Liquid–liquid equilibria for ternary mixtures of 2,2-dimethyl-1,3-dioxolane-4-methanol with n-heptane, toluene, ethanol and water

Fluid Phase Equilibria 405 (2015) 107–113

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Liquid–liquid equilibria for ternary mixtures of 2,2-dimethyl-1,3-dioxolane-4-methanol with n-heptane, toluene, ethanol and water Marina Yakovleva, Eugeny Vorobyov, Igor Pukinsky, Igor Prikhodko, George Kuranov ∗ , Natalia Smirnova Institute of Chemistry, Saint Petersburg State University, Universitetsky pr., 26, 198504 St. Petersburg, Russian Federation

a r t i c l e

i n f o

Article history: Received 6 March 2015 Received in revised form 7 July 2015 Accepted 10 July 2015 Available online 20 July 2015 Keywords: Liquid–liquid equilibria 2,2-Dimethyl-1,3-dioxolane-4-methanol Ternary mixtures NRTL UNIFAC

a b s t r a c t Liquid–liquid equilibria (LLE) data are presented for three ternary systems: 2,2-dimethyl-1,3-dioxolane4-methanol (DMDM) + n-heptane + ethanol, and DMDM + n-heptane (or toluene) + water. The most of the measurements were performed at 293.15 K and atmospheric pressure, some data obtained relate to 273.15 K. The phase diagrams for the ternary system containing n-heptane and water show the extended heterogeneous area between the water–hydrocarbon side of the concentration triangle and the n-heptane-DMDM side. Much smaller regions of immiscibility with the critical points are observed for the ternary mixtures DMDM + toluene + water and DMDM + n-heptane + ethanol. The experimental LLE data were correlated applying the NRTL model. The UNIFAC interaction parameters for CH2 O groups of DMDM were estimated on the base of LLE in the DMDM + n-heptane + ethanol system. The UNIFAC model was applied to predict the LLE diagrams for ternary DMDM + n-heptane (or toluene) + water solutions. Both NRTL and UNIFAC models with the estimated parameters have provided satisfactory results. © 2015 Elsevier B.V. All rights reserved.

1. Introduction In this paper we present the results of the LLE experimental study and modeling performed for multicomponent systems containing 2,2-dimethyl-1,3-dioxolane-4-methanol (DMDM). In our preceding work [1] the results of the LLE study were given for multicomponent mixtures of 2,2-dimethyl-1,3-dioxolane (DMD) with n-heptane, toluene, ethanol and water. New UNIFAC parameters were estimated to describe interactions of DMD ether groups with water, OH and CH2 groups. During the last years polyol derivatives have found many new applications as solvents and as additives to gasoline, biofuels, diesel fuels etc., the phase behavior being one of the most important characteristics of liquid mixtures under study. In particular, alkyl-derivatives of 1,3-dioxolane-4-methanol have appeared to be effective and nontoxic icing inhibitors [2,3]; they are considered as perspective additives to gasoline and biofuels increasing their phase stability (the range of homogeneity in water containing systems). A review of the phase equilibria studies for liquid mixtures containing 1,3-dioxolane or its derivatives was given in our preceding paper [1].

∗ Corresponding author. Tel.: +7 911 920 12 77. E-mail address: g [email protected] (G. Kuranov). http://dx.doi.org/10.1016/j.fluid.2015.07.016 0378-3812/© 2015 Elsevier B.V. All rights reserved.

Most of the performed experimental studies of the phase behavior relate to binary mixtures of 1,3-dioxolane or its alkyl-derivatives with water, alkanes, chloroalkanes, alkanols. All studied mixtures of 1,3-dioxolane with hydrocarbons show positive deviations from ideality [4–8] due to the destruction of dipole-dipole interactions between 1,3-dioxolane molecules on hydrocarbon addition. For 1,3-dioxolane mixtures with alkyl derivatives (e.g. chloroalkanes, alkanols) the character of deviations from ideality depends on the balance of two processes: the destruction of dipole–dipole or donor–acceptor interactions between similar molecules and formation of interactions between dissimilar molecules. In systems with light alcohols their self-association due to hydrogen bonding is preferred, and substantial positive deviations from the ideality are observed. With the growth of the alcohol alkyl group the formation of hydrogen bonds between dissimilar molecules becomes more pronounced, and deviations from the ideality become lower. Large positive deviations from ideality are observed for 1,3-dioxolane + water solutions [4,9–11]. The curve of the concentration dependence of the vapor pressure shows that the solutions at 318.15 K are close to the phase splitting. Obviously, the formation of hydrogen bonds between dissimilar molecules in 1,3-dioxolane + water solutions cannot compensate the breaking of hydrogen bonds between water molecules. Incorporation of alkyl radicals in 1,3-dioxolane molecules results in increased positive deviations from ideality for aqueous

