Determination of critical temperatures for mixtures of alkylbenzenes

Article abstract of DOI:10.1134/S0965544107060114

The liquid-vapor critical temperatures of benzene mixtures with 1,3-di-tert-butylbenzene, 1,4-di-tert-butylbenzene, and 1,3,5-tri-tert- butylbenzene; a mixture of di-tert-butylbenzene isomers; and a toluene mixture with 3,5-di-tert-butyltoluene were determined over the entire range of composition by means of the amouule method. It was found that the excess critical temperature of the mixtures is related to the critical volumes of the substances. The capabilities of several calculation methods for predicting the critical temperature of mixtures were analyzed on the basis of published data and the obtained results. The Lee-Kesler rules of mixtures were refined by introducing binary interaction parameters.

Full text of DOI:10.1134/S0965544107060114

ISSN 0965-5441, Petroleum Chemistry, 2007, Vol. 47, No. 6, pp. 434–441. © Pleiades Publishing, Ltd., 2007.
Original Russian Text © I.A. Nesterov, A.G. Nazmutdinov, V.S. Sarkisova, T.N. Nesterova, N.N. Vodenkova, 2007, published in Neftekhimiya, 2007, Vol. 47, No. 6, pp. 466–473.
Determination of Critical Temperatures
for Mixtures of Alkylbenzenes
I. A. Nesterov, A. G. Nazmutdinov, V. S. Sarkisova, T. N. Nesterova, and N. N. Vodenkova
Samara State Technical University, Samara, Russia
e-mail: kinterm@samgtu.ru
Received February 7, 2007
Abstract—The liquid–vapor critical temperatures of benzene mixtures with 1,3-di-tert-butylbenzene, 1,4-di-
tert-butylbenzene, and 1,3,5-tri-tert-butylbenzene; a mixture of di-tert-butylbenzene isomers; and a toluene
mixture with 3,5-di-tert-butyltoluene were determined over the entire range of composition by means of the
ampoule method. It was found that the excess critical temperature of the mixtures is related to the critical vol-
umes of the substances. The capabilities of several calculation methods for predicting the critical temperature
of mixtures were analyzed on the basis of published data and the obtained results. The Lee–Kesler rules of mix-
tures were refined by introducing binary interaction parameters.
DOI: 10.1134/S0965544107060114
The critical temperature (T ) is not only a quantity of
1,4-Di-tert-butylbenzene was prepared via the alky-
c
independent value in the establishment of the relation lation of benzene with isobutylene in the presence of
of the properties of substances to their molecular struc- 87% H SO (10–15 vol %). The reaction was carried
2
4
ture; it is also the key property of modern prediction out in a thermostated flask equipped with a stirrer, a
methods based on the law of corresponding states reflux condenser, and a thermometer with a continuous
isobutylene supply to the reaction mixture emulsified
by vigorous stirring. The synthesis temperature did not
exceed 40°ë. The yield of 1,4-diTBB was 80–85 mol %
on a converted benzene basis. The reaction mixture also
contained 10–15% TBB and an insignificant amount of
benzene and isobutylene oligomers. After completion
of the synthesis, the reaction mixture was allowed to
settle and the organic layer was separated by decanta-
tion and was cooled to a temperature of 10°ë. Precipi-
tated 1,4-diTBB crystals were filtered off, washed with
water to neutral reaction, and recrystallized from etha-
nol (90–99 vol %). Pure 1,4-diTBB was isolated via
vacuum distillation.
[
1, 2]. Since new information for the database of exper-
imental critical temperatures is gathered very slowly,
special attention is given to improvement in methods
for the prediction of critical temperatures. In order to
verify the workability of calculation methods and to
modernize them, it is necessary to have experimental
data on the critical temperatures of the most informa-
tive mixtures. It is binary mixtures of this kind that
were the objects of study in the present work. These
mixtures are formed by benzene with 1,3-di-tert-butyl-
benzene
1,4-diTBB), and 1,3,5-tri-tert-butylbenzene (1,3,5-
triTBB); by diTBB isomers; and by toluene with
,5-di-tert-butyltoluene (3,5-diTBT). That is, we con-
(1,3-diTBB),
1,4-di-tert-butylbenzene
(
3
1,3-Di-tert-butylbenzene and 1,3,5-tri-tert-butyl-
sidered alkylbenzenes with strongly different extents of benzene (or 3,5-di-tert-butyltoluene) were prepared via
the alkylation of benzene (or toluene) with 1.5–2-fold
excess of tert-butyl chloride synthesized according to a
known procedure [3] from tert-butanol and concen-
trated HCl. The alkylation was carried out in the pres-
hindering of the aromatic ring by alkyl substituents.
The critical temperatures of these mixtures were deter-
mined for the first time and over the entire range of their
composition.
ence of 10–15 (5–7) wt % AlCl at a temperature of 0°ë
3
in a thermostated flask with stirring for 10–20 (5–7) h.
