Description of Thermodynamic Behavior of the Systems Formed by

Ind. Eng. Chem. Res. 2008, 47, 3253-3264

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Description of Thermodynamic Behavior of the Systems Formed by Alkyl Ethanoates with 1-Chloroalkanes Using the COSMO-RS Methodology Contributing with New Experimental Information Juan Ortega,* and Elena Marrero Laboratorio Termodina´ mica y Fisicoquı´mica, Parque Cientı´fico-Tecnolo´ gico, UniVersidad de Las Palmas de Gran Canaria, Canary Islands, Spain

Jose´ Palomar Seccio´ n de Ingenierıá Quı´mica (Dpto. de Quı´mica Fı´sica Aplicada). UniVersidad Auto´ noma de Madrid, Cantoblanco, 28049 Madrid, Spain

For this work, V Em and HEm have been measured at a temperature of 298.15 K and at atmospheric pressure for a set of binary mixtures composed of seven alkyl ethanoates (from methyl to octyl, except heptyl) and six 1-chloroalkanes (C4 to C9). Of the 42 binary mixtures, measurements have only been made for systems for which the excess quantities have not been published previously. Except for the octyl ethanoate +1-chlorobutane system, with V Em < 0, and hexyl ethanoate+1-chlorobutane, with V Em ≈ 0, the mixtures present expansive effects. In the case of the enthalpies, methyl ethanoate+1-chloroalkane mixtures are all endothermic and evolve toward H Em < 0 as the alkanolic part of the ethanoate increases, and mixtures of octyl ethanoate+1chloroalkane are all totally exothermic. The COSMO-RS model, based on quantum chemical calculations, has been used to explain the behavior of these mixtures, which estimate the enthalpic effects as a result of the inter/intramolecular interactions of the two types of ester/chloroalkane molecules. The results obtained with the COSMO-RS give a good qualitative prediction with an explanation of the different effects that determine the behavior of these mixtures, especially the influence, in both the pure substance and the mixture, of the increased chain length in both types of compound. Application of two different versions of the UNIFAC method gives acceptable results, although with the original version of Dang and Tassios10 it was necessary to determine new parameters using the experimental database of this work. 1. Introduction After analyzing the results of research into binary systems of dihalides (Cl, Br, I) with esters,1-5 some conclusions were proposed. It is not easy to interpret the structural behavior of these systems, and even less so with the modeling achieved with a group-contribution engineering method. Hence, to expand our knowledge in this area we decided to study again the interactions that affect these mixtures, verifying the antecedents of systems containing mono- and/or alkyl polyhalides. In the case of the mono-chloroalkanes, there are some publications in the literature about mixtures of alkyl esters (methyl to propyl) with 1-chloroalkanes (pentane to octane),6-9 whereas the dihalide mixtures have been mentioned previously.1-5 In these works, it was observed that the modelization of excess enthalpies, HEm, using the UNIFAC model,10,11 showed discrepancies that became larger with increasing the number of carbon atoms in the compounds involved in the binary mixture. There are several explanations for these differences, one being that the interaction parameters are inadequate, having been obtained from a short experimental database. Another possible reason would be if the model employed uses an average value for parameters that correspond to interactions of functional groups, and these values depend on the results of estimations based on the systems used and the quality of the experimental data used in the regression. To compensate this second consideration, in a previous article5 it was proposed, not for the first time,12 that the interaction parameters vary with the chain length of the * To whom correspondence should be addressed. E-mail: [email protected].

compounds of the mixture. Another reason for this, also suggested in several works, is the different nature of the halogen atom in the mono- and dihalogenated compounds, which has clear repercussions on the modeling. For all of these reasons, it is necessary to conduct a thorough and in depth analysis and to correct, where required, even if only partially, some of the deficiencies mentioned. It is a priority to provide new experimental data for mixtures of high molecular weight compounds to expand on current knowledge of these fluid systems and increase the utility of the modelization. In this stage of the project, we have only focused on binary systems of alkyl ethanoates with 1-chloroalkanes, even including binary mixtures of two long-chain compounds. More specifically, for this work values of V Em and H Em have been measured at a temperature of 298.15 K for the following set of binary mixtures empirically described by {CH3COOCuH2u + 1 (u)16, 8) + CH3(CH2)V - 2CH2Cl (V ) 4-9)}. As background data, there are several articles in the literature that include V Em and HEm values at the temperature indicated because the quality of the data is an essential factor in modeling. There are V Em data for {methyl or ethyl ethanoates+1-chloroalkane (Cl5-Cl8)},6,9 of HEm for {methyl, or ethyl, or propyl ethanoates+1-chloroalkane (Cl5-Cl8)}7,8 and also values of isobaric liquid-vapor equilibria for {methyl, or ethyl ethanoates+1-chloroalkane (Cl5, Cl6)}.13 Finally, data have also been found for V Em and H Em at 298.15 K (for methyl, or ethyl ethanoate+1-chlorobutane).14-16 For the modeling, we follow a different approach from previous studies1-5 because estimations with the two versions of UNIFAC10,11 and the values assigned to the different

10.1021/ie071467m CCC: $40.75 © 2008 American Chemical Society Published on Web 03/29/2008

