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J. Chem. Thermodynamics 37 (2005) 1138–1143

Quaternary (liquid + liquid) equilibria for (water + 1,1-dimethylethyl methyl ether + diisopropyl ether + toluene)

at the temperature 298.15 K

Yao Chen *, Yanhui Dong, Zhongjuan Pan

Department of Chemistry, Jinan University, Guangzhou 510632, China

Received 5 November 2004; received in revised form 19 January 2005; accepted 2 February 2005

Available online 5 March 2005

Abstract

(Liquid + liquid) equilibrium tie-lines were measured for one ternary system {x1H2O + x2CH3C(CH3)2OCH3 +

(1 � x1 � x2)(CH3)2CHOCH(CH3)2} and one quaternary system {x1H2O + x2CH3C(CH3)2OCH3 + x3(CH3)2CHOCH

(CH3)2 + (1 � x1 � x2 � x3)C6H5CH3} at T = 298.15 K and P� = 101.3 kPa. The experimental (liquid + liquid) equilibrium results

have been satisfactorily correlated by modified and extended UNIQUAC models both with ternary and quaternary parameters in

addition to binary ones.

� 2005 Elsevier Ltd. All rights reserved.

Keywords: (Liquid + liquid) equilibria; Oxygenate additives; Ternary mixtures; Quaternary mixtures

1. Introduction

The materials 1,1-dimethylethyl methyl ether

(MTBE, methyl tert-butyl ether) and diisopropyl ether

(DIPE) are considered as blending agents for new re-

formulated gasoline. To assess the solubility of these

oxygenate additives in aqueous-hydrocarbon mixtures,

we continue to study the multicomponent (liquid + li-

quid) equilibria for aqueous aromatic mixtures withMTBE or DIPE. There is much variety in the ternary (li-

quid + liquid) equilibria with aqueous MTBE and DIPE

mixtures [1–4], but not enough for the quaternary (liquid

+ liquid) equilibria with the MTBE and DIPE mixtures

[5,6].

In this work, we present (liquid + liquid) equilibria

for one ternary mixture of water + MTBE + DIPE and

one quaternary mixture of water + MTBE + DIPE +toluene measured at T = 298.15 K. The measured results

0021-9614/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jct.2005.02.002

* Corresponding author. Tel.: +8620 8522 0223; fax: +8620 8522

1697.

E-mail address: tlirq@jnu.edu.cn (Y. Chen).

are correlated with modified UNIQUAC and extendedUNIQUAC models having binary, ternary, and quater-

nary parameters [7,8]. The binary and ternary parame-

ters constituting the quaternary mixtures are obtained

from binary and ternary phase equilibria whose experi-

mental values are available from the following litera-

tures: (vapour + liquid) equilibria, (toluene + DIPE)

at T = (339.70 to 381.19) K [9], (MTBE + DIPE) at

T = (338.05 to 325.95) K [10], (MTBE + toluene)at T = 333.15 K [11]; mutual solubilities at T =

298.15 K, (DIPE + water) [3], (toluene + water) [12],

(MTBE + water) [2]; ternary (liquid + liquid) equilibria

at T = 298.15 K, (water + MTBE + toluene) [1], and

(water + DIPE + toluene) [4].

2. Experimental

The MTBE was supplied by Tedia Company, Inc.

with nominal minimum mass fraction purity of 0.998.

Toluene was provided from Guangzhou Chemical

Reagent Factory, with mass fraction purity of 0.995.

Y. Chen et al. / J. Chem. Thermodynamics 37 (2005) 1138–1143 1139

The DIPE was obtained from Tianjin Chemical Reagent

Institute with mass fraction purity of 0.990. Water was

provided from Jinan University with mass fraction puri-

ties of 0.999. The g.c. analysis did not detect any appre-

ciable peaks, and determined the mass fraction purities

of 0.995 for DIPE, and >0.998 for MTBE and toluene.Quaternary (liquid + liquid) equilibrium measurements

were carried out at the temperature (298.15 ± 0.01) K.

