Excess molar volumes and excess molar enthalpies of the binary mixtures of 1,2-dichloropropane with di- and triethylene glycol mono-alkyl ethers at T = 298.15 K

Fluid Phase Equilibria 285 (2009) 30–35

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Excess molar volumes and excess molar enthalpies of the binary mixtures of 1,2-dichloropropane with di- and triethylene glycol mono-alkyl ethers at T = 298.15 K Dipak Sen, Moon Gab Kim ∗ School of Applied Chemical Engineering, Kyungpook National University, 386 Gajangdong, Sangju 742-711, Republic of Korea

a r t i c l e

i n f o

Article history: Received 13 January 2009 Received in revised form 8 May 2009 Accepted 19 June 2009 Available online 27 June 2009 Keywords: Excess molar properties Redlich–Kister equation Thermodynamic models 1,2-Dichloropropane Di- and triethylene glycol mono-alkyl ethers

a b s t r a c t E E The excess molar volumes Vm and excess molar enthalpies Hm at T = 298.15 K and atmospheric pressure for the binary systems of 1,2-dichloropropane (1,2-DCP) with di- and triethylene glycol mono-alkyl ethers have been determined by measuring density and heat flux, respectively. The density has been measured by using a digital vibrating-tube densimeter, whereas heat flux measurements have been carried out by using an isothermal calorimeter with a flow-mixing cell. The diethylene glycol mono-alkyl ethers are 2(2-alkoxyethoxy)ethanols: diethylene glycol mono-propyl ether (DEGMPE), diethylene glycol mono-butyl ether (DEGMBE), and the triethylene glycol mono-alkyl ethers are 2-(2-(2-alkoxyethoxy)ethoxy)ethanols: triethylene glycol mono-methyl ether (TEGMME), triethylene glycol mono-ethyl ether (TEGMEE), and E E triethylene glycol mono-butyl ether(TEGMBE). It was found that both Vm and Hm values of the binary mixtures are negative over the whole composition range except for the mixture with very high mole fraction of 1,2-DCP(x1 ) in both DEGMPE and DEGMBE. In the case of 2-(2-(2-alkoxyethoxy)ethoxy)ethanols, E E the negative values of Vm and Hm continue to increase with an increase of the alkyl chain length of these E alkoxyethanols. The minimum values of Vm shift from −0.1939 cm3 mol−1 for the mixture with DEGMPE to E −0.40 cm3 mol−1 for the mixture with TEGMBE at x1 = 0.40–0.50. Also, the minimum negative values of Hm have been shown ranging from −472.9 J mol−1 (DEGMBE) to −800.5 J mol−1 (TEGMBE) at x1 = 0.40–0.50. E E The experimental results of both Hm and Vm were fitted to the Redlich–Kister equation. The experimental E Hm data were also fitted to three local-composition models (Wilson, NRTL, and UNIQUAC). It was found that among these three models, the NRTL equation provides the most appropriate correlating result. © 2009 Elsevier B.V. All rights reserved.

1. Introduction In the past few years, substantial attempts have been made on the measurement, analysis and interpretation of basic thermodynamic properties such as excess volume and density [1,2], viscosity [3], excess volume and enthalpy [4,5], and excess enthalpy [6] of binary mixtures containing alkoxyethanols. The literature E and reveals that no efforts have been made to provide the Vm E Hm values of these higher alkoxyethanols: DEGMPE, DEGMBE, TEGMME, TEGMEE and TEGMBE with particular 1,2-DCP. This paper is a continuation of our systematic program [7–11] based on the measurements of excess properties of binary mixtures containing 1,2-DCP, which is used as solvent for oil, fats, resin and rubber [12]. Alkoxyethanols, CH3 (CH2 )n –O–(CH2 –CH2 O)m –CH2 –CH2 OH (n = 2, 3 when m = 1 and n = 0, 1, 3 when m = 2) are self-associated compounds due to the interaction between their OH terminal