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interactions of the systems chosen, of ester/alkane,17 alkane/ chloride,7 and ester/chloride,7 would not give very different results from those that would be expected following the considerations of previous works.7,17 However, information derived from other models, based on theoretical considerations supported by quantum chemical approximations, would contribute to developing a better formula for the group-contribution models. For this reason, in this work we used the recent ab initio COSMO-RS methodology18 to estimate the H Em of the mixtures considered here. In general, the group-contribution methods require a large number of experimental data, whereas COSMO-RS is a quantum chemical approximation method and can predict the thermodynamic properties of pure fluids and mixtures from structural data of the individual molecules. COSMO calculates thermodynamic data from the polarity surface distribution of the mixture components, obtained from quantum chemical calculations based on the polarizable continuum model. The different intermolecular interactions, in other words electrostatic interactions, hydrogen bonds and dispersion forces are represented as functions of the polarity surface of the systems’ compounds. Using a statistical thermodynamic procedure, COSMO-RS transforms polarity molecular data into standard thermodynamic quantities. The COSMO-RS methodology has been efficiently used to predict equilibria data of gas-liquid, vapor-liquid, and liquid-liquid phases of halocarbonated compounds19 and presents some advantages over classical groupcontribution methods,20 such as (a) providing a qualitative and quantitative description of the different physicochemical interactions between the molecules of pure compounds and mixtures, facilitating the interpretation of the behavior of these fluids; (b) including in the calculation the effects associated with intramolecular interactions and proximity effects associated with the hydrogen bonds; (c) the fact that it can be used to resolve differences between isomers and, therefore, to estimate their contribution to the properties of the mixture; and (d) to provide a better description of the temperature dependence of the properties. Application of the COSMO-RS, as an alternative to a frequently used method such as UNIFAC, is indicated when there are insufficient experimental data, or, as occurs here, when additional information is required about the behavior of the fluid systems. Therefore, with the extensive experimental information provided in this work for the (alkyl ethanoates +1-chloroalkanes) systems, we study here, for the first time, its efficiency to estimate the H Em of these mixtures, observing the method’s contributions to the description of these types of systems, and its extension to other binary systems containing alkyl di- or polyhalides.

Table 1. Physical Properties of Pure Substances at T ) 298.15 and Comparison with Those from Literature

compound C4H9Cl C5H11Cl C6H13Cl C7H15Cl C8H17Cl C9H19Cl CH3COOCH3 CH3COOC2H5 CH3COOC3H7 CH3COOC4H9 CH3COOC5H11 CH3COOC6H13 CH3COOC8H17

supplier

mass fraction

F/ (kg‚m-3) exp.

880.87 880.75f 880.90e Fluka >99% 877.15 877.11a 877.10d Fluka >99% 873.42 873.50a 873.90d Aldrich 99% 871.24 870.98a 871.80d Fluka >98% 868.64 868.61a 869.20d Aldrich 99% 867.44 866.80d Fluka 927.08 926.73g 927.90e Fluka >99.5% 894.48 894.24h 894.55e Aldrich 99% 882.27 882.60d 882.55i Aldrich 99.7% 876.16 876.60d 876.36e Aldrich 99% 872.13 872.19b 871.90d Aldrich 99% 868.46 867.90d 868.60c Aldrich g99% 864.20 861.30d

Aldrich

99%

nD

lit.

exp.

lit.

1.4005 1.3999f 1.4001e,d 1.4101 1.4090a 1.4104d 1.4180 1.4177a 1.4179d 1.4235 1.4236a 1.4241d 1.4285 1.4284a 1.4287d 1.4330 1.4322d 1.3585 1.3585g 1.3589e 1.3693 1.3700h 1.3698e 1.3815 1.3828d 1.3816i 1.3922 1.3918d 1.4010 1.4000b 1.4008d 1.4071 1.4073d 1.4069c 1.4176 1.4180d

a Ref 21. b Ref 22. c Ref 23. d Ref 24. e Ref 25. f Ref 26. g Ref 4. h Ref 27. i Ref 28.

external circulation bath, model Phenix II, that provides the desired temperature controlled to within (0.01 K. Excess molar volumes, V Em, were calculated from direct measurements of the densities of the pure products and mixtures, at a temperature of T ) (298.15 ( 0.01) K. Densities were measured in an Anton Paar digital densimeter, model DMA-58, with an uncertainty of (2 × 10-2 kg‚m-3, previously calibrated with water and nonane according to our standard laboratory procedure. The samples were prepared by weighing into 10 cm3 hermetically sealed vials to prevent evaporation and injecting the pure substances with a 2 cm3 Hamilton syringe in different proportions to achieve the values of each point (x, V Em). A Mettler balance H51AR was used with a precision of (10-5 g. The uncertainty in the mole fraction was below 5 × 10-5 and the uncertainty in the VEm was below (2 × 10-9 m3‚mol-1 in all cases. The HEm values are direct measurements obtained calorimetrically in a Calvet type microcalorimeter, Setaram model MS80D, carried out at T ) (298.15 ( 0.002) K. In this case, the paired results (x, HEm) were estimated with uncertainties of (2 × 10-4 for the mole fraction and (1 J‚mol-1 for H Em, respectively.

2. Experimental Section 2.1. Materials. All of the products used, alkyl ethanoates and 1-chloroalkanes were supplied by Fluka and Aldrich and were of maximum commercial grade. Before use, they were degasified with ultrasound and kept for several hours with a 0.3 nm molecular sieve. The quality of the pure substances was verified by measuring some physical properties, such as the refractive index nD, and the density F, at T ) 298.15 K. The values obtained for the products are shown in Table 1 together with those recorded in the literature, and the comparison was acceptable in all cases. The good quality of substances was confirmed by GC. 2.2. Apparatus and Procedure. Refractive indices nD for the pure compounds were measured in an Abbe refractometer by Zuzi, model 320, with an uncertainty of (0.0002 units. The equipment was thermostated with water from a Haake

3. Results Experimental values of V Em and H Em, measured at atmospheric pressure and at a temperature of 298.15 K for the set of binary mixtures described by for {xCH3COOCuH2u + 1 (u ) 1 a 6, 8) + (1 - x) CH3(CH2)V - 2CH2Cl (V ) 4 a 9)} are presented, respectively, in Tables S1 and S2. These tables do not include data of binary mixtures (methyl ethanoate, or ethyl or propyl +1-Cl5 to 1-Cl8) published in previous studies.6-9 The correlation of both mixing quantities, expressed generically as Y Em/(J‚mol-1 or m3‚mol-1), was carried out with the following equation,

Y Em ) z(1 - z)

x

∑i Ai - 1zi - 1 where z ) x + k(1 - x)

(1)

