Application of the extended real associated solution (ERAS) model to excess molar volumes of binary...

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Application of the extended real associated solution (ERAS) model to excess molarvolumes of binary mixtures of (alkoxyethanols+1-alkanol)

Amalendu Pal a, Harsh Kumar b,⁎, Shanti Lal Oswal c

a Department of Chemistry, Kurukshetra University, Kurukshetra-136 119, Haryana, Indiab Department of Chemistry, Dr B R Ambedkar National Institute of Technology, Jalandhar-144 011 Punjab, Indiac R & D, Biochemistry Division, Span Diagnostic Limited, 173-B, New Industrial Estate, Udhana, Surat-394 120, Gujarat, India

a b s t r a c ta r t i c l e i n f o

Article history:Received 12 February 2010Received in revised form 23 June 2010Accepted 9 July 2010Available online 17 July 2010

Keywords:Excess molar volumeAlkoxyethanols1-AlkanolsERASBinary liquid mixtures

Excess molar volumes of binary mixtures of diethylene glycol monomethyl ether or triethylene glycolmonomethyl ether or diethylene glycol monoethyl ether or triethylene glycol monoethyl ether+1-alkanolat 298.15 K and atmospheric pressure over whole composition range have been used for application ofextended real associated solution (ERAS) model which accounts for hydrogen bonding effects as well as forfree volume effects in associating mixtures. The ERAS model results obtained by adjusting the modelparameters indicates strong hydrogen bonding effects between unlike molecules. The value of crossassociation constant KAB illustrates the fact that cross associates are more pronounced in mixture of lower1-alkanol.

© 2010 Elsevier B.V. All rights reserved.

1. Introduction

Hydrogen bonded systems are very interesting because hydrogenbonds play a very vital role in chemical, physical, and biologicalprocess. The description of the thermodynamic properties ofassociated mixtures using association model (effects arising fromhydrogen bonding) [1–4] and equation of state contribution (freevolume effects arising from differences of the van der Waalsinteractions between different molecules) [5,6] were described inthe same time by Treszczanowicz and Benson [7] and Heintz [8]. Boththe models apply the Flory equation of state theory [5], but differ inmodel of association contributions as well as in the method ofapproximation of hypothetical monomer of self-associated compo-nent. Both these models are quite successful in describing volumetricproperties of alkanol+alkane mixtures [7–18]. The model due toHeintz [8] popularly known as extended real associated solutionmodel (ERAS) applicable to alkanol+alkane or associating compo-nent (A, alkanol) and other weakly associating component (B,alkylamine) [19,20]. In addition, cross-association (AiB or AiBj) inthe mixture can also be accounted for.

The ERAS model has been utilized to quantitatively interpretthermodynamic properties Hm

E , GmE , and Vm

E and to account for thecompeting effects present in the binary mixtures 1-alkanol+amine[21–37], 1-alkanol+linear and branched ether [38–47], 1-alkanol+

cyclic ether [48,49], 1-alkanol+acetonitrile [50,51], 1-alkanol+polyether [52], and ethyl ethanoate+1-alkanol [53,54].

Alkoxyethanols are a very interesting class of compounds due topresence of oxygen (–O–) and hydroxyl (–OH) group in the samemolecule, which allows self-association via inter- and intramolecularH-bonds [55–57]. The properties of binary liquid mixtures containingalkoxyethanols as one of the components are generally explained onthe basis of solvent structure stabilization (interstitial accommoda-tion), solute-solvent interaction (hydrogen bonding, structure break-ing etc.), and solute-solute association (hydrophobic interaction). Lotof attempts have been made to describe quantitatively the propertiesof these mixtures using experimental data in our laboratory [58–63].Moreover, the study of themixtures containing alkoxyethanols and 1-alkanols is very important due to the interaction between thecomponents. There exist very strong and chemical interactionsbetween oxygen (–O–) of ether, which acts as an electron donorand hydroxyl group (–OH) of 1-alkanol. In the present paper we haveexamined the ERAS model to estimate excess molar volume of higheralkoxyethanol+1-alkanol binary mixtures as it is applicable to twoassociating components and also accounts for the cross-associationbetween them. The alkoxyalkanols considered include diethyleneglycol monomethyl ether (DEGMME), triethylene glycol monomethylether (TEGMME), diethylene glycol monoethyl ether (DEGMEE), andtriethylene glycol monoethyl ether (TEGMEE). This will help to havedeeper understanding of interactions present in the mixture compo-nents. To our knowledge, the applicability of ERAS model to somelower alkoxyethanol+1-alkanol mixtures has only been examined byGonzalez et al., [46].

Journal of Molecular Liquids 156 (2010) 154–164

⁎ Corresponding author. Tel.: +91 181 2690301x2207.E-mail addresses: [email protected], [email protected] (H. Kumar).

0167-7322/$ – see front matter © 2010 Elsevier B.V. All rights reserved.doi:10.1016/j.molliq.2010.07.004

Contents lists available at ScienceDirect

Journal of Molecular Liquids

j ourna l homepage: www.e lsev ie r.com/ locate /mol l iq


2. Theory

2.1. Extended real associated solution (ERAS) model

As per ERAS model, any excess function ZE is the combination of thetwo additive terms so called chemical contribution (ZEchem) and physicalcontribution (ZEphy) which arise from hydrogen bonding effects andnon-polar Vander Waals interactions between unlike moleculesincluding free volume effect, respectively and is represented as:

ZE = ZEphy + ZEchem ð1Þ

where ZE=excess molar volume, VE or excess molar enthalpy, HE.The assumption made in the frame of ERAS model that only

consecutive association occurs, which is described by a chemicalequilibrium constant KA, according to the equations:

Am + A↔KA Am + 1 ð2Þ

Bm + B↔KB Bn + 1 ð3Þ

where m and n ranges from 1 to ∞, are the degree of self association.The cross-association between two self associated components A andB is represented as:

Am + Bn ↔KAB AmBn ð4Þ

The association constant Ki (i=A, B and AB) are assumed to beindependent of the chain length. Their temperature dependence isgiven by:

Ki = K0 exp − Δh�iR

� �1T− 1

T0

� �� ð5Þ

where K0 is the equilibrium constant at standard temperature T0(298.15 K), R is the gas constant and Δhi* is the enthalpy for thereactions given by the Eqs. (2)–(4), which corresponds to thehydrogen bonding energy. These reactions are also characterized bythe volume change Δvi* related to formation of linear chains.