The experimental apparatus is schematically shown in

figure 1. The quaternary mixtures were prepared by mix-

ing the binary mixtures whose compositions are M1, M2

and M3 with water and then toluene stepwise to cover

the two-phase region. The M1, M2 and M3 are approx-

imately 0.25, 0.50, 0.75, respectively, indicating the molefraction of DIPE in MTBE. The mixtures in the equilib-

rium glass cell were stirred vigorously by using a mag-

netic stirrer for 4 h, and settled for 4 h which were

sufficient to separate into two layers. The headspace of

the cell was filled with dry nitrogen gas to prevent con-

tamination with moisture. The samples, withdrawn from

the upper and lower phases in the cell by using a micro-

syringe, were analyzed by a gas chromatograph (Shang-hai Analyses Apparatus Factory, GC-122) equipped

with a thermal conductivity detector. A stainless steel

column (2 m long, 3 mm i.d.) packed with Porapak QS

was used to separate each component. The oven temper-

atures of the injection port and detector were set at

T = 473 K, and the final temperature of the oven was

kept at T = 453 K. The hydrogen flow rates for both

the separation and reference columns were set at1.0 ml s�1. The peak area of the components, measured

with a chromatopac (Zhejiang university, MR98S), was

calibrated by gravimetrically weighted mixtures. Three

analyses were made for each sample to obtain a mean

value. The accuracy of the measurements was estimated

within ±0.001 mole fraction.

FIGURE 1. Schematic diagram for LLE measurement.

3. Results and analyses

Tables 1 and 2 list the experimental ternary and

quaternary tie-line results for {x1H2O + x2CH3C

(CH3)2OCH3 + (1 � x1 � x2)(CH3)2CHOCH(CH3)2}

and {x1H2O + x2CH3C(CH3)2OCH3 + x3(CH3)2CH-OCH(CH3)2 + (1 � x1 � x2 � x3)C6H5CH3} at T =

298.15 K. Following a classification of the plane of the

quaternary (liquid + liquid) equilibrium surface [13]

these mixtures, composed of three pairs of type 2 of

the ternary (liquid + liquid) equilibria for (water + DI-

PE + MTBE) and (water + toluene + MTBE or +

DIPE) mixtures, show type 2 of the quaternary

(liquid + liquid) equilibria behavior. The experimentalresults were represented by using modified UNIQUAC

and extended UNIQUAC models including ternary

and quaternary parameters in addition to binary param-

eters. The binary parameters for the miscible mixtures

were obtained from binary experimental (vapour + li-

quid) equilibrium data reduction taking into

account the vapor-phase non-ideality and the Poynting

correction [14]. Vapour pressures of the pure compo-nents were obtained from the Antoine equation whose

constants were taken from the literature values [15,16].

Pure liquid molar volumes were calculated by the

modified Rackett equation [17]. Second virial coeffi-

cients were estimated by the method of Hayden-O�Con-nell [18]. Table 3 shows the molecular structural

parameters of pure components. Values of molecular

size and area parameters r and q for pure componentswere taken from Prausnitz et al. [2,3,14]. The values

of q 0 used in the modified UNIQUAC and extended

UNIQUAC models, fixed to obtain a good representa-

tion for binary and ternary phase equilibria

studied previously, were obtainable from the references

[7,8].

Table 4 shows the constituent binary parameters, a12and a21, of the modified UNIQUAC model and those ofthe extended UNIQUAC model, along with the root-

mean-square deviations between the experimental and

most probable calculated values of the measured vari-

ables (dP for pressure, dT for temperature, dx for li-

quid-phase mole fraction, and dy for vapor-phase mole

fraction). The root-mean-square deviations between

the experimental and calculated values were obtained

from a regression analysis based on the maximum like-lihood principle, where the standard deviations are ta-

ken as 0.133 kPa in pressure, 0.05 K in temperature,

0.001 in liquid phase mole fraction, and 0.003 in vapor

phase mole fraction [14]. The binary parameters for

the mutual solubility were obtained by solving the isoac-

tivity of each component in two liquid phases (I and II)

and the mass balance [19]

