Application of the Flory Theory and of the Kirkwodâ Buff Formalism to

Ind. Eng. Chem. Res. 2009, 48, 7417–7429

7417

Application of the Flory Theory and of the Kirkwod-Buff Formalism to the Study of Orientational Effects in 1-Alkanol + Linear or Cyclic Monoether Mixtures Juan Antonio Gonza´lez,* Nicola´s Riesco,† Ismael Mozo, Isaıás Garcıá De La Fuente, and Jose´ Carlos Cobos G.E.T.E.F., Departamento de Fı´sica Aplicada, Facultad de Ciencias, UniVersidad de Valladolid, 47071 Valladolid, Spain

Orientational effects present in binary mixtures of 1-alkanols with linear or cyclic monoethers have been studied using the Flory model and the Kirkwood-Buff formalism. The alcohols considered are those from methanol to 1-decanol, and the ethers are the following: dimethylether (DME), diethylether (DEE), dipropylether (DPE), dibutylether (DBE), tetrahydrofuran (THF), and tetrahydropyran (THP). In terms of the Flory model, orientational effects have been investigated by analyzing the concentration dependence of the interaction parameter, X12, and comparing the deviations obtained between experimental molar excess enthalpies, HEm, and calculated values with an X12 parameter determined from HEm measurements at equimolar composition. Due to the facts that structural effects are relevant for many of the considered mixtures and their excess molar volumes, VEm, are negative, we have also determined the excess molar internal energies, UEV,m, and X12 parameters from these data. From the X12 variation with the alkanol size, we have shown than interactions between unlike molecules are nearly constant along a homologous series with a given ether. In the framework of the Kirkwood-Buff theory, the study has been developed through the Kirkwood-Buff integrals and related local mole fractions, obtained from vapor-liquid equilibria and VEm data available in the literature. Ideal compressibilities for the mixtures were assumed. Although the Flory model does not describe the complex structural effects present in the investigated mixtures and fails when predicting VEm, both theories provide consistent results on the orientational effects in these solutions. In addition, the results are in agreement with those previously obtained from the ERAS model. Systems involving linear monoethers are mainly characterized by orientational effects related to the self-association of the alcohol, in such way that the mentioned effects decrease when the size of the alcohol is increased in solutions with a given ether. Orientational effects become more relevant when the chain length of the linear monoether mixed with a fixed 1-alkanol increases. It has been shown that dispersive interactions merely differ by size effects for solutions of 1-alkanol (from 1-propanol) and DPE, or DBE. Systems with cyclic monoethers are characterized by a strengthening of dipolar interactions and a weakening of association effects. As a result, orientational effects are weaker in this type of solution. It is remarkable that mixtures with the longer 1-alkanols (from 1-hexanol) show a behavior close to random mixing. Random mixing is also observed when the temperature increases, as in the case of 1-propanol or 1-butanol + diethylether systems at 323.15 K. 1. Introduction Oxaalkanes represent an important class of molecules from a theoretical point of view. As a matter of fact, these molecules are formally obtained by replacing one or several CH2 groups in an alkane by O atoms (e.g., cyclohexane, oxane, 1,3-dioxane, 1,4-dioxane, 1,3,5-trioxane). A large variety of homomorphic molecular species can be so obtained which differ in the number and relative positions of the same functional group. The study of mixtures with oxaalkanes makes it possible to examine the influence of some interesting effects on their thermodynamic properties, as well as the behavior of any theoretical model when predicting such properties. So, linear oxaalkanes, CH3(CH2)u-1-O-(CH2)V-1-CH3, allow the study of the steric effect of alkyl groups; linear acetals, CH3-(CH2)u-1-O-CH2O-(CH2)V-1-CH3, the proximity effect of two -O- groups; linear polyoxaalkanes, CH3-O-(CH2-CH2-O)u-CH3, the effect of increasing number of oxyethylene groups, cyclic ethers, the ring strain. 1-Alkanol + oxaalkane mixtures are particularly * To whom correspondence should be addressed. E-mail: jagl@ termo.uva.es. Fax: +34-983-423136. Tel.: +34-983-423757. † Department of Earth Science and Engineering, Imperial College London, Exhibition Road, London, SW7 2AZ, U.K.

interesting due to their complexity, a consequence of the selfassociation of the alkanols partially destroyed by the active molecules of ethers and of the new intermolecular OH · · · O bonds created. So, the treatment of this class of systems is a severe test for any theoretical model. The purely physical model DISQUAC,1 based on the rigid lattice theory developed by Guggenheim,2 has been successfully applied to the theoretical study of interactions in 1-alkanol + oxaalkane mixtures,3,4 assuming structure-dependent interaction parameters. The Dortmund version of UNIFAC,5 which ignores proximity or steric effects, fails to describe, for the mixtures mentioned above, very sensitive properties to molecular structure as HEm or molar excess E heat capacity at constant pressure,3 Cp,m . Unfortunately, both DISQUAC and UNIFAC are based on rigid-lattice theories and no change in the volume upon mixing is assumed. A model E E widely applied to simultaneously represent Hm and Vm (excess 6 molar volume) is the so-called ERAS model, which combines the real-association solution model7-9 (chemical contribution) with a physical term derived from the Flory equation of state.10 Although a variety of 1-alkanol + linear monoether systems have been investigated using ERAS,11-15 the more complete treatment has been recently presented by us.16 On the other hand,