EXPERIMENTAL
After completion of the reaction, the alkylate con-
taining 1–3 wt % TBB, 8–11 % 1,3-diTBB (10–20%
Used in the experiments were benzene, toluene, and
ethylbenzene samples of the reagent grade for chroma-
tography, with a purity of 99.9% (GLC) and in-house trace amounts of the substrate was separated from the
synthesized tert-butylbenzenes (TBB) and tert-butyl- catalyst complex and treated with a mixture of ice and
toluenes (TBT), namely, 1,3-di-tert-butylbenzene, 15% HCl for decomposition of the dissolved residual
,4-di-tert-butylbenzene, 1,3,5-tri-tert-butylbenzene, catalyst. The organic layer was separated, washed with
and 3,5-di-tert-butyltoluene. a sodium bicarbonate solution and water, and dried over
3
1
-TBT), 7–10% 1,4-diTBB (7–12% 4-TBT), 70–80%
,3,5-triTBB (55–70% 3,5-diTBT), impurities, and
1
4
34

DETERMINATION OF CRITICAL TEMPERATURES
435
Na SO or CaCl . The alkylate was fractionated by
∆ícm, ä
2
4
2
sharp rectification under vacuum on a laboratory frac-
tionating column.
The tert-butylbenzenes used had the following
purity according to GLC data: 1,3-diTBB, 98.3%
40
- 1
3
5
-
-
-
-
2
30
25
3
4
5
(
1,4-diTBB as the only impurity); 1,4-diTBB, 99.9%;
2
1
1
0
5
0
5
0
5
1
,3,5-triTBB, 99.7%; and 3,5-diTBT, 99.8 wt %.
- 6
- 7
The critical temperatures were determined by means
-
-
8
9
of the ampoule method, monitoring the disappearance
of the meniscus upon heating and its appearance upon
cooling [4]. The schematic of the setup and the experi-
mental procedure were reported in the previous paper
0
.2
0.4
0.6
0.8
1.0
-
X , mole (mass) fractions
1
[4]. tert-Butylbenzenes are unstable under the condi-
tions of long-term exposure to high temperatures,
unlike the methyladamantanes studied earlier [4],
Fig. 1. Excess critical temperatures of the (1) benzene–eth-
ylbenzene, (2, 9) benzene–isopropylbenzene, (3) benzene–
1
,3-di-tert-butylbenzene, (4) benzene–1,4-di-tert-butylben-
zene, (5) toluene–3,5-ditert-butyltoluene, (6) benzene–
,3,5-tri-tert-butylbenzene, and (7) 1,3-di-tert-butylben-
which possess í values close to those of TBB. There-
Ò
fore, because of the considerable thermal degradation
of the tert-butyl substituents, it was necessary to exer-
cise a special approach, the maximum allowable reduc-
tion in the time of the experiment.
1
zene–1,4-di-tert-butylbenzene mixtures against the compo-
sition expressed in mole fractions, and the (8) toluene–3,5-
ditert-butyltoluene and (9) benzene–isopropylbenzene mix-
tures with the composition expressed in mass fractions.
The quality of most test mixtures was monitored
gas-chromatographically both before and after the
experiment. The results of monitoring of the composi-
tion of the test compounds before and after the mea-
these mixtures are 4.7 and 3.4 K, respectively. For all
other alkylbenzene mixtures examined, the values of
surements of í , the values of the critical temperatures,
Ò
∆T are much lower, not exceeding 2 K at maximum.
cm
and the measurement time are presented in Table 1.
We complemented the existing database of Kay
binary interaction parameters [1] with some structures
that have been absent from it.
The analysis was carried out on a Kristall-2000M
work station operated by means of the version 2.2
Chromatec-Analytic software and equipped with a
flame-ionization detector and a quartz capillary column
The Lee–Kesler mixing rules
(
30 × 0.00025 m) with the bonded OV-101 liquid phase
1
V
cm
1/3
1/3
3
1/2
Tcm = -----------
y y (V + V ) (T T )
i j ci cj ci cj
and a split ratio of 1 : 40. The carrier-gas (helium) flow
rate was 2 ml/min. The evaporator temperature was
∑∑
8
i
j
3
50°ë, the detector temperature was 300°ë, and the
are recommended in [1] for normal liquids and are
extensively used for predicting most intermolecular
interaction-dependent properties with the use of meth-
ods based on the law of corresponding states. We
attempted to apply the mixing rule in the original ver-
sion [1]; however, the results turned out to be worse that
column oven temperature was programmed from 30 to
1
50°ë K at a heating rate of 5°C/min.