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solutions and in the appearance of a solubility gap. Incorporation of hydroxyl groups in molecules of 1,3-dioxolane derivatives changes significantly the phase behavior of the aqueous solutions and favors a good mutual miscibility. There are few studies devoted to phase equilibria modeling for mixtures containing substituted dioxolanes. The VLE data correlation using the NRTL model was performed for binary mixtures of 4-methyl-1,3-dioxolane with methanol, propylene glycol and acetone [12]. The ability to correlate VLLE data for binary mixtures of water with 2-methyl-1,3-dioxolane or with 2,4-dimethyl-1,3dioxolane applying the UNIQUAC model was studied in [13]. The present work is aimed at the study of the influence of hydroxyl groups in DMDM molecules on the phase behavior of systems containing this dioxolane derivative. The results of the LLE study are presented for the following ternary systems: DMDM + n-heptane + ethanol, DMDM + n-heptane + water and DMDM + toluene + water. The study includes both experimental measurements of the LLE and the phase equilibria modeling by NRTL and UNIFAC models. The presented results are new, and they extend the available information on the phase behavior and thermodynamic excess functions of mixtures containing 1,3-dioxolane derivatives. 2. Experimental 2.1. Chemicals Information on the source, purity, density, and refractive index of the chemicals used is presented in Table 1. Densities were measured with DM 45 Mettler Toledo vibrating-tube densimeter automatically thermostated within ±0.01 K. Refractive indices were measured with refractometer RL-1 (PZO, Poland). The water content in ethanol and in DMDM was controlled by the Karl Fisher (KF) titration method (Mettler Toledo, V20). The purity of organic solvents was estimated by the gas chromatography (GC) method. To get pure ethanol its aqueous rectificate was subjected to the azeotropic rectification with added benzene. Distilled water was used in the experiments. DMDM was purified by vacuum rectification. The densities and refractive indices of n-heptane, toluene, ethanol and water corresponded to the standard literature values. 2.2. Procedures applied in the LLE studies The preliminary tests in the temperature range 243.15–313.15 K have shown that DMDM + ethanol, DMDM + water and DMDM + toluene binaries demonstrate the complete mutual miscibility of the components, whereas the limited miscibility is observed for DMDM mixtures with n-heptane. So, the experimental LLE measurements were performed for the ternary systems: DMDM + n-heptane + ethanol, DMDM + n-heptane + water and DMDM + toluene + water. The study of the systems containing both DMDM and water meets some difficulties due to chemical interactions between the