10.1021/ie9004354 CCC: $40.75  2009 American Chemical Society Published on Web 06/22/2009

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Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009

only mixtures of 1-alkanol + 2,5,8-trioxanonane or + 2,5,8,11tetraoxadodecane have been studied using ERAS17 under the assumption that the polyethers are self-associated, which seems to be not very pertinent. The lack of a systematic treatment of 1-alkanol + polyoxaalkane mixtures underlines the difficulty in studying such mixtures in the framework of ERAS. This may be related to the existence of strong dipolar interactions in the mentioned solutions, also encountered in the case of 1-alkanol + cyclic ether mixtures.4 Such interactions may explain the discrepancies between experimental results and ERAS calculations.4 The Flory model is commonly used to describe simultaE E and Vm of systems of one slightly polar compound neously Hm (N,N,N-trialkylamine18 or monoether19) + alkanes) or involving two polar compounds as 1-alkanol + 1-alkanol20 or 2-methoxyethanol + hydroxyether.21 The theory has been also applied to predict isobaric expansion coefficient, RP, isentropic, κS, or isothermal, κT, compressibilities and speeds of sound, u, of simple systems, as those involving two alkanes or of the type cyclohexane or benzene + n-alkane.22-24 The Flory model provides good results for the systems mentioned above, as they are characterized by random mixing, which is a basic assumption of the theory. This important feature has made it possible to investigate order creation and order destruction processes in B + Cn mixtures25-28 (B is usually a nonpolar or slightly polar compound, with spherical or platelike shape). As any order effects are ignored in the theory, deviations from this behavior lead to differences between experimental values for magnitudes E E E E E and Vm , Cp,m , (∂Vm /∂T)P, or -(∂Vm /∂P)T and theoretical as Hm results, which are ascribed to order effects. The main conclusion of these studies is the existence of a short orientational order in long chain alkanes, which does not appear in highly branched isomeric alkanes or short chain alkanes. Recently, we have shown that the model application can be extended in two ways. First, the theory provides rather accurate predictions on RP κS, κT, and u of complex mixtures as alkoxyethanol + dibutylether or + 1-butanol.29 Second, it is possible to investigate the existence of orientational effects in these complex mixtures by studying the variation of the X12 parameter with the composition.30 At this end, we have reported previously an expression which allows a more easy X12 determination at a given mole E value at that composition.30 fraction from the experimental Hm The aim of this work is to gain insight into the orientational and structural effects present in 1-alkanol + linear or cyclic monoether mixtures through the application of the Flory model. For a more complete study, and in order to check the results, the present solutions are also investigated, when the needed experimental data are available, in terms of the Kirkwood-Buff formalism.31-33 As far as we know, only systems with tetrahydrofuran and ethanol or 1-propanol have been treated on the basis of this theory.34 The alcohols considered in our study are those from methanol to 1-decanol, and the ethers are the following: dimethylether (DME), diethylether (DEE), dipropylether (DPE), dibutylether (DBE), tetrahydrofuran (THF), and tetrahydropyran (THP). So, we are investigating, not a few systems, but different homologous series, in such way that regularities can be observed and discussed. 2. Theories 2.1. Flory Model. In this section, we present a brief summary of the model. More details are given in the original works.10,35-38 The main features of the theory are as follows: (i) Molecules are divided into segments. A segment is an arbitrarily chosen isomeric portion of the molecule. The number of segments per

molecule of component i is denoted by ri, and the number of intermolecular contact sites per segment by si. (ii) The mean intermolecular energy per contact is proportional to -η/Vs (where η is a positive constant characterizing the energy of interaction for a pair of neighboring sites and Vs is the volume of a segment). (iii) When stating the configurational partition function, it is assumed that the number of external degrees of freedom of the segments is lower than 3, in order to take into account the restrictions on the precise location of a given segment by its neighbors in the same chain. (iv) Random mixing is assumed: the probability of having species of kind i neighbors to any given site is equal to the site fraction, θi (θi ) siriNi/srN; where N ) N1 + N2 is the total number of molecules and r and s are the total number of intermolecular segments and contact sites per segment, respectively). For a very large total number of contact sites, the probability of formation of an interaction between contacts sites belonging to different liquids is θ1θ2. Under these hypotheses, the Flory equation of state is given by j 1/3 jV j V 1 P ) 1/3 j j j j T V T V -1

(1)

j ) V/V*; P j ) P/P*, and T j ) T/T* are the reduced where V volume, pressure, and temperature, respectively. Equation 1 is valid for pure liquids and liquid mixtures. For pure liquids, the reduction parameters, V*, i P*, i and T* i can be obtained from experimental data, such as RPi and κTi. For mixtures, the corresponding parameters are calculated as follows: V* ) x1V1* + x2V2* T* )

(2)

φ1P1* + φ2P2* - φ1θ2X12 φ1P1* T1*

+

(3)