Ind. Eng. Chem. Res., Vol. 47, No. 9, 2008 3255 Table 2. Coefficients Ai and k, and Standard Deviation s, Obtained for Eq 1 mixture YEm

kv

A0

)

109‚VEm/(m3

A1

A2

s

mixture

‚mol-1)

kh YEm

xCH3COOCH3 + (1 - x) C4H9Cl (1 - x) C5H11Cl 9 (1 - x) C6H13Cl 9 (1 - x) C7H15Cl 9 (1 - x) C8H17Cl 9 (1 - x) C9H19Cl

1.314 1.520 1.727 1.933 2.141 2.346

2889 3407 4187 4860 5613 5978

-1487 -1552 -3409 -4653 -6721 -6990

506 165 1542 2270 3991 3599

xCH3COOC2H5 + (1 - x) C4H9Cl (1 - x) C5H11Cl 6 (1 - x) C6H13Cl 6 (1 - x) C7H15Cl 6 (1 - x) C8H17Cl 6 (1 - x) C9H19Cl

1.067 1.234 1.402 1.569 1.737 1.904

1664 2205 2619 3057 3431 3991

-302 -731 -1281 -2044 -2603 -3878

xCH3COOC3H7 + (1 - x) C4H9Cl (1 - x) C5H11Cl (1 - x) C6H13Cl (1 - x) C7H15Cl (1 - x) C8H17Cl (1 - x) C9H19Cl

0.908 1.050 1.193 1.335 1.478 1.620

1032 1270 1601 1891 2285 2614

x1CH3COOC4H9 + (1 - x1) C4H9Cl (1 - x1) C5H11Cl (1 - x1) C6H13Cl (1 - x1) C7H15Cl (1 - x1) C8H17Cl (1 - x1) C9H19Cl

0.793 0.917 1.042 1.166 1.291 1.415


A0 )

A1

A2

s

HEm/(J‚mol-1)

2 5 7 3 4 7

x1CH3COOCH3 + (1 - x1) C4H9Cl (1 - x1) C5H11Cl 8 (1 - x1) C6H13Cl 8 (1 - x1) C7H15Cl 8 (1 - x1) C8H17Cl 8 (1 - x1) C9H19Cl

0.921 1.078 1.237 1.395 1.553 1.711

1812 1816 2740 3916 4721 5750

269 1578 574 -1789 -2286 -3756

161 -542 -113 1516 1172 1439

3 4 2 2 4 8

160 241 460 939 1171 2108

7 1 1 2 2 5

x1CH3COOC2H5 + (1 - x1) C4H9Cl (1 - x1) C5H11Cl 7 (1 - x1) C6H13Cl 7 (1 - x1) C7H15Cl 7 (1 - x1) C8H17Cl 7 (1 - x1) C9H19Cl

0.915 1.071 1.229 1.386 1.543 1.700

1102 1271 1944 2392 3565 3762

-564 552 -339 -339 -2699 -1840

961 -431 89 -262 1002 42

3 3 4 4 11 8

-593 -181 -521 -933 -1416 -2142

508 38 160 445 652 1222

4 3 3 4 7 3

x1CH3COOC3H7 + (1 - x1) C4H9Cl (1 - x1) C5H11Cl8 (1 - x1) C6H13Cl 8 (1 - x1) C7H15Cl 8 (1 - x1) C8H17Cl 8 (1 - x1) C9H19Cl

0.788 0.923 1.058 1.193 1.329 1.464

421 612 969 1499 1952 2243

-287 438 571 -403 -1014 -962

719 -109 -579 310 586 212

3 2 3 4 3 5

453 769 1023 1239 1347 1759

-60 -76 -223 -350 -40 -1042

82 71 135 149 -179 581

2 2 2 2 6 4


0.693 0.812 0.931 1.050 1.170 1.289

-1 355 613 1018 1035 1337

-238 -398 -430 -1227 -150 -561

272 292 321 1177 -13 283

1 1 1 1 4 5

0.705 0.816 0.927 1.037 1.149 1.259

210 393 770 990 1146 1207

-36 406 -224 -385 -376 -240

17 -259 174 181 128 27

1 4 2 3 2 3


0.620 0.726 0.833 0.939 1.046 1.152

-12 -29 92 355 609 818

-1465 -800 -22 -239 -580 -598

1334 952 74 299 629 564

4 4 1 2 1 2


0.633 0.732 0.832 0.931 1.031 1.130

24 310 468 670 793 910

-24 -77 7 -212 -181 -167

-42 148 13 148 110 -2

0 1 1 2 2 2


0.559 0.655 0.751 0.847 0.944 1.039

-266 -53 21 -94 263 628

-589 -948 -916 -122 -365 -757

-311 419 883 394 452 631

3 4 2 3 2 1


0.527 0.610 0.693 0.776 0.859 0.941

-229 42 230 346 463 518

97 13 -82 -108 -70 54

-242 8 111 164 89 -67

1 0 1 1 1 2


0.481 0.564 0.647 0.729 0.812 0.895

-561 -282 -135 -146 -81 -55

700 -423 -1103 -845 -734 -315

-2314 -739 544 572 783 364

5 5 5 2 2 1

using in all cases a second-order polynomial equation. Depending on whether the correlation is done on the pairs of values (x, V Em) or (x, H Em), a different fixed value will be used for the parameter k, determined as indicated in other previous studies,1-5 denominated kv for the first case and kh for the second case. Knowing the densities of the pure compounds, the values of these parameters are easily calculated from

kv )

V om,2(T) V om,1(T)

)

M2F1(T)

(2)