RESULTS AND DISCUSSION
Table 1 lists the experimental values of the critical in the case of application of Kay’s rule and the Higashi
temperatures with their standard deviations ( = 0.05); method. To increase the efficiency of this widely used
the coefficients (Ä for the Redlich–Kister equation method, we complement the above equation with the
1
–3
[5] calculated for the test mixtures; the binary interac- parameters of binary interactions
tion parameters for the three mixing rules that we have
selected: the quadratic form of Kay’s rule [1, 4], Lee–
Kesler rule [1] with the binary interaction parameters
that we introduced, and the Higashi rule [6, 7]; and the
1
1/3
1/3
3
1/2
Tcm = -----------
k y y (V + V ) (T T ) ,
ij i j ci cj ci cj
∑∑
8V
cm
i
j
where k = k = 1, and k are determined via the least-
mean absolute deviations in í estimated by these
ii
jj
ij
Ò
square treatment of experimental data.
methods.
The Higashi binary interaction parameters, being
surprisingly simple:
A dramatic decrease in the level of critical tempera-
tures on passing from mole to mass fractions indicates
that the critical temperatures of mixtures (T ) are
cm
Tcm = θ T + θ T + 2θ θ ∆ ,
1
c1
1
c2
1
2
T
related to the critical volumes (V ) of individual sub-
c
stances. Figure 1 depicts the dependence of the excess
critical temperatures on the mass fractions of the com-
ponents only for the benzene–isopropylbenzene and
toluene–3,5-diTBT systems characterized by the high-
est values of ∆T . The maximal values of ∆T for
2/3
ci
x V
i
where θ = --------------------- , i = 1, 2,
i
2
2
cj
/3
xjV
∑
cm
cm
i = 1
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

4
36
NESTEROV et al.
Table 1. Results of investigation of the critical temperatures of alkylbenzene mixtures
Composition X /X , wt %
Tcm exp – Tcm calcd
1
2
Experimenttime,
c
Tcm exp, K
before
after
experiment
min
a
b
I
II
III
experiment
Benzene–ethylbenzene (A = 15.567, A = 6.9172, A = 33.055, /∆Tcm, av/ = 0.7)
1
2
3
Binary interaction parameters
1.016
0.0
1.009
0.0
2.700
0.0
0
.0/99.9
617.55
1
3
4
4
7
7
9.70/80.30
8.04/61.96
3.88/56.12
5.23/54.77
0.45/29.55
8.16/21.84
–
–
–
–
–
–
596
522
326
50
441
221
607.3 ± 0.3
597.2 ± 0.2
593.5 ± 0.1
590.3
581.2 ± 0.3
575.7 ± 0.2
562.05
0.0
0.2
–0.3
–2.6
2.6
0.3
0.2
–0.3
–2.7
2.3
1.2
2.3
–2.7
–0.3
0.2
1.5
0.0
1.2
0.0
0.3
0.0
9
9.9/0.0
Mean absolute error, /∆Tcm, av/, K
0.9
0.9
0.9
Benzene–isopropylbenzene [8] (A = 49.014, A = 16.374, A = –8.4171, /∆Tcm, av/ = 0.3)
1
2
3
Binary interaction parameters
1.042
1.027
0.0
–0.9
–0.1
0.2
0.5
–0.1
0.8
11.99
0.0
–0.7
0.1
0.2
0.4
–0.2
0.7
–1.0
0.0
0
.0/
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
–
631.0
622.4
614.4
596.8
590.0
584.7
582.3
578.0
562.05
0.0
–2.2
–1.1
0.6
1.3
0.8
1.7
–0.1
0.0
2
3
6
7
7
8
8
1.73/
9.89/
6.66/
4.96/
9.94/
3.28/
5.73/
–0.9
0.0
1
.0/
Mean absolute error, /∆Tcm, av/, K
0.9
0.4
0.4
Benzene–1,3-di-tert-butylbenzene (A = 114.26, A = 27.690, A = 2.6223, /∆Tcm, av/ = 0.0)
1
2
3
Binary interaction parameters
1.096
1.048
0.0
1.2
0.2
–0.6
0.0
16.85
0.0
1.3
0.3
–0.6
0.0
0
.0/98.3
687.6
0.0
–2.8
0.3
1.2
0.0
5
.92/94.08
6.41/84.29
49.49/48.65
52.63/46.36
345
215
224
681.9 ± 0.3
638.4 ± 0.3
626.3 ± 0.1
562.05
4
4
0.02/59.98
8.79/51.21
9
9.9/0.0
Mean absolute error, /∆Tcm, av/, K
0.9
0.4
0.5
Benzene–1,4-di-tert-butylbenzene (A = 109.09, A = 36.852, A = 66.507, /∆Tcm, av/ = 0.5)
1
2
3
Binary interaction parameters
1.093
1.048
0.0
1.0
–1.0
–0.3
2.5
15.40
0.0
1.1
–1.0
–0.4
2.4
0
.0/99.9
702.9
0.0
–2.8
–1.6
4.3
4.8
0.0
1
2
5
9
3.89/86.11
9.25/70.75
6.73/43.27
0.50/9.50
14.69/67.91
28.48/65.60
58.05/41.62
91.34/8.60
254
417
304
359
684.3 ± 0.2
660.1 ± 1.3
621.4 ± 0.3
577.3 ± 0.2
562.05
9
9.9/0.0
0.0
0.0
Mean absolute error, /∆Tcm, av/, K
2.3
0.8
0.8
Benzene–1,3,5-tri-tert-butylbenzene (A = 141.88, A = 89.374, A = 70.146, /∆Tcm, av/ = 0.0)
1
2
3
Binary interaction parameters
1.122
0.0
1.065
0.0
24.28
0.0
0
.0/99.7
700.5
7
.51/92.49
8.47/64.11
32.09/63.87
73.38/26.62
570
639
316
690.7 ± 0.4
658.6 ± 0.2
600.1 ± 0.6
562.35
–6.7
0.9
9.5
–0.5
–0.9
1.8
–0.2
–0.9
1.4
3
7
0.51/69.49
3.38/26.62
9
9.9/0.0
0.0
0.0
0.0
3
.4
0.6
0.5
Mean absolute error, /∆Tcm, av/, K
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

DETERMINATION OF CRITICAL TEMPERATURES
437
Table 1. (Contd.)
