
of formation of benzene, toluene, and 1,3-dimethylben-
3
3
3
3
3
3
3
o
zene) and –0.42 kJ/mol (from ∆ H (g, 298 K) of tolu-
f
m
ene, 1,3-dimethylbenzene, and 1,3,5-trimethyleben-
zene) at the level of errors in the formation enthalpies
from 0.54 to 1.4 kJ/mol.
4
-Isopropyltoluene
The role of the relative significance of different con-
o
1.94f
2.06f
1.92f
2.07f
1.84g
1.83g
3
3
4
4
2
3
33
73
23
73
93
13
35
26
30
26
2
2
3
2
2.11
2.21
2.04
2.18
2.04
2.01
1.96
2.03
2.07
tributions to ∆ S (r, T) of reaction (1) is illustrated in
r
m
i
Fig. 1. From the diagram in the figure, it follows that the
contribution to the symmetry of the molecules is deter-
mining.
Data on the enthalpies of formation of 1,4- and
,3-diethylbenzenes are represented only by the calcu-
1
1.096
lated values (Table 4); moreover, the scatter in these
estimates reaches 2 kJ/mol. Thus, chemical equilibrium
is the only source of information on the magnitude of
the effect of the interaction between the ethyl substitu-
ents on the aromatic ring.
333
1.80g
1.088
1.88g
1.93g
3
3
53
83
1.081
1.071
*
n is the number of determinations of equilibrium constants; m is
the number of series of experiments; the confidence intervals
characterize a divergence between serial values of equilibrium
constants at m > 1 and represent the error of the primary experi-
ment in a series at m = 1.
a [2]; b [3]; c this work; d this work; e [5]; f [6]; g [7]; h [8]; i [9];
j [10]; and k [11].
The published data on the liquid-phase equilibrium
at 298 K on AlCl [5] and at 443 K on zeolite [11] have
3
been complemented in this work and are presented in
Table 1. The values of K were calculated with the use

of the results of the approximation of the experimental

–í data [14] (Table 2) and are reliable enough despite
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

4
46
NESTEROV et al.
Table 2. Results of the approximation of experimental p–T data
Coefficients of equation (1)
Compound
Tb, K
p -p , Pa
in fin
3
A
B
C
10 × D
1
1
3
4
1
1
1
1
,3-Dimethylbenzene
,4-Dimethylbenzene
-Isopropyltoluene
412.302
411.544
448.096
450.264
454.253
456.903
476.32
144-3541200
642-3501000
4117-104884
12026-104552
6425-104018
6422-104018
14-101325
111.4343
115.2534
–384.2800
138.9890
107.5120
112.8617
128.5371
75.75673
–8594.180
–8690.371
7346.640
–16.08437
–16.73104
66.69395
–20.37853
–14.98980
–15.89761
–18.1489
–9.25049
15.23
16.03
–87.64
19.03
11.55
12.74
13.55
1.889
-Isopropyltoluene
–10370.95
–9551.819
–9734.693
–10988.9
–9417.44
,3-Diethylbenzene
,4-Diethylbenzene
,3-Diisopropylbenzene
,4-Diisopropylbenzene
483.443
11-104626
Table 3. Results of the approximation of experimental equilibrium constants
Coefficients
Coefficients
o
m
o
m
o
m
of the equation
o
m
of the equation ln
∆r
S
∆ H
∆rS
Reac-
∆ H
r
(
r
3
–1
3
–1
ln(K ) = a × 10 × T + b
ln(K ) = a × 10 × T + b
tion T , K
x
p
av
l, T ),
(l, Tav),
J/(mol K)
(g, Tav),
kJ/mol
(g, Tav),
J/(mol K)
av
no.
kJ/mol
a
b
a
b
1
,4-Dimethylbenzen
1,3-Dimethylbenzene (1)
1
1
374
401
0.1322
0.7155 –1.10 ± 1.43 5.95 ± 3.83
0.0571
1,3-Diethylbenzene (2)
0.4724 –0.93 ± 0.22 3.93 ± 0.64 0.1251 0.5088
0.8884
–0.47 ± 0.41 7.39 ± 1.05
1
,4-Diethylbenzene
2
2
350
350
0.1120
0.0294
–1.04 ± 0.22 4.23 ± 0.65
–0.92 ± 0.05* 4.59*
1
,4-Diisopropylbenzene
1,3-Diisopropylbenzene (3)
0.1256 0.5213
3
3
338
338
0.5522 –0.24 ± 0.14 4.59 ± 0.43
–1.04 ± 0.13 4.33 ± 0.40
–1.19 ± 0.02* 3.91*
1
,4-Di-tert-butylbenzene
1,3-Di-tert-butylbenzene (4)
4
4
354
354
–0.1520
–0.0888
0.6015
1.26 ± 0.16 5.00 ± 0.45 0.1480 0.3215
–1.23 ± 0.15 2.67 ± 0.44
–1.23 ± 0.07* 3.11*
4
-Isopropyltoluene
3-Isopropyltoluene (5)
–0.0500 0.8668
5
5
364
0.8994
0.74 ± 0.26 7.48 ± 0.73
0.42 ± 0.26 7.21 ± 0.73
–0.05 ± 0.08* 5.86*
o
m
*
The entropy change was calculated by the method of statistical thermodynamics; the enthalpy is the average value of ∆ H (g, T ) cal-
r
av
o
r m
culated for all K values (Table 1) with the use of calculated ∆ S (g, Ti).
p
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