∗ Corresponding author. Tel.: +82 54 530 1332; fax: +82 54 536 1330. E-mail address: mg [email protected] (M.G. Kim). 0378-3812/$ – see front matter © 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2009.06.018

group and oxygen ether atoms via inter- and intra-hydrogen bonds. These glycol ether solvents have been used in the coating industry because of their good coupling ability and solubility for coating resins [13]. Likewise, 1,2-DCP is a polar compound having a dipole moment 1.87 (D) [14] at T = 298.15 K. In spite of its modest polarity, 1,2-DCP is insoluble in water, probably because of its inability to form hydrogen bonds. It is soluble in typical organic solvents of low polarity like benzene, ether, and chloroform. Molecules are held together by van der Waals force of attraction and dipole–dipole interaction. The non-ideal behaviors of these mixtures containing polar and self-associated components are significantly observed on the mixing process because of their difference in molecular size, hydrogen-bonding and dipole–dipole interaction between unlike molecules. The aim of this paper is to collect the set of values of excess E and H E of these binary mixtures at T = 298.15 K and properties, Vm m atmospheric pressure over the whole concentration range. In this context, the determinations of the excess properties are considered of primary interest, as these properties are essential in characterizing the type and magnitude of the molecular interactions on

D. Sen, M.G. Kim / Fluid Phase Equilibria 285 (2009) 30–35

the mixing process. The sign, magnitude, and symmetry of these quantities are the direct result of bond breaking and rearranging during the mixing process and any effect arising from energetic interactions between both like and unlike molecules will be directly reflected in the enthalpy data and their representations, which is essential when studying new theoretical approaches to the pure liquid and liquid mixtures. Moreover, a knowledge of these excess molar properties can be useful in predicting the solution behavior of 1,2-DCP in higher alkoxyethanols. The secondary aspect is to examine the effect of the addition of (–OC2 H4 –) group or alkyl chain length in alkoxyethanol molecules on molecular interaction E and H E at T = 298.15 K in these binary mixtures with 1,2-DCP. The Vm m were correlated by the Redlich–Kister equation [15]. We also tested the thermodynamic models (Wilson, NRTL, and UNIQUAC) [16–18] E values, to based on the local-composition, for the experimental Hm investigate which models show the best correlation of the excess enthalpy together with the standard deviation and to calculate their parameters.

31

which was operated under suction mode and equipped with an automatic sample changer (model SP3, Anton Paar, Graz, Austria). Prior to measuring the refractive index and density, calibrations have been done by using HPLC grade water for the refractometer and HPLC grade water and air for the densimeter at working condition. Samples were prepared by weighing the liquids in approximately 50 cm3 well-sealed glass-vials, taking due precaution to minimize the evaporation losses. All the weighing were performed by a digital electronic balance with a precision ±1.5 × 10−5 g (model AT-201, Mettler Toledo, Switzerland). The uncertainty of the mole fraction of the samples was estimated to be less than ±1 × 10−4 . From these data, excess molar volumes of the binary mixtures were determined according to the following relation:

2 E Vm (cm3

2. Experimental

mol

−1

)=

i=1

−

2

(xi Mi )

i=1

(1)

(xi Mi /i )

where xi , Mi , , and i are the mole fraction, molar mass, density of mixtures and density of component i, respectively. The uncertainty for the excess volume measurement is less than ±5 × 10−4 cm3 mol−1 . E were determined with an Excess molar enthalpies Hm isothermal calorimeter (model CSC-4400, Calorimetry Sciences Corporation, UT, U.S.A.) with a newly designed flow-mixing assembly kit (model CSC-4442, CSC, UT, U.S.A.). Two digital HPLC pumps with a precision of 0.2% (Acuflow Series II, Fisher Scientific, U.S.A.) were used to deliver liquid components at constant volumetric flow rates to the mixing cell of the calorimeter. The working pressure of the mixing cell in the calorimeter was controlled at p = 101.3 kPa by a back-pressure regulator (Grove Valves & Regulator Co., Stafford, TX, U.S.A.). The magnitude of the measured heat signal is an important factor that has to be taken into account when determining the total volumetric flow rate for a set of experiments. In this study, the selected values were 0.5 cm3 min−1 for all the measurements. To eliminate the uncertainties in the volumetric flow rate due to the fluctuations in ambient temperature, liquid components were kept in double glass-lined jacketed bottles controlled by circulating coolant from a Haake digital circulating bath (model Series-9100, PolyScience, IL, U.S.A.) with an accuracy of ±0.01 K. Details of an isothermal flow calorimeter, the calibrations of both pumps and calorimeter, the reliability of the apparatus, and the experimental E , have been described procedure to determine the experimental Hm in a previous work [8,9,21]. The uncertainty of the mole fraction was estimated to be less than ±1 × 10−3 . Similarly, the uncertainty of our calorimetric measurements can be estimated to be E ± 0.5–1.0)J mol−1 . (Hm