ðc xiÞI ¼ ðc xiÞII ; ð1Þ

i i

TABLE 1

Equilibrium phase compositions in mole fraction (x) for the ternary of

H2O(1) + CH3C(CH3)2OCH3(2) + (CH3)2CHOCH(CH3)2(3) mixtures

at T = 298.15 K

Phase I Phase II

x1 x2 1 � x1 � x2 x1 x2 1 � x1 � x2

0.1014 0.8986 0.0000 0.9909 0.0091 0.0000

0.0980 0.7732 0.1288 0.9932 0.0068 0.0000

0.0899 0.5505 0.3596 0.9943 0.0054 0.0003

0.0818 0.4582 0.4600 0.9953 0.0041 0.0006

0.0655 0.3571 0.5774 0.9890 0.0055 0.0055

0.0443 0.2751 0.6806 0.9961 0.0025 0.0014

0.0488 0.2529 0.6983 0.9966 0.0022 0.0012

0.0437 0.1581 0.7982 0.9975 0.0011 0.0014

0.0207 0.0604 0.9189 1.0000 0.0000 0.0000

TABLE 2

Experimental (liquid + liquid) equilibrium results for the quaternary mixture

Phase I

x1 x2 x3 1 � x1 � x2 � x3

{x1H2O + x2CH3C(CH3)2OCH3 + x3(CH3)2CHO

M1 : x03 ¼0.0550 0.6042 0.2156 0.1252

0.0812 0.5203 0.1857 0.2128

0.0463 0.4389 0.1463 0.3685

0.0214 0.3725 0.1337 0.4724

0.0177 0.3310 0.1123 0.5390

0.0292 0.2884 0.0995 0.5829

0.0204 0.2613 0.0887 0.6296

0.0195 0.2346 0.0848 0.6611

0.0221 0.2163 0.0751 0.6865

0.0162 0.1978 0.0675 0.7185

0.0159 0.1936 0.0643 0.7262

0.0159 0.1647 0.0549 0.7645

M2 : x03 ¼0.0490 0.3968 0.4266 0.1276

0.0158 0.3644 0.3961 0.2238

0.0243 0.2890 0.3130 0.3737

0.0287 0.2405 0.2558 0.4750

0.0173 0.2122 0.2245 0.5461

0.0153 0.1858 0.1939 0.6050

0.0147 0.1740 0.1806 0.6306

0.0149 0.1509 0.1584 0.6758

0.0142 0.1388 0.1449 0.7020

0.0132 0.1301 0.1345 0.7218

0.0116 0.1163 0.1220 0.7501

0.0146 0.1031 0.1075 0.7748

M3 : x03 ¼0.0367 0.1884 0.6311 0.1438

0.0229 0.1751 0.5737 0.2283

0.0227 0.1409 0.4550 0.3814

0.0185 0.1156 0.3739 0.4920

0.0184 0.1038 0.3278 0.5500

0.0147 0.0906 0.2856 0.6091

0.0153 0.0767 0.2495 0.6585

0.0178 0.0731 0.2325 0.6766

0.0152 0.0668 0.2121 0.7059

0.0117 0.0612 0.1942 0.7329

0.0124 0.0563 0.1767 0.7546

0.0105 0.0492 0.1557 0.7846

TABLE 3

Structural parameters for pure components

Component r q q 0a q 0b

H2O 0.92 1.40 1.283 0.96

CH3C(CH3)2OCH3 4.07 3.63 q0.75 q0.20

(CH3)2CHOCH(CH3)2 4.74 4.09 q0.75 q0.20

C6H5CH3 3.92 2.97 q0.75 q0.20

a Modified UNIQUAC model.b Extended UNIQUAC model.