INTERCONVERSION EQUILIBRIUM OF PARA–META ISOMERIZATION
Table 4. Enthalpies of formation of alkylbenzenes considered in this work
447
0
m
0
∆f
H
(g, 298 K),
∆ H (g, 298 K),
f m
Compound
Reference
Compound
Reference
kJ/mol
kJ/mol
Benzene
Toluene
82.89 ± 0.54
50.17 ± 0.42
17.32 ± 0.75
18.0 ± 1.0
–15.9 ± 1.4
29.8 ± 0.8
–21.8
21
21
21
21
21
22
23
24
23
25
1,3-Diisopropylbenzene
1,4-Diisopropylbenzene
–75.4 ± 1.3
–75.3 ± 1.0
–73.1 ± 1.2
–154.6 ± 1.5
–28.4 ± 2.1
–27.7 ± 1.3
–54 ± 2
18
18
26
18
22
27
29
28
29
28
28
1
,3-Dimethylbenzene
,4-Dimethylbenzene
,3,5-Trimethylbenzene
1
1
1,3,5-Triisopropylbenzene
3-Isopropyltoluene
Ethylbenzene
4-Isopropyltoluene
1
1
,3-Diethylbenzene
,4-Diethylbenzene
3-tert-Butyltoluene
3-tert-Butyltoluene
4-tert-Butyltoluene
1,3-Di-tert-butylbenzene
–20.4
–57.6 ± 1.0
–57 ± 2
–
22.3
Isopropylbenzene
3.9 ± 1.1
–129.2 ± 0.8
–129.2 ± 0.6
1
,4-Di-tert-butylbenzene
the fact that they cover only a part of the temperature 1,3-diethylbenzene molecule as compared to the p-iso-
range (from 373 to 443 K) of the chemical equilibrium mer.
study.
The role of the relative significance of different con-
o
o
m
tributions to ∆ S (g, í) of reaction (2) is illustrated in
The enthalpy ∆ H (g, í ) obtained for reaction (2)
r
m
i
r
av
Fig. 2; from this figure, it follows that two contributions
are determining—that is, the symmetry and the vibra-
tional term—although they are oppositely directed.
via the approximation of the data presented Table 1
is –1.04 ± 0.22 kJ/mol (Table 3) and agrees well with
the value –0.92 ± 0.06 kJ/mol. The latter is the average
o
For 1,4- and 1,3-diisopropylbenzenes, there are cal-
of ∆ H (g, í) values calculated for all values of K
r
m
i

o
m
o
orimetric data on ∆
f
H
(g, 298 K) with an error of 1.0–
(
Table 1) using the entropies ∆ S (g, í) found by
m
r i
1
.3 kJ/mol and a discrepancy in estimates by different
means of statistical thermodynamics calculations with
the use of molecular mechanics and quantum-chemical
authors somewhat exceeding 2 kJ/mol (Table 3). It is
obvious that, as in the case of previous systems, a more
methods. The magnitude of the enthalpy term is signif- detailed determination requires an additional source of
icant and indicates the relative stabilization of the information, such as the chemical equilibrium.
6
Xylenes, 298 K
4
2
0
–
–
2
4
Symmetry
Outer
rotation
Inner
rotation
Vibrations
Total
entropy
Fig. 1. Entropy change for reaction (1) with the entropy terms excluded from the equilibrium constant.
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

