This document summarizes a study on the liquid-liquid equilibrium of the ternary system composed of methanol, benzene, and hexane at different temperatures. Experimental data on the compositions of the coexisting liquid phases are reported at 278.15 K, 283.15 K, and 293.15 K. The data show that increasing the temperature decreases the miscibility gap between the methanol-rich and hexane-rich phases. Models like UNIQUAC and NRTL are able to correlate the experimental equilibrium data reasonably well at the different temperatures, while UNIFAC predicts a larger immiscibility region than observed.

1. Fluid Phase Equilibria 305 (2011) 34–38
Contents lists available at ScienceDirect
Fluid Phase Equilibria
journal homepage: www.elsevier.com/locate/fluid
Influence of temperature on the (liquid + liquid) equilibria of
{methanol + benzene + hexane} ternary system
Mónica B. Gramajo de Doz∗
, Carlos M. Bonatti, María C. Lucena, Diego A. González, Marcos E. Mancilla
Departamento de Física - Facultad de Ciencias Exactas y Tecnología, Universidad Nacional de Tucumán, Avenida Independencia 1800, 4000 Tucumán, Argentina
a r t i c l e i n f o
Article history:
Received 19 November 2010
Received in revised form 23 February 2011
Accepted 25 February 2011
Available online 4 March 2011
Keywords:
Data
Liquid–liquid equilibria
Ternary system
Methanol
Benzene
Hexane
a b s t r a c t
In order to show the influence of temperature on the liquid–liquid equilibria (LLE) of
{methanol (1) + benzene (2) + hexane (3)} ternary system, equilibrium data at T = (278.15, 283.15,
and 293.15) K are reported. The effect of the temperature on liquid–liquid equilibrium is determined
and discussed. Ternary system is available from the literature at T = 298 K. All chemicals were quantified
by gas chromatography using a thermal conductivity detector. The solubility data for methanol + hexane
and the upper critical temperature (UCST) at 308.3 K was reported. The tie line data for the ternary
system were satisfactorily correlated by the Othmer and Tobias method, and the plait point coordinates
for the three temperatures were estimated. Experimental data for the ternary system are compared with
values calculated by the NRTL and UNIQUAC equations, and predicted by means of the UNIFAC group
contribution method. It is found that the UNIQUAC and NRTL models provide similar good correlations
of the equilibrium data at these three temperatures. Finally, the UNIFAC model predicts an immiscibility
region larger than the experimental observed. Distribution coefficients were also analysed through
distribution curves.
© 2011 Elsevier B.V. All rights reserved.
1. Introduction
There are increasing demands for use oxygenated compounds
to produce lead-free gasoline. For this reason, we are study-
ing the phase equilibrium of systems containing hydrocarbons
(benzene, isooctane, toluene, or cyclohexane) and oxygenated
compounds (methanol, ethanol, or methyl tert-butyl ether)
[1–6].
Because of its physical and chemical properties, methanol is a
good candidate for an oxygenated fuel additive. However, methanol
presents partial miscibility with aliphatic hydrocarbons, but not
with aromatic hydrocarbons. Therefore, it is of great importance to
study systems composed by methanol and representative hydro-
carbon of gasoline, establishing the temperature in which the
two-phase region does not exist [7].
In this work, (liquid + liquid) equilibrium (LLE) data have
been obtained for {w1 methanol + w2 benzene + w3 hexane} ternary
system at T = (278.15, 283.15, and 293.15) K with a constancy
in temperature of ±0.05 K, named throughout the text as
{w1 CH4O + w2 C6H6 + w3 C6H14} in order to obtain the behaviour of
blends of hydrocarbons and methanol at three temperatures. The
solubility data for methanol + hexane, the upper critical solution
∗ Corresponding author. Tel.: +54 381 4364093; fax: +54 381 4363004.
E-mail address: mgramajo@herrera.unt.edu.ar (M.B.G.d. Doz).
temperature (UCST) together with bibliographic data for compari-
son [8] was reported.