M1F2(T)

and

( )( ) ( ) ( )( ) ( )

q2 kh ) q1

V om,2

V om,1

2/3

r1 r2

2/3

q2 kvr1 ) q1 r2

2/3

kv ) kq kr

2/3

(3)

where Mi and Fi are, respectively, the molecular weight and the density of the pure compound i. The values of the volume parameters ri, and the surface parameters qi, are determined using a group-contribution method of Bondi.29 Table 2 shows the values obtained for kv and kh, according to the procedure described, for the binary systems of this work. These values are used as fixed quantities in the correlation of the V Em and H Em values relative to the ester composition, x, of each mixture, determining the Ai coefficients for eq 1 by least-squares, minimizing the standard deviations (Y Em) of the corresponding excess quantities. Parts a-g of Figure 1 show the quality of the representations, experimental, and correlation curve, for the V Em for the mixtures studied here, each of which corresponds to a binary system containing each alkyl ethanoate with the six 1-chloroalkanes. Parts i-o of Figure 1 show the same representations for the HEm values. For a better analysis of the results, a representation of the corresponding equimolar excess

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Figure 1. Plot of experimental VEm (a-g) and HEm (i-o) (b), and correlation curves by eq 1 as a function of mole fraction x1 for binary mixtures x1CH3CO2CuH2u + 1 + (1 - x1)1-CVH2V + 1Cl at 298.15 K and comparison with the literature values from Avedis et al.14-16 (4). Labels indicate the V values. (a,i) for u ) 1; (b,j) for u ) 2; (c,k) for u ) 3; (d,l) for u ) 4; (e,m) for u ) 5; (f,n) for u ) 6; (g,o) for u ) 8. (h), Representation of equimolar volumes as a function of V, where (b) are values in this work and (O) are values presented in other works.6-9 Labels indicate the u values.

quantities as a function of the chain length of the halogenated compound will be used, together with data from previous studies,6-9 to complete the dataset studied here. So, part h of Figure 1 shows V Em, whereas that corresponding to HEm will be shown in the following sections. In summary, experimental values obtained in this work show that the mixing processes of the set studied here involve expansion/contraction and are endothermic/exothermic, as a result of different positive/negative effects. The representations show a reduction in the excess quantities with longer alkyl chain lengths for the ethanoate and with diminution of the monochloralkane chain length. 4. Application of the COSMO-RS Model In this work, the COSMO-RS calculations were carried out following a multistep procedure.30 First, the software was used for the Gaussian 03 quantum-chemical calculation31 to generate the COSMO files for each compound studied, with prior optimization of the molecular geometry at computational level

B3LYP/6-311++G**. These files include the ideal screening charges on the molecular surface of each species, calculated by the COSMO continuum solvation model using theory level BVP86/TZVP/DGA1. Next, these files are introduced as input data in the COSMOtherm program32 to calculate the HEm values of the different mixtures at 298.15 K. Depending on the functional density method and the calculation basis chosen, the parametrization of BP_TZVP_ C21_0106 is selected, which is required to calculate the physical-chemical data and contains the intrinsic parameters of COSMOtherm and specific parameters for the chemical elements. Part a of Figure 2 shows the equimolar values of HEm calculated by COSMO-RS together with experimental data. We can see that the values estimated by the model for these mixtures, quantitatively speaking, are very different from experimental values, and do not clearly estimate the enthalpic variation with increased chain length of the chloroalkane, on the one hand, or the increased group number, -CH2- in the

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Figure 2. Plots of equimolar HEm (b), obtained at T ) 298.15 K as a function of chloroalkane chain length V, for binaries xCH3CO2CuH2u + 1 + (1 x)1-CVH2V + 1Cl and theoretical estimations (O) by COSMO-RS using (a) original parameters and (b) optimized parameters in this work.

ethanoate, on the other hand. COSMO-RS is an a priori predictive method and does not require any experimental data of the systems studied. The method depends on a small number of parameters, some of which are physically predetermined.33 These parameters are not associated with functional groups or types of molecules, unless they have been optimized by fitting the COSMO-RS method to the experimental data. Therefore, the resulting parametrization is of general application to predict thermodynamic properties of any type of compound or mixture. However, the authors have demonstrated the value of adjusting the van der Waals interaction parameters in the case of halogen elements34 because, owing to their special polarizability, the van der Waals interactions are not accurately described as sums of the specific terms of each element. Because these types of interactions are known to make an important contribution to the H Em of the mixtures (ester+chloroalkane), in this work the van der Waals parameters were tuned, or adjusted, for the ClCl and H-Cl interaction, to obtain a better prediction of the HEm for the mixtures chosen. Therefore, the original values τ(Cl, Cl) ) -39.60 kJ/mol/nm2 and τ(Cl, H)) -26.06 kJ/mol/ nm2 have been replaced respectively by -47.52 and -46.91 kJ/mol/nm2. These new values produce better estimations and the HEm (a x ) 0.5) are shown in part b of Figure 2. Now, the COSMO-RS method gives a good quantitative and qualitative estimation of the HEm values, providing a better description of the alkylic chain effect of the ethanoate. Hence, for example, for the specific case of the mixture (alkyl ethanoate+1chlorobutane) the HEm values progressively evolve from endothermic to exothermic values as the length of the alkanolic chain of the ethanoate increases. 4.1. COSMO-RS Description for Pure Compounds. One significant advantage of the COSMO-RS methodology is that it shows the charge distribution (σ) over the molecular surface, easily seen by the σ-profile histogram. The σ profile quantifies the density distribution of a charge of a given polarity on the molecular surface, which is used in the statistical thermodynamic procedure of COSMO-RS to obtain the interaction energy between pairs of surface segments. As a result, the σ profile determines the estimation of electrostatic interactions and hydrogen bonds by the COSMO-RS model. In fact, the qualitative analysis of the σ profile of a molecule can be used