4
48
NESTEROV et al.
6
4
2
0
2
4
Ethylbenzenes, 298 K
–
–
Symmetry
Outer
rotation
Inner
Vibrations
Total
entropy
rotation
Fig. 2. Entropy change for reaction (2) with the entropy terms excluded from the equilibrium constant.
6
Isopropylbenzenes, 298 ä
4
2
0
–
–
2
4
Symmetry
Outer
rotation
Inner
rotation
Vibrations
Total
entropy
Fig. 3. Entropy change for reaction (3) with the entropy terms excluded from the equilibrium constant.
The data (Table 1) on the equilibrium of the position 0.02 kJ/mol (statistical thermodynamics and quantum-
isomerization of isopropylbenzenes [8–10] refer to the chemical calculations for the entropy). The magnitude
liquid phase in the presence of AlCl . It is important of the enthalpy term is significant and indicates the rel-
3
ative stabilization of the 1,3-diisopropylbenzene mole-
that there are experimental –í data for this reaction
that completely cover the temperature range of the chem-
ical experiment (298–373 K) and there is no need to use
the calculation procedures for pressures approaching
cule with respect to the p-isomer, as in the case of
1
,3-diethylbenzene.
tert-Butylbenzenes (TBBs) complete the series of
30 Pa.
alkylbenzenes with the variable-effective size of alkyl
substituents. For these compounds, we run a target-ori-
ented experiment; its results reported in [1] made it pos-
o
The enthalpy ∆ H (g, í ) of reaction (3) is –1.04 ±
r
m
av
0
.13 kJ/mol (approximation of Table 1 data) or –1.19 ± sible to compare the enthalpy term of the isomerization
6
4
2
0
2
4
tert-Butylbenzenes, 298 ä
–
–
Symmetry
Outer
rotation
Inner
Vibrations
Total
entropy
rotation
Fig. 4. Entropy change for reaction (4) with the entropy terms excluded from the equilibrium constant.
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