2.1. Materials 1,2-DCP (Fluka, >99%), DEGMPE (Aldrich, >98%), DEGMBE (Fluka, >98%), TEFMME (Fluka, >97%), TEGMEE (Fluka, >90%) and TEGMBE (Fluka, >70%) were used without further purification but degassed by means of an ultrasonic bath. We could not get the highest purity of TEGMBE from any supplier despite our vigorous efforts. HPLC grade water (Fisher Scientific, >99.7%) has been used for the calibration of the refractometer and densimeter. An analysis of all the chemicals by gas chromatography has justified the stated purities of the compounds. The purities of the liquids were also checked by measuring their densities and refractive indices at T = 298.15 K and atmosphere pressure. These values were compared with their corresponding literature values [14,19] as shown in Table 1. Because of scarcity of densities and refractive indices in the literature, the references for some of the densities and refractive indices of di- and triethylene glycol mono-alkyl ethers have been taken from Fluka and Sigma–Aldrich. These results are in good agreement with data in literature. The structural parameters (qi ) [20] of pure components used in UNIQUAC models were also given in Table 1. 2.2. Apparatus and procedure The refractive indices of a pure component were measured using a digital refractometer (model RA-520, Kyoto Electronics, Japan) with an accuracy of ±2 × 10−5 for values ranging from 1.32 to 1.58. The densities of pure components and their binary mixtures were measured by a vibrating-tube densimeter (model DMA 58, Anton Paar, Graz, Austria) with an accuracy ±1 × 10−5 g cm−3 ,

Table 1 for pure components at T = 298.15 K and structural parameters qi, stated purities, and suppliers. Densities , refractive indices n25 D Compound

1,2-DCP DEGMPE DEGMBE TEGMME TEGMEE TEGMBE a b c d e

 (g cm−3 )

n25 D

Exptl.

Lit.

Exptl.

Lit.

1.14903 0.96274 0.94848 1.04330 1.01619 0.98844

1.14936b 0.969c 0.952d 1.04310e 1.020d 0.990d

1.43656 1.42727 1.42998 1.43673 1.43623 1.43973

1.43679b 1.435c 1.432d 1.439d 1.438d 1.441d

Ref. [20]. Ref. [14]. Reference [Sigma–Aldrich] at T = 293.15 K. Reference [Fluka] at T = 293.15 K. Ref. [19].

qi a

Stated purities mass%

Suppliers

3.064 5.768 6.308 6.008 6.548 7.628

>99 >99 >98 >97 >98 >70

Fluka Sigma–Aldrich Fluka Fluka Fluka Fluka

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D. Sen, M.G. Kim / Fluid Phase Equilibria 285 (2009) 30–35

Table 2 E for {1,2-DCP(x1 ) + di- and triethylene glycol mono-alkyl Excess molar volumes Vm ethers(x2 )} at T = 298.15 K.  (J mol−1 )

E Vm (cm3 mol

{1,2-DCP(x1 ) + DEGMPE(x2 )} 0.0540 0.96958 −0.0450 0.1050 0.97629 −0.0852 0.1473 0.98203 −0.1156 0.2030 0.98981 −0.1449 0.2494 0.99653 −0.1640 0.3000 1.00410 −0.1808 0.3488 1.01166 −0.1904 0.4014 1.02011 −0.1939 0.4516 1.02846 −0.1889 0.5005 1.03691 −0.1785

0.5504 0.5995 0.6509 0.7009 0.7520 0.8015 0.8510 0.9018 0.9476

1.04589 1.05507 1.06509 1.07528 1.08618 1.09729 1.10905 1.12184 1.13408

−0.1642 −0.1451 −0.1189 −0.0916 −0.0608 −0.0316 −0.0098 0.0044 0.0098

{1,2-DCP(x1 ) + DEGMBE(x2 )} 0.0520 0.95488 −0.0476 0.1000 0.96107 −0.0934 0.1550 0.96838 −0.1276 0.1997 0.97456 −0.1470 0.2496 0.98176 −0.1692 0.3037 0.98993 −0.1879 0.3497 0.99720 −0.1980 0.4033 1.00602 −0.1997 0.4504 1.01414 −0.1958 0.4998 1.02303 −0.1813