to predict the behavior of the compound in a fluid. For the seven ethanoates studied, part a of Figure 3 presents the σ profile, which can be divided qualitatively into three main regions, separated in part a of Figure 3 by two vertical lines located at the cut-off points for hydrogen bond donors (σHB < -0.0085 e/Å2) and acceptors (σHB > 0.0085 e/Å2). The peaks at 0.01 and 0.013 correspond, respectively, to the oxygens of the ester and the carbonyl groups. Because these peaks are in the highpolarity region (σHB > 0.0085 e/Å2), the groups corresponding to the ethanoate can be considered to be hydrogen bond acceptors. On the other hand, the distribution of charge densities around zero (-0.0085 e/Å2 < σ < 0.0085 e/Å2) correspond to the nonpolar alkylic groups of the ethanoate, assigning positive and negative ones to carbon and hydrogen atoms of the chain, respectively. Part a of Figure 3 shows how the charge density in the nonpolar region of the σ profile increases with the number of atoms in the ethanoate chain, making the σ profile increasingly asymmetrical. This indicates the existence of more repulsive interactions between polar and nonpolar groups of the ethanoate; in other words, a lesser capacity of the compound to interact with itself. This description can be complemented by the representation of the σ potential of these compounds in part b of Figure 3. The σ potential describes the affinity of the solvent concerned to interact with compounds with a charge density of [pX(σ)] with polarity σ. From the results represented in part b of Figure 3, we can see that alkyl ethanoates present strongly attractive interactions with acidic groups and repulsive ones with basic groups. However, the alkyl groups of the ethanoates facilitate interactions with a mild attraction for apolar compounds. Regarding the monochloroalkanes, part c of Figure 3 shows the σ profile of the series chosen for this work. We can observe that the σ profile of these compounds is characterized by the peak produced by the chlorine atom at 0.008 e/Å2 and signals associated with the alkylic groups in the nonpolar zone of the σ profile, the intensity of which increase with the chloroalkane chain. Part d of Figure 3 shows that the σ potential of the monochlorides correspond to a parabola centered at σ ) 0, indicating strong repulsive forces, both with acidic and basic groups. The COSMO-RS results also indicate mildly attractive interactions due to the presence of chloroalkanes in mixtures with compounds of a pronounced apolar nature.


Figure 3. σ profiles and σ potentials of compounds: (a) and (b) correspond, respectively, to the σ profiles and σ potential, for CH3CO2CuH2u + 1. Labels indicate the u values; (c) and (d) correspond, respectively, to the σ profiles and σ potential for 1-CVH2V + 1Cl. Labels indicate the V values.

4.2. COSMO-RS Description of the HmE. We will analyze, using the COSMO-RS model, the effects of the different intermolecular interactions of the mixing components (alkyl ethanoate+1-chloroalkanes) on the HEm. The model will be used to interpret the influence of the addition of a same group, -CH2-, on final values, which implies an endothermic contribution if this group increases the chain length of the 1-chloroalkane and an exothermic contribution if this group is included in the alkyl chain of the ethanoate. Considered separately, the analysis would correspond to: (a) Effect of the 1-Chloroalkane Chain. A previous section refers to COSMO-RS estimations for these mixtures, (Figure 2). The H Em values obtained with the model are the result of summing together the three contributions associated with the interactions H Em (Misfit) polar misfit, HEm (H-Bond) hydrogen bond and H Em (VdW) van der Waals or,

For the mixtures considered here, HEm (H-Bond) ) 0, so the final result would only depend on the other two contributions, according to eq 4, which are shown separately in parts a and b of Figure 4. The values for these interactions make them increasingly repulsive with the increasing chain length of the halogen. The next step involves a more thorough analysis of each of the terms HEm (Misfit) and HEm (VdW), giving in detail, as an example, the calculation for a representative compound such as pentyl ethanoate, which in mixtures with the different chloroalkanes change from exothermic, HEm < 0, to endothermic, HEm > 0, as the length of the halogenated hydrocarbon chain increases (tendency 5 in Figure 2). The contributions of each summand of eq 4 to the final values of HEm are obtained from expressions,

H Em (Misfit) ) x1[H E1 (Misfit)] + x2 [H E2 (Misfit)]

(5)

H Em ) HEm (Misfit) + H Em (H-Bond) + H Em (VdW)

H Em (VdW)) x1[H E1 (VdW)] + x2[H E2 (VdW)]

(6)

(4)

3260


Figure 4. Variation of equimolar HEm at T ) 298.15 K as a function of chloroalkane chain length V, for xCH3CO2CuH2u + 1 + (1 - x)CVH2V + 1Cl, and considering (a) HEm (Misfit) and (b) HEm (van der Waals).

Figure 5. Variation of HEm (Misfit) (2) at T ) 298.15 K with chloroalkane chain length V, for xCH3CO2CuH2u + 1 + (1 - x)1-CVH2V + 1Cl; (a) for pentyl ethanoate and (b) for 1-chloroalkane. (9) HEm (Misfit) of compound in pure state, ( ) HEm (Misfit) of compound in mixture state.

where component 1 ) alkyl ethanoate and component 2 ) 1-chloroalkane and where,

H Ei (Misfit) ) Hi,mixture (Misfit) - Hi,pure (Misfit)

(7)

H Ei (VdW)) Hi,mixture (VdW) - Hi,pure (VdW)

(8)

where i ) component 1 or 2. To calculate HEm (Misfit) in eq 5, in parts a and b of Figure 5 the specific terms of [HE1 (Misfit)] for alkyl ethanoates and of [HE2 (Misfit)] for the chloroalkanes are, respectively, shown. It can be observed that: (i) The contribution of pentyl ethanoate to HEm (Misfit) in eq 5 is exothermic, with HE1 (Misfit) < 0 in part a of Figure 5, whereas chloroalkane contributes endothermically to mixing enthalpy, with HE2 (Misfit) > 0 in part a of Figure 5. To interpret these results from a chemical perspective, we turn to eqs 7-8, which define the HEi (Misfit) of each component on

the basis of its enthalpy in the pure compound and in the mixture. It can be observed in part b of Figure 5 that the electrostatic interactions of the chloroalkane (component 2) are repulsive in both fluids, H2,mixture (Misfit) > 0 and H2,pure (Misfit) > 0, although to a greater extent in the mixture. As a result, the contribution of chloroalkane HE2 (Misfit) to the HEm (Misfit) in eq 5 is endothermic. In the case of pentyl ethanoate, the basic polar groups (CdO and -O-) of the ethanoate present more repulsive interactions between them (in the pure fluid) than the slightly basic Cl- groups of 1-chloroalkane (in the mixture), with a resulting negative contribution of HE1 (Misfit) to HEm (Misfit) in eq 5. (ii) The contribution of both components to the final values of HEm (Misfit) of the mixture is in the opposite direction of the increased number of -CH2- groups, with a positive tendency in the chloroalkanes, part b of Figure 5, and a negative tendency with the alkyl ethanoates, as in part a of Figure 5. In other words, the endothermic contribution of the chloroalkane HE2 (Misfit)