1140 Y. Chen et al. / J. Chem. Thermodynamics 37 (2005) 1138–1143

Xi

xIi ¼Xi

xIIi ¼ 1; ð2Þ

where i is the number of component, x the liquid-phase

mole fraction, c the activity coefficient given by the

s at T = 298.15 K

Phase II

x1 x2 x3 1 � x1 � x2 � x3

CH(CH3)2 + (1 � x1 � x2 � x3)C6H5CH3}

0:25

0.9932 0.0063 0.0005 0.0000

0.9952 0.0048 0.0000 0.0000

0.9964 0.0036 0.0000 0.0000

0.9959 0.0038 0.0003 0.0000

0.9964 0.0033 0.0003 0.0000

0.9955 0.0045 0.0000 0.0000

0.9968 0.0032 0.0000 0.0000

0.9975 0.0025 0.0000 0.0000

0.9979 0.0021 0.0000 0.0000

0.9978 0.0022 0.0000 0.0000

0.9984 0.0016 0.0000 0.0000

0.9986 0.0014 0.0000 0.0000

0:50

0.9970 0.0027 0.0003 0.0000

0.9965 0.0030 0.0005 0.0000

0.9962 0.0030 0.0008 0.0000

0.9980 0.0020 0.0000 0.0000

0.9976 0.0020 0.0004 0.0000

0.9982 0.0018 0.0000 0.0000

0.9982 0.0018 0.0000 0.0000

0.9988 0.0012 0.0000 0.0000

0.9983 0.0017 0.0000 0.0000

0.9988 0.0012 0.0000 0.0000

0.9989 0.0011 0.0000 0.0000

0.9990 0.0010 0.0000 0.0000

0:75

0.9980 0.0016 0.0004 0.0000

0.9965 0.0018 0.0017 0.0000

0.9977 0.0012 0.0011 0.0000

0.9982 0.0011 0.0007 0.0000

0.9987 0.0009 0.0004 0.0000

0.9994 0.0006 0.0000 0.0000

0.9991 0.0006 0.0003 0.0000

0.9992 0.0008 0.0000 0.0000

0.9995 0.0005 0.0000 0.0000

0.9995 0.0005 0.0000 0.0000

0.9995 0.0005 0.0000 0.0000

1.0000 0.0000 0.0000 0.0000

TABLE 4

The results of fitting both models to (vapour + liquid) and (liquid + liquid) equilibria and root-mean-square deviations dP, dT, dx and dy for binary

mixtures

Mixture T/K Model a12/K a21/K dP/kPa T/K 103 Æ dx 103dy

{xC6H5CH3 + (1 � x)(CH3)2CHOCH(CH3)2} 381.19–339.70 Ia �310.42 580.63 0.9 0.4 5.0 15.0

IIb �390.72 662.21 1.0 0.4 6.0 14.9

{xCH3C(CH3)2OCH3 + (1 � x)(CH3)2CHOCH(CH3)2} 338.05–325.95 I �178.45 255.08 0.3 0.1 0.9 5.3

II �219.26 319.95 0.3 0.1 0.9 5.2

{xCH3C(CH3)2OCH3 + (1 � x)C6H5CH3} 333.15 I �222.93 334.43 0.1 0.1 1.2 4.7

II �207.40 337.91 0.1 0.1 1.1 4.7

{xC6H5CH3 + (1 � x)H2O} 298.15 I 1713.30 752.99

II 1540.70 1053.90

{xCH3C(CH3)2OCH3 + (1 � x)H2O} 298.15 I 949.98 110.41

II 767.89 89.725

{x(CH3)2CHOCH(CH3)2 + (1 � x)H2O} 298.15 I 1590.60 166.69

II 1075.00 163.26

a I, modified UNIQUAC model.b II, extended UNIQUAC model.

Y. Chen et al. / J. Chem. Thermodynamics 37 (2005) 1138–1143 1141

modified UNIQUAC or extended UNIQUAC models

previously described in detail [7,8]. For the ternary mix-

tures having a plait point, original UNIQUAC model

predicts generally larger solubility envelope than the

experimental one. Good quantitative description of the

ternary (liquid + liquid) equilibrium mixtures usuallyneeds ternary parameters in addition to the binary

parameters. The ternary parameters, s231, s312 and s123,were obtained by fitting the model to the ternary exper-

imental (liquid + liquid) equilibrium tie-lines and the

quaternary parameters, s2341, s1342, s1243 and s1234, weredetermined from the quaternary experimental (liquid

+ liquid) equilibrium results using a simplex method

[20] by minimizing the objective function:

F ¼ 102 �Xk

minXi

Xj

xexptlijk � xcalcijk

� �2

( ,M

)0:5

;

ð3Þ

TABLE 5

The results of fitting both models with ternary (liquid + liquid) equilibria at

Mixture N

{x1C6H5CH3 + x2CH3C(CH3)2OCH3 + (1 � x1 � x2)H2O} 1

{x1H2O + x2CH3C(CH3)2OCH3 + (1 � x1 � x2)(CH3)2CHOCH(CH3)2}

{x1H2O + x2C6H5CH3 + (1 � x1 � x2)(CH3)2CHOCH(CH3)2} 1

a I, modified UNIQUAC model.b II, extended UNIQUAC model.c Absolute arithmetic mean deviation (mol%).d Root-mean-square deviation (mol%).

where min means minimum values, i = 1 to 3 for ter-

nary mixtures or 1 to 4 for quaternary mixtures,

j = phases I or II, k = 1,2, . . .,n (tie-lines), M = 2ni,

and x = (liquid phase mole fraction). Table 5 presents

the ternary parameters and the root-mean-square devi-

ations of mole fraction of tie-lines between the experi-mental and calculated results for the ternary