φ2P2* T2*

P* ) φ1P*1 + φ2P*2 - φ1θ2X12

(4)

In eqs 3 and 4, φi ) xiV*/∑x i iV* i is the segment fraction and θ2 is alternatively calculated as follows: θ2 ) φ2/(φ2 + S12φ1). S12 is the so-called geometrical parameter of the mixture, which, assuming that the molecules are spherical, is calculated as S12 ) (V*1 /V*2 )-1/3. The energetic parameter, X12, also present in eqs 3 and 4, is defined by similarity with P*i )

siηii

(5)

2V*s 2

as X12 )

s1∆η

(6)

2V*s 2

where ∆η ) η11 + η22 - 2η12. In eqs 5 and 6, V*(reduction s volume for segment) and ηij are changed from molecular units to molar units per segments. X12 is determined from HEm )

(

)

(

x1V1*θ2X12 1 1 1 1 + x1V1*P1* + x2V2*P2* j j1 j j2 j V V V V V

)

(7)

j , is In this equation the reduced volume of the mixture, V obtained from the equation of state Therefore, the molar excess volume can be also calculated:


VEm

j 2) j - φ1V j 1 - φ2V ) (x1V*1 + x2V*2 )(V

(8)

32,33

2.2. Kirkwood-Buff Formalism. This theory describes thermodynamic properties of solutions in an exact manner in the whole concentration range using the Kirkwood-Buff integrals: Gij )

∫

∞

o

(gij - 1)4πr2 dr

(9)

The radial distribution function, gij, denotes the probability of finding a molecule of species i in a volume element at the distance r of the center of a molecule of species j. So, this function provides information about the solution structure on the microscopic level. The product FjGij (Fj is the number density of molecules of species j) represents the average excess (or deficiency) number of molecules j in the whole space around a molecule i with respect to the bulk average. The Gij values can be obtained from FjGij by a process of normalization with respect to concentration and can be interpreted as follows: Gij > 0 represents the excess of molecules of the i type in the space around a given molecule of species j. This means attractive interactions between molecules of i and j. Gij < 0 means that interactions of i-i and j-j are preferred to mutual interactions.32,39 The Kirkwood-Buff integrals can be derived from experimental data of thermodynamic properties such as chemical potential, partial molar volumes, and the isothermal compressibility factor. The resulting equations are the following:32,40 G11 ) RTκT +

j 22 x2V V x1VD x1

(10)

G22 ) RTκT +

j 12 x1V V x2VD x2

(11)

j2 j 1V V VD

(12)

G12 ) G21 ) RTκT -

j i are the mole fraction where R is the gas constant, xi and V and the partial molar volume of component i, respectively (i ) 1, 2); V is the molar volume of the solution; and κT is the isothermal compressibility of the mixture. D is defined as D)1+

( )

x1x2 ∂2GEm RT ∂x 2 1

(13) P,T

Using the Gij quantities, it is possible to estimate the socalled linear coefficients of preferential solvation:41,42 δ011 ) x1x2(G11 - G12)

(14)

δ012 ) x1x2(G12 - G22) δ021 ) x1x2(G12 - G11) δ022 ) x1x2(G22 - G12) which are useful quantities to determine the local mole fractions of the i species around the central j molecule:40-42 δ0ij xij ) xi + Vc

(15)

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Table 1. Flory Parameters of Pure Compounds at T ) 298.15 K a

compoundb

Vi/cm3 mol-1

Rp/10-3 K-1

κT/10-12 Pa-1

3 V*/cm i mol-1

P*/J i cm-3

MeOH EtOH 1-PrOH 1-BuOH 1-PeOH 1-HxOH 1-HpOH 1-OcOH 1-DcOH DME DEE DPE DBE THF THP

40.75c 58.69c 75.16c 91.98d 108.68d 125.31d 141.89e 158.48e 191.58e 69.67c 104.74g 137.68h 170.45i 81.76j 98.19c

1.196c 1.096c 1.004c 0.9493d 0.9090d 0.8805d 0.8599e 0.8442e 0.8272e 1.996c 1.654g 1.261h 1.1336i 1.2265j 1.156k

1248c 1153c 1026c 949.2d 886.5d 842.3d 808.6e 780.9e 740.9e 2514.6f 1967g 1440h 1205.9i 962.3j 990l

31.67 46.32 60.20 74.34 88.45 102.33 116.47 130.45 158.18 49.02 76.57 106 133.74 63.26 76.78

472.9 454.9 454.8 456.4 461.6 465.9 470.6 475.7 488.3 478.1 469.1 440.7 455.2 634.7 569.4

a Vi, molar volume; Rp, isobaric thermal expansion coefficient; κT, isothermal compressibility; V*, i reduction parameter for volume, and P*, i reduction parameter for pressure. b MeOH, methanol; EtOH, ethanol; 1PrOH, 1-propanol; 1-BuOH, 1-butanol; 1-PeOH, 1-pentanol; 1-HxOH, 1hexanol; 1-HpOH, 1-heptanol; 1-OcOH, 1-octanol; 1-DcOH, 1-decanol; DME, dimethylether; DEE, diethylether; DPE, dipropylether; DBE, dibutylether; THF, tetrahydrofuran; THP, tetrahydropyran. c Reference 93. d Reference 53. e Reference 16. f Estimated with the method reported in ref 94. g Reference 50. h Reference 12. i Reference 95. j Reference 15. k Reference 96. l Reference 97.