The expression for VE and HE of the ERAS model extended to thetwo block approach of cross-association [64] are given by [19,20]:

VEERAS = VE

phy + VEchem ð6Þ

VEphy = xAV

�A + xBV

�B

� �VM−KAVA−KBVB

� ð7Þ

VEchem = VM

xAKA Δυ�A KA1−K0

A1

� + xBKB Δυ

�B KB1−K0

B1

� + xAKAB Δυ

�AB

×KB1 1− KAKA1ð Þ

VB = VAð Þ 1− KB KB1ð Þ + KAB KB1

8>><>>:

9>>=>>;

ð8Þ

HEERAS = HE

phy + HEchem ð9Þ

Table 1ERAS parameters of pure components at 298.15 K.

Component KA α (10−3 K−1) κT (TPa−1) Vm (cm3 mol−1) V* (cm3 mol−1) P* (J cm−3) Δhi (kJ mol−1) ΔVi (cm3 mol−1) S (Å−1)

Diethylene glycol monomethyl ether 20 0.849 584.7 118.21 99.28 531 −13.5 −7 1.453Triethylene glycol monomethyl ether 20 0.828 540.4 157.43 132.04 582 −13.5 −7 1.431Diethylene glycol monoethyl ether 20 0.846 633.4 136.37 114.28 500 −13.5 −7 1.437Triethylene glycol monoethyl ether 20 0.842 594.2 175.40 146.50 550 −13.5 −7 1.420Methanol 986 1.201 1206 40.75 32.09 442 −25.1 −5.6 1.649Ethanol 317 1.092 1158.2 58.65 47.12 393 −25.1 −5.6 1.5441-Propanol 197 1.003 1018 75.18 61.28 397 −25.1 −5.6 1.4891-Butanol 175 0.932 940 91.96 75.7 395 −25.1 −5.6 1.4561-Pentanol 153 0.893 883.8 108.68 89.94 401 −25.1 −5.6 1.4331-Hexanol 120 0.87 832 125.32 104.1 412 −25.1 −5.6 1.418

Table 2ERAS parameters at 298.15 K for alkoxyethanol+1-alkanol mixtures.

XAB KAB ΔhAB* ΔVAB*

(J cm−3) (kJ mol−1) (cm3 mol−1)

Diethylene glycol monomethyl ether+methanol 7 114 −45 −13.8Diethylene glycol monomethyl ether+ethanol 7 16 −35 −13.5Diethylene glycol monomethyl ether+1-propanol 7 7.9 −35 −13.3Diethylene glycol monomethyl ether+1-pentanol 7 3.4 −35 −12.5Diethylene glycol monomethyl ether+1-hexanol 8 2.4 −35 −12.4Triethylene glycol monomethyl ether+methanol 7 109 −45 −14.9Triethylene glycol monomethyl ether+ethanol 7 28 −35 −13Triethylene glycol monomethyl ether+1-propanol 7 11.1 −35 −13.4Triethylene glycol monomethyl ether+1-butanol 7 5 −35 −10.7Triethylene glycol monomethyl ether+1-pentanol 7 5 −35 −10.9Triethylene glycol monomethyl ether+1-hexanol 7 4 −35 − 9.4Diethylene glycol monoethyl ether+methanol 7 140 −45 −14.6Diethylene glycol monoethyl ether+ethanol 7 21 −35 −14.3Diethylene glycol monoethyl ether+1-propanol 7 11 −35 −14.3Diethylene glycol monoethyl ether+1-pentanol 7 6.3 −35 −13.7Diethylene glycol monoethyl ether+1-hexanol 9 6.1 −35 −13.3Triethylene glycol monoethyl ether+methanol 7 205 −45 −14.5Triethylene glycol monoethyl ether+ethanol 7 24 −35 −14.4Triethylene glycol monoethyl ether+1-propanol 7 13 −35 −14.5Triethylene glycol monoethyl ether+1-pentanol 8 7.5 −35 −13.5Triethylene glycol monoethyl ether+1-hexanol 8 6.7 −35 −13.5

155A. Pal et al. / Journal of Molecular Liquids 156 (2010) 154–164


Table 3Comparison of experimental Vm

E with ERAS model calculations along with the physicaland chemical contributions for alkoxyethanol+1-alkanol mixtures at 298.15 K.

x1 VEchem VE

phy VEERAS VE

exptl

(cm3 mol−1) (cm3 mol−1) (cm3 mol−1) (cm3 mol−1)

Diethylene glycol monomethyl ether (1)+methanol (2)0.0042 −0.016 −0.008 −0.025 −0.0120.0092 −0.032 −0.018 −0.050 −0.0330.0417 −0.095 −0.076 −0.171 −0.1350.0519 −0.107 −0.091 −0.198 −0.1670.0654 −0.121 −0.109 −0.231 −0.1870.0777 −0.132 −0.125 −0.257 −0.2440.0869 −0.139 −0.135 −0.275 −0.2650.1022 −0.151 −0.151 −0.302 −0.2920.1172 −0.161 −0.164 −0.326 −0.3240.1276 −0.168 −0.173 −0.341 −0.3450.1408 −0.175 −0.183 −0.358 −0.3670.1515 −0.181 −0.189 −0.371 −0.3840.1517 −0.181 −0.190 −0.371 −0.3930.1818 −0.196 −0.207 −0.403 −0.4250.2133 −0.210 −0.219 −0.430 −0.4550.2201 −0.213 −0.222 −0.435 −0.4620.2245 −0.215 −0.224 −0.439 −0.4630.2374 −0.219 −0.227 −0.447 −0.4770.2475 −0.224 −0.229 −0.454 −0.4880.2545 −0.226 −0.231 −0.458 −0.4930.3439 −0.253 −0.239 −0.492 −0.5270.4228 −0.269 −0.232 −0.500 −0.5260.4383 −0.271 −0.229 −0.500 −0.5220.4606 −0.274 −0.225 −0.499 −0.5210.5213 −0.279 −0.210 −0.488 −0.4830.3526 −0.255 −0.239 −0.494 −0.3970.7219 −0.241 −0.133 −0.374 −0.3170.8267 −0.220 −0.086 −0.307 −0.2150.9333 −0.137 −0.034 −0.171 −0.091