The equilibrium concentration for each component was deter-
mined by gas chromatography, using the internal standard method.
Tie lines were also correlated using the Othmer and Tobias’
method [9] and the plait point coordinates at each temperature
are reported.
Furthermore, the experimental results were compared with
those predicted by means of the UNIFAC group contribution
method [10] using the LLE interaction parameters reported by Mag-
nussen et al. [11], and correlated with the NRTL [12] and UNIQUAC
[13] models fitted to those experimental results.
As far as we know, a single work can be found in the literature
regarding LLE data for this ternary system at 298 K [14].
2. Experimental
2.1. Materials
Methanol and benzene were supplied by Merck, while hexane
by Sintorgan (Argentina). The purity of the chemicals was verified
chromatographically using a HP 6890 gas chromatograph with a
TCD detector coupled to a ChemStation and nitrogen as gas carrier,
showing that their mass fractions were higher than 0.998. There-
fore, they were used without further purification. Experimental
results for density, viscosity, and refractive index for the sodium
0378-3812/$ – see front matter © 2011 Elsevier B.V. All rights reserved.
doi:10.1016/j.fluid.2011.02.022

2. M.B.G.d. Doz et al. / Fluid Phase Equilibria 305 (2011) 34–38 35
Table 1
Density , refractive index nD, and viscosity Á values of pure components at 298.15 K.
Chemicals (kg m−3
) nD Á (mPa s)
Exptl. Lit. Exptl. Lit. Exptl. Lit.
Methanol 785.9 786.37a
1.32650 1.32652a
0.542 0.542b
786.45b
1.32661b
0.5513a
0.549c
Benzene 873.7 873.60a
1.49982 1.49792a
0.603 0.6028a
873.56c
1.5009c
Hexane 654.8 654.84a
1.37223 1.37226a
0.302 0.2942a
654.8d
0.301d
a
J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents: Physical Properties and Methods of Purification, 4th ed., Wiley-Interscience, New York (1986).
b
G.E. Papanastasiou, I.I. Zlogas, J. Chem. Eng. Data, 37 (1992) 167–172.
c
F. Li, R. Tang. J. Chem. Thermodyn., 39 (2007) 1530–1537.
d
A. Rodríguez, A.B. Pereiro, J. Canosa, J. Tojo. J. Chem. Thermodyn., 38 (2006) 505–519.
D-line of pure compounds at 298.15 K are summarized in Table 1.
These properties were measured with a KEM DA-300 vibrating tube
densimeter using degassed bidistilled water and dry air as cali-
brating substances in accordance with the supplier instructions, an
Anton Paar Stabinger viscometer (SVM 3000/G2) calibrated by the
manufacturer, and a Leica AR600 refractometer, respectively. The
densimeter and viscometer are equipped with their own Peltier
effect control systems, which maintained the temperature of both
apparatus at ±0.01 K. A thermostatically water bath with a con-
stancy of ±0.01 K was used for refractive index measurements. The
uncertainties were ±0.1 kg m−3 for density, ±0.35% of the measured
value for viscosity, and ±0.00005 for refractive index. For compar-
ison, existing values found in the literature are also included in
Table 1.
2.2. Methods
The experimental procedure used is the same as that reported
in a previous work [4,15]. Consequently, only its essential parts are
reproduced here.
All components in the conjugated phases were quantified by
chromatography applying the internal standard method. Acetone
(C3H6O) (Merck, chromatographic quality) with a mass fraction
purity >0.999 (GC) was the standard compound used for this
purpose. A Hewlett Packard 6890 gas chromatograph with an
automatic injector (Agilent G2613A) directly connected to a Chem-
Station (HP G2070AA) was used. Good separation of the three
components was obtained on a 30 m long × 0.25 mm id × 0.5 ␮m
film thickness capillary column (INNOWax, cross-linked polyethy-
lene glycol, HP 19091N-233). The temperature program used was:
initial temperature 343 K for 2 min, ramp 50 K min−1, and final tem-
perature 473 K for another 1 min. The nitrogen carrier gas flow rate
was electronically kept constant working with a split ratio of 20:1
and with the injector maintained at 453 K. Detection was carried
out by a thermal conductivity detector at 523 K. Three or four anal-
yses were performed for each sample in order to obtain a mean
mass fraction value with repeatability better than 1%.