0.5535 0.6001 0.6494 0.7024 0.7527 0.8024 0.8488 0.9010 0.9479

1.03323 1.04257 1.05296 1.06478 1.07667 1.08922 1.10175 1.11684 1.13148

−0.1650 −0.1478 −0.1227 −0.0945 −0.0620 −0.0335 −0.0168 0.0017 0.0048

{1,2-DCP(x1 ) + TEGMME(x2 )} 0.0554 1.04740 −0.0538 0.1000 1.05082 −0.0945 0.1507 1.05488 −0.1443 0.1999 1.05891 −0.1835 0.2535 1.06343 −0.2177 0.2977 1.06732 −0.2466 0.3483 1.07188 −0.2700 0.4010 1.07680 −0.2880 0.4512 1.08166 −0.3000 0.5013 1.08665 −0.3016

0.5522 0.6013 0.6480 0.7005 0.7514 0.7997 0.8567 0.8993 0.9502

1.09189 1.09716 1.10230 1.10834 1.11440 1.12038 1.12798 1.13384 1.14127

−0.2947 −0.2848 −0.2643 −0.2368 −0.1996 −0.1586 −0.1212 −0.0807 −0.0368

{1,2-DCP(x1 ) + TEGMEE(x2 )} 0.0522 1.02053 −0.0601 0.1019 1.02484 −0.1152 0.1497 1.02919 −0.1694 0.2027 1.03417 −0.2178 0.2538 1.03919 −0.2585 0.3014 1.04406 −0.2902 0.3475 1.04898 −0.3175 0.4037 1.05522 −0.3388 0.4507 1.06069 −0.3507 0.5006 1.06674 −0.3535

0.5530 0.6023 0.6499 0.7036 0.7524 0.8009 0.8494 0.8988 0.9495

1.07337 1.07992 1.08658 1.09448 1.10210 1.11006 1.11849 1.12779 1.13804

−0.3437 −0.3263 −0.3042 −0.2700 −0.2355 −0.1880 −0.1354 −0.0916 −0.0457

{1,2-DCP(x1 ) + TEGMBE(x2 )} 0.0513 ’ −0.0525 0.0919 0.99632 −0.1145 0.1463 1.00135 −0.1759 0.2006 1.00667 −0.2326 0.2501 1.01179 −0.2765 0.3036 1.01768 −0.3231 0.3548 1.02363 −0.3559 0.4015 1.02938 −0.3787 0.4519 1.03595 −0.3948 0.5032 1.04304 −0.4000

0.5498 0.6016 0.6526 0.7010 0.7502 0.8009 0.8510 0.9003 0.9483

1.04990 1.05803 1.06661 1.07535 1.08493 1.09560 1.10721 1.11970 1.13301

−0.3948 −0.3809 −0.3555 −0.3199 −0.2787 −0.2242 −0.1749 −0.1190 −0.0587

 (J mol−1 )

E Vm (cm3 mol

−1

x1

x1

)

−1

)

 N

3

(cm mol

j=1

Aj (2x1 − 1)j−1

−1

or J mol

i=1

)

E E (Qm,expt − Qm,calc )

(N − n)

2

1/2

i

(3)

Table 3 E for {1,2-DCP(x1 ) + di- and triethylene glycol mono-alkyl Excess molar enthalpies Hm ethers(x2 )} at T = 298.15 K.