σ=0.0379 cm3 mol−1

Diethylene glycol monomethyl ether (1)+ethanol (2)0.0242 0.012 −0.041 −0.09 −0.0320.0377 0.003 −0.063 −0.060 −0.0600.0586 0.018 −0.093 −0.075 −0.0810.1005 0.020 −0.142 −0.122 −0.1340.1252 0.019 −0.166 −0.146 −0.1540.1453 0.019 −0.182 −0.163 −0.1720.1605 0.018 −0.193 −0.175 −0.1860.1967 0.016 −0.215 −0.199 −0.2070.2130 0.015 −0.223 −0.208 −0.2150.2359 0.013 −0.233 −0.219 −0.2230.2631 0.010 −0.241 −0.231 −0.2360.2816 0.009 −0.246 −0.238 −0.2420.2993 0.007 −0.249 −0.243 −0.2460.3254 0.004 −0.253 −0.249 −0.2540.4103 −0.004 −0.254 −0.258 −0.2610.4312 −0.006 −0.252 −0.258 −0.2600.4807 −0.011 −0.243 −0.254 −0.2590.5408 −0.016 −0.228 −0.244 −0.2420.6671 −0.025 −0.183 −0.207 −0.1970.7379 −0.027 −0.146 −0.173 −0.1740.8132 −0.029 −0.108 −0.137 −0.1180.8613 −0.027 −0.082 −0.109 −0.0960.9912 −0.006 0.000 −0.006 −0.006

σ=0.0076 cm3 mol−1

Diethylene glycol monomethyl ether (1)+1-propanol (2)0.0121 0.024 −0.008 0.015 −0.0100.0274 0.043 −0.022 0.021 −0.0130.0514 0.063 −0.039 0.024 −0.0240.0809 0.079 −0.058 0.020 −0.0280.1142 0.090 −0.077 0.013 −0.0360.1823 0.102 −0.110 −0.008 −0.0400.2192 0.105 −0.122 −0.017 −0.0400.2609 0.106 −0.133 −0.027 −0.0420.2934 0.106 −0.139 −0.033 −0.0440.3279 0.104 −0.143 −0.039 −0.0450.3612 0.102 −0.146 −0.044 −0.0480.4156 0.098 −0.148 −0.049 −0.0400.4376 0.096 −0.147 −0.051 −0.0400.4593 0.094 −0.146 −0.053 −0.036

Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.5128 0.087 −0.142 −0.054 −0.0380.5725 0.079 −0.129 −0.049 −0.0320.6045 0.075 −0.124 −0.049 −0.0300.6566 0.067 −0.113 −0.046 −0.0260.7444 0.053 −0.090 −0.037 −0.0190.8077 0.042 −0.071 −0.029 −0.0160.8541 0.034 −0.056 −0.022 −0.0140.9266 0.019 −0.025 −0.005 −0.0010.9680 0.010 −0.011 −0.001 −0.002

σ=0.0239 cm3 mol−1

Diethylene glycol monomethyl ether (1)+1-pentanol (2)0.0400 0.105 0.000 0.105 0.0330.0800 0.162 −0.007 0.155 0.0640.0986 0.177 −0.008 0.168 0.0770.1270 0.200 −0.010 0.190 0.0930.1536 0.216 −0.012 0.204 0.1200.1926 0.232 −0.015 0.217 0.1380.2574 0.247 −0.018 0.229 0.1720.3231 0.253 −0.021 0.232 0.2090.3658 0.252 −0.022 0.230 0.2210.4279 0.247 −0.023 0.224 0.2520.4576 0.243 −0.023 0.219 0.2590.4755 0.239 −0.024 0.216 0.2590.5041 0.234 −0.024 0.211 0.2630.5197 0.231 −0.024 0.208 0.2620.6053 0.209 −0.022 0.187 0.2450.6494 0.196 −0.021 0.174 0.2300.6888 0.182 −0.020 0.162 0.2060.8110 0.133 −0.014 0.118 0.1530.8665 0.105 −0.011 0.095 0.1130.9149 0.078 −0.007 0.071 0.0710.9560 0.049 0.000 0.049 0.039

σ=0.057 cm3 mol−1

Diethylene glycol monomethyl ether (1)+1-hexanol (2)0.0300 0.100 0.000 0.100 0.0250.0533 0.147 0.006 0.153 0.0540.0883 0.197 0.009 0.206 0.0990.1302 0.236 0.013 0.249 0.1390.2019 0.277 0.018 0.295 0.2120.2467 0.291 0.019 0.311 0.2590.2929 0.299 0.022 0.321 0.2960.3484 0.303 0.023 0.326 0.3320.3833 0.302 0.023 0.325 0.3400.4514 0.295 0.023 0.318 0.3550.4766 0.290 0.023 0.314 0.3560.5000 0.285 0.023 0.308 0.3570.5264 0.279 0.023 0.302 0.3560.5611 0.269 0.022 0.292 0.3490.6639 0.234 0.019 0.253 0.3060.7482 0.197 0.015 0.212 0.2450.7944 0.173 0.013 0.186 0.2050.8333 0.151 0.010 0.162 0.1690.8715 0.127 0.008 0.136 0.1280.9166 0.095 0.005 0.101 0.0840.9554 0.062 0.000 0.062 0.038

σ=0.0564 cm3 mol−1

Triethylene glycol monomethyl ether (1)+methanol (2)0.0068 −0.029 −0.025 −0.055 −0.0400.0165 −0.061 −0.061 −0.122 −0.0910.0321 −0.096 −0.109 −0.205 −0.1790.0450 −0.118 −0.143 −0.261 −0.2400.0705 −0.152 −0.198 −0.349 −0.3430.0945 −0.177 −0.239 −0.416 −0.4320.1212 −0.199 −0.274 −0.474 −0.5060.1427 −0.216 −0.295 −0.511 −0.5470.1512 −0.222 −0.299 −0.522 −0.5540.1659 −0.232 −0.310 −0.542 −0.5790.1796 −0.240 −0.319 −0.559 −0.5980.1973 −0.250 −0.328 −0.578 −0.6190.2157 −0.259 −0.335 −0.594 −0.6410.2387 −0.271 −0.341 −0.612 −0.659

Diethylene glycol monomethyl ether (1)+1-propanol (2)