INTERCONVERSION EQUILIBRIUM OF PARA–META ISOMERIZATION
449
of di-tert-butylbenzenes with the meta interaction of culated by the Ambrose–Walton method [24] with the
the tert-butyl substituents in TBB molecules.
critical parameters (Table 6) and normal boiling points
(NBP) (Table 2).
o
In this work, ∆ H (g, í ) of reaction (4) serves as
r
m
av.
These systems exhaust the variety of alkylbenzenes
for which not only their chemical para–meta isomeriza-
tion equilibrium have been studied, but also experimen-
tal data on the vapor pressure of the reactants or, at
least, on the NBP of the compounds are available. It is
obvious that, as the structure of the reactant molecules
becomes more complex, it becomes less likely to find
the complete set of experimentally obtained informa-
tion for the description of chemical equilibria in both
liquid- and gas-phase transformations. In this case, an
approach with a minimum of initial information must
inevitably be employed for the prediction of equilib-
rium in the transformations in question.
an important supplement to the data discussed above
and allows the general conclusion that the enthalpy of
para–meta isomerization and, hence, the value of the
enthalpic effect of interaction between 1,3-substituents,
which stabilizes the molecule, depends on the effective
size of the substituents.
An additional support for this conclusion is pro-
vided by the information that is presented in Figs. 1–4
and relates to the contribution of reactions (1)–(4) to
o
m
o
m
∆rS (g, í ). In fact, ∆ H (g, í) of the reaction is
i
r
o
directly related to ∆ S (g, í) at close values of K
r
m
p
(
Table 1) for transformations of the same type. From the
We have shown that a fairly accurate prediction of
the equilibrium is possible for the transformations of
the given type, which includes the calculation (quan-
tum-chemical and by statistical thermodynamics) of
o
data presented in Table 3, it follows that the enthalpy
o
o
∆r H (g, í) and the entropy ∆ S (g, í) of reactions
m
r
m
–1
–1
(1)−(4) regularly change, from 5.5 to 3.1 J mol K and
from –0.47 to 1.23 kJ/mol, respectively, upon passing contributions to ∆
from xylenes to tert-butylbenzenes.
The ratio between the individual contributions to the methods verified for this group of compounds.
S
(g, í) of the reaction of interest
r
m
and the estimation of the NBP of the reactants using the
entropy of the reaction changes in this case (Figs. 1–4).
An increase in the contribution of the vibrational term
The potential of this approach is illustrated by the
material presented in Table 7, which collates the results
of the calculation of the liquid-phase equilibrium con-
stants with the experimental data for the selected sys-
tems. Note that there are no reliable ebulliometric data
on the saturated vapor pressure and normal boiling
point for any component of reactions (6)–(9).
o
leads to a decrease in ∆ S (g, í).
r
m
The entropies of the compounds were calculated by
means of the statistical thermodynamics procedure
using the force-field molecular mechanics method
(Allinger MM2 modernized field) to determine the
As a source of information on the NBP of com-
pounds, we used data obtained using GLC [32]. The
critical parameters were calculated on the basis of the
Randic molecular connectivity indices using the
method described in [30], and the critical pressures
were calculated by the Lydersen method [31]. The val-
ues of the critical properties and the NBP of the com-
pounds used in the calculation of the vapor pressure via
the Ambrose–Walton method [24] are given in Table 6.
geometry of molecules, and rotation barriers, which are
necessary for the calculation of the entropy components
due to both the rotation of the molecule as a whole and
the internal rotation of the groups. The vibration term
of the entropy was calculated by means of the density
functional theory (DFT) with the use of the B3LYP/6-
3
11++G92d,2p) basis set. The application of the
molecular-mechanics method to the calculation of the
rotational terms is caused by the necessity to reduce the
computation time in the matching of the geometric
The procedure used to calculate the equilibrium
parameters used in the entropy terms for the rotation of constants corresponds to the sequence of the presenta-
the molecule as a whole and the internal rotation.
tion of the material in Table 7. Using the statistical ther-
modynamics routine, the rotational (of the molecule as
a whole and groups in the molecule) and vibrational
The coefficients for the equation
o
or
ir
vib
ln∆rS = B(1000/T) + Cln(1000/í) + D(1000/í) (2)
(S + S + S ) contributions to the entropy of the com-
i, m
pounds were calculated; the contribution to the entropy
change (S + S + S ) –(S + S + S ) of the reaction
of the temperature dependence (in the interval 273–598 K),
or
ir
vib
or
ir
vib
fin
in
o
i, m
where ∆rS are the contributions to the entropy due to was determined; the enthalpies of the reactions were
calculated according to Eq. (3) on the basis of the
external and internal rotation or the vibrational term, are
presented in Table 5.
o
obtained data; and, ∆ S (g, í), Kp (calc.), and Kx (calc.)
—
r
from the calculated vapor pressure—were subsequently
found and compared with the experimental values.
A chemical experiment on isopropyltoluenes was
performed in [6, 7] in the presence of AlCl in the liquid
3
In this procedure, only the form of the equation
phase for quite a broad temperature range (293–473 K).
However, this range is covered by experimental
o
or
ir
vib
or
ir
∆
H (g, í) = 0.3253 × [(S + S + + S ) –(S + S +
r
fin
vib
S ) ] – 0.5379 (3) needs to be discussed.

−ídata only for 383–423 K [17]; moreover, these data
in
are not very precise (Table 2). In accordance with the
At present, we consider the linear form to be the
recommendations [1], we used the vapor pressures cal- most appropriate; nonetheless, it should be mentioned
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