Composition X /X , wt %
Tcm exp – Tcm calcd
II
1
2
Experimenttime,
c
Tcm exp, K
before
after
experiment
min
a
b
I
III
experiment
1
,3-Di-tert-butylbenzene–1,4-di-tert-butylbenzene (A = 5.2463, A = 3.6386, A = –34.204, /∆Tcm, av/ = 0.0)
1 2 3
Binary interaction parameters
1.000
1.000
0.0
–0.004
0.0
0
.0/99.9
−
702.9
0.0
–0.1
0.4
3
6
7
1.87/68.13
8.23/31.77
5.95/24.05
−
−
−
−
170
385
299
697.9 ± 0.4
692.9 ± 0.5
690.9 ± 1.0
687.6
–0.1
0.4
–0.1
0.4
–0.4
0.0
–0.4
0.0
–0.4
0.0
9
8.3/0.0
Mean absolute error, /∆Tcm, av/, K
0.2
0.2
0.2
Toluene–3,5-di-tert-butyltoluene (A = 75.140, A = 31.836, A = –3.4323, /∆Tcm, av/ = 1.3)
1
2
3
Binary interaction parameters
1.060
1.029
0.0
9.865
0.0
0
.0/99.8
−
695.5
0.0
–3.9
–1.7
–3.7
–1.0
4.2
7
.07/92.93
7.22/69.29
242
516
149
326
220
277
360
134
296
413
686.2 ± 1.0
676.4 ± 0.6
673.3 ± 0.5
651.6 ± 0.4
655.9 ± 0.6
638.4 ± 0.8
640.2 ± 0.6
619.8 ± 1.9
601.9 ± 0.5
599.5 ± 0.3
591.75
–1.8
0.6
–1.7
0.6
1
1
3
4
5
5
7
9
9
8.41/81.59
9.40/80.60
9.72/60.28
0.44/59.56
1.90/48.10
2.56/47.44
0.88/29.12
1.57/8.43
−
−
–1.5
–1.4
3.6
–1.4
–1.5
3.6
40.21/55.83
40.57/57.34
−
0.0
–1.8
0.7
–1.9
0.6
−
2.5
71.06/28.49
1.6
–0.8
2.0
–0.9
1.9
91.82/8.03
3.1
3.88/6.12
−
−
2.6
1.8
1.8
9
9.9/0.0
0.0
0.0
0.0
Mean absolute error, /∆Tcm, av/, K
Mean absolute error of the entire sample
2.0
1.3
1.3
1.50
0.67
0.66
a
b
c
d
The composition was determined gravimetrically.
The composition was determined chromatographically. The total concentration of unidentified components is x = 100 – X – X , %.
The residence time in the region of critical and near-critical temperatures.
The prediction results for critical temperatures of mixtures with the use of (I) the quadratic form of Kay’s rule [1], (II) the Lee–Kesler mix-
ing rules [1] with the binary interaction parameters that we introduced, and (III) the Higashi mixing rules [6, 7].
1
2
proved to be effective for compounds from different mental data with the Redlich–Kister equation. In this
classes, including polar substances [6, 7, 9, 10].
case, the Lee–Kesler and Higashi methods, which sug-
gest the direct relation of Tcm to the critical volumes of
the compounds, ensure the best prediction; the mean
absolute error over the entire sample (Table 1) is 0.67
and 0.66, respectively, versus 1.50 according to Kay’s
method.
The binary interaction parameters for all methods
and all of the test systems are given in Table 1 as having
been determined from experimental data. The critical
properties of individual compounds used for optimiza-
tion are presented in Table 2.