(2)

−1

E Hm (J mol

−1

x1

E Hm (J mol

{1,2-DCP(x1 ) + DEGMPE(x2 )} 0.060 −146.9 0.119 −250.6 0.147 −296.6 0.202 −374.3 0.255 −429.0 0.306 −467.3 0.355 −485.5 0.402 −490.6 0.447 −482.3 0.511 −449.2

0.552 0.592 0.648 0.702 0.753 0.802 0.848 0.907 0.948

−413.6 −375.5 −308.2 −234.6 −162.1 −94.1 −30.2 26.0 37.8

{1,2-DCP(x1 ) + DEGMBE(x2 )} 0.066 −163.3 0.098 −208.7 0.161 −308.0 0.191 −360.0 0.248 −411.4 0.303 −449.1 0.355 −468.9 0.404 −472.9 0.450 −462.1 0.495 −440.5

0.558 0.598 0.654 0.707 0.757 0.803 0.847 0.902 0.953

−391.6 −356.6 −287.0 −214.9 −143.6 −77.9 −19.0 35.0 41.2

{1,2-DCP(x1 ) + TEGMME(x2 )} 0.061 −179.6 0.091 −236.2 0.150 −381.5 0.206 −496.2 0.260 −586.0 0.311 −658.9 0.360 −708.3 0.407 −742.2 0.452 −757.9 0.496 −758.8

0.558 0.597 0.654 0.707 0.757 0.805 0.851 0.908 0.949

−735.8 −703.7 −638.3 −554.7 −463.8 −366.3 −263.2 −137.1 −60.3

{1,2-DCP(x1 ) + TEGMEE(x2 )} 0.067 −211.7 0.101 −275.0 0.164 −437.0 0.195 −505.3 0.253 −607.3 0.308 −685.4 0.360 −741.8 0.410 −777.7 0.457 −789.4 0.501 −789.8

0.544 0.604 0.660 0.695 0.745 0.807 0.850 0.904 0.954

−775.6 −728.0 −657.2 −603.6 −511.6 −373.8 −274.4 −150.5 −55.0

{1,2-DCP(x1 ) + TEGMBE(x2 )} 0.079 −242.1 0.117 −325.5 0.154 −426.7 0.190 −504.3 0.256 −612.4 0.317 −697.4 0.346 −730.5 0.401 −777.7 0.452 −799.9 0.500 −800.5

0.545 0.606 0.645 0.698 0.746 0.805 0.859 0.907 0.951

−786.6 −737.7 −689.6 −607.8 −515.9 −390.1 −265.8 −155.2 −68.8

x1

E and H E values, Tables 2 and 3 present the experimental Vm m respectively, measured at T = 298.15 K for five binary mixtures of {1,2-DCP + DEGMPE, or +DEGMBE, or +TEGMME, or +TEGMEE, or +TEGMBE} and the results are also shown graphically in Figs. 1 and 2. The composition dependence of experimental excess E (V E or H E ) is described molar properties of the binary systems Qm m m by the following Redlich–Kister equation: n 

−1

where N is the number of experimental points and n is the number of coefficients. All the parameters of Eq. (2) are reported in

3. Results and discussion

E Qm (cm3 mol−1 or J mol−1 ) = x1 x2

where n is the number of parameters, x1 is the mole fraction of 1,2DCP, Aj are adjustable parameters determined by minimizing the sum of squares of the differences between experimental values of E and the corresponding values calculated by Eq. (2) using a nonQm linear regression procedure. The optimal number n of parameters Aj was determined by applying an F-test [22] with an examination of the variation of the standard deviation :

)

)

D. Sen, M.G. Kim / Fluid Phase Equilibria 285 (2009) 30–35

33

Table 4 E E or Hm ) (cm3 mol−1 or J mol−1 ) in Eq. (3) for {1,2-DCP(x1 ) + di- and triethylene glycol Parameters Aj of the Redlich–Kister equation in Eq. (2) with standard deviations, (Vm mono-alkyl ethers(x2 )} at T = 298.15 K. Properties

1,2-DCP(x1 )

E Vm

+DEGMPE(x2 ) +DEGMBE(x2 ) +TEGMME(x2 ) +TEGMEE(x2 ) +TEGMBE(x2 )

E Hm

+DEGMPE(x2 ) +DEGMBE(x2 ) +TEGMME(x2 ) +TEGMEE(x2 ) +TEGMBE(x2 )

A1 (cm3 mol−1 /J mol−1 ) −0.7204 −0.7338 −1.2062 −1.4077 −1.5991 −1832.2 −1763.5 −3043.1 −3175.0 −3205.3

A2 (cm3 mol−1 /J mol−1 )

A3 (cm3 mol−1 /J mol−1 )

0.5117 0.5334 0.0560 0.0899 −0.0137

A4 (cm3 mol−1 /J mol−1 )