where Vc is the volume for the solvation sphere. This value may be roughly estimated41 as the volume of a sphere of radius Rc ) 3r, where r is the radius of the central molecule. This leads to a value of Vc equal to approximately (33 1)Vo ) 26Vo, Vo being the molar volume of the solvated component. 2.2.1. Source of Data. D values were obtained using E Redlich-Kister type expressions for Gm determined from vapor-liquid equilibrium (VLE) data at 298.15 K available E data required for the in the literature.11,12,15,43-49 The Vm calculations were taken from references 14-16, 48, and 50-57. For the methanol + tetrahydrofuran system, VEm values at 303.15 K were used.57 Table 1 collects the isothermal compressibilities of pure compounds, κTi, as well as their molar volumes, Vi. For the mixtures, their isothermal compressibilities were calculated as κT ) Φ1κT1 + Φ2κT2, where Φi is the volume fraction of the component i of the system. That is, when calculating the compressibility of the system, the solution is assumed to be ideal. This assumption does not influence the final calculations of the Kirkwood-Buff integrals.58 The effect of the temperature on Gij has been also examined on the basis of D values obtained from VLE E values data at different temperatures and using the same Vm as above. This introduces a small error to calculate the partial molar volumes of the components, magnitudes which are of secondary importance when Gij values are determined.59 In order to evaluate Vi and κTi values at T * 298.15 K, we have used the well-known equations for the density, F, Rp, and γ () Rp/κT):60 F ) Fo exp(-Ro∆T)

(16)

R ) Ro + Ro2(7 + 4RoT)∆T/3

(17)

γ ) γo - γo(1 + 2RoT)∆T/T

(18)

where ∆T ) T - 298.15 K.

7420


E E Table 2. Molar Excess Enthalpies, Hm , and Internal Energies, UV,m , at Constant Volume at Temperature T and Equimolar Composition for 1-Alkanol + Monoether Systemsa

systemb

T/K

E Hm /J mol-1

MeOH + DME EtOH + DME 1-PrOH + DME 1-BuOH + DME MeOH + DEE EtOH + DEE 1-PrOH + DEE MeOH + DPE EtOH + DPE 1-PrOH + DPE 1-BuOH + DPE

323.15 323.15 323.15 323.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

1-PeOH + DPE 1-HxOH + DPE

298.15 298.15

1-OcOH + DPE 1-DcOH + DPE MeOH + DBE EtOH + DBE 1-PrOH + DBE 1-BuOH + DBE 1-PeOH + DBE 1-HxOH + DBE 1-HpOH + DBE 1-OcOH + DBE 1-DcOH + DBE MeOH + THF EtOH + THF 1-PrOH + THF 1-HxOH + THF 1-HpOH + THF 1-OcOH + THF 1-DcOH + THF MeOH + THP EtOH + THP 1-PrOH + THP 1-PeOH + THP 1-HxOH + THP 1-HpOH + THP 1-OcOH + THP 1-DcOH + THP

298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15 298.15

454 714 815 844 445 611 691 609 716 740 742 702 686 710 702 664 658 788 858 886 865 843 817 772 802 822 532 791 933 995 1070 1129 1241 677 847 922 963 1011 1055 1083 1162

a

E UV,m /J mol-1

648 780 926 699 794 846 869 873 845 851 840 900 939 934 930 916 881 915 942 621 798 936 981 1042 1088 1171

948 988 1018 1030 1075

E X12(Hm )/J cm-3

E X12(UV,m )/J cm-3

49.17 60.18 59.88 55.95 41.74 44.07 42.51 52.53 46.29 39.85 34.96 32.97 28.89 27.29 26.99 22.30 19.82 65.41 52.66 44.71 37.57 32.55 28.62 24.99 24.17 22 51.79 58.79 58.40 45.27 45.28 44.83 44.27 63.04 59.61 54.23 44.31 42.53 41.16 39.56 38

60.12 55.68 56.02 60.27 51.30 45.48 40.47 33.29 28.01 25.23 69.72 55.23 47.37 40.54 35.86 32.03 28.42 27.47 25.09 60.43 59.31 58.59 44.65 44.12 43.25 41.85

43.63 41.56 39.74 37.67 35.22

E c σr(Hm )

ref

0.510 0.189 0.081 0.038 1.01 0.383 0.343 0.430 0.389 0.377 0.346 0.281 0.263 0.328 0.267 0.250 0.216 0.376 0.382 0.414 0.363 0.354 0.329 0.255 0.284 0.265 0.487 0.200 0.084 0.013 0.038 0.063 0.070 0.330 0.291 0.185 0.095 0.075 0.067 0.048 0.015

62 62 62 62 63 63 63 48 51 49 51 64 64 51 64 51 51 65 63 65 65 65 65 63 65 65 66 66 66 67 67 67 67 66 66 66 69 68 68 68 69