Figure 6. Variation of HEm (VdW) (2) at T ) 298.15 K as a function of chloroalkane chain length V, for xCH3CO2CuH2u + 1 + (1 - x)CVH2V + 1Cl; (a) for pentyl ethanoate and (b) for chloroalkane. (9) H Em (VdW) of compound in pure state, ( ) HEm (VdW) of compound in mixture state. Table 3. van der Waals Interaction Parameters (kJ/mol/nm2) for Pairs of Elements, after Optimization

H C O Cl

H

C

O

Cl

-30.28 -23.45 -22.47 -46.91

-34.48 -24.08 -47.27

-9.22 -38.50

-47.52

increases with the chain length. This can be explained by the σ potential of the halide that indicates an increase in the repulsive interactions with basic polar compounds, such as pentyl ethanoate, as the chain length increases. On the other hand, the repulsions of pentyl ethanoate in the mixture decrease with the length of the 1-chloroalkane, obtaining more negative values of HE1 (Misfit), which can be explained by the pentyl ethanoate σ potential that indicates slightly attractive interactions with nonpolar groups that must increase in the mixture with the 1-chloroalkane chain. The net result of contributions of opposite sign, HE1 (Misfit) and HE2 (Misfit), for the mixture of (pentyl ethanoate +1-chloroalkane), is a change from being initially exothermic to being endothermic with increased chloroalkane chain length. In other words, the contribution of chloroalkane to HEm (Misfit) is more important as the alkyl chain length increases. Following a similar procedure, we can analyze the contribution of van der Waals interactions in the final values of HEm of the chosen group of mixtures (pentyl ethanoate+1-chloroalkane, eq 4). Figure 6 can be used to interpret the values of HEm (VdW) in the mixture, in terms of the contribution of each component, according to eq 6, observing that: (i) These contributions occur again, with HE1 (VdW) < 0 and E H2 (VdW) > 0. We can interpret these results by examining eq 8. From the Hi,pure (VdW), calculated from the van der Waals interaction parameters of Table 3, we can deduce that the interaction of both components is attractive, both for the pure fluid and for the mixtures (parts a and b of Figure 6). However, the van der Waals interactions of the chloroalkane in the mixture decrease in the mixture relative to the pure component (part b of Figure 6). Consequently, the chloroalkane has a positive enthalpy HE2 (VdW), with an endothermic contribution to the total excess enthalpy of the mixture. This result is assigned to the smallest contribution of the Cl-Cl terms of interaction, for

which the parameter τ(Cl, Cl) is the largest in Table 3. For the HE1 (VdW) of the pentyl ethanoate, part a of Figure 6 shows that this component presents stronger interactions between the van der Waals and the chloroalkane molecules than with its own molecules, which is associated with appearance of the van der Waals interactions with Cl- in the mixture. Therefore, the van der Waals interactions of the pentyl ethanoate contribute exothermically to the total excess enthalpy of the mixture. (ii) In the case of the van der Waals interactions, HEm (VdW) decreases with the increased chain length of the 1-chloroalkane, whereas the corresponding contribution of the pentyl ethanoate increases. The difference between the van der Waals interactions of the chloroalkane in the pure fluid and in the mixture decreases with its chain length, which is associated with an increase in the relative contribution of the τ(Cl, H) term in the mixture, also a significant value in Table 3. On the other hand, the relative contribution of the van der Waals interactions of the pentyl ethanoate with the Cl- group decreases with the length of the chloroalkane chain, giving less-negative HE1 (VdW) values as the chain length increases. The net result in HEm (VdW) of the contribution of both components (tendency 5 in part b of Figure 4) indicates that the van der Waals interactions of the ethanoate are important for the short-chained 1-chloroalkanes, and the contribution of the chloroalkane increases with the alkylic chain length. (b) Effect of the Alkyl Ethanoate Chain. Separately, we discuss the influence of the alkyl ethanoate chain on the HEms. In parts a and b of Figure 2, which present the equimolar HEm for these mixtures, we can observe that for a given alkane the values decrease regularly as the alkyl chain of the ethanoate increases. Parts a and b of Figure 4 show the contributions to HEm (Misfit) polar misfit and HEm (VdW) van der Waals, interactions in which in both cases are more attractive when we increase the chain length of the ethanoate group. An opposite effect is produced with increasing the length of the chloroalkane chain (parts a and b of Figure 4). As an example, we can describe the influence of the ethanoate chain in mixtures with 1-chlorobutane, selected because they evolve from endothermic values, HEm > 0, to exothermic ones, HEm < 0, as the ethanoate chain increases, points with ν ) 4 in part b of Figure 2. As discussed previously, parts a and b of Figure 7 show that:

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Figure 7. Variation of HEm (Misfit) (2) at T ) 298.15 K with ethanoate chain length u, for xCH3CO2CuH2u + 1 + (1 - x)CVH2V + 1Cl; (a) for alkyl ethanoate and (b) for chlorobutane. (9) HEm (Misfit) of compound in pure state, ( ) HEm (Misfit) of compound in mixture state.

Figure 8. Variation of HEm (VdW) (2) at T ) 298.15 K with ethanoate chain length u, for x CH3CO2CuH2u+1 + (1 - x)CVH2V + 1Cl; (a) for alkyl ethanoate and (b) for 1-chlorobutane. (9) HEm (VdW) of compound in pure state, ( ) HEm (VdW) of compound in mixture state.

