Thermodynamics of 1-alkanol+linear polyether mixtures

J. Chem. Thermodynamics 59 (2013) 195–208 Contents lists available at SciVerse ScienceDirect J. Chem. Thermodynamics journal homepage: www.elsevier.com/locate/jct Thermodynamics of 1-alkanol + linear polyether mixtures Juan Antonio González ⇑, Ángela Mediavilla, Isaías García De la Fuente, José Carlos Cobos G.E.T.E.F., Departamento de Física Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain a r t i c l e i n f o Article history: Received 3 October 2012 Received in revised form 20 November 2012 Accepted 6 December 2012 Available online 31 December 2012 Keywords: 1-Alkanol Polyether Calorimetric data Volumetric data Interactions Dipolar Flory a b s t r a c t Experimental densities, q, and speeds of sound, u, have been measured at (293.15–303.15) K for the systems methanol, 1-butanol or 1-decanol + 3,6,9-trioxaundecane using a vibrating-tube densimeter and sound analyzer Anton Paar model DSA-5000. These values were used to calculate excess molar volumes, V Em , excess adiabatic compressibilities, jES , and excess speeds of sound, uE. Data available in the literature on excess molar enthalpies, HEm , and on excess molar isobaric heat capacities, C Ep;m , of 1-alkanol + linear polyether mixtures indicate that: (i) interactions are mainly of dipolar type, particularly for solutions with longer 1-alkanols; (ii) the ability of the ether to break the alcohol self-association increases with the number of CH2CH2O groups in the oxaalkane. The enthalpies of the alcohol-ether interactions, DHOHO, have been determined. In mixtures with a given polyether, DHOHO increases with the alcohol size. For 1-alkanol + CH3O(CH2CH2O)nCH3 systems, DHOHO decreases for increased n values. Alcoholether interactions are stronger in mixtures with linear polyethers than in those with monoethers.V Em data show the existence of free volume effects in solutions including methanol or These effects  ethanol.  E become more important for large n values, which is supported by values of @V@Tm . The Flory model P has been used to investigate orientational effects in the systems under study. It is shown that orientational effects are relevant in mixtures with methanol or ethanol, and that the behaviour of the remaining systems is close to that of random mixing. Solutions with 3,6-dioxaoctane slightly differ from this trend and are characterized by weak orientational effects. We have also applied the Flory model to 1-alkanol + PEG-250, or +PEG-350 mixtures, which behave similarly to those including linear polyethers. Orientational effects are much stronger in 1-alkanol + linear monoether systems, and are roughly independent of the mixture components. Results obtained in this work are consistent with those obtained previously when applying the Kirkwood–Buff formalism. Ó 2012 Elsevier Ltd. All rights reserved. 1. Introduction Interest on alcohol + ether mixtures is consequence of their wide variety of applications. This type of systems is used as gasoline additives due to their octane-enhancing and pollution reducing properties [1,2]. Solutions of alcohols (refrigerant) with absorbents as polyethers or polyethylene glycols (PEG) have been proposed as working fluids for absorption refrigerant machines in order to improve the cycle machine [3]. Alkanol + ether mixtures are industrially relevant because alkanols are basic components in the synthesis of oxaalkanes and therefore are contained as an impurity. Mixtures of short chain 1-alkanols with linear polyethers are also interesting as can be considered as simple models of the complex systems water + PEG, widely used in biochemical and biomedical processes [4]. From a theoretical point of view, the study of 1-alkanol + ether mixtures is particularly important due to their complexity, related to the partial destruction of the H-bonds between alcohol molecules by the active ether molecules, and to the new ⇑ Corresponding author. Tel.: +34 983 423757; fax: +34 983 423136. E-mail address: jagl@termo.uva.es (J.A. González). 0021-9614/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2012.12.007 OH–O bonds created upon mixing [5,6]. On the other hand, in solutions formed by 1-alkanol and a linear polyether, strong dipole-dipole interactions can be expected. Note the rather high upper critical solution temperatures of the mixtures 2,5,8,11-tetraoxadodecane + dodecane or of 2,5,8,11,14-pentaoxapentadecane + decane (280.81 K and 291,98 K, respectively [7]). This may explain that, in order to attain a better representation of the thermodynamic properties of the 1-propanol + 2,5,8-trioxanonane, or +2,5,8,11-tetraoxadodecane systems by means of the ERAS model [8], these polyethers were treated as self-associated compounds [9]. The present work is part of a general experimental and theoretical investigation on 1-alkanol + linear or cyclic polyether mixtures. Thus, we have provided excess molar volumes, V Em , [10–14] and enthalpies, HEm [15–17] for this type of systems. In addition, we have investigated solutions of methanol, ethanol or 1-propanol with some linear or cyclic polyethers [18] using the Kirkwood–Buff formalism [19]; and 1-alkanol + 1,3-dioxolane, or +1,3-dioxane, or +1,4-dioxane, or +1,3,5-trioxane systems [6] in terms of the DISQUAC [20] and ERAS models. It should be mentioned that we have also developed detailed studies on 1-alkanol + linear or cyclic monoether mixtures using different theories (DISQUAC, ERAS, 196 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 Flory [21] or the Kirkwood–Buff integrals) [5,6,22]. As continuation, we report now densities, speeds of sound, adiabatic compressibilities, and the corresponding excess functions V Em ; uE , and jES , for the methanol, 1-butanol or 1-decanol + 3,6,9-trioxaundecane mixtures over the temperature range (293.15–303.15) K. V Em data at 298.15 K for the methanol or 1-butanol systems are available in the literature [13,23]. The Flory model has also been applied to the investigated solutions in order to gain insight into their interactions and structure. We have already shown that this theory is an appropriate tool for the study of orientational effects in liquid solutions [22,24–27]. 2. Experimental 2.1. Materials 3,6,9-Trioxaundecane (Chromasolv for HPLC P 99%), 1-butanol (Chromasolv plus for HPLC P 99.7%) and 1-decanol (Assay P 99%) were from Sigma Aldrich, and methanol (Assay P 99.8% GC) was from Fluka and used without further purification. The q and u values of the pure liquids are in good agreement with those reported in the literature (table 1). and the error in the final mole fraction is estimated to be less than ±0.0001. Conversion to molar quantities was based on the relative atomic mass Table of 2005 issued by IUPAC [28]. The densities and speeds of sound of both pure liquids and of the mixtures were measured using a vibrating-tube densimeter and sound analyzer, Anton Paar model DSA-5000, automatically thermostated within ±0.01 K. Temperature measurements were taken using a Pt-100, calibrated at the triple point of water (0.01 °C) and at the melting point of gallium (29.7646 °C) according to the ITS-90 scale. The calibration of the densimeter was carried out with deionised double-distilled water, heptane, octane, isooctane, cyclohexane and benzene, using q values from the literature [29–31]. The