E E and UV,m at equimolar compostion are also included. b For definitions, see Table 1. c Equation 24. The interaction parameters calculated from Hm

From eqs 19 and 20

3. Estimation of the Flory Energetic Parameter E Here, we report an expression to determine X12 from a Hm measurement at a given composition, which is an improvement of the equation previously given to calculate X12 from E at x1) 0.5.61 For the sake of simplicity, we use the soHm called pj ≈ 0 approximation of the equation of state, which is a good approximation at atmospheric pressure:

j 1/3 j) V -1 T j 4/3 V

x1P*1 V*1 x2P*2 V*2 1 + + (x1P*1 V*1 + x2P*2 V*2 j1 j2 j V V V x1V*1 θ2X12)

x1P*1 V*1 + x2P*2 V*2 - x1V*1 θ2X12 x2P*2 V*2 x1P*1 V*1 + T*1 T*2

E j is j Tj as a function of Hm . As V From eq 22, we can obtain V j j , and a function of T (eq 19), it is possible to determine T using now eq 21, we finally obtain

( )

x1P*1 V*1 1 X12 )

( )

j1 j2 T T + x2P*2 V*2 1 j j T T x1V*1 θ2

(23)

(20)

Properties of the pure compounds’ molar volumes, RPi and V*i κTi, and the corresponding reduction parameters, P*and i (i ) 1, 2), needed for calculations are listed in Table 1. X12 E values determined from Hm data at x1) 0.5 available in the 48,49,51,62-69 literature are collected in Table 2.

(21)

4. Results

and eq 3 can be written as follows: T* )

x1P*1 V*1 x2P*2 V*2 1 j + x2P*2 V*2 T j 2) (x P*V*T + + j1 j2 jT j 1 1 1 1 V V V (22)

(19)

Equation 7 can be rearranged as HEm )

HEm )

E E and Vm obtained from the Flory model using Results for Hm X12 values at x1 ) 0.5 are listed in Tables 2 and 3, respectively.

Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009 E Vm ,

Table 3. Molar Excess Volumes, at 298.15 K and Equimolar Composition for 1-Alkanol + Monoether Systemsa E Vm (0.5)/cm3 mol-1 b

system

exp

Floryc

ref

MeOH + DEE EtOH +DEE 1-PrOH +DEE MeOH + DPE EtOH + DPE 1-PrOH + DPE 1-BuOH + DPE 1-HxOH + DPE 1-OcOH + DPE 1-DcOH + DPE MeOH + DBE EtOH + DBE 1-PrOH + DBE 1-BuOH + DBE 1-PeOH + DBE 1-HxOH + DBE 1-HpOH + DBE 1-OcOH + DBE 1-DcOH + DBE MeOH + TFH EtOH + THF 1-PrOH + THF 1-HxOH + THF 1-HpOH + THF 1-OcOH + THF 1-DcOH + THF 1-PeOH + THP 1-HxOH + THP 1-HpOH + THP 1-OcOH + THP 1-DcOH + THP

-0.7883 -0.6540 -0.899 -0.339 -0.294 -0.3907 -0.468 -0.5845 -0.635 -0.664 -0.186 -0.149 -0.1846 -0.239 -0.300 -0.342 -0.368 -0.382 -0.396 -0.261 -0.0216 -0.008 0.0402 0.0806 0.1186 0.1999 0.0455 0.0696 0.1121 0.1578 0.2569

0.441 0.572 0.511 0.625 0.692 0.624 0.533 0.312 0.072 -0.101 0.739 0.789 0.772 0.700 0.611 0.540 0.415 0.369 0.245 0.435 0.732 0.913 1.015 1.062 1.089 1.106 0.867 0.893 0.903 0.897 0.882

50 50 55 48 51 52 51 52 51 51 14 14 52 53 53 53 16 16 16 57 54 15 56 56 56 70 69 56 56 56 69

7421

E where N () 19) is the number of data points and Hm,exp E represents the smoothed Hm values calculated at ∆x1 ) 0.05 in the composition range [0.05, 0.95] from polynomial expansions given in the original works.48,49,51,62-69 In order to obtain a detailed information on the concentration dependence of X12, we have calculated this magnitude using eq 23 and HEm,exp values. The X12(x1) variation is estimated from the equation:

∆i ) 100

|

Xmax,min (x1) - X12(x1 ) 0.5) 12 X12(x1 ) 0.5)

|

(25)

where Xmax 12 is the maximum absolute value of the X12(x1) function min in the range [0.05, 0.45] (i ) 1) and X12 is the minimum absolute value in the range [0.55, 0.95] (i ) 2). The corresponding values are listed in Table 4 (see also Figures 4 and 5). Values of the Kirkwood-Buff integrals and of the local mole fractions are collected in Table 5. Figures 6 and 7 show Gij results for some selected systems.

a Comparison of experimental (exp) results with Flory calculations. For definitions, see Table 1. c Values obtained using interaction E parameters determined from Hm at equimolar composition (Table 2). b

Figure 2. HEm for the 1-alkanol (1) + DME (2) mixtures at 323.15 K. Points, experimental results:62 (b), methanol; (9), 1-butanol. Solid lines, Flory calculations using interaction parameters from Table 2.