components (the products of the reaction of hydrolysis are glycerol and acetone). The effect of the hydrolysis on the phase behavior grows with temperature and water content, and at elevated temperatures it becomes quite significant. Our preliminary measurements have shown that the effect of the hydrolysis on the composition of the coexisting phases produced in the experiments at 293.15 K can be neglected (at least, during the time of the studies) though it is not so at significantly higher temperatures. Temperatures 293.15 and 273.15 K were chosen for our studies of the phase behavior of the mixtures. The isothermal titration method [15] was applied to determine the LLE phase boundaries (the run of the binodal curve in the concentration triangle) in the ternary systems, the temperature in the vessel being maintained constant within ±0.05 K. A known amount of the prepared by weight liquid mixture (homogeneous or heterogeneous) is thermostated in the 10 ml glass vessel, and the titrant is added drop by drop under stirring until a change of the phase state is observed. The mass of the added titrant was determined by weighing the vessel ejected from the thermostated jacket and dried outside. The resulting material balance of the substances gives the point on the binodal curve. Refractive indices of the obtained saturated solutions were measured at 298.15 K, exceeding the temperature of titration—in order to avoid a possible cloudiness of the mixture on the prism  of the refractometer. —mole fraction (xi ) of The dependencies “refractive index n25 D the components along the binodal” were plotted. These dependencies were necessary further to determine the tie-lines in ternary systems. The accuracy of the phase boundaries determination was within 0.5 mol%. The compositions of the coexisting liquid phases in ternary heterogeneous systems were determined as follows. The mixtures prepared by weight, with the compositions presumably close to the middle of the tie-line, were thermostated in the glass cell and vigorously agitated by a magnetic stirrer for at least 1 h. Then the sample was left quiet to attain the complete measure their refractive indices. The refractive indices together with known dependencies n25 − xi along the binodal curve allows to find the compositions D of coexisting phases. The point presenting the overall composition of the ternary mixture should lie on the liquid–liquid tie line, and this point served to control the accuracy of the estimated compositions of the coexisting layers. In some cases (when the run of the n25 − xi curve for one of the phases was unfavorable for determinD ing its composition) the overall composition played the role of an auxiliary point in determining the tie-line. The mean experimental uncertainty in the equilibrium phase compositions did not exceed 1–2 mol%.

3. Results of the LLE measurements The LLE data at 293.15 K for all investigated ternary systems and the LLE phase boundary data for DMDM + n-heptane + ethanol system at 273.15 K are summarized in Tables 2–3 and in Figs. 1–4.

Table 1 Properties of the pure compoundsa . Compound

CAS registry no

Source

Purity (mass fraction)

Purification method

Analysis method

DMDMb n-Heptane Toluene Ethanol Water

100-79-8 142-82-5 108-88-3 64-17-5 7732-18-5

Acros Vekton Vekton Vekton

>0.990 >0.998 >0.998 >0.998 >0.999

Vacuum rectification None None Azeotropic rectification Distillation

GC, KF GC GC GC, KF

a b

Standard uncertainties (u) are u() = 0.1 kg m-3 , u(nD 20 ) = 1 × 10-4 . The IUPAC chemical name for DMDM is 1,3-dioxolane-4-methanol, 2,2-dimethyl.

Density (kg m−3 ) (293.15 K 101.3 kPa)

Refractive index nD 20

Exp.

Lit. [14]

Exp.

Lit. [14]

1069.3 683.8 866.9 789.5 998.2

1064.0 684.0 866.0 790.0 998.0

1.4358 1.3876 1.4969 1.3614 1.3330

1.436 1.387 1.496 1.362 1.333

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109

Table 2 Experimental equilibrium mole fractions xi in the saturated solutionsa for ternary systems at T = 293.15 K, and at T = 273.15 Kb , p = 101.3 kPa (binodal curve data). DMDM + n-heptane + ethanol

DMDM + n-heptane + water

DMDM + toluene + water

xD

xH

xE

nD 25

xD

xH

xW

0.756 0.667 0.557 0.472 0.414 0.366 0.312 0.228 0.165 0.106 0.054 0.013

0.244 0.264 0.314 0.375 0.431 0.481 0.546 0.647 0.737 0.825 0.911 0.987

0.000 0.069 0.129 0.153 0.155 0.153 0.142 0.125 0.098 0.069 0.035 0.000

1.4203 1.4160 1.4103 1.4058 1.4029 1.4002 1.3975 1.3933 1.3906 1.3881 1.3863 1.3856

0.037 0.054 0.086 0.122 0.196 0.233 0.350 0.456 0.520 0.580 0.610 0.655 0.674 0.725 0.746 0.760 0.759 0.756

0.004 0.004 0.006 0.007 0.008 0.010 0.011 0.017 0.027 0.035 0.048 0.064 0.073 0.103 0.128 0.167 0.208 0.244

0.959 0.942 0.908 0.871 0.7916 0.757 0.639 0.527 0.453 0.385 0.342 0.281 0.253 0.172 0.126 0.073 0.033 0