156 A. Pal et al. / Journal of Molecular Liquids 156 (2010) 154–164


Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.2660 −0.283 −0.345 −0.628 −0.6750.2905 −0.293 −0.346 −0.639 −0.6830.3304 −0.306 −0.344 −0.649 −0.6830.3950 −0.323 −0.331 −0.654 −0.6700.5286 −0.338 −0.283 −0.620 −0.5920.6134 −0.333 −0.241 −0.574 −0.5160.6919 −0.306 −0.198 −0.504 −0.4280.7767 −0.284 −0.143 −0.427 −0.3100.8634 −0.232 −0.089 −0.321 −0.1790.9347 −0.157 −0.043 −0.199 −0.076

σ=0.0576 cm3 mol−1

Triethylene glycol monomethyl ether (1)+ethanol (2)0.0092 −0.005 −0.028 −0.033 −0.0260.0198 −0.008 −0.059 −0.067 −0.0590.0409 −0.015 −0.116 −0.130 −0.1140.0595 −0.019 −0.156 −0.175 −0.1560.0866 −0.025 −0.205 −0.230 −0.2120.1126 −0.029 −0.243 −0.273 −0.2550.1398 −0.035 −0.275 −0.309 −0.2940.1672 −0.039 −0.299 −0.339 −0.3310.2010 −0.045 −0.322 −0.367 −0.3650.2173 −0.047 −0.330 −0.378 −0.3760.2327 −0.049 −0.337 −0.386 −0.3850.2475 −0.052 −0.342 −0.393 −0.3950.2752 −0.055 −0.348 −0.404 −0.4100.3094 −0.059 −0.352 −0.412 −0.4180.3475 −0.063 −0.352 −0.415 −0.4250.3840 −0.067 −0.348 −0.414 −0.4280.4261 −0.070 −0.339 −0.409 −0.4250.4662 −0.073 −0.326 −0.399 −0.4130.5150 −0.076 −0.308 −0.384 −0.3930.5696 −0.078 −0.283 −0.361 −0.3560.6299 −0.078 −0.252 −0.330 −0.3270.6988 −0.075 −0.212 −0.287 −0.2760.7659 −0.072 −0.164 −0.237 −0.2250.8790 −0.056 −0.088 −0.145 −0.1200.9439 −0.038 −0.042 −0.079 −0.060

σ=0.0124 cm3 mol−1

Triethylene glycol monomethyl ether (1)+1-propanol (2)0.0148 0.016 −0.023 −0.007 −0.0170.0411 0.030 −0.059 −0.029 −0.0440.0707 0.039 −0.093 −0.054 −0.0680.0999 0.044 −0.125 −0.081 −0.0920.1305 0.047 −0.150 −0.103 −0.1150.1605 0.049 −0.169 −0.121 −0.1220.1940 0.049 −0.187 −0.137 −0.1390.2215 0.050 −0.198 −0.148 −0.1470.2577 0.049 −0.209 −0.159 −0.1530.2856 0.049 −0.214 −0.165 −0.1600.3076 0.048 −0.217 −0.169 −0.1620.3246 0.048 −0.219 −0.171 −0.1650.3310 0.047 −0.219 −0.172 −0.1660.3604 0.046 −0.220 −0.174 −0.1670.4076 0.044 −0.218 −0.175 −0.1710.4523 0.041 −0.213 −0.172 −0.1700.5173 0.037 −0.201 −0.164 −0.1620.5818 0.033 −0.184 −0.151 −0.1420.6693 0.026 −0.149 −0.123 −0.1250.7572 0.020 −0.116 −0.095 −0.0940.8579 0.013 −0.071 −0.058 −0.0610.9278 0.008 −0.031 −0.024 −0.036

σ=0.0076 cm3 mol−1

Triethylene glycol monomethyl ether (1)+1-butanol (2)0.0802 0.134 −0.107 0.028 0.0070.1433 0.173 −0.159 0.014 0.0110.1963 0.193 −0.188 0.005 0.0170.265 0.209 −0.210 −0.001 0.0220.3385 0.219 −0.219 −0.001 0.0290.4209 0.223 −0.217 0.006 0.0350.4708 0.223 −0.210 0.013 0.0380.529 0.219 −0.198 0.021 0.040

(continued on next page)

Triethylene glycol monomethyl ether (1)+methanol (2)

Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.5845 0.213 −0.183 0.031 0.0450.6768 0.197 −0.147 0.050 0.0460.7335 0.183 −0.125 0.058 0.0440.7789 0.169 −0.106 0.063 0.0420.8335 0.149 −0.082 0.067 0.0350.9081 0.109 −0.047 0.063 0.0260.9671 0.059 −0.015 0.045 0.012

σ=0.0231 cm3 mol−1

Triethylene glycol monomethyl ether (1)+1-pentanol (2)0.0067 0.025 0.000 0.025 0.0060.0442 0.103 −0.012 0.091 0.0260.0816 0.146 −0.020 0.126 0.0480.1371 0.184 −0.036 0.147 0.0820.2065 0.210 −0.048 0.163 0.1220.2567 0.221 −0.053 0.167 0.1400.3002 0.226 −0.057 0.169 0.1600.3147 0.227 −0.058 0.169 0.1700.3353 0.228 −0.059 0.169 0.1770.3528 0.229 −0.059 0.169 0.1790.3768 0.229 −0.060 0.168 0.1820.3800 0.229 −0.060 0.168 0.1840.4011 0.228 −0.061 0.167 0.1850.4160 0.227 −0.061 0.167 0.1870.4460 0.225 −0.061 0.165 0.1910.4538 0.225 −0.061 0.164 0.1890.4934 0.220 −0.059 0.161 0.1860.5454 0.213 −0.057 0.155 0.1810.6071 0.201 −0.053 0.147 0.1620.6682 0.186 −0.048 0.138 0.1470.7390 0.165 −0.040 0.125 0.1110.8215 0.134 −0.025 0.109 0.0790.8990 0.096 −0.015 0.082 0.0470.9598 0.054 0.000 0.054 0.018