In order to obtain the uncertainty in the equilibrium mass frac-
tion values, we prepare several ternary mixtures with very well
known concentrations by mass. These mixtures were analysed
with the chromatographic method, and their chromatographic con-
centrations were compared with those obtained by mass. This
comparison shows that the reported mass fraction values have an
uncertainty of ±0.001.
The upper critical solution temperature (UCST) for
methanol + hexane binary system was determined using the
constant-composition method [16]. The heterogeneous binary
liquid sample was prepared in 16 mL sample vials equipped with
cap, septa and a Teflon coated magnetic bar to provide an intense
stirring. The sample was brought into thermal equilibrium in a
water bath, and subjected to changes in temperature with heating
rates of about 0.1 K min−1. The temperature was read when the
transition was achieved. Measurements repeated of temperature
at which the opalescence of sample disappeared gave the same
value within ±0.1 K.
3. Results and discussion
Experimental results for density, viscosity, and refractive index
for the sodium D-line of pure compounds at 298.15 K with those
reported in the literature are summarized in Table 1.
Fig. 1 shows the solubility curve of the methanol + hexane binary
system, the upper critical solution temperature (UCST) at 308.3 K,
together with bibliographic data for comparison [8].
Table 2 lists the (liquid + liquid) equilibrium, expressed in
mass fraction, of {w1 CH4O + w2 C6H6 + w3 C6H14} ternary system
at T = 278.15, 283.15, and 293.15 K with a constancy in temper-
ature of ±0.05 K. Fig. 2 shows experimental ternary equilibrium
data and plait points (PP) calculated with the Othmer and Tobias’
method at the three temperatures studied here, together with LLE
data reported by Nagata [14] for comparison.
As can be seen, a good trend agreement is achieved among all
temperatures. In this plot binodal curve and tie lines were omitted
in order to avoid confusion.
Experimental, correlated and predicted results at 293.15 K are
shown in Fig. 3 for comparison. For the other temperatures, similar
plots were obtained. Therefore, they were not shown.
Fig. 1 shows that this ternary system can be classified as type
1 in the Treybal’s classification, because only one pair of partially
miscible liquids is present [16]. Also, tie lines were satisfactorily
correlated using the Othmer and Tobias’ method [9] that provides
the plait point coordinates at each temperature.
260
270
280
290
300
310
320
0.0 0.2 0.4 0.6 0.8 1.0
CH4O
T(K)
UCST
Fig. 1. Experimental coexistence temperature-composition (mass fraction of
methanol) curve for {CH4O + C6H14} binary system and the upper critical solution
temperature and ᭹ from Ref. [8].

3. 36 M.B.G.d. Doz et al. / Fluid Phase Equilibria 305 (2011) 34–38
Table 2
Experimental data of {w1 CH4O + w2 C6H6 + w3 C6H14} ternary system at three temperatures; wi denotes mass fraction.