accuracy for the q and u measurements are ±1  105 g  cm3 and ± 0.1 m  s1, respectively, and the corresponding precisions are ±1  106 g  cm3 and ± 0.01 m  s1. The experimental technique was checked by determining V Em and u of the standard mixtures: cyclohexane + benzene at the temperatures (293.15, 298.15 and 303.15) K and 2-ethoxyethanol + heptane at 298.15 K. Our results agree well with published values [32–35]. The accuracy in V Em is believed to be less than ð0:01 V Em; max þ 0:005Þ cm3  mol , where 1 V Em; max denotes the maximum experimental value of the excess 2.2. Apparatus and procedure Binary mixtures were prepared by mass in small vessels of about 10 cm3. Caution was taken to prevent evaporation, molar volume with respect to the mole fraction. The accuracies of uE and jES are estimated to be 0.015  juEj and 0:02  jES , respectively. TABLE 1 Physical propertiesa of pure compounds at temperature T and atmospheric pressure: q, density; u, speed of sound; aP, isobaric thermal expansion coefficient; jS, adiabatic compressibility; jT, isothermal compressibility; and CP, isobaric heat capacity. Property T/K Exp. Lit. Exp. Lit. Exp. Lit. Exp. Lit. q/g  cm3 293.15 0.79155 0.80989 0.80956b 0.82995 0.9063b 0.78720 0.80647 0.80575b 0.8064g 0.82695 0.8302c 0.83028e 0.82698e 0.8268c 0.90673 298.15 0.90288 303.15 0.78244 0.80222 0.80196b 0.8023g 0.82315 0.82285j 0.89722 0.90150b 0.90281h 0.9033i 0.8966b 293.15 298.15 303.15 298.15 1118 1101.4 1086.6 1.16 0.78172b 0.7915d 0.78637b 0.78720f 0.7868g 0.78172b 0.78248d 0.7820d 1119k 1102k 1086k 1.196b 1256.2 1239.6 1223.8 0.95 1257 k 1241k 1224k 0.948b 1397.1 1380.3 1364.1 0.82 293.15 298.15 303.15 298.15 1010.7 1047.3 1082.5 1246.7 1009k 1047k 1083k 1248b 782.4 806.9 832.2 947 782k 806k 832k 942b 617 635 653 738 u/m  s1 aP/103  K1 jS/TPa1 jT/TPa 1 CP/J  mol1  K1 a Methanol 81.47b 298.15 Uncertainties, e, are: e(q) = ±0.01 kg  m Reference [29]. Reference [99]. d Reference [100]. e Reference [101]. f Reference [102]. g Reference [103]. h Reference [10]. i Reference [104]. j Reference [105]. k Reference [106]. l Reference [107]. m Reference [108]. n Reference [109]. o Reference [110]. p Reference [5]. q Reference [111]. r Reference [112]. b c 1-Butanol ; e(u) = ±0.1 m  s 3 1-Decanol 177.07b 3,6,9-Trioxaundecane 1380.0 j 1364.5j 0.843m 0.819n 635.1j 654.2j 740.9p 1259.4 1239.9 1221.8 1.05 694.9 720.5 746.2 891.4 372.98r ; e(aP) = ±0.025  aP; e(jS) = ±0.0002  jS; e(jT) = ±0.012  jT; and for pressure, e(P) = ±0.1 kPa. 1 1241.9l 1.077l 1.07o 720 900q 897m 347.5 i 197 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 their V Em value for the methanol system is 9% higher than that provided here (figure 1). 3. Experimental results 3.1. Equations The thermodynamic properties for which values are derived most directly from the experimental measurements are the density, q, the molar volume, V, and the isentropic compressibility, jS. Values of aP (isobaric thermal expansion coefficient) for pure compounds were obtained from a linear dependence of q with T. Assuming that the absorption of the acoustic wave is negligible, jS can be calculated using the Newton-Laplace’s equation: jS ¼ 1 qu2 ð1Þ : For an ideal mixture at the same temperature and pressure than the system under study, the values Fid of the thermodynamic property, F, are calculated using the equations [32,36,37]: F id ¼ x1 F 1 þ x2 F 2 ðF ¼ V; C P Þ; ð2Þ and F id ¼ /1 F 1 þ /2 F 2 ðF ¼ aP ; jT Þ; ð3Þ xi V i V id where Cp is the isobaric heat capacity, /i ¼ the volume fraction, jT, the isothermal compressibility, and Fi, the F value of component i, respectively. For jS and u, the ideal values are calculated according to [36,37]: jidS ¼ jidT  TV id aid2 P C id P ; ð4Þ and uid ¼  1 id id S q j 1=2 ; ð5Þ where qid = (x1M1 + x2M2)/Vid (Mi, molecular mass of the i component). In this work, we have determined the excess functions: F E ¼ F  F id ; ð6Þ 3.2. Experimental results Table 2 lists values of densities, calculated V Em and of u vs. x1, the mole fraction of the 1-alkanol. Table 3 contains the derived quantities jES and uE. The data were fitted by unweighted least-squares polynomial regression to the equation: ð7Þ i¼0 where F stands for the properties cited above. The number of coefficients k used in Eq. (7) for each mixture was determined by applying an F-test [38] at the 99% confidence level. Table 4 lists the parameters Ai obtained in the regression, together with the standard deviations r, defined by: rðF E Þ ¼ 2 1=2 1 X E ; F cal  F Eexp Nk  4.1. Flory model The main hypotheses of the theory are the following [21,39– 42]. (i) Molecules are divided into segments, which are arbitrarily chosen isomeric portions of the molecule. (ii) The mean intermolecular energy per contact is proportional to g/vs (where g is a positive constant which characterizes the energy of interaction for a pair of neighbouring sites and vs is the segment volume). (iii) When stating the configurational partition function, the number of external degrees of freedom of the segments is considered to be lower than 3. This is necessary to take into account restrictions on the precise location of a given segment by its neighbours in the same chain. (iv) Random mixing is assumed. The probability of having species of kind i neighbours to any given site is equal to hi, the site fraction. In the case of very large total number of contact sites, the probability of formation of an interaction between contacts sites belonging to different liquids is h1h2. Under these hypotheses, the Flory equation of state is given by: PV V 1=3 1 ¼  ; T V 1=3  1 VT ð9Þ where V ¼ V=V  ; P ¼ P=P  and T ¼ T=T  are the reduced volume, pressure and temperature, respectively. Eq. (9) is valid for pure liquids and liquid mixtures. For pure liquids, the reduction parameters, V i , P i and T i are obtained from aPi and jTi data. The corresponding expressions for reduction parameters for mixtures are given elsewhere [25]. HEm is determined from HEm ¼ x1 V 1 h2 X 12 V þ x1 V 1 P1  1 V1  1 V  þ x2 V 2 P 2  1 V2  ð8Þ where N is the number of direct experimental values. Results on V Em and jES are shown graphically in figures 1 and 2. The present V Em data for the methanol solution at 298.15 K are in good agreement with those previously measured in our laboratory [13] (figure 1). For the 1-butanol mixture, our V Em data are also in good agreement with those reported by Pal and Kumar [23]. However, at x1 = 0.5, 1 V  : ð10Þ All the symbols have their usual meaning [25] The reduced volume of the mixture, V, in Eq. (10) is obtained from the equation of state. Therefore, the molar excess volume can be also calculated:
V Em ¼ x1 V 1 þ x2 V 2 ðV  u1 V 1  u2 V 2 Þ: for F = V, jS and u. k1 X F E ¼ x1 ð1  x1 Þ Ai ð2x1  1Þi ; 4. Theory ð11Þ 4.1.1. Estimation of the Flory interaction parameter X12 is determined from a HEm measurement at given composition from the equation [22,24,25]: X 12 ¼     x1 P1 V 1 1  TT1 þ x2 P2 V 2 1  TT2 x1 V 1 h2 ð12Þ ; For the application of this expression, it must be noted that VT is a function of HEm : HEm ¼ x1 P1 V 1 V1 þ x2 P2 V 2 V2 þ 1 VT x1 P1 V 1 T 1 þ x2 P2 V 2 T 2