σ=0.0324 cm3 mol−1

Triethylene glycol monomethyl ether (1)+1-hexanol (2)0.0158 0.059 0.000 0.059 0.0260.0556 0.144 0.000 0.144 0.0700.1158 0.213 0.000 0.213 0.1320.1699 0.249 0.000 0.249 0.1780.2295 0.274 0.000 0.274 0.2230.2972 0.289 0.000 0.289 0.2650.3638 0.296 −0.006 0.289 0.3000.3724 0.296 −0.006 0.289 0.3030.3891 0.296 −0.006 0.289 0.3080.4037 0.296 −0.006 0.289 0.3100.4054 0.296 −0.006 0.289 0.3120.4316 0.295 −0.007 0.288 0.3150.4586 0.292 −0.007 0.286 0.3180.4838 0.289 −0.007 0.282 0.3190.5240 0.283 −0.007 0.276 0.3140.5727 0.273 −0.007 0.266 0.3050.6465 0.253 −0.006 0.247 0.2790.7199 0.227 0.000 0.227 0.2360.7749 0.203 0.000 0.203 0.1900.8378 0.169 0.000 0.169 0.1440.9004 0.128 0.000 0.128 0.0950.9579 0.075 0.000 0.075 0.041

σ=0.0388 cm3 mol−1

Diethylene glycol monoethyl ether (1)+methanol (2)0.0150 −0.064 −0.022 −0.086 −0.0580.0290 −0.102 −0.042 −0.144 −0.1100.0453 −0.135 −0.062 −0.197 −0.1700.0635 −0.164 −0.081 −0.244 −0.2300.0825 −0.188 −0.098 −0.286 −0.2820.0968 −0.203 −0.109 −0.312 −0.3200.1162 −0.222 −0.122 −0.344 −0.3600.1328 −0.237 −0.132 −0.369 −0.4000.1565 −0.255 −0.144 −0.399 −0.4300.1883 −0.277 −0.156 −0.432 −0.4780.2230 −0.297 −0.165 −0.462 −0.5140.2545 −0.313 −0.170 −0.483 −0.539


Triethylene glycol monomethyl ether (1)+1-butanol (2)



Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.2732 −0.322 −0.173 −0.494 −0.5500.2963 −0.331 −0.174 −0.506 −0.5590.3215 −0.341 −0.175 −0.516 −0.5630.3418 −0.348 −0.175 −0.523 −0.5670.3746 −0.357 −0.173 −0.531 −0.5690.4139 −0.366 −0.169 −0.536 −0.5490.5000 −0.369 −0.156 −0.525 −0.5130.5678 −0.378 −0.142 −0.519 −0.4650.6335 −0.372 −0.121 −0.493 −0.4190.7119 −0.351 −0.099 −0.450 −0.3500.7839 −0.319 −0.076 −0.396 −0.2820.8744 −0.251 −0.046 −0.296 −0.1760.9418 −0.164 −0.018 −0.182 −0.086

σ=0.0566 cm3 mol−1

Diethylene glycol monoethyl ether (1)+ethanol (2)0.0131 −0.007 −0.018 −0.025 −0.0190.0393 −0.016 −0.049 −0.066 −0.0660.0666 −0.024 −0.081 −0.105 −0.1100.0959 −0.032 −0.107 −0.139 −0.1490.1265 −0.039 −0.129 −0.169 −0.1820.1448 −0.043 −0.141 −0.184 −0.2010.1701 −0.049 −0.154 −0.203 −0.2190.2089 −0.057 −0.170 −0.227 −0.2490.2336 −0.061 −0.178 −0.239 −0.2600.2582 −0.065 −0.184 −0.249 −0.2690.3157 −0.074 −0.193 −0.267 −0.2780.3309 −0.077 −0.194 −0.270 −0.2840.3654 −0.081 −0.194 −0.276 −0.2860.3770 −0.083 −0.194 −0.277 −0.2870.4002 −0.085 −0.193 −0.278 −0.2900.4535 −0.090 −0.188 −0.278 −0.2770.5030 −0.094 −0.180 −0.274 −0.2670.5612 −0.097 −0.167 −0.264 −0.2460.6218 −0.098 −0.147 −0.245 −0.2220.6971 −0.096 −0.123 −0.219 −0.1820.7619 −0.089 −0.100 −0.189 −0.1480.8662 −0.075 −0.059 −0.134 −0.0770.9726 −0.031 −0.011 −0.042 −0.014

σ=0.0217 cm3 mol−1

Diethylene glycol monoethyl ether (1)+1-propanol (2)0.0080 0.006 −0.004 0.003 −0.0050.0243 0.014 −0.010 0.004 −0.0100.0449 0.020 −0.022 −0.002 −0.0210.0613 0.023 −0.029 −0.006 −0.0270.0733 0.024 −0.034 −0.010 −0.0310.0873 0.025 −0.039 −0.014 −0.0360.1053 0.026 −0.046 −0.020 −0.0390.1244 0.026 −0.052 −0.026 −0.0460.1422 0.025 −0.057 −0.032 −0.0520.1637 0.025 −0.062 −0.038 −0.0570.1932 0.023 −0.069 −0.046 −0.0640.2244 0.021 −0.075 −0.054 −0.0720.2494 0.019 −0.079 −0.059 −0.0760.2619 0.018 −0.081 −0.063 −0.0800.2835 0.016 −0.083 −0.067 −0.0820.3099 0.014 −0.086 −0.072 −0.0840.3203 0.013 −0.086 −0.074 −0.0840.3427 0.011 −0.088 −0.077 −0.0850.3540 0.009 −0.088 −0.079 −0.0850.3976 0.005 −0.089 −0.084 −0.0840.4346 0.002 −0.089 −0.087 −0.0810.4863 −0.003 −0.087 −0.089 −0.0740.5371 −0.007 −0.083 −0.091 −0.0670.5743 −0.010 −0.079 −0.090 −0.0620.6359 −0.015 −0.073 −0.087 −0.0560.6943 −0.018 −0.064 −0.082 −0.0460.7542 −0.020 −0.054 −0.074 −0.0370.8040 −0.022 −0.044 −0.066 −0.0290.8833 −0.020 −0.023 −0.044 −0.0170.9445 −0.016 −0.012 −0.027 −0.010

σ=0.0208 cm3 mol−1

Diethylene glycol monoethyl ether (1)+methanol (2)

Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


Diethylene glycol monoethyl ether (1)+1-pentanol (2)0.0219 0.041 0.000 0.041 0.0100.0432 0.065 0.000 0.065 0.0160.0629 0.081 0.005 0.086 0.0290.0886 0.096 0.007 0.103 0.0420.1202 0.109 0.009 0.118 0.0520.1482 0.117 0.010 0.127 0.0670.1702 0.121 0.011 0.133 0.0770.2041 0.126 0.013 0.138 0.0790.2358 0.128 0.014 0.142 0.1000.2684 0.129 0.014 0.143 0.1110.3086 0.128 0.015 0.144 0.1210.3398 0.127 0.015 0.142 0.1260.3676 0.125 0.016 0.140 0.1300.4053 0.121 0.016 0.137 0.1360.4382 0.117 0.015 0.133 0.1440.4511 0.116 0.015 0.131 0.1430.4722 0.113 0.015 0.128 0.1450.4858 0.111 0.015 0.126 0.1460.5084 0.107 0.015 0.122 0.1450.5463 0.101 0.014 0.115 0.1440.5747 0.096 0.014 0.109 0.1410.6016 0.091 0.013 0.104 0.1360.6373 0.084 0.012 0.096 0.1310.6795 0.076 0.011 0.086 0.1260.7188 0.067 0.010 0.077 0.1140.7511 0.060 0.009 0.069 0.1010.7960 0.050 0.007 0.058 0.0880.8527 0.037 0.000 0.037 0.0630.9389 0.017 0.000 0.017 0.0270.9728 0.008 0.000 0.008 0.015

σ=0.0365 cm3 mol−1

Diethylene glycol monoethyl ether (1)+1-hexanol (2)0.0367 0.060 0.013 0.073 0.0300.0626 0.084 0.021 0.105 0.0490.1273 0.118 0.045 0.163 0.0950.1895 0.134 0.061 0.195 0.1270.2324 0.139 0.069 0.208 0.1500.2790 0.141 0.077 0.218 0.1680.3420 0.139 0.084 0.223 0.2000.3913 0.136 0.087 0.222 0.2050.3961 0.135 0.087 0.222 0.2080.4168 0.133 0.088 0.220 0.2150.4312 0.131 0.088 0.219 0.2180.4553 0.128 0.088 0.216 0.2190.5000 0.121 0.087 0.208 0.2190.5474 0.112 0.085 0.197 0.2200.5920 0.103 0.081 0.184 0.2100.6195 0.097 0.078 0.176 0.2050.6566 0.089 0.074 0.163 0.1900.7091 0.077 0.066 0.143 0.1730.7649 0.063 0.056 0.119 0.1480.8030 0.053 0.049 0.102 0.1300.8671 0.037 0.029 0.066 0.0950.9176 0.023 0.019 0.042 0.0600.971 0.008 0.007 0.015 0.025

σ=0.0348 cm3 mol−1

Triethylene glycol monoethyl ether (1)+methanol (2)0.0150 −0.071 −0.044 −0.115 −0.0700.0360 −0.133 −0.094 −0.227 −0.1710.0685 −0.195 −0.152 −0.346 −0.3040.0874 −0.222 −0.177 −0.399 −0.3700.1013 −0.239 −0.193 −0.432 −0.4200.1190 −0.259 −0.209 −0.468 −0.4710.1353 −0.276 −0.222 −0.498 −0.5070.161 −0.299 −0.238 −0.537 −0.5680.1845 −0.319 −0.249 −0.568 −0.6140.2162 −0.342 −0.259 −0.600 −0.6500.2572 −0.368 −0.265 −0.633 −0.6820.2741 −0.377 −0.266 −0.643 −0.6900.2825 −0.381 −0.266 −0.648 −0.6940.3285 −0.403 −0.265 −0.668 −0.705



HEphy = xAV

�A + xBV

�B

� � KAP�A

VA

+KBP

�B

VB

− P�MVM

!ð10Þ

VEchem =

xAKA Δh�A KA1−K0

A1

� + xBKB Δh

�B KB1−K0

B1

� + xAKAB Δh

�AB

×KB1 1− KA KA1ð Þ

VB = VAð Þ 1− KBKB1ð Þ + KAB KB1− P�MV

EcHem

V2M

8>>><>>>:

9>>>=>>>;

ð11Þ

KA and KB are the equilibrium constants. KAB and ΔhAB* are theassociation constants and hydrogen bond energy from the cross-association. ØA1 and ØB1 are the hard core volume fraction of thecomponent in the mixture. They have to be calculated numericallyfrom the solution of the following coupled equations:

KA =KA1

1−KAKA1ð Þ2 1 +VAKABKB1

VB 1−KBKB1ð Þ� �

ð12Þ

KB =KB1

1−KBKB1ð Þ2 1 +KABKA1

1−KAKA1ð Þ� �

ð13Þ

Here ØA and ØB are the stoichiometric hard-core volume fractionsof the components.

2.2. ERAS parameters

The physical contribution ZphyE in ERASmodel is derive from Flory's

equation of state [5,6], which is assumed to be valid not only for purecomponents but also for the mixture.

PiV i

T i

=V1=3i

V1=3i −1

− 1

V i T i

ð14Þ

Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.3881 −0.424 −0.256 −0.680 −0.7020.4181 −0.432 −0.249 −0.682 −0.6870.4778 −0.442 −0.233 −0.675 −0.6560.5536 −0.448 −0.207 −0.655 −0.5810.6387 −0.437 −0.169 −0.606 −0.4830.6962 −0.053 −0.145 −0.197 −0.4140.7622 −0.389 −0.116 −0.505 −0.3250.8792 −0.287 −0.060 −0.348 −0.1700.9468 −0.175 −0.023 −0.198 −0.079

σ=0.0855 cm3 mol−1

Triethylene glycol monoethyl ether (1)+ethanol (2)0.0118 −0.009 −0.028 −0.038 −0.0270.0260 −0.018 −0.058 −0.076 −0.0550.0450 −0.027 −0.097 −0.124 −0.0910.0626 −0.034 −0.125 −0.159 −0.1310.0870 −0.042 −0.158 −0.201 −0.1710.1130 −0.050 −0.187 −0.237 −0.2180.1438 −0.058 −0.213 −0.271 −0.2630.1834 −0.067 −0.237 −0.305 −0.3120.2085 −0.072 −0.248 −0.321 −0.3320.2235 −0.075 −0.254 −0.329 −0.3400.2477 −0.079 −0.260 −0.339 −0.3550.2537 −0.081 −0.261 −0.342 −0.3640.2805 −0.085 −0.265 −0.350 −0.3780.3175 −0.089 −0.267 −0.357 −0.3840.3591 −0.095 −0.266 −0.361 −0.3890.4158 −0.100 −0.258 −0.358 −0.3860.4629 −0.103 −0.247 −0.351 −0.3720.5244 −0.106 −0.229 −0.335 −0.3490.5964 −0.106 −0.203 −0.309 −0.3130.6532 −0.104 −0.175 −0.278 −0.2740.7449 −0.097 −0.133 −0.230 −0.2070.8661 −0.075 −0.073 −0.148 −0.1100.9266 −0.055 −0.034 −0.089 −0.060