0.839b 0.741b 0.586b 0.462b 0.383b 0.276b 0.186b 0.134b 0.084b 0.017b

0.161b 0.132b 0.182b 0.248b 0.322b 0.433b 0.563b 0.685b 0.791b 0.983b

0.000b 0.127b 0.232b 0.290b 0.298b 0.291b 0.251b 0.181b 0.125b 0.000b

a b

nD 25 1.3608 1.3665 1.3781 1.3885 1.4030 1.4075 1.4155 1.4211 1.4233 1.4241 1.4260 1.4244 – 1.4238 1.4232 1.4219 1.4204 1.4186

xD

xT

xW

nD 25

0.129 0.200 0.282 0.309 0.310 0.290 0.260 0.223 0.186 0.143

0.005 0.020 0.092 0.214 0.345 0.501 0.608 0.700 0.779 0.838

0.866 0.780 0.626 0.477 0.345 0.209 0.132 0.077 0.035 0.019

1.3921 1.4096 1.4260 1.4422 1.4570 1.4649 1.4707 1.4750 1.4810 1.4868

Standard uncertainties (u) are u(T) = 0.1 K, u(x) = 5 × 10-4 , u(nD 25 ) = 1 × 10−4 . T = 273.15 K.

Consistency of the experimental LLE data for the systems with critical (plait) point was confirmed by the Othmer–Tobias correlation [16]:

 ln

1 − x2˛ x2˛



 = A + B ln

ˇ

1 − x3



(1)

ˇ

x3

where xi ˛ and xi ˇ are the mole fractions of component i in the phase ˛ and the phase ˇ, respectively. It should be noted that this empirical correlation is not capable to treat the ternaries having two pairs

of partly miscible components and exhibiting the phase diagrams without critical point; thus the Othmer–Tobias correlation was not applied to the ternary DMDM (1) + n-heptane (2) + water (3) system. The fitting parameters of Eq. (1) (A and B) for two systems studied were determined using a linear least-squares method, and they are reported in Table 4 together with the correlation coefficients R2 and the standard deviations . The results correspond to linear correlation (1) which indicates a satisfactory quality of the experimental data.

Table 3 Experimental equilibrium mole fractions xi in the coexisting liquid phases for the ternary systems; T = 293.15 K, p = 101.3 kPa (tie-lines)a . Phase ˛

Phase ˇ

DMDM + n-heptane + ethanol xD

xH

0.716 0.250 0.280 0.632 0.300 0.582 0.553 0.317 0.359 0.496 0.431 0.416 DMDM + n-heptane + water xH xD 0.181 0.010 0.013 0.296 0.024 0.510 0.069 0.664 0.146 0.755 DMDM + toluene + water xT xD 0.057 0.003 0.005 0.126 0.010 0.170 0.056 0.255 a

xE

nD 25

xD

xH

xE

nD 25

0.034 0.088 0.118 0.130 0.145 0.153

1.4183 1.4142 1.4116 1.4100 1.4071 1.4035

0.025 0.050 0.072 0.085 0.129 0.190

0.960 0.916 0.880 0.857 0.791 0.702

0.015 0.034 0.048 0.058 0.080 0.108

1.3860 1.3864 1.3869 1.3874 1.3890 1.3916

xW 0.809 0.691 0.466 0.267 0.099

nD 25 1.4010 1.4124 1.4227 1.4251 1.4226

xD 0.008 0.008 0.010 0.010 0.012

xH 0.988 0.988 0.985 0.985 0.960

xW 0.004 0.004 0.003 0.003 0.002

nD 25 1.3853 1.3853 1.3854 1.3854 1.3855

xW 0.940 0.869 0.820 0.689

nD 25 1.3700 1.3921 1.4025 1.4190

xD 0.010 0.061 0.137 0.244

xT 0.985 0.928 0.842 0.645

xW 0.005 0.011 0.021 0.111

nD 25 1.4916 1.4890 1.4835 1.4720

Standard uncertainties (u) are u(T) = 0.1 K, u(x) = 0.001, u(nD 25 ) = 1 × 10−4 .