0.4593 0.3946 0.3533 0.4164 0.4474

1222.3 1185.0 334.0 348.7 298.7

 (cm3 mol−1 /J mol−1 )

0.1483 0.1455 0.0996 0.1264 0.0531

1084.1 1074.1 1035.8 1024.6 956.8

0.0012 0.0027 0.0024 0.0023 0.0032

678.6 846.1 680.4 811.8 858.0

4.1 5.2 5.1 5.9 4.4

E and H E together with the standard deviations of the Table 4 for Vm m fits. E data were also used to investigate the suitThe experimental Hm ability of thermodynamic models as a function of temperature and composition at constant pressure. In this study, three kinds of models (Wilson, NRTL, and UNIQUAC) based on a local-composition theory, have been tested. The excess enthalpy, which indicates the temperature dependence of the excess Gibbs free energy, can be correlated via the Gibbs–Helmholtz equation:



E Hm

= −RT

2

∂(GE /RT ) ∂T



(4) P,x

From Eq. (4), the resulting expressions for the excess enthalpy can be derived by substituting GE /RT for the corresponding excess Gibbs free energy equations. The Wilson, NRTL and UNIQUAC E are given by the following Eqs. (5)–(7), respecexpressions of Hm tively:

E Fig. 1. Excess molar volumes Vm for {1,2-DCP(x1 ) + di- and triethylene glycol monoalkyl ethers(x2 )} at T = 298.15 K. Experimental results: () TEGMBE; (䊉) TEGMEE; () TEGMME; () DEGMBE; () DEGMPE; (—) calculated with Eq. (2) using parameters listed in Table 4.

E = x1 x2 Hm

   12 12

x1 + 12 x2

+

21 21 x2 + 21 x1



(5)

where 12 = V2 /V1 exp(−12 /RT), 12 = V1 /V2 exp(−21 /RT), and Vi is the molar volume of the component i:



E = RTx1 x2 Hm

+

x2 + x1 exp(˛21 )(1 − ˛21 ) {x1 exp(˛21 ) + x2 }2

x1 + x2 exp(˛12 )(1 − ˛12 ) {x2 exp(˛12 ) + x1 }2

21



12

(6)

where ˛ is the non-randomness parameter;  12 = g12 /RT and  21 = g21 /RT:



E Hm

= q1 x1

where

qi

2 21 u21 1 + 2 21 is

a





+ q2 x2

structural

1 12 u12 2 + 1 12

parameter



(7) of

component 

 12 = exp(−u12 /RT),  21 = exp(−u21 /RT), and i = xi qi /

xj qj .

j=1

E Fig. 2. Excess molar enthalpies Hm for {1,2-DCP(x1 ) + di- and triethylene glycol mono-alkyl ethers(x2 )} at T = 298.15 K. Experimental results: () TEGMBE; (䊉) TEGMEE; () TEGMME; () DEGMPE; () DEGMBE; (—) calculated with Eq. (2) using parameters listed in Table 4.

i,

The adjustable parameters of each model, 12 = a21 − a11 (J mol−1 ) and 21 = a12 − a22 (J mol−1 ) in the Wilson equation, g12 = g12 − g22 (J mol−1 ), g21 = g21 − g11 (J mol−1 ) and a in the NRTL equation, and u21 = u12 − u22 (J mol−1 ) and u21 = u21 − u11 (J mol−1 ) in the UNIQUAC equation, are listed in Table 5 together with standard deviations. Usually, the molecular packing effect caused by several factors such as self-association (inter- or intra-molecular interaction) and the physical interaction (van der Waals interaction and dipole–dipole interaction) between like molecules increase the volume. On the other hand, charge transfer type force, a structural effect that arises from the geometrical fitting of one component into other component due to the different molar volumes and free volumes of pure components or interactions between unlike

34

D. Sen, M.G. Kim / Fluid Phase Equilibria 285 (2009) 30–35

Table 5 Adjustable parameters: (12 and 21 ), Wilson equation in Eq. (5); (g12 , g21 and ˛), NRTL equation in Eq. (6); (u12 and u21 ), UNIQUAC equation in Eq. (7) and standard −1 E Jmol ) in Eq. (3) for {1,2-DCP(x1 ) + di- and triethylene glycol mono-alkyl ethers(x2 )} at T = 298.15 K. deviations, (Hm System:1,2-DCP(x1 )