σ=0.0222 cm3 mol−1

Triethylene glycol monoethyl ether (1)+1-propanol (2)0.0158 0.004 −0.013 −0.009 −0.0100.0338 0.005 −0.032 −0.027 −0.0320.0499 0.005 −0.045 −0.039 −0.0470.0821 0.004 −0.067 −0.064 −0.0720.1117 0.001 −0.084 −0.082 −0.0900.1421 −0.001 −0.097 −0.099 −0.1070.1855 −0.005 −0.113 −0.118 −0.1320.2039 −0.007 −0.122 −0.128 −0.1410.2156 −0.008 −0.124 −0.132 −0.1480.2287 −0.009 −0.127 −0.136 −0.1530.2467 −0.010 −0.131 −0.141 −0.1580.2718 −0.013 −0.134 −0.147 −0.1630.3362 −0.018 −0.135 −0.152 −0.1650.3682 −0.020 −0.135 −0.155 −0.1650.4062 −0.023 −0.134 −0.156 −0.1610.4517 −0.025 −0.130 −0.156 −0.1550.5178 −0.029 −0.123 −0.151 −0.1400.5799 −0.031 −0.112 −0.143 −0.1250.6685 −0.032 −0.094 −0.127 −0.0970.7891 −0.031 −0.064 −0.095 −0.0620.9049 −0.023 −0.026 −0.048 −0.027

σ=0.0153 cm3 mol−1

Triethylene glycol monoethyl ether (1)+1-pentanol (2)0.0084 0.016 0.000 0.016 0.0080.0277 0.040 0.000 0.040 0.0180.0514 0.058 0.008 0.066 0.0320.0996 0.079 0.013 0.093 0.0570.1385 0.089 0.016 0.106 0.0750.1731 0.095 0.018 0.114 0.0870.2400 0.099 0.022 0.122 0.1050.2663 0.100 0.023 0.123 0.1090.3368 0.099 0.024 0.123 0.1200.3498 0.098 0.024 0.123 0.1220.3996 0.095 0.024 0.119 0.1250.4199 0.094 0.024 0.118 0.129


Triethylene glycol monoethyl ether (1)+methanol (2)

Table 3 (continued)

x1 VEchem VE

phy VEERAS VE

exptl


0.4864 0.088 0.023 0.111 0.1270.5371 0.082 0.022 0.104 0.1250.5944 0.076 0.020 0.096 0.1190.6928 0.062 0.016 0.079 0.0960.7326 0.056 0.015 0.071 0.0850.7877 0.048 0.012 0.059 0.0700.8324 0.040 0.009 0.049 0.0500.9002 0.028 0.000 0.028 0.032

σ=0.0189 cm3 mol−1

Triethylene glycol monoethyl ether (1)+1-hexanol (2)0.0148 0.026 0.006 0.032 0.0100.0435 0.056 0.015 0.071 0.0300.0705 0.073 0.024 0.096 0.0480.1145 0.089 0.042 0.132 0.0730.1473 0.098 0.051 0.149 0.0880.1792 0.103 0.058 0.161 0.1050.2242 0.107 0.066 0.173 0.1280.2767 0.109 0.073 0.181 0.1500.2919 0.109 0.074 0.183 0.1600.3244 0.108 0.077 0.185 0.1760.3574 0.107 0.078 0.185 0.1870.4161 0.102 0.079 0.182 0.1990.4744 0.097 0.078 0.175 0.2070.5528 0.087 0.074 0.161 0.2050.6176 0.078 0.067 0.145 0.1890.6949 0.066 0.058 0.123 0.1630.7681 0.053 0.046 0.099 0.1250.8336 0.041 0.029 0.070 0.0950.9110 0.025 0.016 0.042 0.0500.9657 0.012 0.000 0.012 0.019

σ=0.0364 cm3 mol−1

σ represent standard deviation between experimental data and ERAS results of VmE .

Triethylene glycol monoethyl ether (1)+1-pentanol (2)



where i=A, B, M (mixture). In Eq. (14) V i=Vi /V�i ; Pi=Pi /Pi*; T i=Ti /

Ti*; are the reduced volume, pressure and temperature, respectively.All the reduction parameters of pure components can be determinedknowing the experimental data for molar volume V, thermalexpansion coefficient α, isothermal compressibility κT, providedsuitable association parameters, Ki, Δvi*, Δhi* are known. The reductionparameters for the mixtures PM*, TM* and VM* are calculated frommixingrules [19,20,25]as follows

P�M = KAP�A + KBP

�B−XABKAθB ð15Þ

T�M =P�M

KAP�A = T

�M + KBP

�B = T

�M

ð16Þ

V�M = xAV

�A + xBV

�B ð17Þ

XAB is an interaction parameter characterizing the difference ofdispersive intermolecular interaction between A and B. Ø i and θi arethe hard-core volume fraction and the surface fraction of thecomponent i [8].

3. Results and discussion

The ERAS reduction parameters for pure 1-alkanols (methanol,ethanol, 1-propanol, 1-butanol, 1-pentanol, and 1-hexanol) at298.15 K are available in the literature [8,13]. For determination ofERAS reduction parameters: characteristic volume V*, characteristicpressure P* and characteristic temperature T*, the values of thermalexpansion coefficient α, isothermal compressibility κT, molar volumeVm, surface to volume ratio S, equilibrium constant K, self-associationenthalpy Δh* and self-association volume ΔV * of DEGMME, DEGMEE,TEGMME, and TEGMEE at 298.15 K are required. Experimentally α, κT,and Vm have been determined [58–63]. The values of surface tovolume ratio S were estimated from group volumes and surfaces asrecommended by Bondi [65]. The values of K, Δh* and ΔV * for higher

Fig. 1. VE at 298.15 K for diethylene glycol monomethyl ether (1)+methanol (2) (a); +ethanol (2) (b); +1-propanol (2) (c); +1-pentanol (2) (d); +1-hexanol (2) (e). (●, VEexptl.;