(i) The enthalpy misfit of both components in the mixture, HE1,mixture (Misfit) and HE2,mixture (Misfit), and in the pure component, HE1,pure (Misfit) and HE2,pure (Misfit), present positive values. As with the previous case, the repulsive interactions of the chloroalkane are greater in the mixture than in the pure compound, whereas in the ethanoate the opposite occurs, resulting in the chloroalkane making an endothermic contribution, HE2 (Misfit) > 0, as in part b of Figure 7, and the ethanoate an exothermic one, HE1 (Misfit) < 0, as in part a of Figure 7. (ii) As the ethanoate chain length increases, the contribution of the chloroalkane HE2 (Misfit) is diminished, as in part b of Figure 7, whereas that of the ethanoate HE1 (Misfit) increases, as in part a of Figure 7, an opposite effect to that described in the previous analysis (influence of the chloroalkane chain). The effect in HE2 (Misfit) is due to the decreased enthalpy misfit of the chlorobutane in the mixture. On the basis of the σ potential of the alkyl ethanoate, this result can be interpreted as an

increase in mildly attractive interactions with the nonpolar chain length of the chloroalkane as the ethanoate chain increases. On the other hand, the effect on HE1 (Misfit) is due to the fact that in spite of both HE1,pure (Misfit) and HE1,mixture (Misfit) increasing in value with the ethanoate chain length, the second does so to a greater extent. The σ potential of the alkyl ethanoate indicates an increase in repulsive interactions as the chain length of the ethanoate increases, explaining this result. In part a of Figure 4, it can be observed how the net result of HEm (Misfit) as a sum of HE1 (Misfit) and HE2 (Misfit) is an increasingly endothermic misfit enthalpy as the ethanoate chain increases in length. For the longer ethanoates, the ethanoate and the chloroalkane make a similar contribution, producing a misfit enthalpy close to zero for these mixtures. Studying the contribution of the van der Waals interactions in parts a and b of Figure 8, for both components this interaction is attractive for the pure fluid and for the mixtures. Coinciding with the previous analysis, it can be concluded that the van der


Figure 9. Variation of equimolar HEm (b) at T ) 298.15 K with chloroalkane chain length V, for xCH3CO2CuH2u + 1 + (1 - x)CVH2V + 1Cl and theoretical estimations: (0) by UNIFAC10 with optimized parameters in this work, and (4) by UNIFAC.11

Waals interactions of the chlorobutane in the pure compound are greater in the mixture, part b of Figure 8, whereas the opposite occurs for the alkyl ethanoate, part a of Figure 8, giving contributions of HE2 (VdW) > 0 and HE1 (VdW) < 0, respectively, to the van der Waals excess enthalpy of the mixture. However, as the ethanoate chain increases in length, the value of HE2 (VdW) increases due to the smaller contribution of the τ(Cl, Cl) term in the mixture, whereas HE1 (VdW) diminishes as a result of the increased relative contribution of the τ(Cl, H) term in the mixture. 5. Conclusions Excess properties, V Em and HEm, have been determined experimentally for a set of binary systems (alkyl ethanoates +1chloroalkanes). The COSMO-RS method was used to obtain information to define the behavior of this type of systems and to support concepts established in previous works with groupcontribution models. The COSMO-RS methodology describes the HEm of the mixtures (alkyl ethanoate + chloroalkane) on the basis of the different electrostatic and van der Waals interactions established in the pure fluids and in the mixtures. The electrostatic interactions between chloroalkane and alkyl ethanoate species are always repulsive because both are polar molecules of a basic nature and increase for the case of the ester because of the high basicity of the oxygenated groups. In contrast, van der Waals interactions are always attractive and increase with the relative weight of the -Cl in the fluid. The different weights of these interactions in the pure components and in the mixture results in a complex description of HEm as a function of each component. Hence, the chloroalkane contributes endothermically to the mixture because, on the one hand, its polar misfit interactions are more repulsive with the ethanoate than with itself, whereas its van der Waals interactions are more attractive in the pure compound than in the mixture. Ethanoate, however, has an opposite influence, contributing exothermically to the mixture through both its misfit and also its van der Waals interactions. The increased number of -CH2- in a component

implies greater misfit and van der Waals contributions of this component in the mixture. Consequently, the mixture becomes more endothermic if the alkylic chain of the chloroalkane increases and more exothermic if the ethanoate chain increases. Although COSMO-RS cannot predict the volumetric behavior owing to the lack of an equation of state, the considerations made to explain energetic effects can also help to explain VEm and how these values change with the chain length of the compounds involved (part h of Figure 1). An expansion takes place with the increased chain length of the chloroalkane because, as well as increasing the net endothermic contribution of the chloroalkane, there is also an increase in the intramolecular empty spaces because of steric impediments of the different ester/chloroalkane molecules. This effect is opposite to the effect of the increased ethanoate chain length on the VEm, with an increased exothermic effect in the mixture and a better final fit of the compounds’ molecules in the final mixture. In fact, for the longest chain ester mixture (octyl ethanoate) and the shortest chloroalkane chain (1-chlorobutane), contractions occur, V Em < 0, as shown in part h of Figure 1. To give continuity to our research line described in previous works, although these models are fundamentally different, we do not rule out the possibility of using the information acquired in the application of COSMO-RS to improve application of the UNIFAC model. For this purpose, we show here application of the UNIFAC model in its two most recent versions to estimate HEm. The version of Dang and Tassios,10 with the interaction parameters for CH3COO/CH2 determined by Ortega et al.,17 and for CH3COO/Cl by Ortega et al.,7 does not give negative values for HEm. The results corresponding to the version of Gmehling et al.,11 are shown in Figure 9 and are an improvement on the previous results, although with a lower quality of the estimation than that of the COSMO-RS. For this work, we recalculated the interaction parameters for ethanoate/chloride for the version of Dang and Tassios,10 using the database provided in this work. Regression of the set of values (x, HEm) produced new parameters, aCH3COO/Cl ) -1.33, and aCl/CH3COO ) 39.56, that improve the results obtained, as shown in Figure 9, which are now very similar to those estimated by the version of Gmehling et al.11 Acknowledgment The authors gratefully acknowledge the financial support received from the Ministerio de Educacioń y Ciencia (Spain) for the Project CTQ2006-12027. Supporting Information Available: Tables containing the experimental values of excess molar volumes and excess molar enthalpies. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Ortega, J.; Marrero, E.; Toledo, F. J.; Espiau, F. Thermodynamic study of (alkyl esters+R,ω-alkyl dihalides) I: HEm and VEm for 25 binary mixtures {xCu-1H2u-1CO2C2H5 +(1 - x)R,ω-ClCH2(CH2)V-2CH2Cl}, where u ) 1 to 5, R ) 1, and V ) ω ) 2 to 6. J. Chem. Thermodyn. 2005, 37, 1332-1346. (2) Ortega, J.; Navas, A.; Plaćido, J.; Toledo, F. J. Thermodynamic study of (alkyl esters+R,ω-alkyl dihalides) II: HEm and VEm for 25 binary mixtures {xCu - 1H2u - 1CO2 C2H5 + (1 - x) R,ω-BrCH2(CH2)V - 2CH2Br}, where u ) 1 to 5, R ) 1, and V ) ω ) 2 to 6. J. Chem. Thermodyn. 2006, 38, 585-598. (3) Ortega, J.; Marrero, E.; Toledo, F. J. Thermodynamic study of (alkyl esters+ R,ω-alkyl dihalides) III: HEm and V Em for 20 binary mixtures