T (K) Overall compositions Methanol-rich phase Hexane-rich phase
w1 w2 w3 w1 w2 w3 w1 w2 w3
278.15 0.4166 0.0000 0.5834 0.739 0.000 0.261 0.054 0.000 0.946
0.4072 0.0246 0.5682 0.704 0.027 0.269 0.050 0.021 0.929
0.3980 0.0481 0.5539 0.658 0.055 0.287 0.058 0.040 0.902
0.3879 0.0681 0.5440 0.615 0.070 0.315 0.067 0.065 0.868
0.3785 0.0875 0.5340 0.587 0.085 0.328 0.093 0.091 0.816
0.3598 0.1048 0.5354 0.542 0.106 0.352 0.108 0.104 0.788
0.3502 0.1272 0.5226 0.482 0.128 0.390 0.129 0.126 0.745
0.3483 0.1493 0.5024 0.373 0.149 0.478 0.202 0.153 0.645
PPa
0.336 0.159 0.505 0.336 0.159 0.505
283.15 0.4277 0.0000 0.5723 0.700 0.000 0.300 0.063 0.000 0.937
0.4121 0.0249 0.5630 0.672 0.024 0.304 0.076 0.026 0.898
0.3935 0.0451 0.5614 0.631 0.044 0.325 0.088 0.046 0.866
0.3807 0.0653 0.5540 0.602 0.058 0.340 0.110 0.075 0.815
0.3797 0.0872 0.5331 0.540 0.084 0.376 0.128 0.092 0.780
0.3695 0.1030 0.5275 0.500 0.100 0.400 0.151 0.109 0.740
PPa
0.372 0.133 0.495 0.372 0.133 0.495
293.15 0.4056 0.0000 0.5944 0.661 0.000 0.339 0.084 0.000 0.916
0.4067 0.0248 0.5685 0.607 0.024 0.369 0.101 0.026 0.873
0.3998 0.0469 0.5533 0.546 0.045 0.409 0.117 0.050 0.833
0.3875 0.0697 0.5428 0.489 0.065 0.446 0.191 0.079 0.730
PPa
0.380 0.090 0.530 0.380 0.090 0.530
“Zero” means that the component is absent.
a
Estimated plait point by the Othmer and Tobias’ method.
Material balances were performed for each tine line at each
temperature in order to check the consistency of the equilibrium
experimental data reported in Table 2 [17]. These calculations
show that our data satisfy the mass balance within an average
absolute deviation of 0.83, 2.32, and 0.38% at (278.15, 283.15,
0.00
0.05
0.10
0.15
0.20
0.00 0.25 0.50 0.75 1.00
C6H14 (3)
C6H6(2)
PP
PP
PP
Fig. 2. Experimental LLE data of {w1 CH4O + w2 C6H6 + w3 C6H14} ternary system. ᭹,
278.15 K; , 283.15 K; , 293.15 K; , 298,15 K from Ref. [13]. PP, plait point. In order
to avoid confusion, binodal curves, tie lines and overall compositions were omitted.
0.00
0.25
0.50
0.00 0.25 0.50 0.75 1.00
C6H14 (3)
C6H6(2)
PP
PP
PPPP
Fig. 3. (Liquid + liquid) equilibrium of the ternary system
{w1 CH4O + w2 C6H6 + w3 C6H14} at T = 278.15 K. ᭹, Experimental; ×, NRTL; ,
UNIQUAC; ♦, UNIFAC; +, global compositions.
and 293.15) K with a greatest deviation of 2.4, 4.2, and 0.7%,
respectively.
The LLE data for the ternary system studied here were corre-
lated by the UNIQUAC and NRTL activity coefficient models, using
an iterative computer program developed by Sørensen [18] that
minimizes the values of the following objective functions:
Fa =
k
˙
i
˙ aI
ik
− aII
ik
/ aI
ik
− aII
ik
2
+ Q
n
˙P2
n , (1)
Fx =
k
˙ min
i
˙
j
˙ xijk − ˆxijk
2
+ Q
n
˙P2
n , (2)
Here aI,II
ik
are the activities obtained from the experimental concen-
trations, I and II are the phases, xijk and ˆxijk are the experimental
mole fraction values of the liquid phase and of the calculated tie
line lying close to the considered experimental line, respectively,
where i represents the components, j the phases, and k the tie lines.
Pn and Q are the parameter and the constant values in the penalty
term, respectively.
This penalty term was established to reduce the risk of mul-
tiple solutions associated with high parameter values. The values
of the penalty terms were chosen taking into account Sorensen’s
recommendation [18]. Table 3 shows the structural parameters of
the pure components taken from literature [19] and the optimised
binary interaction parameters of the UNIQUAC and NRTL models,
for the ternary system. The non-randomness parameter ˛ij for the
NRTL equation is also given.