ð13Þ and that from the equation of state, V ¼ VðTÞ. More details have been given elsewhere [22,24,25]. Eq. (12) is generalization of that previously given to calculate X12 from HEm at x1 = 0.5 [43]. Properties of the pure compounds at 298.15 K, molar volumes, aPi and jTi, and the corresponding reduction parameters, Pi and V i ði ¼ 1; 2Þ, needed for calculations are listed in table 5. X12 values determined from experimental HEm data at x1 = 0.5 are collected in table 6. 5. Theoretical results Results on HEm and V Em obtained from the Flory model using X12 values at x1 = 0.5 are listed in tables 6 and 7, respectively. 198 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 2 Densities, q, molar excess volumes, V mE , and speeds of sound for 1-alkanol(1) + 3,6,9-trioxaundecane(2) mixtures at temperature T and atmospheric pressure.a x1 q/g  cm3 V Em =cm3  mol 0.1141 0.1553 0.1987 0.2490 0.2972 0.3651 0.3841 0.4206 0.4696 0.5133 0.90490 0.90405 0.90307 0.90179 0.90038 0.89801 0.89727 0.89572 0.89332 0.89089 0.2584 0.3334 0.4122 0.4958 0.5674 0.6493 0.6697 0.7054 0.7407 0.7679 0.1296 0.1589 0.1917 0.2627 0.2904 0.3505 0.3925 0.4241 0.4639 0.5181 0.90000 0.89940 0.89867 0.89683 0.89602 0.89401 0.89241 0.89101 0.88909 0.88601 0.1058 0.1571 0.1991 0.2309 0.2886 0.3249 0.3748 0.4216 0.4730 0.5164 u/m  s1 q/g  cm3 V Em =cm3  mol u/m  s1 Methanol(1) + 3,6,9-trioxaundecane(2); T = 293.15 K 1259.4 0.5624 0.88761 1259.4 0.6126 0.88369 1259.2 0.6545 0.87981 1258.6 0.6980 0.87507 1257.7 0.7575 0.86711 1255.9 0.8037 0.85925 1255.2 0.8469 0.85024 1253.7 0.9023 0.83503 1251.3 0.9467 0.81874 1248.6 0.7774 0.7781 0.7666 0.7421 0.6891 0.6228 0.5461 0.4015 0.2485 1244.7 1240.0 1235.1 1229.0 1218.6 1208.1 1196.0 1175.4 1153.6 0.2671 0.3254 0.3878 0.5042 0.5472 0.6274 0.6773 0.7034 0.7353 0.7625 Methanol(1) + 3,6,9-trioxaundecane(2); T = 298.15 K 1240.0 0.5637 0.88297 1239.9 0.6132 0.87912 1239.7 0.6207 0.87844 1239.0 0.6959 0.87083 1238.5 0.7434 0.86468 1237.1 0.8007 0.85537 1235.8 0.8481 0.84546 1234.4 0.9005 0.83108 1232.6 0.9476 0.81397 1229.3 0.7749 0.7791 0.7754 0.7465 0.7062 0.6336 0.5437 0.4029 0.2457 1225.8 1221.2 1220.4 1210.9 1203.0 1190.8 1177.7 1158.6 1135.9 0.89527 0.89427 0.89331 0.89258 0.89089 0.88971 0.88788 0.88591 0.88340 0.88090 0.1943 0.3005 0.3783 0.4440 0.5250 0.5737 0.6323 0.6809 0.7225 0.7441 Methanol(1) + 3,6,9-trioxaundecane(2); T = 303.15 K 1221.5 0.5681 0.87747 1221.5 0.6092 0.87433 1221.4 0.6548 0.87007 1220.9 0.6984 0.86535 1220.4 0.7448 0.85928 1219.5 0.8012 0.84999 1218.2 0.8484 0.84019 1216.5 0.9007 0.82594 1214.1 0.9489 0.80825 1211.5 0.7616 0.7724 0.7530 0.7313 0.6902 0.6103 0.5274 0.3922 0.2244 1207.7 1204.1 1199.0 1193.3 1185.6 1173.9 1161.1 1142.6 1119.6 0.1284 0.2205 0.3190 0.3623 0.4157 0.4529 0.4963 0.5481 0.6523 0.7018 0.90130 0.89611 0.88985 0.88686 0.88292 0.87996 0.87635 0.87171 0.86130 0.85573 0.0785 0.1330 0.1774 0.1943 0.2115 0.2145 0.2193 0.2196 0.2134 0.2018 1-Butanol(1) + 3,6,9-trioxaundecane(2); T = 293.15 K 1262.2 0.7934 0.84415 1263.3 0.8942 0.82914 1264.1 0.9397 0.82136 1264.3 1264.5 1264.4 1264.4 1264.3 1263.6 1263.3 0.1654 0.1069 0.0689 1262.1 1260.2 1258.9 0.1245 0.2149 0.3175 0.4078 0.4543 0.5047 0.5543 0.6137 0.6973 0.7951 0.89677 0.89176 0.88538 0.87900 0.87540 0.87125 0.86684 0.86113 0.85218 0.84007 0.0789 0.1285 0.1754 0.2015 0.2109 0.2177 0.2191 0.2151 0.2028 0.1697 1-Butanol(1) + 3,6,9-trioxaundecane(2); T = 298.15 K 1242.5 0.8466 0.83280 1243.8 0.9449 0.81686 1244.9 1245.5 1245.6 1245.7 1245.7 1245.5 1245.3 1244.5 0.1407 0.0621 1243.9 1241.7 0.0738 0.1419 0.2180 0.3020 0.3764 0.5002 0.5541 0.6056 0.6997 0.7961 0.89447 0.89096 0.88673 0.88157 0.87651 0.86690 0.86216 0.85729 0.84732 0.83544 0.0445 0.0826 0.1235 0.1606 0.1862 0.2101 0.2115 0.2118 0.1974 0.1667 1-Butanol(1) + 3,6,9-trioxaundecane(2); T = 303.15 K 1223.5 0.8493 0.82796 1224.8 0.8896 0.82180 1225.9 0.9431 0.81286 1227.0 1227.7 1228.3 1228.4 1228.5 1228.4 1227.9 0.1363 0.1093 0.0655 1227.4 1226.8 1225.8 0.0632 0.1084 0.2052 0.2940 0.90186 0.89794 0.88979 0.88249 0.0739 0.1195 0.1859 0.2288 1-Decanol(1) + 3,6,9-trioxaundecane(2); T = 293.15 K 1267.1 0.7863 0.84492 1272.6 0.8872 0.83776 1284.5 0.9441 0.83382 1295.5 0.1696 0.0987 0.0455 1363.0 1378.8 1388.1 1 x1 1 199 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 2 (continued) x1 q/g  cm3 V Em =cm3  mol 0.3930 0.4943 0.5430 0.5932 0.6872 0.87457 0.86666 0.86292 0.85911 0.85212 0.2528 0.2602 0.2571 0.2496 0.2206 0.0605 0.1110 0.1588 0.2062 0.3020 0.3947 0.5040 0.5920 0.6553 0.89798 0.89368 0.88969 0.88579 0.87808 0.87077 0.86239 0.85580 0.85116 0.0715 0.1206 0.1572 0.1862 0.2269 0.2520 0.2544 0.2408 0.2199 u/m  s1 q/g  cm3 x1 V Em =cm3  mol 1-Decanol(1) + 3,6,9-trioxaundecane(2); T = 298.15 K 1247.8 0.7443 0.84472 1254.1 0.7923 0.84132 1260.1 0.8362 0.83823 1266.1 0.8836 0.83493 1278.3 0.9400 0.83105 1290.4 1305.0 1317.3 1326.4 0.89300 0.88954 0.88523 0.88099 0.87394 0.86702 0.85829 0.85560 0.84746 Experimental and theoretical values for HEm are compared graphically in figures 3–7. For the sake of clarity, Table 6 also includes the relative standard deviations for HEm defined as 2 !2 31=2 E E   X H  H 1 m; exp m;calc 5 ; rr HEm ¼ 4 N HEm; exp ð14Þ where N (=19) is the number of data points, and HEm; exp stands for the smoothed HEm values calculated at Dx1 = 0.05 in the composition range [0.05, 0.95] from polynomial expansions given in the original works. In order to obtain detailed information on the concentration dependence of X12, this magnitude has been determined using Eq. (12) and the mentioned HEm; exp values at Dx1 = 0.05. The X12(x1) variation is estimated from the equation: Di ¼ jDX 12 jmax i ; jX 12 ðx1 ¼ 0:5Þj u/m  s1 1 1308.1 1321.4 1327.9 1334.7 1348.1 1-Decanol(1) + 3,6,9-trioxaundecane(2); T = 303.15 K 0.0715 1229.6 0.7409 0.84090 0.1076 1234.8 0.7915 0.83736 0.1487 1241.6 0.8318 0.83456 0.1823 1248.3 0.8856 0.83089 0.2218 1260.0 0.9364 0.82744 0.2442 1271.7 0.2455 1287.6 0.2421 1292.7 0.2177 1308.7   1 E E Uncertainties, e, are: eðx1 Þ ¼ 0:0001; e V m ¼ 0:01 V m; max þ 0:005 cm3  mol ; eðuÞ ¼ 0:1 m  s1 ; eðPÞ ¼ 0:1 kPa. 0.0605 0.1016 0.1540 0.2064 0.2953 0.3846 0.5006 0.5369 0.6486 a 1 ð15Þ where jDX 12 jmax is the maximum absolute value of the X12(x1)  X12 i (x1 = 0.5) difference in the ranges [0.05,0.45] (i = 1) and [0.55,0.95] (i = 2). The corresponding values are listed in table 8 (see also figure 8). 6. Discussion Hereafter, we are referring to thermodynamic properties at equimolar composition and T = 298.15 K. 6.1. Calorimetric data For a deeper understanding of the interactions and structure of 1-alkanol + linear polyether mixtures, we must start showing a brief summary of the main features of 1-alkanol + alkane, or +linear monoether systems [5]. In the case of solutions with a given monoether, HEm increases from methanol to ethanol or 1-propanol and then smoothly decreases. This variation is similar to that observed for 1-alkanol + fixed n-alkane mixtures. In addition, the HEm curves are skewed towards low mole fractions of the alcohol 0.1845 0.1555 0.1285 0.0940 0.0483 1339.5 1347.0 1353.8 1361.4 1370.4 0.1783 0.1502 0.1283 0.0871 0.0494 1322.6 1330.4 1336.7 1345.4 1353.5 in both types of mixtures, and their C Ep;m values are high and posi1 tive. For example, C Ep;m =J  mol  K1 ¼ 11:7 for ethanol + heptane [44], and 7.2 for ethanol + methyl butyl ether [45]. All these features point out that self-association of the1-alkanol plays an  important role in such solutions. However, TSEm ¼ HEm  GEm values of 1-alkanol + alkane, or +linear monooxalkane largely