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{xCu - 1H2u - 1CO2C4H9 + (1 - x)R,ω-ClCH2(CH2)V-2CH2Cl}, where u ) 1 to 5, R ) 1, and V ) ω ) 2 to 6. J. Chem. Thermodyn. 2006, 38, 11391149. (4) Ortega, J.; Navas, A.; Plaćido, J. Thermodynamic study of (alkyl esters + R,ω-alkyl dihalides) IV: HEm and VEm for 25 binary mixtures {xCu - 1H2u - 1CO2CH3 + (1 - x) R,ω-BrCH2(CH2)V-2CH2Br}, where u ) 1 to 5, R ) 1, and V ) ω ) 2 to 6. J. Chem. Thermodyn. 2007, 39, 128141. (5) Ortega, J.; Marrero, E. Thermodynamic study of (alkyl esters+R,ωalkyl dihalides) V: HEm and VEm for 25 binary mixtures {xCu - 1H2u - 1CO2CH3 + (1 - x) R,ω-ClCH2 (CH2)V - 2CH2Cl}, where u ) 1 to 5, R ) 1, and V ) ω ) 2 to 6. J. Chem. Thermodyn. 2007, 39, 742-757. (6) Ortega, J.; Matos, S.; Paz-Andrade, M. I.; Fernandez, J. Excess molar volumes of ethyl formate+1-chloroalkane at 298.15 K. J. Chem. Eng. Data 1987, 32, 464-466. (7) Ortega, J.; Matos, S.; Paz-Andrade, M. I.; Fernandez, J.; Pias, L. Analysis of excess enthalpies of ester+1-chloroalkanes with two group contribution models: Primary parameters. Fluid Phase Equilib. 1988, 43, 295-316. (8) Ortega, J. Measurements and analysis of excess enthalpies of alkyl acetates+1-chloroalkanes using the UNIFAC model. Ber. Bunsen-Ges. Phys. Chem. 1988, 92, 1146-1149. (9) Ortega, J.; Penã, J. A.; Matos, S. Int. DATA Ser., Sel. Data Mixtures., Ser. A. 1989, 85-96. (10) Dang, D.; Tassios, D. P. Prediction of enthalpies of mixing with a UNIFAC model. Ind. Eng. Chem. Process Des. DeV. 1986, 25, 22-31. (11) Gmehling, J.; Li, M.; Schiller, M. A modified UNIFAC model.2. Present parameter matrix and results for different thermodynamics properties. Ind. Eng. Chem. Res. 1993, 32, 178-193. (12) Ortega, J.; Plaćido, J. Study on the binary mixtures of alkyl alfa, omega-dihalogenated (chlorine, bromine, iodine) with n-alkanes. An improvement by considering the variation of the interaction parameters with the chain length. Fluid Phase Equilib. 1995, 109, 205-225. (13) Ortega, J.; Penã, J. A. Vapor-liquid equilibria of methyl or ethyl acetate with 1-chloropentane or 1-chlorohexane at 101.32 kPa pressure. J. Chem. Eng. Jap. 1994, 27, 351-356. (14) Avedis, G.; Roux, A. H. M.; Grolier, J-P. E. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1990, 2-5. (15) Avedis, G.; Roux, A. H. M.; Grolier, J-P. E. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1990, 79-81. (16) Avedis, G.; Roux, A. H. M.; Grolier, J-P. E. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1991, 175-176. (17) Ortega, J.; Legido, J. L.; Fernandez, J.; Pıás, L.; Paz Andrade, M. I. Measurements and analysis of excess enthalpies of ester+n-alkane using the UNIAFC model. Ber. Bunsen-Ges. Phys. Chem. 1991, 95 (2), 128135. (18) Klamt, A. COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Design, 1st ed; Elsevier: Amsterdam, The Netherlands, 2005. (19) Eckert, F.; Klamt, A. Prediction of halocarbon thermodynamics with COSMO-RS Fluid Phase Equilib. 2003, 210, 117-141. (20) Klamt, A.; Eckert, F. COSMO-RS: A novel and efficient method for the a priori prediction of thermophysical data of liquids. Fluid Phase Equilib. 2000, 172, 43-72. (21) Matos, J. S.; Ortega, J.; Garcıá, M. V. Int. DATA Ser., Sel. Data Mixtures, Ser. A 1991, 3, 216-223.

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ReceiVed for reView October 30, 2007 ReVised manuscript receiVed December 22, 2007 Accepted February 14, 2008 IE071467M

Description of Thermodynamic Behavior of the Systems Formed by

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