Goodness of fit, as measured by the r.m.s. deviation in mole
fraction F, is given by
F = 100 ˙
k
˙
i
˙
j
(xijk − ˆxijk)
2
/2nM
1/2
, (3)
where n is the number of components in the system. The r.m.s.
relative error in the solute distribution ratio Ä is given by
Ä = 100
k
(Äk − ˆÄk)
2
/M
1/2
, (4)
These residuals are listed in Table 3 for these two models. Here,
xijk is the experimental mole fraction of the ith component in the
jth phase on the kth tie line, ˆxijk is the corresponding calculated

4. M.B.G.d. Doz et al. / Fluid Phase Equilibria 305 (2011) 34–38 37
Table 3
Residuals F and Ä for UNIQUAC, NRTL, and UNIFAC models, optimised param-
eters of the UNIQUAC and NRTL equations, and non-randomness parameter (˛ij),
of the ternary system {w1 CH4O + w2 C6H6 + w3 C6H14} at T = (278.15, 283.15, and
293.15) Ka
.
F (%) Ä (%) i,j aij
b
(K) aji
b
(K) ˛ij
T = 278.15 K UNIQUAC
0.4 15.8 1,2 31.253 38.186
1,3 9.9347 662.79
2,3 −177.65 206.39
T = 283.15 K
0.2 9.2 1,2 430.75 39.399
1,3 3.5881 625.55
2,3 108.34 201.11
T = 293.15 K
0.5 26.7 1,2 113.18 −19.500
1,3 −2.2098 626.72
2,3 −58.388 −55.072
T = 278.15 K NRTL
0.4 13.9 1,2 733.98 −484.95 0.2
1,3 408.09 488.03
2,3 −277.72 86.358
T = 283.15 K
0.2 10.2 1,2 −123.12 −102.74 0.3
1,3 462.90 476.12
2,3 −410.33 −65.451
T = 293.15 K
0.5 24.9 1,2 587.66 −273.10 0.3
1,3 460.70 469.61
2,3 20.396 −334.24
T = 278.15 K UNIFAC
12.4 45.4
T = 283.15 K
12.2 16.0
T = 293.15 K
14.0 12.6
a
The following UNIQUAC structural parameters were used [12]: for CH4O,
r = 1.4311 and q = 1.4320; for C6H6, r = 3.1878 and q = 2.400; for C6H14, r = 4.4998 and
q = 3.856.
b
aij = (uij − uji)/R for the UNIQUAC equation, where uij is the UNIQUAC binary
interaction parameter (J mol−1
); R = 8.31451 J K−1
mol−1
; aij = (gij − gji)/R for the NRTL
equation, where gij is the energy of interaction between an i–j pair of molecules
(J mol−1
).
value, and Äk and ˆÄk are the experimental and calculated solute
distribution ratios, respectively, given by w2
/w2
.
In order to apply the UNIFAC group contribution method, hex-
ane, benzene, and methanol were subdivided in functional groups,
as it is usually done.
The goodness of fit in terms of the residuals F and Ä was sat-
isfactory for the UNIQUAC and NRTL models, although this last
residual shows relatively high values for the highest temperature
studied here due to the large relative error associated with low con-
centrations of some compounds in both phases (compare w23 and
w21 values reported in Table 2 at 293.15 K with those at the other
temperatures). Taking into account both residuals, the UNIQUAC
equation fitted to the experimental data is more accurate than the
NRTL model for this ternary system, as can be seen in Table 3.
On the other hand, the UNIFACmodel was not able to predict nei-
ther qualitatively nor quantitatively the LLE for this system, since it
predicts an immiscibility region much larger than the experimental
observed for the three temperatures studied here, particularly for
the methanol-rich phase. Predicted results were shown in Fig. 3.
On the other hand, the NRTL and UNIQUAC equations fitted to
the experimental results are considerably more accurate than the
UNIFAC method taking into account both overall errors, F and Ä
(see Table 3), as usually happens.
Fig. 4 shows distribution curves at all the temperatures stud-
ied here for this ternary system, the mass fraction of benzene in
the hexane-rich phase (w23) is plotted against the mass fraction of
benzene in the methanol-rich phase (w21).