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Fig. 1. The LLE phase diagram for DMDM + n-heptane + ethanol system at T = 293.15 K: the experimental binodal curve and tie-lines, and the results of modeling using the NRTL and UNIFAC.

Fig. 2. The LLE phase diagram for DMDM + n-heptane + ethanol system at T = 273.15 K: the experimental binodal curve and the results of modeling using the NRTL and UNIFAC.

Fig. 3. The LLE phase diagram for DMDM + n-heptane + water system at T = 293.15 K: the experimental binodal curve and tie-lines, and the results of modeling using the NRTL and UNIFAC.

M. Yakovleva et al. / Fluid Phase Equilibria 405 (2015) 107–113

111

Fig. 4. The LLE phase diagram for DMDM + toluene + water system at T = 293.15 K: the experimental binodal curve and tie-lines, and the results of modeling using the NRTL and UNIFAC.

3.1. DMDM + n-heptane + ethanol mixtures In the system DMDM + n-heptane two components are partly miscible, and, thus, in the ternary system in some concentration range two liquid phases coexist (which become identical in the critical point). The heterogeneous area for the ternary system is rather small (Fig. 1). The results presented in Table 2 and Fig. 1 show that all data obtained are in a good agreement between themselves. Fig. 1 and Table 3 where the compositions of the coexisting liquid phases are given show that the distribution of ethanol between the n-heptane and DMDM phases is in favor of the DMDM one. At lower temperature the heterogeneous area becomes larger (Fig. 2). 3.2. DMDM + n-heptane + water mixtures The system is formed by homogeneous binary mixtures of DMDM with water and by two binary systems with miscibility gaps: DMDM + n-heptane and n-heptane + water. The mutual solubility of water and heptane is very small: about 0.001 mol% of water in n-heptane and 10−5 mol% of n-heptane in water at 293.15 K [17]. The ternary system has the wide heterogeneous region between two branches of the binodal, each of the branches going from the water + n-heptane side of the concentration triangle to the DMDM + n-heptane side. Near the apex of pure water the homogeneous area is quite narrow and this area expands on DMDM addition. The homogeneous area and the bimodal branch near the apex of pure n-heptane are extremely small. Therefore the LLE tie-lines are directed approximately to the apex of pure n-heptane (Fig. 3). 3.3. DMDM + toluene + water mixtures The mutual solubility of toluene and water is higher than that of n-heptane and water but, nevertheless, it is very low: about Table 4 The Othmer–Tobias parameters for ethanol (1) + DMDM (2) + n-heptane (3) and DMDM (1) + toluene (2) + water (3) systems at 293.15 K, p = 101.3 kPaa . System

A

B

R2



Ethanol (1) + DMDM (2) + n-heptane(3) DMDM (1) + toluene (2) + water(3)

0.760

0.539

0.998

0.03

0.903

0.949

0.997

0.13

a

The correlation coefficients R2 and the standard deviations  are presented.

0.002 mol% of water in toluene and 10−4 mol% of toluene in water [17] at 293.15 K. The system DMDM + toluene + water is quite different from the system containing n-heptane. It is formed by only one binary with miscibility gap (toluene + water) and by two homogeneous binary systems with DMDM. The heterogeneous area for this ternary system (Fig. 4) is smaller than that for the system with n-heptane but larger than the area for the system DMDM + nheptane + ethanol. Fig. 4 and Table 3 where the compositions of the coexisting liquid phases are given demonstrate that DMDM is distributed nearly equally between the toluene and water layers. 4. LLE Modeling Phase behavior modeling for the ternary systems under study was carried out applying the NRTL [18] and UNIFAC [19] models—like in our preceding study for solutions of DMD [1]. 4.1. Modeling using NRTL According to the NRTL model each binary system of components i and j is characterized by three parameters—the non-randomness parameter ˛ij and interaction parameters Aij and Aji . These parameters are usually evaluated basing on the experimental data for binary systems. With the known parameters for the binaries one can try to predict the phase diagrams of multi-component systems. To estimate parameters for DMDM + n-heptane binary system we used the experimental LLE data obtained in the present work. For water + toluene and water + n-heptane solutions the literature data on the mutual solubility of components in the binaries were used [17]. There are no experimental isothermal vapor–liquid equilibrium data for n-heptane + ethanol mixtures at 293.15 K. NRTL parameters based on VLE data at 303.15 and 313.15 K predict a miscibility gap at 293.15 K in this system which is not experimentally observed. So, to estimate NRTL parameters for the n-heptane + ethanol system we used the activity coefficient values calculated applying the UNIFAC model with the set of parameters presented in [20]. This way permits to decrease the number of adjustable parameters estimated from the ternary data. In the binary systems DMDM + ethanol, DMDM + water, DMDM + toluene there are no miscibility gaps, and no VLE data available for them. Therefore, the binary parameters for these systems were found using the experimental tie lines for the ternary systems DMDM + n-heptane + ethanol, DMDM + n-heptane + water