differ. Thus, for the 1-propanol + hexane system, GEm ¼ 1295 [46], HEm ¼ 533 [47] and TSEm ¼ 762 (all values in J  mol1), while for the 1-propanol + dipropyl ether solution, GEm ¼ 840 [48], HEm ¼ 714 [48] and TSEm ¼ 74 (values also in J  mol1). The much higher TSEm values and the lower C Ep;m values of monoether systems reveal the existence of dipolar interactions in such solutions [5]. On the other hand,HEm (monoether) > HEm (alkane), which indicates that linear monoethers are more active molecules when breaking the alcohol self-association [5]. For mixtures with a given linear polyether, HEm increases with the chain length of the 1-alkanol (table 6, figures 3–7), C Ep;m values are lower than for solutions with alkanes or linear monoethers (C Ep;m ¼ 4:4 J  mol 1  K1 for 1-propanol + 2,5,8- TSEm trioxanonane [45]), and values are rather high and positive, although they strongly depend on the alcohol and ether sizes. For systems containing 2,5,8-trioxanonane, GEm ð308:15 KÞ=J  mol 1 [49]; HEm =J 1  mol ¼ 283 (methanol) and 313 (1-propanol) ¼ 440 (methanol) and 1214 (1-propanol) [50]. Therefore, TSEm =J  mol  157 (methanol) and 901 (1-propanol). For the methanol + 2,5,8,11-tetraoxadodecane system, 1 GEm ð303:15 KÞ ¼ 59 J  mol TSEm 1 [51]; HEm ¼ 581 J  mol 1 [52] and 1  522 J  mol . Such features show that dipolar interactions are very important in this type of solutions, and that their contribution to HEm increases with the alcohol size. If 2,5-dioxahex- ane solutions are considered, the HEm curve is shifted to lower mole fractions of methanol, while for mixtures with the remainder 1-alkanols, the corresponding HEm curves are nearly symmetrical [15] (figure 3, see also figures 4 and 5). That is, association effects are more relevant in the methanol system. 200 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 3 Excess speeds of sound, uE, and excess adiabatic compressibilities, jES , of 1-alcohol(1) + 3,6,9-trioxaundecane(2) mixtures at 298.15 K and atmospheric pressurea . x1 uE/m  s1 0.1296 0.1589 0.1917 0.2627 0.2904 0.3505 0.3925 0.4241 0.4639 0.5181 0.5637 0.6132 0.6207 0.6959 0.7434 0.8007 0.8481 0.9005 0.9476 Methanol(1) + 3,6,9-trioxaundecane(2) 7.2 8.7 10.5 14.3 15.7 18.7 20.8 22.2 24.1 26.3 28.0 29.7 29.8 31.4 31.7 30.8 28.5 23.3 15.3 0.1245 0.2149 0.3175 0.4078 0.4543 0.5047 0.5543 0.6137 0.6973 0.7951 0.8466 0.9449 1-Butanol(1) + 3,6,9-trioxaundecane(2) 3.1 4.8 6.4 7.4 7.7 8.0 8.1 8.1 7.9 6.9 6.0 3.0 0.0605 0.1110 0.1588 0.2062 0.3020 0.3947 0.5040 0.5920 0.6553 0.6922 0.7443 0.7923 0.8362 0.8836 0.9400 1-Decanol(1) + 3,6,9-trioxaundecane(2) 0.3 0.6 0.8 1.1 1.6 2.2 2.6 2.8 2.7 2.6 2.5 2.1 1.8 1.3 0.7 jES =TPa1 TABLE 4 Coefficients Ai and standard deviations, r (FE) (Eq. 8) for representation of the F E a property at temperature T and atmospheric pressure for 1-alcohol(1) + 3,6,9-trioxaundecane(2) systems by Eq. (7). 9.63 11.80 14.28 19.64 21.73 26.25 29.50 31.75 34.76 38.59 41.70 45.10 45.47 49.72 51.70 52.51 50.79 44.20 31.22 3.95 6.27 8.43 9.83 10.36 10.79 11.07 11.09 10.99 9.84 8.62 4.31 T/K Property FE 293.15 V Em 298.15 303.15 293.15 298.15 303.15 293.15 298.15 303.15 a b V Em uE jES V Em V Em V Em uE jES V Em V Em V Em uE jES V Em A0 A1 A2 A3 Mehanol(1) + 3,6,9-trioxaundecane(2) 3.036 0.95 0.45 0.48 A4 0.55 r(FE)b 0.002 0.002 3.017 0.98 0.61 0.66 102.5 150.2 80.2 134 60 100 70  183 2.956 1.03 0.44 0.58 0.005 1-Butanol(1) + 3,6,9-trioxaundecane(2) 0.881 0.14 0.04 0.24 0.002 50 190 0.085 0.48 0.001 0.866 0.178 0.093 0.15 31.87 42.98 8.1 14.4 8.7 13 10.1  15 0.838 0.199 0.09 0.16 0.001 1-Decanol(1) + 3,6,9-trioxaundecane(2) 1.043 0.06 0.08 0.18 0.002 6 9 0.03 0.04 1.017 0.12 0.07 0.12 0.001 10.38 14.15 6.5 4.7 1.8 2.1 3.6 4 0.03 0.03 0.989 0.13 0.07 0.11 0.002 F E ¼ V Em , units: cm3  mol1; FE = uE, units: m  s1; F E ¼ jES , units: TPa1. units are the same that for FE. 0.68 1.17 1.53 1.90 2.64 3.25 3.65 3.67 3.50 3.36 3.06 2.57 2.13 1.51 0.85
E Uncertainties, e, are: e(x1) = ±0.0001; eðuE Þ ¼ 0:015  juE j; e jS ¼ 0:02  jES ; eðPÞ ¼ 0:1 kPa. a Interestingly, for mixtures with a fixed 1-alkanol, the HEm variation with the selected solvent (alkane, linear mono or polyether) depends on the alcohol considered. In the case of methanol solutions, HEm ðlinear monoetherÞ > HEm (linear polyether). Thus, 1 HEm =J  mol ¼ 445 (diethyl ether [50]); 338 (2,5-dioxahexane [15]); 609 (dipropyl ether [53]); 440 (2,5,8-trioxanonane [50]); 788 (dibutyl ether) [54]; 344 (3,6-dioxaoctane [50]). For mixtures including the remainder 1-alkanols, HEm increases in the sequence: alkane < linear monoether < linear polyether. For 1-propanol solutions: 685 (octane) [55] < 864 (dibutyl ether) [54] < 1123 (3,6,9-trioxaundecane [16]) (all values in J  mol1). The lower HEm values of methanol + linear polyether mixtures reveal the existence of strong interactions between unlike molecules (see below), which may also explain, at least partially, the rather large and negative V Em values of these systems (table 7). It is remarkable that HEm of mixtures formed by a given 1-alkanol and CH3–O–(CH2CH2O)nCH3 FIGURE 1. V Em at 298.15 K and atmospheric pressure for 1-alkanol(1) + 3,6,9trioxaundecane(2) mixtures. Symbols: experimental results: () (this work); (j) [13], (O) [23], methanol; (.), (this work), (h) [23], 1-butanol; (), 1-decanol (this work). Full lines, results from Redlich–Kister expansions using parameters listed in table 4. increases with n. In the case of 1-propanol mixtures, 1 HEm =J  mol ¼ 1040 ðn ¼ 1Þ [15] < 1214 (n = 2) [50] < 1401 (n = 3) [8] < 1514 (n = 4) [56]. In addition, the HEm curves become shifted to higher concentrations of the alcohol for increased n values (figures 3–7). Therefore, one can conclude that the ability of polyethers to disrupt the alcohol self-association increases with n. Dielectric measurements support this conclusion [57]. Let’s now evaluate the enthalpy of the OH–O interactions in 1alkanol + linear polyether mixtures. The starting equation is [5,58– 61]: 201 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 molar enthalpy at infinite dilution of the first component) of 1-alkanol or ether + heptane systems. So, E;1 DHOHO ¼ HE;1 m1 ð1  alkanol þ linear polyetherÞ  H m1 ð1  alkanol þ heptaneÞ  HE;1 m1 ðlinear polyether þ heptaneÞ FIGURE 2. jES at 298.15 K and atmospheric pressure for 1-alkanol(1) + 3,6,9trioxaundecane(2) mixtures. Symbols: experimental results (this work): (), methanol; (j), 1-butanol; (N), 1-decanol. Full lines, results from Redlich–Kister expansions using parameters listed in table 4. HEm ¼ DHOHOH þ DHOO þ DHOHO ð16Þ which merely expresses that, neglecting structural effects [62,63], HEm is the result of three contributions: two of them DHOHOH,DHOO, are positive and are related to the breaking of alkanol-alkanol and ether-ether interactions upon mixing, respectively; DHOHO is a negative contribution due to the new OH–O interactions created during the mixing process. Eq. (16) may be extended to x1 ? 