E Figure 1. Hm for the 1-octanol (1) + oxaalkane (2) mixtures at 298.15 K. Points, experimental results: (b), DPE;51 (9), THP.68 Solid lines, Flory calculations using interaction parameters from Table 2.

E A comparison between experimental Hm and theoretical values are shown graphically in Figures 1-3. For the sake of clarity, E Table 2 also includes the relative standard deviations for Hm defined as

E σr(Hm ))

[ ( 1 N

∑

E E Hm,exp - Hm,calc E Hm,exp

)]

2 1/2

(24)

Figure 3. HEm for the 1-alkanol (1) + THF (2) mixtures at 298.15 K. Points, experimental results: (b), methanol;66 (9), 1-hexanol.67 Solid lines, Flory calculations using interaction parameters from Table 2.

7422


E Table 4. Variations of the X12 Values, ∆i, Obtained from Hm Data at 298.15 K of 1-Alkanol + Monoether Mixtures in the Concentration Ranges [0.05, 0.5] (i ) 1) and [0.5, 0.95] (i ) 2) Calculated According to Equation 25

systema MeOH + DME EtOH + DMEb 1-PrOH + DMEb 1-BuOH + DMEb MeOH + DEE EtOH + DEE 1-PrOH + DEE MeOH + DPE 1-PrOH + DPE 1-PeOH + DPE 1-HxOH + DPE 1-DcOH + DPE MeOH + DBE 1-PrOH + DBE 1-BuOH + DBE 1-PeOH + DBE 1-HxOH + DBE 1-HpOH + DBE 1-OcOH + DBE 1-DcOH + DBE MeOH + THF EtOH + THF 1-PrOH + THF 1-HxOH + THF 1-HpOH + THF 1-OcOH + THF 1-DcOH + THF MeOH + THP EtOH + THP 1-PrOH + THP 1-PeOH + THP 1-HxOH + THP 1-HpOH + THP 1-OcOH + THP 1-DcOH + THP b

a

∆1

∆2

ref

1.015 0.484 0.193 0.087 2.282 1.503 1.184 1.462 1.304 0.992 1.115 0.566 1.617 1.447 1.317 1.243 1.152 1.168 0.989 0.868 0.799 0.386 0.149 0.018 0.052 0.081 0.118 0.921 0.837 0.281 0.265 0.177 0.148 0.129 0.027

0.505 0.297 0.053 0.011 0.730 0.395 0.396 0.476 0.437 0.280 0.365 0.174 0.349 0.444 0.399 0.387 0.360 0.217 0.309 0.301 0.549 0.238 0.086 0.025 0.077 0.081 0.095 0.348 0.390 0.279 0.102 0.126 0.127 0.075 0.032

62 62 62 62 63 63 63 48 49 64 51 51 65 65 65 65 65 63 65 65 66 66 66 67 67 67 67 66 66 66 69 68 68 68 69

For definitions, see Table 1.

Figure 4. Flory interaction parameters, X12, for 1-alkanol (1) + oxaalkane E (2) mixtures at 298.15 K. Points, values determined from Hm at different mole fractions, x1 (see text): (b) methanol + THP;66 (9), 1-propanol + THP;66 (2), 1-hexanol + THP;68 (1), 1-decanol + THP;69 (O), 1-hexanol E + THF.67 Solid and dashed lines, X12 values calculated from Hm at x1 ) 0.5 (Table 2).

5. Discussion Hereafter, we are referring to thermodynamic properties at equimolar composition and T ) 298.15 K.

Figure 5. Flory interaction parameters, X12, for 1-alkanol (1) + DME (2) E mixtures at 323.15 K. Points, values determined from Hm at different mole fractions,62 x1 (see text): (b) methanol; (9), 1-butanol. Solid or dashed lines, E X12 values calculated from Hm at x1 ) 0.5.

5.1. 1-Alkanol + Linear Monoether Systems. It is known that the disruption, upon mixing, of interactions between like E molecules contributes positively to Hm and that negative contributions to this excess function come from the creation of interactions between unlike molecules. Positive contributions E are here due to the breaking of the alkanol-alkanol and to Hm ether-ether interactions, while negative contributions come from the creation of the alkanol-ether interactions. For a given E (dipropylether or dibutylether) > 1-alkanol (* methanol), Hm E E (heptane). So, for 1-propanol systems, Hm (dipropylether)49 Hm 15 E -1 ) 740 > Hm(heptane) ) 597 J mol . This reveals that ether molecules are more active that those of alkane when breaking the self-association of the alcohols and that the new OH · · · O interactions created are weaker than the H-bonds between alcohol molecules.16 E The large σr(Hm ) values obtained for these mixtures (Table 2) reveal the existence of strong orientational effects. Accordingly, ∆i (i ) 1, 2) values are also large (Table 4), particularly those for i ) 1. That is, orientational effects seem to be stronger at low alcohol concentration. This may be due to alkanol selfassociation plays an important role in the present solutions, as is supported by the following features. (i) For a given ether, E increases from methanol to ethanol or 1-propanol, and then Hm slowly decreases; i.e., the observed variation is similar to that of 1-alkanol + fixed n-alkane systems.16 (ii) As in these E mixtures, the Hm curves are also skewed toward low mole E is positive fractions of the alcohol (Figures 1 and 2). (iii) Cp,m and quite high (e.g., for the ethanol + methyl butylether E system,71 Cp,m ) 7.18 J mol-1 K-1. E is also the result of several opposing effects. Changes in the Vm self-association of the alcohol or interactions between like molE E ecules lead to an increased Vm ; negative contributions to Vm arise from interactions between unlike molecules or structural effects such as changes in free volume or interstitial accommodation.72-75 In the case of 1-alkanol + given alkane mixtures, these contributions are sensitive to the lengths of the component molecules.74 For systems with the shorter 1-alkanols (e.g., ethanol, 1-propanol), VEm is positive over the whole concentration range due to the effects of the disruption of the H-bonds and the fact that nonspecific interactions are predominant over the less significant contribution from structural effects. In contrast, the latter are dominant for