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M. Yakovleva et al. / Fluid Phase Equilibria 405 (2015) 107–113 Table 6 UNIFAC group assignment in this study.

Table 5 NRTL model parameters Aij , Aji and ˛ij .

DMDM n-Heptane Toluene Ethanol Water a

DMDM

n-Heptane

Toluene

Ethanol

Water

Substance

Main group

Subgroups and their numbers

0 1123 33.01 −1083 770.6

233.30.3a 0 – 403.1 3610

351.1−0.27a – 0 – 2672

1546−0.03a 394.40.39a – 0 –

−207.40.3a 10980.155a 17810.14a – 0

DMDM

“CH2 ”

2 “CH3 ” 1 “CH2 ” (in CH2 OH group) 1 “C” 1 “DCH2 O” (in the cycle) 1 “CHO” (in the cycle) 1 “OH” 1 “CH3 ” 1 “CH2 ” 1 “OH” 2 “CH3 ” 5 “CH2 ” 5 “ACH” 1 “ACCH3 ” 1 “H2 O”

Non-randomness parameter ˛ij .

and DMDM + toluene + water. The estimated interaction parameters and non-randomness parameter ˛ij are presented in Table 5. average absolute deviation calculated as The

N 2 3 exp calc  = 1/6N i=1 j=1 k=1 xijk − xijk

for

“DCH2 O”

Ethanol

“OH” “CH2 ”

n-Heptane

“OH” “CH2 ” “ACH” “ACCH3 ” “H2 O”

Toluene Water

DMDM + n-

heptane + ethanol system is 3 mol%. With the parameters from Table 4 the binodal curve for DMDM + n-heptane + ethanol solutions at 273.15 K was predicted. For each of two temperatures under consideration the calculated curve is rather close to the experimental one, but the asymmetry of the latter is not properly reproduced (Figs. 1 and 2). The maximum deviation from the experimental binodal curve is 4 mol%. The results of the LLE correlation for DMDM + n-heptane + water and DMDM + toluene + water systems are presented in Figs. 3 and 4, and they are quite satisfactory. The average absolute deviations of the calculated equilibrium compositions of the liquid phases from the experimental are 0.4 mol% for DMDM + n-heptane + water and 1 mol% for DMDM + toluene + water. The maximum deviations from the experimental binodal curve are 1 mol% and 2 mol%, respectively. 4.2. Modeling using UNIFAC Table 6 shows how molecules of the substances studied in the present work were divided into the main structural groups and subgroups, the subgroups have the same interaction energy parameters and differ between themselves only by the geometric characteristics. For example, DMDM molecule includes ether groups “DCH2 O” (with DCH2 O and CHO subgroups), one hydroxyl group “OH”, and “CH2 ” groups (with two methyl groups, one methylene and one “C” groups in a molecule): The geometrical and energy parameters for most of the groups under consideration were taken from literature [20]. But these parameters for ether groups relate only to linear or cyclic monoethers (tetrahydrofuran). The calculations using these values of parameters give a poor prediction for the DMDM + nheptane + ethanol system (Fig. 1). The failure is obviously due to ignoring the intramolecular interactions of two conjugated oxygen atoms in 1,3-dioxolane molecule and in its derivatives. In [1] new UNIFAC parameters were estimated for interactions between the ether group “DCH2 O” in cyclic diether (DMD) and other groups.