0.00
0.10
0.20
0.00 0.10 0.20
w 21
w23
PP
PP
PP
Fig. 4. Distribution curves of benzene between methanol and hexane in the
{w1 CH4O + w2 C6H6 + w3 C6H14} ternary system. w23, mass fraction of benzene in
the hexane-rich phase; w21, mass fraction of benzene in the methanol-rich phase.
᭹, 278.15 K; , 283.15 K; , 293.15 K; , 298,15 K from Ref. [13]. PP, plait point.
Fig. 4 reveals that the distribution coefficients are close to 1 at
these three temperatures, and return to the 45◦ diagonal, corre-
sponding to the plait point at each temperature.
4. Conclusions
(Liquid + liquid) equilibrium of the ternary system
{w1 CH4O + w2 C6H6 + w3 C6H14} was investigated at T = (278.15,
283.15, and 293.15) K.
From our experimental results, we conclude that the mutual
solubility of methanol in hexane is larger than that of hexane in
methanol at any of the temperatures studied here. Additionally,
this ternary system shows that the solubility increases when tem-
perature increases. Therefore, the heterogeneous region becomes
smaller when temperature increases as can be seen in Fig. 2. The
temperature at which system becomes homogeneous corresponds
to the Upper Critical Solution Temperature (UCST) of binary mix-
ture methanol + hexane.
As can be seen, the solubility of this ternary system is sensitive
to changes in a short range of temperature. A plausible explana-
tion to this thermal behaviour can be obtained keeping in mind
the chemical nature of the blended species. Methanol is a highly
antagonistic to hydrocarbons [20].
The UNIQUAC and NRTL models show low values of both resid-
uals, particularly for the residual F, although for Ä is high at
T = 293.15 K (see Table 3) due to low concentrations of some com-
pounds in both phases. Furthermore, taking into account both
residuals, the NRTL equation is more accurate than the UNIQUAC
one, except at T = 293.15 K.
Moreover, the data regressed using the UNIFAC group contri-
bution method show considerable deviations from experimental
results, since it predicts an immiscibility region much larger than
that experimentally observed at the three temperatures studied
here.
List of symbols
a activity obtained directly from the model by insertion of
the experimental concentrations (Eq. (1))
aij, aji parameters of the UNIQUAC and NRTL models
F r.m.s. deviation in mole fraction given by Eq. (3)
Fa, Fx objective functions given by Eqs. (1) and (2)
LLE liquid–liquid equilibria
Äk experimental solute distribution ratio (Eq. (4))
ˆÄk calculated solute distribution ratio (Eq. (4))
Ä r.m.s. relative error in the solute distribution ratio given
by Eq. (4)
M number of tie lines (Eqs. (3) and (4))
n number of the components in the system (3 or 4)
nD refractive index for the sodium D line

5. 38 M.B.G.d. Doz et al. / Fluid Phase Equilibria 305 (2011) 34–38
Pn parameter in the penalty term (Eqs. (1) and (2))
Q constant value in the penalty term (Eqs. (1) and (2))
r.m.s. root mean square deviation
wi mass fraction of component i
xijk experimental mole fraction of the ith component in the
jth phase on the kth tie line (Eqs. (2) and (3))
ˆxijk calculated mole fraction of the ith component in the jth
phase on the kth tie-line (Eqs. (2) and (3))
wi
mass fraction of the ith component in the methanol
phase
wi
mass fraction of the ith component in the organic phase
Subscripts
i lower index-denoting components (1–3)
j lower index-denoting phases ( or )
k lower index denoting tie lines (1–M)
methanol-rich phase
hexane-rich phase
Greek letters
˛ij non-randomness parameter for the NRTL equation
density (kg m−3)
Á viscosity (mPa s)
Ä solute distribution ratio
Acknowledgement
Financial support from the Consejo de Investigaciones de la Uni-
versidad Nacional de Tucumán, Argentina (CIUNT, grant 26/E418)
is gratefully acknowledged.
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