0 [5,61,64] to evaluate DHOHO, the enthalpy of the H-bonds between 1-alkanols and linear polyethers in the studied solutions. In such case, DHOHOH and DHOO can be replaced by HE;1 m1 (partial excess ð17Þ This is a rough estimation of DHOHO due to: (i) HE;1 m1 data used were calculated from HEm measurements over the entire mole fraction range. (ii) For 1-alkanol + n-alkane systems, it was assumed that HE;1 m1 is independent of the alcohol, a common approach when applying association theories [8,65–68]. We have used in this work 1 [69–71]. From inspection of DHOH-O results HE;1 m1 ¼ 23:2 kJ  mol collected in table 9, some interesting conclusions can be stated. (i) For a given polyether, DHOHO slightly increases with the 1-alkanol size, that is, interactions between unlike molecules become weaker, probably because the OH group is more sterically hindered in longer 1-alkanols. The contribution to HEm from the breaking of the etherether interactions increases with the aliphatic surface of the alcohol, as HEm of polyether + n-alkane mixtures also increases with the chain length of the alkane. The HEm values of solutions involving 2,5,8,11tetraoxadodecane are (in J  mol1) [72]: 1704 (heptane) < 1877 (octane) < 2110 (decane) < 2214 (dodecane). This may explain the observed HEm increase, much steeper when replacing methanol by ethanol, than when this alcohol is replaced by 1-propanol (table 6; figures 3, 5, 7). (ii) In the case of mixtures containing the same 1-alkanol and 2,5-dioxahexane or 3,6-dioxaoctane, no meaningful difference is encountered between the corresponding DHOHO values. However, HEm (2,5-dioxahexane) > HEm (3,6-dioxaoctane) (table 6), which is due to a higher DHOO term in the case of 2,5-dioxahexane solution, i.e., to a higher positive contribution to HEm from the breaking of the ether-ether interactions.Note that HE;1 m1 (2,5-dioxahexane + heptane) = 5.48 kJ  mol1 [73] > HE;1 (3,6-dioxaoctane + m1 heptane) = 4.53 kJ  mol1 [74].The same behaviour is expected for mixtures with 2,5,8-trioxanonane, or 3,6,9-trioxaundecane.(iii) The increase of n in the ether when is mixed with a certain 1-alkanol leads to lower DHOHO values, that is, to stronger interactions between unlike molecules.However, HEm increases in the opposite sequence (see above).This variation is parallel to that of DHOO (table 9).In fact, for CH3-O-(CH2CH2O)nCH3 + heptane mixtures, TABLE 5 Flory parametersa of pure compounds at T = 298.15 K and atmospheric pressure. a b c d e f g h Compound Vi/cm3  mol1 ap/103  K1 jT/TPa1 V i =cm3  mol Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Octanol 1-Nonanol 1-Decanol 2,5-Dioxahexane 3,6-Dioxaoctane 2,5,8-Trioxanonane 3,6.9-Trioxaundecane 2,5,8,11-Tetraoxadodecane 2,5,8,11,14-Pentaoxapentadecane 40.75b 58.69b 75.16b 91.98c 108.68c 125.31c 141.89d 158.48d 174.97e 191.58d 104.34b 141.33g 142.93f 179.68h 181.72f 221.02f 1.196b 1.096b 1.004b 0.9493c 0.9090c 0.8805c 0.8599d 0.8442d 0.8398e 0.8272d 1.268f 1.225g 1.060f 1.05h 0.965f 0.921f 1248b 1153b 1026b 949.2c 886.5c 842.3c 808.6d 780.9d 752e 740.9d 1114.5f 1140.5g 821.6f 891.4h 707.1f 589.6f 31.67 46.32 60.20 74.34 88.45 102.33 116.47 130.45 144.14 158.18 80.25 109.38 118.25 142.84 146.49 179.51 1 P i =J  cm3 472.9 454.9 454.8 456.4 461.6 465.9 470.6 475.7 490.6 488.3 573.4 534.6 610.6 555.7 626.1 706.1 Vi, molar volume, ap, isobaric thermal expansion coefficient; jT, isothermal compressibility; V i , reduction parameter for volume and P i , reduction parameter for pressure. Reference [29]. Reference [92]. Reference [5]. Reference [113]. Reference [114]. Reference [87]. [This work]. 202 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 6 Molar excess enthalpies, HEm at 298.15 K, atmospheric pressure and equimolar composition for 1-alkanol(1) + polyether(2) systems. The interaction parameters, X12, calculated from HEm at equimolar composition are also included. 1-Alkanol HEm =J  mol X12/J  cm3  rr HEm  a Reference Polyether: 2,5-dioxahexane 31.02 55.74 60.40 57.70 59.44 57.38 55.62 55.15 54.62 53.91 0.963 0.172 0.070 0.055 0.033 0.019 0.020 0.027 0.028 0.022 15 15 15 9 15 15 15 15 15 15 Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 344 742 870 842 877 941 Polyether: 3,6-dioxaoctane 29.55 47.60 46.31 38.9 36.22 35.35 0.370 0.419 0.206 0.121 0.084 0.116 50 50 50 115 115 115 Methanol Ethanol 1-Propanol 1-Heptanol 440 962 1214 1222 1624 Polyether: 2,5,8-trioxanonane 38.03 0.626 61.54 0.140 63.91 0.062 64.33 0.024 54.51 0.043 50 50 50 9 50 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol 1123 1254 1312 1406 1475 1636 Polyether: 3,6,9-trioxaundecane 55.82 0.102 53.36 0.053 49.36 0.035 47.80 0.072 45.99 0.007 44.31 0.016 16 16 16 17 16 16 1-Propanol Polyether: 2,5,8,11-tetraoxadodecane 1401 69.50 0.0156 9 Methanol 1-Propanol 1-Butanol 1-Pentanol Polyether: 2,5,8,11,14-pentaoxapentadecane 581 47.20 0.356 1597 75.92 0.028 1853 74.81 0.026 1986 70.37 0.063 52 56 56 56 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Octanol 1-Nonanol 1-Alkanol HE;1 ¼ 5:48ðn ¼ 1Þ [73] < 8.16 (n = 2) [75] < 10.84 (n = 3) m;1 =kJ  mol [72] < 13.33 (n = 4) [76].Consequently, HEm of polyether + heptane mixtures also increases with n:1285 (n = 1) [73] < 1621 (n = 2) [75] < 1704 (n = 3) [72] < 1897 (n = 4) [76] (values in J  mol1).Interestingly, these values seem to be slightly higher than those of1-hexanol + CH3–O–(CH2CH2O)nCH3 mixtures (table 6), which suggests the importance of dipolar interactions in solutions including longer 1-alkanols. Experimental work is undertaken to investigate carefully this point. On the other hand, alcohol–oxaalkane interactions are stronger in mixtures with linear polyethers than in systems with linear monoethers. For example, DHOHO/kJ  mol1 = 21.1 and 16.40 for the methanol + diethyl ether, or 1-propanol + dibutyl ether mixtures, respectively [5]. 1 Flory 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol Polyether:2,5-dioxahexane 0.499 0.314 0.481 0.194 0.783 0.197 0.068 1.020 0.071 0.067 0.069 0.014 1.139 0.064 1.188 0.113 1.226 0.168 1.250 0.278 1.216 13 116 13 23 10 117 116 9 23 116 12 14 14 Methanol Ethanol 1-Propanol 1-Hexanol 1-Nonanol Polyether: 3,6-dioxaoctane 0.717 0.305 0.433 0.697 0.385 0.825 0.303 0.825 0.183 13 13 10 12 14 Polyether: 2,5,8-trioxanonane 0.611 0.212 0.542 0.258 0.642 0.223 0.068 0.909 0.067 0.138 0.268 0.369 1.322 0.559 13 23 13 23 10 9 23 12 14 14 Methanol Ethanol 1-Propanol Methanol Ethanol Relative standard deviation (Eq. (14)). Reference V Em (0.5)/cm3  mol1 Exp. 338 803 1040 993 1174 1263 1340 1433 1517 1588 Methanol Ethanol 1-Propanol a 1 TABLE 7 Molar excess volumes, V Em at 298.15 K, atmospheric pressure and equimolar composition for 1-alkanol(1) + polyether(2) systems. Comparison of experimental (Exp.) results with Flory calculations using interaction parameters listed in Table 6. 1-Propanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Nonanol 1-Decanol Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol Methanol 6.2. Volumetric data Ethanol For 1-alkanol + given alkane mixtures, it is well known that the different contributions to V Em , such as changes in the alcohol selfassociation, breaking of interactions between like molecules, or structural effects (changes in free volume, or interstitial accommodation) are sensitive to the lengths of the mixture components 1-Propanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol Polyether: 3,6,9-trioxaundecane 0.754 0.686 0.769 0.430 0.397 0.304 0.857 0.324 0.216 0.989 0.209 0.149 1.046 0.0283 1.116 0.178 0.254 this work 23 13 13 23 10 94 this work 23 23 12 14 this work Polyether: 5,8,11-trioxapentadecane 0.683 0.661 0.415 0.419 0.352 0.364 0.276 0.239 0.233 0.188 0.078 13 116 13 23 10 116 23 116 12 14 14 Polyether: 2,5,8,11-tetraoxadodecane 0.718 0.655 0.351 0.337 0.199 0.821 0.120 0.142 0.311 0.430 0.668 13 23 13 23 117 9 23 12 14 14 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 203 TABLE 7 (continued) 1-Alkanol Exp. Methanol Ethanol 1-Hexanol 1-Heptanol 1-Nonanol Reference V Em (0.5)/cm3  mol1 Flory Polyether: 2,5,8,11,14-pentaoxapentadecane 0.797 0.004 0.426 0.308 0.453 0.723 13 13 12 14 14 FIGURE 5. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + 2,5,8trioxanonane(2) mixtures. Symbols: experimental results: (), methanol [50]; (j), ethanol [50]; (N), 1-propanol [9]; (.), 1-heptanol [50]. Solid lines, results from the Flory model using interaction parameters listed in table 6. FIGURE 3. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + 2,5-dioxahexane(2) mixtures. Symbols: experimental results: (), methanol [15]; (j), 1propanol [9]; (N), 1-pentanol [15]; (.), 1-heptanol [15]; (), 1-nonanol [15]. Solid lines, results from the Flory model using interaction parameters listed in table 6. FIGURE 6. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + 3,6,9trioxaundecane(2) mixtures. Symbols: experimental results [16]: (), 1-propanol; (j), 1-pentanol; (N), 1-heptanol; (.), 1-nonanol. Solid lines, results from the Flory model using interaction parameters listed in table 6. FIGURE 4. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + 3,6dioxaoctane(2) mixtures. Symbols: experimental results: (), methanol [50]; (j), 1-butanol [115]; (N), 1-hexanol [115]. Solid lines, results from the Flory model using interaction parameters listed in table 6. [77]. Thus, V Em is positive over the whole concentration range when the effects of the disruption of the H-bonds between alcohol molecules and non-specific interactions are predominant over the less significant contribution from structural effects. If the latter are dominant, as for solutions including long chain 1-alkanols and short alkanes, where interstitial accommodation exists, V Em becomes negative [77–79]. The V Em variation of 1-alkanol + fixed linear monoether mixtures is similar to that of the corresponding systems with heptane [5]. For a given alcohol, V Em (heptane) > V Em 204 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 8 Variations of the X12 parameter, Di, or 1-alkanol(1) + polyether(2) mixtures in the concentration ranges [0.05, 0.5] (i = 1) and [0.5,0.95] (i = 2) calculated according to Eq. (25). 1-Alkanol (linear monoether), due to the existence of interactions between unlike molecules, which are stronger in methanol systems. The more negative V Em values for the systems including longer 1-alkanols may be explained in terms of interstitial accommodation of the ether molecules in the alcohol structure [5], as in solutions with heptane occurs. In contrast, V Em increases with the 1-alkanol size in mixtures containing a given polyether (table 7). In such case, V Em is negative for systems with shorter 1-alkanols, and become positive for solutions with longer alcohols (table 7, figure 1). Negative V Em values can be here related to the existence of interactions between unlike molecules. However, free volume effects are also present, particularly for mixtures with methanol or ethanol, as the concentration dependence of V Em reveals. In fact, the V Em curves of such solutions are shifted to higher mole fractions of the alkanol, the smaller mixture component ([13], figure 1). A similar behaviour is encountered in alkane + alkane mixtures [80–83]. It is remarkable that for 1-alkanol + fixed polyether mixtures, V Em and HEm vary similarly with the alkanol size. This means that the observed V Em variation can be ascribed to changes in the interactional effects, essentially a less negative contribution due to the weakening of the alkanol-ether interactions and higher positive contributions to V Em from the breaking of interactions between like molecules, For example, in the case of solutions with 1 2,5,8,11-tetraoxadodecane, V Em =cm3  mol ¼ 0:749 (heptane), 0.976 (octane), 1.281 (decane) [84], 1.477 (dodecane) [85]. Next, V Em of 1-alkanol + CH 3-(CH 2)u1-O-(CH2CH 2O)n(CH 2)u1CH3 mixtures decreases when u increases (n constant) (table 7), which is consistent with a lower positive contribution to V Em from the breaking of the ether-ether interactions (see above). The same behaviour is observed for CH3-(CH2)u1-O-(CH2CH2O)n (CH2)u11 CH3 + heptane mixtures: V Em =cm3  mol ¼ 1:092ðn ¼ u ¼ 1Þ [86], 0.743 (n = 1;u = 2) [87]. The V Em variation with n (u fixed) strongly depends on the 1-alkanol size (table 7). Thus, for systems with methanol or ethanol and D2 Reference 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Octanol 1-Nonanol 15 15 15 9 15 15 15 15 15 15 Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Alkanol + 3,6-dioxaoctane 0.531 0.366 1.307 0.484 0.456 0.257 0.269 0.151 0.240 0.032 0.220 0.066 50 50 50 115 115 115 Methanol Ethanol 1-Propanol FIGURE 7. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + linear polyether(2) mixtures. Symbols: experimental results: (), methanol(1) + 2,5,8,11, 14-pentaoxapentadecane(2) [52]; (j), 1-propanol(1) + 2,5,8,11-tetraoxadodecane(2) [9]; (N), 1-propanol(1) + 2,5,8,11,14-pentaoxapentadecane(2) [56]; (.), 1butanol(1) + 2,5,8,11,14-pentaoxapentadecane(2) [56]; (), 1-pentanol(1) + 2,5,8, 11,14-pentaoxpentadecane(2) [56]. Solid lines, results from the Flory model using interaction parameters listed in table 6. D1 1-Alkanol + 2,5-dioxahexane 0.956 0.759 0.473 0.218 0.195 0.067 0.092 0.086 0.103 0.010 0.036 0.034 0.029 0.032 0.023 0.067 0.024 0.041 0.031 0.041 1-Heptanol 1-Alkanol + 2,5,8-trioxanonane 0.596 0.660 0.285 0.164 0.158 0.034 0.038 0.041 0.057 0.122 50 50 50 9 50 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Heptanol 1-Nonanol 1-Alkanol + 3,6,9-trioxaundecane 0.135 0.154 0.066 0.067 0.038 0.061 0.027 0.011 0.012 0.016 0.027 0.052 16 16 16 17 16 16 1-Propanol 1-Alkanol + 2,5,8,11-tetraoxadodecane 0.043 0.018 9 Methanol 1-Propanol 1-Butanol 1-Pentanol 1-Alkanol + 2,5,8,11,15-pentaoxapentadecane 0.225 0.503 0.038 0.057 0.027 0.067 0.231 0.049 52 56 56 56 methanol ethanol 1-Propanol u ¼ 1; V Em is negative and decreases when n increases, the opposite behaviour to that observed for HEm . This reveals an increase of free volume effects, as it is also noted by the fact that the V Em curves are progressively shifted to higher mole fractions of the alcohol (smaller component) when n increases [13]. For mixtures with longer 1alkanols, say 1-hexanol, V Em is positive and increases with n, as HEm does. Contributions to V Em from interactional effects are here predominant. It is interesting to compare V Em results for systems including the same 1-alkanol and linear mono or polyethers of similar size. For example, V Em (3,6-dioxaoctane)/cm3  mol1 = 0.717 (methanol) [13], 0.303 (1-hexanol) [12]; V Em (2,5,8-trioxanonane)/cm3  mol1 = 0.611 (methanol) [13], 0.268 (1-hexanol) [12]; V Em (dipropyl ether)/cm3  mol1 = 0.339 (methanol) [53], 0.584 (1-hexanol) [88]. The lower V Em values for methanol + polyether mixtures could be ascribed to stronger interactions between unlike molecules, as HEm values are also lower than for solutions with linear monoethers. For longer 1-alkanols, V Em is higher for mixtures with polyethers due to the large positive contribution to V Em from the disruption of the ether-ether interactions. Note that V Em (heptane)/cm3  mol1 = 0.256 (dipropyl ether) [89], 0.743 (3,6dioxaoctane) [87], 0.902 (2,5,8-trioxanonane) [90]. However, an interesting exception is found when comparing V Em values of methanol or ethanol + 2,5-dioxahexane, or +diethyl ether systems. V Em (2,5-dioxahexane)/cm3  mol1 =  0.499 (methanol); 0.194 205 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 9 Partial excess molar enthalpies, HE;1 1 , at T =298.15 K at atmospheric pressure for solute(1) + organic solvent(2) mixtures, and hydrogen bond interaction enthalpy, DHOHO, for 1-alkanol(1) + linear polyether(2) systems. H1E;1 =kJ  mol 2,5-Dioxahexane + heptane 3,6-Dioxaoctane + heptane 2,5,8-Trioxanonane + heptane 3,6,9-Trioxaundecane + heptane 2,5,8,11-Tetraoxadodecane + heptane 2,5,8,11,14Pentaoxapentadecane + heptane Methanol + 2,5-dioxahexane Ethanol + 2,5-dioxahexane 1-Propanol + 2,5-dioxahexane 5.48 [73] 4.53 [74] 8.16 [75] 5.75 [118] 10.84 [72] 13.33 [76] 1-Butanol + 2,5-dioxahexane 1-Pentanol + 2,5-dioxahexane 1-Hexanol + 2,5-dioxahexane 1-Heptanol + 2,5-dioxahexane 1-octanol + 2,5-dioxahexane 1-Nonanol + 2,5-dioxahexane Methanol + 3,6-dioxaoctane Ethanol + 3,6-dioxaoctane 1-Propanol + 3,6-dioxaoctane 1-Butanol + 3,6-dioxaoctane 1-Pentanol + 3,6-dioxaoctane 1-Hexanol + 3,6-dioxaoctane Methanol + 2,5,8-trioxanonane Ethanol + 2,5,8-trioxanonane 1-Propanol + 2,5,8-trioxanonane FIGURE 8. Flory interaction parameters, X12, for 1-alkanol(1) + linear polyether(2) mixtures at 298.15 K. Points, values determined from HEm at different mole fractions (see text): () methanol(1) + 2,5-dioxahexane(2) [15] (j), 1-propanol(1) + 3,6,9trioxaundecane(2) [16]; (N), 1-pentanol(1) + 3,6.9-trioxaundecane(2) [16] Solid lines, X12 values calculated from HEm at x1 = 0.5 (table 6). 1-Heptanol + 2,5,8-trioxanonane 1-Propanol + 3,6,9-trioxaundecane 1-Butanol + 3,6,9-trioxaundecane 1-Pentanol + 3,6,9-trioxaundecane 1-Hexanol + 3,6,9-trioxaundecane 1-Heptanol + 3,6,9-trioxaundecane 1-Nonanol + 3,6,9-trioxaundecane 1-Propanol + 2,5,8,11-tetraoxadodecane Methanol + 2,5,8,11,14pentaoxapentadecane 1-Propanol + 2,5,8,11,14pentaoxapentadecane 1-Butanol + 2,5,8,11,14pentaoxapentadecane 1-Pentanol + 2,5,8,11,14pentaoxapentadecane (ethanol) [13]; V Em (diethyl ether)/cm3  mol1 = 0.788 (methanol), 0.654 (ethanol) [91].  E It is also pertinent to examine the magnitude Ap ¼ @V (table @T p 10). Its sign is the result of the variation in the balance of association/solvation and structural effects with temperature, and depends on the size and shape of the component molecules. For systems with short 1-alkanol and long n-alkane, Ap is positive over the whole concentration range (association effects are dominant). For mixtures of long 1-alkanol and a short n -alkane, Ap shows negative values in the concentration region where interstitial accommodation is important. Similar trends are encountered for 1-alkanol + linear monoether mixtures [5]. For dibutyl ether systems, Ap/cm3  mol1  K1 varies in the order: 0.003 (1-propanol) [11,88] > 0.001 [92] (1-butanol) > 0.0002 [92] (1-pentanol) > 0.0009 [92] (1-hexanol) > 0.002 (1-heptanol) [5] > 0.003 (1octanol) [5] > 0.005 [5] (1-decanol). This clearly remarks that association effects are more relevant for those mixtures including shorter 1-alkanols. In the case of linear polyether + alkane mixtures, Ap is usually positive and decrease with the size of the oxaalkane in such way that for the 2,5,8,11,14-pentaoxapentadecane + heptane or +cyclohexane systems becomes negative [93], as consequence of dominant structural effects. For 1-alkanol + 3,6,9-trioxaundecane mixtures, Ap decreases with the alcohol size: 0.002 (methanol) > 0.0016 (1-propanol) > 0.0011 (1-butanol) > 0.0016 (1-hexanol)  0.0014 (1-decanol) cm 3  mol1  K1 [this work, 11,12,94]. This is probably due to a weakening of association/solvation effects. The higher Ap values of 1-propanol + linear polyether mixtures compared to those of 1-hexanol solutions [10–12] can be explained similarly. For 1-propanol systems, we note that Ap changes as follows: 2,5-dioxahexane < 2,5,8-trioxanonane < 2,5,8,11-tetraoxadodecane > 2,5,8,11, 14-pentaoxapentadecane (table 10). This suggests that structural effects are enough important in the pentaether mixture to provide a meaningful negative contribution to Ap at high temperatures. The negative Ap (303.15 K) value of the 1-propanol + PEG-250 mixture (0.001 cm3  mol1  K 1 [95]) is consistent with this statement. System a 2.24 4.30 4.74 4.28 5.25 5.55 6.20 6.45 7.32 7.75 1.40 4.71 4.47 3.94 4.25 4.79 2.77 4.08 4.75 4.23 6.80 4.01 4.38 4.78 5.18 5.67 6.31 4.06 2.38 [15] [15] [15] [9] [15] [15] [15] [15] [15] [15] [50] [50] [50] [115] [115] [115] [50] [50] [50] [9] [50] [16] [16] [16] [17] [16] [16] [9] [52] 1 DHOHO/ kJ  mol1 26.4 24.4 23.9 24.4 23.4 23.1 22.5 22.2 21.4 20.9 26.3 23 23.3 23.8 23.5 22.9 28.6 27.3 26.6 27.1 24.6 24.9 24.6 24.2 23.8 23.3 22.6 30 34.2 4.64 [56] 31.9 5.54 [56] 31 8.48 [56] 28 value obtained from HE data over the whole concentration range. Values of jES and uE reported in table 3 are rather low. The sign of these magnitudes is consistent with that of V Em . Mixtures characterized by negative V Em values are less compressible than the ideal solution, while the speed of sound is larger. The concentration dependence of the jES , uE and V Em curves is also similar. Note that for the methanol mixture, the curves are very skewed to high mole fractions of the alcohol (figures 1 and 2). Finally, it should be mentioned that, at 303.15 K, jES of the methanol + 2,5,8,11,14-pentaoxapentadecane system is-44 TPa1 [96]. That is, it seems that the behaviour of 1-alkanol + polyether mixtures regarding to jES and uE magnitudes is close to that of ideal solution. 6.3. Results from Flory model with methanol or ethanol are characterized by large  Systems  r HEm values (table 6), which reveals the existence of strong ori- entational effects, particularly in mixtures including methanol. For the remaining solutions, the rather low rðHEm Þ values obtained indicate that the random mixing hypothesis is attained in large extent (see below). Mixtures with 1-alkanols (from 1-propanol) and 3,6-dioxaoctane slightly differ from this behaviour and are charac- 206 J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 TABLE 10  E Variation of excess molar volume with temperature, @V@Tm , for 1-alkanol(1) + linear P polyether(2) mixtures at 298.15 K and atmospheric pressure. System 103 1-Propanol + 2,5-dioxahexane 1.23 1.1 1.1 1.6 1-Hexanol + 2,5-dioxahexane 1-Propanol + 2,5,8trioxanonane 1-Hexanol + 2,5,8-trioxanonane Methanol + 3,6,9trioxaundecane 1-Propanol + 3,6,9trioxaundecane 1-Butanol + 3,6,9trioxaundecane 1-Hexanol + 3,6,9trioxaundecane 1-Decanol + 3,6,9trioxaundecane 1-Propanol + 5,8,11trioxapentadecane 1-Hexanol + 5,8,11trioxapentadecane 1-Propanol + 2,5,8,11tetraoxadodecane 1-Propanol + 2,5,8,11,14pentaoxapentadecane  @V Em 3 @T P =cm   mol 1  K1 Reference [117] [10,11] [11,12] [117] 2.1 1.75 2.0 [10,11] [11,12] This work 1.6 [94] 1.5 1.07 [10,11] This work 1.6 [11,12] 1.4 This work 1.75 [94] 2.9 1.05 [10,11] [11,12] 2.24 [117] 1.07 [117] FIGURE 9. HEm at 298.15 K and atmospheric pressure for 1-alkanol(1) + PEG(2) mixtures. Symbols: experimental results: (), methanol(1) + PEG-250(2) [52]; (j), 1-propanol(1) + PEG-350(2) [56]; (N), 1-butanol(1) + PEG-350(2) [56]; (.), 1-pentanol(1) + PEG-350(2) [56]. Solid lines, results from the Flory model using interaction parameters listed in table 11. 