—, VEERAS; - - -, VE

phy.; ∙∙∙∙∙∙∙, VEchem.).



alkoxyalkanols reported by Gonzalez et al. [66] were used to calculatethe ERAS reduction parameters. The properties and ERAS parametersfor alkoxyalkanols and 1-alkanols are collected in Table 1. Normallythe unknown parameters KAB, ΔhAB* , ΔvAB* and XAB are obtained from asimultaneous adjustment to experimental data of Vm

E and HmE . In the

absence ofHmE data for presently investigatedmixtures, we have taken

cross-association hydrogen bond energy ΔhAB* of methanol withalkoxyalkanol as 45 kJ mol-1 and of other alkanols with alkoxyalkanolas 35 kJ mol−1 as recommended by Gonzalez et al., [46]. The optimumvalues of unknown parameters KAB, ΔvAB* and XAB were obtained byadjusting Vm

E subject to additional restriction 7bXABb9 J cm−3. Thevalues of cross-parameters are listed in Table 2.

The ERAS results are compared with experimental VmE data along

with physical and chemical contributions in Table 3 and Figs. 1–4. The

standard deviations are in the range 0.0076 to 0.0855 cm3 mol−1,with average values of 0.0335 cm3 mol−1. For most of the systemsstandard deviations are below 0.038 cm3 mol−1except for mixturesDEGMME+1-pentanol and+1-hexanol, DEGMEE+methanol,TEGMME + methanol, and TEGMEE + methanol for which thedeviations are more. The ERAS model describes the compositiondependence of Vm

E properly. The strongly negative VmE curves are

dominated by the chemical contribution and in case of higher alkanol,the curve are shifted to the higher alkanol concentration range. TheVmE (min) values are quite similar for the experimental data [60–64]

with the lower alkanols.The ERAS cross-parameter KAB (Table 2) needed to fit Vm

E dependsupon chain length of alkanol, it decreases with increase in chainlength of alkanol, drastically from methanol to ethanol. Similar was

Fig. 2. VE at 298.15 K for triethylene glycol monomethyl ether (1)+methanol (2) (a); +ethanol (2) (b); +1-propanol (2) (c); +1-butanol (2) (d); +1-pentanol (2) (e);+ 1-hexanol (2) (f). (●, VE

exptl.; —, VEERAS; - - -, VE

phy.; ∙∙∙∙∙∙∙, VEchem.).



the observationwith alkyl amines with alkanols [27,28]. Due to stronginductive effect of the alkyl group in alkanol, there may be weakinteraction to the ether –O– group and the –OH group of higheralkanol. It is consistent with the formation of strong complex withmethanol than the other alkanols [67]. For a given alkanol system, KAB

(TEGMEE)NKAB(DEGMEE)NKAB(DEGMME)NKAB(TEGMME); i.e. alka-nol–alkoxyalkanol interactions tends to weaker in the sequenceTEGMEENDEGMEENDEGMMENTEGMME. On the other hand, ΔvAB*

(DEGMME)NΔvAB* (DEGMEE)≈ΔvAB* (TEGMEE)NΔvAB* (TEGMME),which may be attributed to that the packing effect, which may bemore important inmixtures with TEGMEE and TEGMME. The negativevalues of ΔvAB* parameter obtained in this work for alkanol+alkoxyalkanol are also more negative than those obtained for

1-alkanol+linear monoether (ΔvAB* ≈-12 cm3 mol−1) [46,47] char-acterizing very strong interactions and packing effect between unlikemolecules.

4. Conclusions

Excess molar volumes of twenty-one alkoxyethanol+1-alkanolmixtures have been examined in the framework of the ERAS model.The standard deviations between experimental and ERAS modelvalues are in the range 0.0076 to 0.0855 cm3 mol−1 with an averagevalue of 0.0335 cm3 mol−1. The ERAS model gives an adequatequantitative representation of Vm

E for presently investigated alkox-yalkanol+1-alkanol binary mixtures. We know that while estimating

Fig. 3. VE at 298.15 K for diethylene glycol monoethyl ether (1)+methanol (2) (a); +ethanol (2) (b); +1-propanol (2) (c); +1-pentanol (2) (d); +1-hexanol (2) (e). (●, VEexptl.;


phy.; ∙∙∙∙∙∙∙, VEchem.).



ERAS parameters only consecutive linear self-association is consid-ered, while model does not take into account dipole–dipoleinteraction and ring formation in alkoxyalkanol. Moreover in presentsystems Vm

E varies for a common alkoxyalkanol from negative topositive. In most cases it predict correct sign however compositiondependence is not quantitative but only qualitative. Such behav-iour has also been observed earlier in case of alkoxyalkanol+alkoxyalkanol systems. This probably reflects a weakness of thepresent treatment which essentially assume site of specific interac-

tions associated with different parts averaged over the molecule andthat a single energy parameter can be used to describe theinteractions between unlike molecule.

References

[1] H. Renon, J.M. Prausnitz, Chem. Eng. Sci. 22 (1967) 299.[2] H.V. Kehiaian, Bull. Acad. Pol. Sci. 16 (1968) 165.[3] H.V. Kehiaian, A. Treszczanowicz, Bull. Acad. Pol. Sci. 16 (1968) 171.[4] C.B. Kretschmer, R. Wiebe, J. Chem. Phys. 22 (1954) 1697.

Fig. 4. VE at 298.15 K for triethylene glycol monoethyl ether (1)+methanol (2) (a); +ethanol (2) (b); +1-propanol (2) (c); +1-pentanol (2) (d); +1-hexanol (2) (e). (●, VEexptl.;


phy.; ∙∙∙∙∙∙∙, VEchem.).



[5] P.J. Flory, R.A. Orwell, A. Vrij, J. Am. Chem. Soc. 86 (1964) 3507.[6] P.J. Flory, J. Am. Chem. Soc. 87 (1965) 1833.[7] A.J. Treszczanowicz, G.C. Benson, Fluid Phase Equilib. 89 (1985) 117.[8] A. Heintz, Ber. Bunsenges. Phys. Chem. 89 (1985) 172.[9] A.J. Treszczanowicz, T. Treszczanowicz, Thermochim. Acta 237 (1994) 277.

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Application of the extended real associated solution (ERAS) model to excess molar volumes of binary...

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