4
50
NESTEROV et al.
o
Table 5. Coefficients of equation (1) for contributions to Sm, i (g, T), J/(mol K)
Compound
Contribution
A
B
C
D
1
1
1
1
1
1
1
1
3
4
,3-Dimethylbenzene
I
II
173.38692
119.7602
36.5595
25.03911
17.69353
4.844942
265.0338
25.03911
17.60152
4.812871
257.5387
24.6033
–0.15378
2.094958
–4.32661
–57.5417
–0.15378
2.020043
–4.35438
–63.6043
–0.50654
2.626301
–36.5012
–67.7603
–0.50654
2.676418
–42.1888
–68.6219
–3.9279
–4.08699
–2.88292
–0.79028
16.64064
–4.08699
–2.86824
–0.78338
17.82855
–4.01837
–2.98958
–0.1948
III
IV
I
–18.1545
173.38692
119.1726
36.46228
–11.6082
176.63734
126.7409
129.6799
–30.761
,4-Dimethylbenzene
,3-Diethylbenzene
II
III
IV
I
II
18.32955
–16.1317
362.1126
24.6033
III
IV
I
21.19879
–4.01837
–2.9987
,4-Diethylbenzene
176.63734
125.7706
134.0429
–27.0364
182.11431
131.1319
202.1161
–18.9164
182.11431
130.7269
195.819
II
18.39549
–23.3252
361.0428
20.43969
18.83279
–52.64
III
IV
I
1.00198
21.32205
–3.34253
–3.07248
5.642514
24.98811
–3.34253
–3.08392
4.115881
25.09005
–2.6688
,3-Diisopropylbenzene
,4-Diisopropylbenzene
,3-Di-tert-butylbenzene
,4-Di-tert-butylbenzene
-Isopropyltoluene
II
3.042924
–88.0162
–86.3661
–3.9279
III
IV
I
448.1698
20.43969
18.91069
–45.6074
447.7541
16.32016
19.20202
48.40152
520.4204
16.32016
19.19898
36.01921
517.3181
–0.00204
–0.00637
–30.4799
369.5845
–0.00205
–0.00637
–36.5207
369.2447
II
3.103824
–80.9367
–86.9123
–7.32582
3.34656
III
IV
I
–15.5274
187.17857
134.1915
147.1162
–5.82892
187.17857
134.4036
153.8704
–0.06466
195.0082
139.6636
151.211
II
–3.1325
III
IV
I
–23.025
–8.53619
31.25333
–2.6688
–117.965
–7.32582
3.344556
–35.8231
–120.086
–20.7892
–12.4773
–50.9346
–62.9981
–20.7892
–12.4773
–55.9246
–63.3882
II
–3.13221
–5.20518
31.59949
0.000652
0.001048
3.302536
19.52106
0.000653
0.001048
4.352075
19.64978
III
IV
I
II
III
IV
I
–31.5582
195.0082
139.3144
154.7076
–30.3493
-Isopropyltoluene
II
III
IV
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

INTERCONVERSION EQUILIBRIUM OF PARA–META ISOMERIZATION
451
Table 6. Physicochemical properties used for the prediction of vapor pressure of alkylbenzenes
Compound
T*, K
T*, K
ps*, atm
b
c
3
4
1
1
1
1
1
1
-Isopropyltoluene
448.096a
450.264‡
485b
647.45
650.58
680
28.90
28.90
23.84
23.84
20.41
20.41
20.18
20.18
-Isopropyltoluene
-Isopropyl-3-propylbenzene
-Isopropyl-4-propylbenzene
,3-Di-sec-butylbenzene
,4-Di-sec-butylbenzene
-Butyl-3-sec-butylbenzene
-Butyl-4-sec-butylbenzene
489b
686
508b
696
519b
711
514b
700
523b
719
*
The critical temperatures and critical pressures were calculated according to Randic [30] and Lydersen [31], respectively.
See Table 2; [32].
a
b
that the form of the equation can vary when new exper-
imental data appear.
CONCLUSIONS
On the basis of the results of the study and analysis
Since the results of this work showed the enthalpy of experimental and published data, it was found that
0
∆rH (g, í) of para–meta isomerization to be a variable the enthalpy term of the interaction of alkyl substituents
in the meta position on the aromatic ring is a variable
quantity dependent on the structure of the alkyl substit-
uents.
quantity dependent on the structure of the reactant mol-
ecules, the coefficients for Eq. (3) were determined via
0
the approximation of all ∆ H (g, í) for reactions (1)–
r
0
(
5). The values of ∆ H (g, í) used in this operation
It was shown that the liquid-phase equilibrium con-
were calculated for each temperature of the study of the stants of the para–meta isomerization of alkylbenzenes
r
0
can be predicted with an error of 10 ± 3 rel % (at reac-
tant vapor pressures of at least 30 Pa) using the follow-
ing combination of calculation methods: force-field
molecular mechanics (Allinger modified MM2 field)
for the geometry optimization of molecules and the cal-
culation of the rotation barrier of the groups; the
method based on the density functional theory for the
calculation of the vibrational spectrum of molecules;
Randic molecular connectivity indices and the method
equilibrium from the values of K (Table 1) and ∆ S (g, í)

r
m
found according to the statistical thermodynamics pro-
cedure.
The results presented in Table 7 show that the pre-
diction of the liquid-phase equilibrium constants is sat-
isfactory. The error in the determination of K (at reac-
ı
tant vapor pressures of at least 30 Pa) is 10 ± 3 rel %
even with the use of quite limited initial information, described in [30] for the critical temperature; the Lyder-
the normal boiling points determined for the com- sen index for the critical pressure, and the Ambrose–
pounds using GLC.
Walton method for the vapor pressures.
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