+DEGMPE(x2 ) +DEGMBE(x2 ) +TEGMME(x2 ) +TEGMEE(x2 ) +TEGMBE(x2 )

Wilson

NRTL

UNIQUAC

12 (J mol−1 )

21 (J mol−1 )

 (J mol−1 )

g12 (J mol−1 )

g21 (J mol−1 )

˛

 (J mol−1 )

u12 (J mol−1 )

u21 (J mol−1 )

 (J mol−1 )

1555.5 1618.3 −124.0 −42.1 74.6

−2464.1 −2570.6 −2240.2 −2455.8 −2702.7

70.5 73.5 40.0 40.0 36.8

8777.8 8642.9 6881.1 7393.4 7484.6

−4311.5 −4177.2 −3564.8 −3891.5 −4047.4

0.17 0.18 0.29 0.26 0.24

4.1 6.7 4.1 5.1 5.5

−874.4 −833.1 −1178.2 −1180.8 −1144.4

745.1 715.8 943.8 951.7 934.9

126.6 134.7 54.3 66.0 82.6

molecules are the most common factors that contribute to volume contraction. Fig. 1 shows that experimental excess molar volumes at T = 298.15 K for the binary mixtures of {1,2-DCP + di- and triethylene glycol mono-alkyl ethers}are negative over the whole composition range except for two binary mixtures, {1,2-DCP + DEGMPE, or +DEGMBE} with a high mole fraction of 1,2-DCP, and decrease with alkyl chain length and addition of (–OC2 H4 –) in the alkoxyethanols. E shift from −0.1939 cm3 mol−1 Also, the minimum values of Vm for the mixture with DEGMPE to −0.40 cm3 mol−1 for the mixE values for ture with TEGMBE at (x1 = 0.4–0.5). The negative Vm whole binary mixtures can be described on the basis of differences in molecular volume/free volume between liquid components and unlike molecular interaction caused by dipole–dipole interaction. All alkoxyethanol molecules in our present work are much bigger than 1,2-DCP. As a result, empty spaces due to the formation of the asymmetric structure of alkoxyethanols are created around their environment on the mixing process. As a consequence of dipole–dipole interaction between unlike molecules, these spaces easily permit a 1,2-DCP molecules into their enviE < 0. ronment, resulting macroscopically in contraction or in Vm E is slightly positive for both However, in a 1,2-DCP rich region, Vm binary mixtures containing DEGMPE and DEGMBE. Unlike the 2(2-(2-alkoxyethoxy)ethoxy)ethanols, these alkoxyethanols consist lower number of (–OC2 H4 –) group in their molecules, which in turn decreased interaction between unlike molecules in the mixture. Accordingly, a lower number of 2-(2-alkoxyethoxy)ethanols, in a 1,2-DCP rich region, cannot provide sufficient empty space to introduce a large number of 1,2-DCP molecules in the resulting mixture. As a matter of fact, a slightly expansion effect can be observed E . Thus, negative V E values for {1,2to show positive values of Vm m DCP + di- and triethylene glycol mono-alkyl ethers }are found to vary in the following order: DEGMPE < DEGMBE < TEGMME < TEGMEE < TEGMBE E plotted against Fig. 2 shows the experimental values of Hm x1 together with fitted curves by using Redlich–Kister polyE values are negative over nomial. Like excess volume, all Hm the whole composition range except for the those with high mole fraction of 1,2-DCP in both systems containing DEGMPE E values for the binary mixtures and DEGMBE. All the Hm of {1,2-DCP + 2-(2-(2-alkoxyethoxy)ethoxy)ethanols} are almost symmetrical and considerably lower than those for the corresponding 2-(2-alkoxyethoxy)ethanols mixtures. For {1,2-DCP + 2E (x ) curves are asymmetrical; (2-alkoxyethoxy)ethanols} the Hm 1 E values are displaced toward a low 1,2-DCP contheir minimum Hm E shift from centration (x1 = 0.400). Also, the minimum values of Hm −472.9 J mol−1 for the mixture with DEGMBE to −800.5 J mol−1 for E values of the mixture with TEGMBE at (x1 = 0.5). The negative Hm mixtures containing 1,2-DCP increase in this sequence:

DEGMBE < DEGMPE < TEGMME < TEGMEE < TEGMBE E values are negative when the interaction between Mostly, Hm the unlike molecules are stronger than that of like molecules

E values indiand vice-versa [23]. The experimental results of Hm cate that interaction between 1,2-DCP and 2-alkoxyethanols is stronger than the total interaction of 1,2-DCP-1,2-DCP and alkoxyethanol–alkoxyethanol. This effect can be explained on the basis of a steric hindrance and unlike molecular interaction. When associated 1,2-DCP interacts with big and associated alkoxyethanols molecules, the steric hindrance may be overcome by the unlike molecular dipole–dipole interaction. The bigger the alkoxyethanol molecule is, the easier it will be to associate with the small 1,2-DCP molecule. TEGMBE is the biggest one of the alkoxyethanols, so it is quite favorable to associate with 1,2-DCP, which in turn lead E . As a consequence, H E values in to the maximum negative Hm m these mixtures become more negative with the introduction of the (–OC2 H4 –) group and with the increase of the alkyl chain length in the alkoxyethanol molecules. Insertion of the (–OC2 H4 –) part in the alkoxyethanol molecules increases not only the size but also the polar interaction between the unlike molecules. Being smaller size and lower in numbers, unlike molecular interaction due to dipole–dipole interaction is not much significant in both systems containing DEGMPE and DEGMBE, at very low mole fraction of 2(2-alkoxyethoxy)ethanols. Consequently, breaking of the hydrogen bond of these alkoxyethanols occurs at their very low concentration with little absorption of energy to mix with 1,2-DCP and accordingly a slight positive deviation from the ideality can be observed. Contrary to the results from the mixtures of {1,2-DCP + 2E (2-(2-alkoxyethoxy)ethoxy)ethanols}, Hm values become less negative with an increase in the alkyl chain-length of 2-(2alkoxyethoxy)ethanols. The results of this work indicate in general that the longer the alkyl group of the 2-(2-alkoxyethoxy)ethanols, the weaker is the interaction with 1,2-DCP, and it most definitely appears as though the long alkyl groups shield the oxygen E values atom of the given compounds. As a matter of fact, Hm for DEGMPE is less than that of DEGMBE. This effect is, however, nearly unaffected for such binary mixtures which consist alternately of very small and large molecules as in {1,2-DCP + 2(2-(2-alkoxyethoxy)ethoxy)ethanols}.

4. Conclusion E and H E show the negative deviation from the Both Vm m ideality except for the binary mixtures consisting of 2-(2alkoxyethoxy)ethanols. In the binary mixtures {1,2-DCP + DEGMPE, E and H E are slightly positive in a 1,2-DCP rich or +DEGMBE}, both Vm m E and H E values for the binary mixtures region. Both negative Vm m containing 2-(2-(2-alkoxyethoxy)ethoxy)ethanols go on increasing with an increase of the alkyl chain length of alkoxyethanols. On the E values decrease from the binary mixture containing other hand, Hm E values show the reverse result for DEGMBE to DEGMPE while Vm these mixtures. The Redlich–Kister polynomial was successfully correlated with E and H E data. For all mixtures, good agreeboth the experimental Vm m E and calculated H E values as a ments between experimental Hm m function of mole fraction derived only from NRTL models were obtained in accordance with standard deviations. The Wilson and

D. Sen, M.G. Kim / Fluid Phase Equilibria 285 (2009) 30–35

UNIQUAC models have not been found to be appropriate to correlate the experimental excess enthalpy. List of symbols Aj adjustable parameters for Redlich–Kister equation GE Gibb’s free energy E excess molar enthalpy Hm Mi molar mass of component i qi structural parameter in UNIQUAC equation R universal gas constant volume parameter in UNIQUAC equation ri uij energy parameter in UNIQUAC E Vm excess molar volume mole fraction of 1,2-dichloropropane x1 Greek letters ˛ parameter in NRTL related to non-randomness in the mixture i area fraction of component i  density ij energy parameters in Wilson binary parameters in Wilson ij  standard deviation binary parameters in NRTL and UNIQUAC  ij Subscripts/superscripts E excess properties m molar property i, j components of a mixture

35

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