7423

Table 5. Kirkwood-Buff Integrals, Gij, and Local Mole Fractions, xij, at Temperature T and Mole Fraction x1 for 1-Alkanol + Monoether Mixtures system MeOH + DEE

a

T/K

x1

G11/cm3 mol-1

G22/cm3 mol-1

G12/cm3 mol-1

x11

x12

298.15

0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8 0.2 0.4 0.6 0.8

570 346.3 147.2 18.1 525.2 263.9 139.3 31.7 1255.6 948.5 526.6 152.1 1014 795.3 454.9 134.4 1220.7 767.9 244.3 28.5 801.8 429.8 109.6 -22 716.3 285.6 29.9 -57.4 584.6 234.9 23.2 -58.5 513.8 115.8 -64.8 -111.5 304.3 -16.4 -130.2 -154 206.3 -35.8 -133.7 -157.1 1378.3 709.7 253.6 37.4 1394.4 559.4 130.4 -19.2 800.2 326.4 12.4 -91.1 259.8 155.8 59.1 -8.4 70.11 23.7 -19.3 -44.9 25.5 -22.5 -55.1 -68.9

-100.7 -91.4 -74.2 -60.3 -106.5 -104.4 -94 -73.5 -134.3 -114.9 -65.3 20.1 -138.9 -124.6 -82.2 -12.4 -118.3 -90.6 -61.9 -21.7 -126.8 -91.1 -47.3 -27.1 -119.9 -80.9 -60.3 -23.9 -127.2 -95.6 -72.6 -34.2 -104.8 -55 -43.6 -24.5 -91.4 -36.6 -20.2 15 -103.4 -52.4 -30.5 -4.2 -160.7 -128.5 -87.7 10.7 -151.4 -112.2 -87.3 -7.1 -145.1 -82.3 -52.7 -20.4 -79.7 -70.6 -56.7 -29.3 -79.4 -72.1 -61.6 -53.9 -75.7 -64.7 -55.3 -53.3

-90 -132.2 -142.7 -123.5 -55.6 -97.4 -122.5 -127 -129.9 -230.2 -287.7 -262.8 -112.3 -199.8 -259.9 -241.5 -188.7 -287.6 -246.7 -199.3 -188.3 -252.8 -220.4 -182.5 -220.6 -254.1 -207.9 -174.9 -198.6 -232 -202.5 -175.9 -264.5 -265.6 -200.9 -164.2 -284.2 -261.3 -199.8 -166 -258.1 -249.6 -200.1 -166.6 -229.2 -300.2 -287.3 -266.9 -287.5 -321.4 -266.6 -241.2 -290.1 -341.6 -271.5 -216.9 -73.8 -103 -109.2 -99.8 -78.9 -94.2 -95.4 -87.7 -95.3 -103.3 -96.8 -86.2

0.299 0.508 0.666 0.821 0.252 0.473 0.653 0.821 0.409 0.667 0.784 0.863 0.365 0.619 0.759 0.885 0.348 0.566 0.677 0.824 0.281 0.484 0.640 0.813 0.263 0.454 0.624 0.808 0.251 0.446 0.662 0.808 0.238 0.428 0.610 0.803 0.223 0.414 0.604 0.800 0.218 0.412 0.604 0.800 0.332 0.524 0.666 0.825 0.312 0.488 0.640 0.815 0.253 0.449 0.629 0.806 0.250 0.459 0.638 0.814 0.216 0.418 0.612 0.804 0.210 0.410 0.605 0.801

0.201 0.396 0.594 0.796 0.200 0.400 0.598 0.797 0.200 0.392 0.585 0.787 0.201 0.395 0.588 0.790 0.197 0.387 0.588 0.792 0.197 0.389 0.589 0.793 0.196 0.388 0.591 0.793 0.197 0.391 0.592 0.794 0.193 0.386 0.589 0.794 0.191 0.385 0.588 0.792 0.193 0.387 0.589 0.793 0.197 0.391 0.589 0.790 0.195 0.389 0.580 0.792 0.195 0.386 0.588 0.793 0.200 0.396 0.594 0.795 0.200 0.397 0.596 0.797 0.198 0.396 0.595 0.797