Note that the data for the benzene–1,3,5-triTBB,
benzene–1,4-diTBB and toluene–3,5-diTBT systems
have a greater error in the case of application of Kay’s
rule. This deviation may be due to the large values of
the corresponding critical volumes of the compounds.
An analysis of the results (Table 1) shows that the
use of the binary interaction parameters of all of the
types in question is effective for the systems of alkyl-
benzenes having different molecular structures up to
the complete hindrance of the aromatic ring by alkyl
substituents, the mean absolute error in all cases is
For this reason, it is necessary to consider the corre-
comparable to the error of approximation of experi- lation of the binary interaction parameters with the crit-
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

4
38
NESTEROV et al.
Table 2. Critical properties of hydrocarbons used for analysis of experimental data
3
3
Compound
Benzene
Tc, K
Vc, cm /mol
Compound
1,3-diTBB
Tc, K
Vc, cm /mol
562.05 [2]
591.75 [2]
617.15 [2]
631.0 [2]
256 [2]
316 [2]
374 [2]
434.7 [2]
687.6 [11]
702.9 [11]
700.5 [11]
695.5 [11]
672e
672e
877e
726e
Toluene
1,4-diTBB
Ethylbenzene
Isopropylbenzene
1,3,5-triTBB
3
,5-diTBT
Cyclohexane
Methane
Ethane
553.5 [2]
296.88 [2]
98.6 [2]
1,3-Dimethyladamantane
1,3,5-Trimethyladamantane
2-Methylpentane
706.7 [4]
701.9 [4]
497.50 [2]
433.75 [2]
530.10 [2]
559.60 [2]
587.00 [2]
571.45 [2]
611e
190.56 [2]
305.32 [2]
369.83 [2]
469.70 [2]
507.60 [2]
617.70 [2]
145.5 [2]
200.0 [2]
311.0 [2]
368.0 [2]
624.0 [2]
366.7 [2]
303.2 [2]
421.0 [2]
488.2 [2]
529.0 [2]
Propane
2,2-Dimethylpropane
2-Methylhexane
n-Pentane
n-Hexane
n-Decane
2-Methylheptane
2-Methyloctane
e
Calculated according to the Lydersen method [1].
ical volumes of the compounds involved in the interac- ladamantane and cyclohexane–1,3,5-trimethyladaman-
tion. This approach was practiced by Kay [1] and tane systems studied earlier [4] (Fig. 2c) fit well the
turned out to be successful for the relevant group of general correlation. We suppose that, to resolve this
compounds. Of a broad set of combinations of binary- problem, it is necessary to complement the array of
mixture components, Kay distinguished two groups of experimental data with information on mixtures of
substances related by independent equations. More- alkanes for which 0.5 > V /V > 2.
ci
cj
over, all organic compounds were approximated by the
same universal equation.
Although works on the perfection of experimental
methods for determining the critical temperatures of
substances that have low thermal stability continue
The models that we selected for study and comple-
mented with published data (Table 3) for alkane mix-
tures [5, 12, 13] make it possible to partly explain the
cause of this unity. From Fig. 2a, it follows that the Kay
binary interaction parameters for the mixtures of ter-
tiary alkylbenzenes with benzene or toluene form an
individual series that diverges from the alkane–alkane
series, for which data are well consistent with the gen-
eral correlation given in [1] for organic substances.
Thus, the general correlation equations for binary inter-
action parameters should be used with a great care, bet-
ter, after their experimental verification. It is likely that
such correlations will be more rigorous for compounds
from the same class belonging to normal liquids or
compounds that are close in nature and their intermo-
lecular interaction energy monotonically varies with a
change in the size of molecules in the molecular vol-
umes of substances.
[
14–16], not everything is directly measurable. In some
cases, an indirect approach appears to be fruitful. Let us
give an example.
There are two values of the critical temperature for
,4-diTBB: Steele [17] obtained a value of 708 K by
1
means of the DSC technique, and we determined it by
the ampule method to be 702.9 K [11]. The discrepancy
of 5 K is beyond the limits of the error of the methods.
The temperature level used, however, did not rule out
the partial degradation and consolidation of molecules.
The experimental data for the benzene–1,4-diTBB sys-
tem can serve as a source of additional information in
this case. At a 1,4-diTBB concentration up to 70 wt %
(
50 mol %) in this system, the critical temperature of
the mixture is 40 K or more below the í of 1,4-diTBB,
Ò
a fact that is very important in the case of high-temper-
ature experiments.