(liquid + liquid) equilibria. Figure 2 compares the

experimental and calculated (liquid + liquid) equilibria

of the ternary mixtures making up the quaternary

mixtures {x1H2O + x2CH3C(CH3)2OCH3 + x3(CH3)2-

CHOCH(CH3)2 + (1 � x1 � x2 � x3)C6H5CH3}. App-

reciable differences in solubility envelope between two

ternary mixtures (water + MTBE + toluene) and(water + DIPE + toluene) are observed in figure 2 by

superimposing one on the other. Also, the mutual sol-

ubilities of water in MTBE rich-region are larger than

those of water in DIPE rich-region. As shown in figure

2, DIPE dissolves into water less than MTBE. These

T = 298.15 K

o. of tie-lines Ternary parameters Deviations

Ia IIb Ia IIb

3 s231 = �1.1172 s231 = �0.00172 0.20c 3.13

s132 = �1.9836 s132 = �6.9795 0.67d 4.19

s123 = 0.00321 s123 = 0.00625

9 s231 = 0.01139 s231 = �0.56586 0.42 4.10

s132 = �1.2032 s132 = 0.35230 0.45 5.44

s123 = 3.8481 s123 = �11.168

2 s231 = 0.22581 s231 = �0.07082 0.16 4.23

s132 = 0.35329 s132 = �0.01161 0.19 6.48

s123 = �3.0509 s123 = �0.13301

TABLE 6

The results of fitting both models to the quaternary (liquid + liquid) equilibria at T = 298.15 K

Mixture No. of tie-lines Quaternary parameters Deviations

Ia IIb Ia IIb

{x1H2O + x2H3C(CH3)2OCH3 + x3(CH3)2CHOCH(CH3)2(1 � x1 � x2 � x3)C6H5CH3}

36 s2341 = 2.3367 s2341 = 0.8419 0.18c 0.52

s1342 = �38.0985 s1342 = 4.8323 0.28d 0.67

s1243 = 64.3726 s1243 = 30.5706

s1234 = 0.8216 s1234 = �74.4782

a I, modified UNIQUAC model.b II, extended UNIQUAC model.c Absolute arithmetic mean deviation (mol%).d Root-mean-square deviation (mol%).

FIGURE 2. Experimental and calculated (liquid + liquid) equilibria of three ternary mixtures making up (water + MTBE + DIPE + toluene) at

T = 298.15 K. –�–�–, experimental tie-line; —, calculated tie-line using the modified UNIQUAC model with binary and ternary parameters taken

from tables 4 and 5.

1142 Y. Chen et al. / J. Chem. Thermodynamics 37 (2005) 1138–1143

differences may be explained by the intermolecular

interactions of water with MTBE and DIPE. The pres-

ence of an extra methylidyne group in DIPE compared

with MTBE increases more hydrophobicity of the ether

and consequently weakens the attractive interactions

between water and the oxygen atom in the ether. Table

6 summarizes the calculated results for the quaternary

mixtures obtained in fitting the modified UNIQUACmodel and the extended UNIQUAC model with bin-

ary, ternary and quaternary parameters to the quater-

nary (liquid + liquid) equilibria.

4. Conclusions

(Liquid + liquid) equilibrium tie-lines were measuredfor one ternary system {x1H2O + x2CH3C(CH3)2-

OCH3 + (1 � x1 � x2)(CH3)2CHOCH(CH3)2} and one

quaternary system {x1H2O + x2CH3C(CH3)2OCH3 + x3(CH3)2CHOCH(CH3)2 + (1 � x1 � x2 � x3)C6H5CH3}

at T = 298.15 K and P� = 101.3 kPa. The experimental

quaternary (liquid + liquid) equilibria were success-

fully correlated by using both models including bin-

ary, ternary and quaternary parameters. The

quaternary (liquid + liquid) equilibrium results calcu-

lated by the modified UNIQUAC and the extended

UNIQUAC models are in good agreement with the

experimental results.

Acknowledgments

Supported by Foundation of Ministry of Education

of China (2002-247), Foundation of Scientific Research

from Guangdong Province of China (2003C33101) and

Foundation of Jinan University of China (640071).

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JCT 04/234