Unfortunately, with this set of parameters we could not predict immiscibility in binary system DMDM + n-heptane. All trials to get the single set of parameters for both DMD and DMDM failed. Evidently, it is due to the inability of the group-contribution approach to take into account intramolecular interactions between oxygen atoms and hydroxyl group in DMDM molecule. For this reason we had to estimate, using the experimental data obtained in our study, the parameters of interaction between ether group “DCH2 O” in DMDM and other groups. The interaction energy parameters for groups DCH2 O–CH2 and DCH2 O–OH were evaluated basing on the experimental LLE data for the DMDM + nheptane + ethanol system. The set of the interaction parameters was determined by minimizing the differences between the experimental mole fractions of the components in the coexisting liquid phases and the calculated ones for all the tie lines. The estimated parameters are presented in Table 7 together with those determined previously [20]. The average absolute deviation of the calculated equilibrium compositions of the liquid phases from the experimental mole fractions for this system is 3 mol%. The maximum deviation from the experimental binodal curve is 6 mol%. It is rather significant but much lower than in the case of using the original UNIFAC parameters (33 mol%) (Fig. 1). Using the parameters presented in Table 6 we have predicted the LLE binodal curve for the DMDM + n-heptane + ethanol system at 273.15 K. The calculated curve is close to the NRTL results (Fig. 2), but for better representation one needs to take into account the temperature dependency of the parameters. The estimated group interaction parameters permit to predict with a good accuracy the LLE in the ternary system DMDM + nheptane + water without re-estimation of the parameters of interactions between “DCH2 O” and “H2 O” groups (Fig. 3). The average absolute deviation of the calculated equilibrium compositions of the liquid phases from the experimental mole fractions for this system is 2 mol%. The maximum deviation from the experimental binodal curve is 2 mol%. The deviations between the calculated and experimental values are more significant in the case of the

Table 7 UNIFAC group interaction parameters used in this work.

CH2 ACH ACCH2 OH H2 O DCH2 O *

CH2

ACH

ACCH2

OH

H2 O

DCH2 O

0 156.5 104.4 328.2 342.4 877*

−114.8 0 −146.8 −9.21 372.8 52.13

−115.7 167.0 0 1.27 203.7 65.69

644.6 703.9 4000 0 −122.4 274.6*

1300 859.4 5695 28.73 0 212.8

262.7* 32.14 213.1 2485* 64.42 0

Parameters were estimated in the present work.

M. Yakovleva et al. / Fluid Phase Equilibria 405 (2015) 107–113

original set of UNIFAC parameters, including parameters for groups DCH2 O–CH2 and DCH2 O–OH. The maximum deviation from the experimental binodal curve is 25 mol%. The experimental data available are not sufficient to re-estimate parameters of interactions between DCH2 O and ACH, ACCH2 groups, so we used the original set of parameters for these groups to predict LLE in the ternary DMDM + toluene + water system. The maximum deviation from the experimental binodal curve in this case is 4 mol% (Fig. 4). However, slope of the calculated tie lines differs significantly from the experimental ones and the average absolute deviation of the calculated compositions of the coexisting liquid phases from the experimental ones is 20 mol%. 5. Conclusions The experimental data obtained in the present study give information on the mutual solubilities of components in ternary mixtures of 2,2-dimethyl-1,3-dioxolane-4-methanol with water, hydrocarbon (n-heptane or toluene) and ethanol. The results of calculations applying the UNIFAC model demonstrate that with the interaction parameters for linear ethers or with those for cyclic monoether (tetrahydrofuran) the LLE cannot be satisfactorily predicted for mixtures of DMDM with ethanol and n-heptane. In the present study new UNIFAC parameters were estimated for interactions of DMDM ether groups with OH and CH2 groups. With the new parameters a satisfactory representation of the LLE for the ternary mixtures under consideration was achieved. The values of the parameters give evidence of some interdependence of ether and hydroxyl groups in a DMDM molecule. Evidently, the interdependence of neighboring functional polar groups in a molecule affects the energies of their interactions with other groups, and this can restrict the range of applicability of the group-contribution approach for systems containing such molecules.

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