0:281ðN S ¼ 18Þ [22] and TABLE 11 Molar excess enthalpies, HEm at 298.15 K, atmospheric pressure and equimolar composition for 1-alkanol(1) + PEG(2) a systems. The interaction parameters calculated from HmE at equimolar compostion are also included. 1-Alkanol HEm =J  mol Methanol + PEG-250 1-Propanol + PEG-350 1-Butanol + PEG-350 1-Pentanol + PEG-350 608 1437 1721 1973 1 X12/J  cm3 48.15 64.36 64.78 64.62  rr HEm 0.293 0.075 0.080 0.078 b Reference 52 56 56 56 a Flory calculations using the following parameters for the PEGs. PEG-250: V = 271.17cm3  mol1 [119]; ap = 8.83  104  K1 [119] jT = 580 TPa1 [119,120]; ⁄ V = 221.69 cm 3  mol1; P⁄ = 679.2 J  cm3; PEG-350: V = 313.91cm3  mol1 [121]; ap = 7.84  104  K1 [121] jT = 490TPa1 [121]; V⁄ = 261.21cm 3  mol1; P⁄ = 687.8 J  cm3.   terized by weak orientational effects. Note that r HEm values of these mixtures are higher than those of the corresponding systems with 2,5-dioxahexane (table 6). This could be due to the oxygen atoms are more screened in 3,6-dioxaoctane molecules in such way that the creation of interactions between unlike molecules becomes more difficult, which could lead to enhanced effects related to the self-association of 1-alkanols. For methanol+CH3O(CH2CH2O)nCH3 mixtures, orientational effects decrease when n is increased, probably due to a certain compensation between effects related to interactions between like molecules and those ascribed to interactions between unlike molecules. A comparison between Flory results for 1-alkanol + linear mono or polyether mixtures is necessary. We define the mean rel  P    r HEm ¼ ative standard deviation as r rr HEm =NS (NS, number    r HEm ¼ of systems). For mixtures with monoethers, r 0:335ðN S ¼ 26Þ [22]; while for polyether mixtures,   E r r Hm ¼ 0:142ðNS ¼ 32Þ (this work). If solutions with methanol   r r HEm ðmonoetherÞ ¼ or ethanol are not considered,   r r HEm ðpolyetherÞ ¼ 0:059ðNS ¼ 25Þ (this work). This clearly shows that orientational effects are stronger in mixtures involving linear monoethers. It is remarkable that this type of effects are roughly independent of the 1-alkanol in systems with linear monoethers. Polyether mixtures behave differently and orientational effects are much relevant in those systems with methanol or ethanol. We have applied also the model to 1-alkanol + PEG-250, or +PEG-350 mixtures (table 11, figure 9), which show similar trends to those encountered in systems with linear polyethers. Thus, orientational effects are stronger in the methanol + PEG-250 solution,   characterized by a larger r HEm value. The HEm of this system de- creases with increased T values: 608J  mol1 [52] (T = 298.15 K); 576 J  mol1 [97] (T = 303.15 K), which suggests that the mentioned orientational effects are mainly of dipolar type. For the remaining 1-alkanol + PEG-350 systems, their behaviour is close to that of random mixing. With regard to systems including 2,5,8,11,14-pentaoxapentadecane, solutions with PEGs show higher and more asymmetrical HEm curves (figures 7 and 9). This confirms our previous statement on the increase of CH2CH2O groups in the ether increases its ability to break the alcohol selfassociation. On the other hand, in mixtures with a given 1-alkanol, the X12 parameter increases with the alcohol size up to 1-propanol or 1butanol and then decreases (table 6). It is known that HEm is the result of   two contributions: one related to interactional effects U EV;m , and another linked to structural effects (equation of state (eos) contribution). Thus [62,63]: HEm ¼ U EV;m þ T aP V Em jT : ð18Þ In the classical Flory theory, HEm is also expressed as the sum of an interactional term (directly dependent on X12) and of a term which depends on the characteristic and reduced parameters of the pure compounds and of V Em (eos contribution) [39]. Table 7 shows that the V Em values predicted by the model are positive and much higher J.A. González et al. / J. Chem. Thermodynamics 59 (2013) 195–208 than the experimental ones, which, according to Eq. (18), leads to overestimated values of the eos contribution. This is particularly important for solutions with long chain 1-alkanols and may explain the lower X12 values for such systems. The very large V Em values obtained from the Flory model reveal that the interactional contribution to this magnitude is overestimated and that structural effects (free volume effects) are not properly taken into account. Nevertheless, the theory describes correctly the parallel variation of HEm and V Em for mixtures with a given polyether when the alkanol size is increased, or the V Em decrease for 1-alkanol+CH3O(CH2CH2O)nCH3 mixtures when n is increased. The application of the Kirkwood–Buff formalism to methanol or 1-propanol+linear polyether systems shows that the local mole fractions of alcohols (x11) are higher than the bulk ones (x1) [18]. Differences between x11 and x1 are more relevant at low 1-alkanol concentrations and decrease when replacing methanol by 1-propanol [18]. Interestingly, the x11 values are lower than those of systems with linear monoethers [22]. Figure 8 shows the concentration dependence of X12. Typically, for the methanol+2,5-dioxahexane mixture, where effects related to the alcohol self-association are very important, X12 changes rapidly with x1. For the 1-propanol + 3,6,9-trioxaundecane sys  tem such dependence is much weaker (see the low r HEm value of this system, table 6). On the other hand, the X12 values at the concentration range [0.05,0.45] are higher than X12 at x1 = 0.5. That is, the model overestimates the interactions between unlike molecules in that region, which is agreement with the findings obtained from the application of the Kirkwood–Buff integrals. We finish with a comment on the results obtained when using a generalized statistical thermodynamic formalism based on an eos type theory of H-bonds in fluid systems [98]. The model predicts a contribution to HEm which is much lower to that ascribed to physical effects. At equimolar composition and 298.15 K, the former contribution is 100 J  mol1 for the 1-propanol + 2,5-dioxahexane mixture and decreases for the corresponding 1-butanol solution (ca. 0 J  mol1) [98]. On the other hand, the H-bond contribution to HEm is s-shaped, with positive values at lower mole fractions of the 1-alcohol. We newly see that effects related to alcohol self-association are more relevant in that region. 7. Conclusions Experimental q; u; V Em ; jES and uE values have been reported for methanol, 1-butanol or 1-decanol + 3,6,9-trioxaundecane systems. HEm and C Ep;m data of 1-alkanol + linear polyether mixtures reveal that interactions are essentially of dipolar type, particularly for solutions with longer 1-alkanols. Interactions between unlike molecules become weaker when the alcohol size is increased in mixtures with a given polyether. For 1-alkanol + CH3O(CH2CH2O)nCH3 systems, such interactions are stronger for increased n values, although the ability of the ether to break the alcohol self-association increases with n. V Em data show the existence of free volume effects in solutions including methanol or ethanol. These effects are more important for large n values. 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