The result of analysis of the dependence for the
We treated the experimental results for the benzene–
Lee–Kesler binary interaction parameters (Fig. 2b) 1,4-diTBB system by means of the Lee–Kesler and
leads to the same conclusion: alkanes and tert-alkyl- Higashi methods, as the most accurate of those consid-
benzenes form independent series. As regards the ered in this work, over the range 562.1–660.6 K
Higashi parameters (Fig. 2c), such a conclusion is not (Table 1). Using the binary interaction parameters cal-
obvious. It cannot be ruled out that the groups of com- culated by the equations for alkylbenzenes (Figs. 2b,
pounds under consideration obey a general law, espe- 2c) as L = 1.045 and ∆T = 16.05, we obtained values
ij
cially, in the view that the cyclohexane–1,3-dimethy- of 703.5 and 701.2 K, respectively for the í of
Ò
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

DETERMINATION OF CRITICAL TEMPERATURES
439
Table 3. Results of analysis of published experimental data on the critical temperatures of hydrocarbon mixtures
f
f
Tcm exp – Tcm calc , K
Tcm exp – Tcm calc , K
X , mole
X , mole
1
1
T , K
T , K
cm
cm
fraction
fraction
I
II
III
I
II
III
Cyclohexane–1,3-dimethyladamantane [4]
Cyclohexane–1,3,5-trimethyladamantane [4]
(
A = 82.272, A = 33.864, A = –7.0476, /∆Tcm, av/ = 0.6) (A = 88.286, A = 24. 212, A = –27.630, /∆Tcm, av/ = 0.1)
1
2
3
1
2
3
Binary interaction
parameters
1.064
1.033
7.964
Binary interaction
parameters
1.075
1.039
11.03
1
.0000
.9349
.7073
.4625
.2010
.0556
.0000
553.5
568.3
619.3
654.8
685.5
701.4
706.7
0.0
–0.1
4.2
–1.1
–3.4
–1.0
0.0
0.0
–1.5
2.3
–0.7
–1.7
–0.2
0.0
0.0
–1.5
2.2
–0.8
–1.7
–0.3
0.0
0.0000
0.3534
0.5078
0.7572
0.8485
1.0000
701.9
668.5
648.8
609.2
591.4
553.5
0.0
–2.4
–1.2
2.4
3.3
0.0
0.0
–0.1
–0.6
0.1
0.8
0.0
0.0
–0.1
–0.6
0.1
0.8
0.0
0
0
0
0
0
0
Mean absolute error
1.4
0.9
0.9
Mean absolute error
1.6
0.3
0.2
Methane–ethane [5]
n-Pentane–n-hexane [5]
(
A = 58.320, A = 15.342, A = –11.784, /∆Tcm, av/ = 0.0)
(A = 7.500, A = 4.500, A = 0.000, /∆Tcm, av/ = 0.0)
1
2
3
1
2
3
Binary interaction
parameters
1.121
1.107
15.36
Binary interaction
parameters
1.008
1.005
1.658
0
.0000
.2000
.4000
.6000
.8000
.0000
305.4
290.9
272.8
251.3
225.0
190.5
0.1
–1.1
–1.0
0.4
1.9
–0.1
0.8
0.1
–0.2
–0.5
0.0
0.8
–0.1
0.3
0.1
0.0
–0.4
–0.1
0.7
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
507.7
500.8
494.0
486.9
478.9
469.7
0.1
–0.4
–0.2
0.2
0.4
0.0
0.1
–0.4
–0.2
0.2
0.4
0.0
0.1
–0.4
–0.2
0.2
0.4
0.0
0
0
0
0
1
–0.1
0.2
Mean absolute error
Mean absolute error
0.2
0.2
0.2
Ethane–propane [12]
n-Pentane–n-decane [5]
(
A = 23.187, A = 6.0368, A = –2.6261, /∆Tcm, av/ = 0.3)
(A = 118.12, A = 59.375, A = 0.0001, /∆Tcm, av/ = 0.0)
1
2
3
1
2
3
Binary interaction
parameters
1.035
1.025
5.105
Binary interaction
parameters
1.109
1.073
26.51
0
.0000
.1202
.2398
.3598
.4803
.5807
.6603
.7389
.8205
.8997
.0000
369.8
364.0
358.0
352.5
344.1
337.9
333.1
327.5
321.4
314.1
305.3
0.0
–0.6
–0.7
0.3
–0.8
–0.3
0.4
0.7
1.0
0.1
0.0
0.0
–0.4
–0.4
0.6
–0.7
–0.4
0.2
0.4
0.7
–0.1
0.0
0.0
–0.4
–0.4
0.6
–0.7
–0.4
0.2
0.4
0.6
–0.1
0.0
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
617.7
601.3
584.0
560.1
523.9
469.7
0.0
–5.7
–2.8
2.9
5.7
0.0
0.0
–2.8
–1.2
1.2
1.8
0.0
0.0
–2.5
–1.0
1.0
1.3
0.0
0
0
0
0
0
0
0
0
0
1
Mean absolute error
2.9
1.2
1.0
Mean absolute error
0.5
0.3
0.3
Propane–2-methylpentane [5]
2,2-Dimethylpropane–n-hexane [5]
(
A = 72.207, A = 16.121, A = 0.55339, /∆Tcm, av/ = 0.0)
(A = 16.309, A = –5.0208, A = 1.1393, /∆Tcm, av/ = 0.0)
1
2
3
1
2
3
Binary interaction
parameters
1.083
1.051
10.72
Binary interaction
parameters
1.017
1.013
3.419
0
.0000
.2000
.4000
.6000
.8000
.0000
497.7
482.0
463.0
439.0
408.5
369.8
0.2
–1.5
–0.8
0.8
1.6
0.0
0.2
0.1
0.2
0.0
–0.3
0.0
0.2
0.1
0.2
0.0
–0.4
0.0
0.0000
0.2000
0.4000
0.6000
0.8000
1.0000
507.7
496.0
482.2
467.0
450.7
433.8
0.1
0.5
0.2
–0.2
–0.5
0.1
0.1
0.7
0.3
–0.3
–0.6
0.0
0.1
0.7
0.3
–0.3
–0.6
0.1
0
0
0
0
1
Mean absolute error
0.8
0.1
0.2
Mean absolute error
0.3
0.3
0.3
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

4
40
NESTEROV et al.