4
52
NESTEROV et al.
Table 7. Results of the prediction of chemical equilibrium
o
o
T, K
∆S*
∆ H (g, T)* ∆ S (g, T)*
Kp (calc)
p /p
Kx (calc)
Kx (exp)
*
∆, %
r
r
fin in
4
-tert-Butyltoluene
3-tert-Butyltoluene (6)
2
2
3
2
3
3
3
3
98
83
03
79
03
23
43
63
1.57
1.57
1.40
1.60
1.40
1.25
1.12
1.01
–0.02
–0.02
–0.08
–0.01
–0.08
–0.13
–0.17
–0.21
7.33
7.33
7.16
7.37
7.16
7.01
6.89
6.77
2.44
1.19
1.21
1.18
1.21
1.18
1.16
1.14
1.13
2.05
2.02
2.06
2.01
2.06
2.10
2.12
2.14
1.778a
1.984a
1.964a
2.094a
2.011a
2.005a
2.290a
2.382a
–15
–2
–5
4
2.44
2.44
2.44
2.44
2.44
2.43
2.42
–3
–5
7
10
1
-Isopropyl-4-propylbenzene
1-Isopropyl-3-propylbenzene (7)
3
3
3
4
33
63
93
23
–1.22
–1.18
–1.14
–1.10
–0.93
4.54
4.58
4.62
4.66
2.42
2.36
2.30
2.26
1.18
1.16
1.14
1.12
2.05
2.04
2.02
2.01
2.25
2.20
2.18
2.16
9
7
7
7
–0.92
–0.91
–0.90
1
,4-Di-sec-butylbenzene
1,3-1,3-Di-sec-butylbenzene (8)
3
3
3
33
63
93
–1.76
–1.80
–1.89
–1.11
–1.12
–1.15
4.01
3.96
3.88
2.42
2.34
2.27
1.60
1.51
1.45
1.51
1.54
1.57
1.78
1.72
1.78
15
10
12
1
-Butyl-4-sec-butylbenzene
1-Butyl-3-sec-butylbenzene (9)
3
3
3
33
63
93
–1.38
–1.40
–1.44
–0.99
–0.99
–1.01
4.38
4.36
2.42
2.35
2.29
1.49
1.42
1.36
1.63
1.66
1.68
1.997
2.021
2.100
18
18
20
4.32
or
ir
ir
vib
∆
∆r
S* was calculated as (S + S + Svib)fin – (Sor + S + S ) .
in
o
H
(g, T)* in l J/mol was calculated according to Eq. (3).
∆rS (g, T)*; was calculated as (S + S + S )fin – (S + S + Svib)in + Rln (σfin – σ ), where σ is the symmetry numbers of molecules.
o
or
ir
vib
or
ir
in
Kx(exp)* was obtained in this work.
∆
, % was calculated as 100(Kx(exp) – Kx(calc))/Kx(exp)
.
a – [1].
PETROLEUM CHEMISTRY Vol. 48 No. 6 2008

INTERCONVERSION EQUILIBRIUM OF PARA–META ISOMERIZATION
453
As a source of information on the normal boiling 14. A. F. Forziati, W. R. Norris, and F. D. Rossini, J. Res.
Natl. Bur. Stand. 43, 555 (1949).
5. D. Ambrose, J. Chem. Thermodyn. 19, 1007 (1987).
points, GLC data can be used.
1
1
6. B. D. Smith and R. Srivastava, Thermodynamic Data for
Pure Compounds. Part A. Hydrocarbons and Ketones.
Physical Science Data (Elsevier, Amsterdam, 1986),
Vol. 25.
7. T. Boublik, V. Fried, and E. Hala, The Vapour Pressures
of Pure Substances (Elsevier, Amsterdam, 1984).
ACKNOWLEDGMENTS
This work was supported by the Russian Federation
Ministry for Education and Science under the 2006–
1
2
208 program “Development of the scientific potential
of the higher school,” project no. RNP.2.1.1.1.1198.
1
1
8. S. P. Verevkin, Thermochim. Acta 316, 131 (1998).
9. F. W. Melpolder, J. E. Woodbridge, and C. E. Heading-
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