Table 3. (Contd.)
f
f
Tcm exp – Tcm calc , K
Tcm exp – Tcm calc , K
X , mole
X , mole
1
1
T , K
T , K
cm
cm
fraction
fraction
I
II
III
I
II
III
2
-Methylpentane–2-methylhexane [13]
2-Methylpentane–2-methylheptane [13]
(
A = 8.5645, A = 0.78821, A = 5.2895, /∆Tcm, av/ = 0.1)
(A = 18.899, A = 9.4274, A = 16.203, /∆Tcm, av/ = 0.3)
1
2
3
1
2
3
Binary interaction
parameters
1.009
1.007
3.180
Binary interaction
parameters
1.060
1.014
5.077
0
.0000
.1207
.3326
.5473
.7210
.9080
.0000
530.43
527.3
521.3
514.3
508.7
501.5
497.75
0.3
0.1
0.0
–0.3
0.2
0.2
0.3
0.2
0.1
0.0
0.0
0.1
0.0
0.0
0.1
0.2
0.3
0.2
0.0
–0.3
0.2
0.2
0.3
0.2
0.0000
0.1375
0.3286
0.5698
0.7547
0.9206
1.0000
559.7
554
0.1
0.4
–1.6
0.2
0.9
1.1
0.3
0.7
0.1
0.6
–1.4
0.1
0.7
0.9
0.3
0.6
0.1
0.6
–1.4
0.1
0.6
0.9
0.3
0.6
0
0
0
0
0
1
542.4
529.8
517.7
505.1
497.75
Mean absolute error
Mean absolute error
2
-Methylhexane–2-methylheptane [13]
2-Methylheptane–2-methyloctane [13]
(
A = 7.8774, A = 2.5267, A = 14.724, /∆Tcm, av/ = 0.2)
1
2
3
Binary interaction
parameters
1.010
1.008
3.767
Binary interaction
parameters
(1.0)
(1.0)
(9.5)
0
0
0
0
0
0
1
.0000
.1301
.3236
.5363
.7768
.9074
.0000
559.6
557.3
552.0
545.9
538.8
534.8
530.43
0.0
0.4
–0.3
–0.5
0.3
0.0
0.4
–0.3
–0.5
0.2
0.0
0.4
–0.3
–0.5
0.2
0.0000
0.1384
0.3938
0.5976
0.7854
0.9272
1.0000
582.87
577.4
560.9
543.7
525.1
507.3
497.75
–4.1
–2.1
–0.6
0.4
1.5
0.5
–4.1
–1.5
–0.2
0.1
0.9
0.1
–4.1
–1.5
–0.2
0.1
0.8
0.1
1.1
0.3
1.0
0.3
1.0
0.3
0.3
0.3
0.3
Mean absolute error
0.4
0.4
0.4
2
-Methylhexane–2-methyloctane [13]
2-Methylpentane–2-methyloctane [13]
Binary interaction
parameters
(1.0)
(1.0)
(5.5)
Binary interaction
parameters
(1.0)
(1.0)
(0.54)
0
0
0
0
0
0
1
.0000
.1270
.3516
.5675
.7519
.9199
.0000
582.87
579.9
571.2
559.8
548.6
537
–4.1
–2.0
–0.2
0.3
0.7
0.9
–4.1
–1.9
–0.1
0.2
0.5
0.8
–4.1
–1.9
–0.1
0.2
0.5
0.7
0.0000
0.1080
0.3224
0.5235
0.7265
0.9075
1.0000
582.87
581.1
576.9
572.7
568.1
562.9
559.7
–4.1
–3.2
–1.8
–0.6
0.5
–4.1
–3.2
–1.8
–0.6
0.5
–4.1
–3.2
–1.8
–0.6
0.5
0.6
0.1
0.5
0.1
0.5
0.1
530.43
0.3
0.3
0.3
f
The prediction results for critical temperatures of mixtures with the use of (I) the quadratic form of Kay’s rule [1], (II) the Lee–Kesler mix-
ing rules [1] with the binary interaction parameters that we introduced, and (III) the Higashi mixing rules [6, 7].
1
.4-diTBB. The average value 702.4 K is consistent tion, there are experimental data [13] for 2-methyloc-
with the results of direct determination and, what is tane mixtures. These data can be used for the estimation
more important, complements the array of data on í of
Ò
of the critical temperature of 2-methyloctane if the
information region is limited to a temperature of 573 K.
By means of calculating the binary interaction parame-
ters via the equations given in Figs. 2b and 2c, we
1
,4-diTBB.
The situation in the alkane group is close to the one
discussed above. The values of í adopted for individ-
Ò
obtain the following set of í values for 2-MO, in K:
ual compounds in the literature agree well with the
results of studies of the critical temperatures for almost
all mixtures (Tables 2, 3). However, this is not the case
Ò
5
86.6 and 587.1, 587.1 and 588.5, and 587.2 and 587.1
with the use of the Lee–Kesler and Higashi methods as
for 2-methyloctane (2-MO) for which these are two applied to the systems 2-methylpentane–2-MO, 2-
known values, 587.00 [2] and 582.87 K [13]. In addi- methylhexane–2-MO, and 2-methylheptane–2-MO,
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007

DETERMINATION OF CRITICAL TEMPERATURES
441
kij
ACKNOWLEDGMENTS
(
a)
1.14
This work was supported by the Program “Develop-
ment of the Scientific Potential of Higher School
(2006–2008),” RNP.2.1.1.1198.
y = 0.1118x + 0.8842
1
.12
.10
.08
.06
.04
.02
.00
1
1
1
1
1
1
-
-
1
2
y = 0.0536x + 0.9454
- 3
REFERENCES
1
2
3
4
5
. R. C. Reid, J. M. Prausnitz, and T. K. Sherwood, The
Properties of Gases and Liquids (McGraw-Hill, New
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Properties of Gases and Liquids (McGraw-Hill, New
York, 2001).
Lij
(
b)
1
1
1
1
1
.08
y = 0.0736x + 0.921
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Experimentierkunst (Johann Ambrosius Barth, Leipzig,
.06
.04
.02
.00
-
-
-
1
2
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1
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(2006)].
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Thermophysical and Thermochemical Data (CRC, Boca
Raton, 2000).
∆
T
6
7
. Y. Higashi, J. Chem. Eng. Data 42, 1269 (1997).
(
c)
3
0
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Data 49, 1615 (2004).
2
2
1
1
5
0
5
0
5
0
y = 22.48x + 24.184
8
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Eng. Chem. Res., 42, 6531 (2003).
-
1
- 2
y = 9.6358x + 9.2477
9. K. Otake, Y. Uchida, M. Yasumoto, et al., J. Chem. Eng.
-
3
Data 49, 1643 (2004).
10. M. Yasumoto, Y. Uchida, K. Ochi, et al., J. Chem. Eng.
Data 50, 596 (2005).
1
.0
1.5
2.0
2.5
3.0
3.5
Vi /V
11. I. A. Nesterov, T. N. Nesterova, A. G. Nazmutdinov,
et al., Zh. Fiz. Khim. 80, 2032 (2006).
j
1
1
1
2. L. Freitas, G. Platt, and N. Henderson, Fluid Phase
Fig. 2. Binary interaction parameters according to the
Equilib. 225, 29 (2004).
(
a) Kay, (b) Lee–Kesler, and (c) Higashi mixing rules for
3. J. A. Abara, D. W. Jennings, W. B. Kay, and A. S. Teja, J.
(1) alkylbenzenes, (2) methyladamantanes, and (3) alkanes.
Chem. Eng. Data 33, 242 (1988).
4. E. D. Nikitin, A. P. Popov, and Y. G. Yatluk, J. Chem.
Eng. Data 51, 1335 (2006).
respectively. The average value is 587.5 K, which is
practically the same as that adopted in [2].
15. D. M. Von Niederhausern, G. M. Wilson, and N. F. Giles,
J. Chem. Eng. Data 51, 1986 (2006).
Thus, the results of the study on the critical temper-
atures of the mixtures not only are important as such but 16. W. V. Steele, J. Chem. Thermodyn. 27, 135 (1995).
also can be a source of information for estimation of íÒ 17. W. V. Steele, R. D. Chirico, S. E. Knipmeyer, and
of thermally unstable compounds.
A. Nguyen, J. Chem. Eng. Data 42, 1021 (1997).
PETROLEUM CHEMISTRY Vol. 47 No. 6 2007