388.15

MeOH + DPEb

298.15

323.15

EtOH + DPEc

298.15

1-PrOH + DPEd

298.15

1-BuOH + DPEc

298.15

323.15

1-HxOH + DPEe

298.15

1-OcOH + DPEf

298.15

323.15

1-PrOH + DBEg

298.15

1-BuOH + DBEh

298.15

1-HxOH + DBEi

298.15

MeOH + THFj

298.15

EtOH + THFk

298.15

1-PrOH + THFl

298.15

a E b E c E d E e . Ref 48 for VLE and Vm . Ref 11 for VLE; ref 51 for Vm . Ref 49 for VLE; ref 52 for Vm . Ref 12 for VLE; ref Ref 43 for VLE; ref 50 for Vm E f E g E h E i E j 52 for Vm . Ref 12 for VLE; ref 51 for Vm . Ref 47 for VLE; ref 52 for Vm . Ref 44 for VLE; ref 53 for Vm . Ref 47 for VLE; ref 53 for Vm . Ref 45 E k E l E for VLE; ref 57 for Vm. Ref 46 for VLE; ref 54 for Vm. Ref 15 for VLE and Vm.

systems with long chain 1-alkanols and short alkanes, which show E values.74-76 This has been explained assuming that, negative Vm

as the length of the 1-alkanol is increased, the negative effect accompanying the fitting of the n-alkane molecules into the alkanol

7424


UEV,m ) HEm -

Figure 6. Kirkwood-Buff integrals, Gij, for 1-alkanol (1) + DPE (2) systems at 298.15 K. Solid lines: methanol. Dashed lines: 1-octanol.

Figure 7. Kirkwood-Buff integrals, Gij, for 1-propanol (1) + oxaalkane (2) systems at 298.15 K. Solid lines: DPE. Dashed lines: THF.

multimer structure becomes progressively more important and E predominates for sufficient long alkanol molecules. The Vm variation of 1-alkanol + fixed linear monoether mixtures is similar to that of the corresponding systems with heptane.16 For 1-propanol solutions, VEm(heptane)76 ) 0.297 > VEm(dipropylether)52 ) -0.3907 E (heptane) > cm3 mol-1. The fact that, for a given alcohol, Vm E Vm(dipropylether) is due to the existence of interactions between unlike molecules, which are stronger in methanol systems16 (see E values below, Table 2). On the other hand, the more negative Vm for the systems with longer 1-alkanols may be explained in terms of interstitial accommodation of the ether molecules in the alcohol structure, as occurs in solutions with heptane. This complex behavior is poorly represented by the Flory model, which provides E values (Table 3); i.e., structural effects are ignored by the large Vm theory. E On the other hand, it is pertinent here to remember that Hm is the result not only of interactional effects but also of structural E . effects. The former are more properly considered using UV,m E E Neglecting terms of higher order in Vm, UV,m is displayed to a good approximation with77,78

Rp E TV κT m

(26)

E where (Rp/κT)TVm is termed the equation of state contribution E and Rp and κT are the isobaric thermal expansion to Hm coefficient and the isothermal compressibility of the mixture, respectively. Due to the lack of experimental data, these quantities (M ) Rp, κT) have been calculated from the M ) Φ1M1 + Φ2M2 equation (Mi is the property of the pure compound i). This is a good approximation for the studied mixtures in view of their rather low |∆Rp| and |∆κS| values.16,53 E E Table 2 shows that UV,m > Hm . Consequently, the interaction E measurements is lower than that parameter obtained from Hm E data, and interactions between like calculated from UV,m molecules are undervalued when they are estimated from the former. This should be taken into account when examining, e.g., the X12 variation with the alcohol size (see below). 5.1.1. Effect of Increasing the Chain Length of the E 1-Alkanol in Systems with a Given Ether. The lower UV,m values obtained for mixtures with methanol reveal that interactions between unlike molecules are stronger for such solutions. E is nearly constant, for systems For DPE or DBE mixtures, UV,m with longer 1-alkanols (Table 2). This seems to indicate that the different interactional contributions mentioned above are E ) and ∆i (i ) counterbalanced. Tables 2 and 4 show that σr(Hm 1, 2) values usually decrease. So, orientational effects become weaker for solutions involving longer alkanols. This may be ascribed to (i) the lower self-association of long chain 1-alkanols. This is indicated by the decrease of the difference between the cohesive energy density, Dce ) (∆Hvap - RT)/V (∆Hvap, enthalpy of vaporization), and the internal pressure, Pint ) (∂U/∂V)T ) TRP/κT - P (Table 6). Dce is a measure of the total molecular cohesion per cubic centimeter of a given solvent, while Pint is a measure of the change in internal energy of a solvent when it undergoes a very small isothermal expansion, which does not disrupt all the intermolecular interactions associated with 1 mol of the solvent, but those interactions vary most rapidly near the equilibrium separation in it79-81 Typically, such interactions are dispersion, repulsion, and dipole-dipole interactions.79-81 In terms of the ERAS model, the equilibrium constant of selfassociation, KA, changes as follows:6,82 985 (methanol) > 197 (1-propanol) > 120 (1-hexanol) > 88 (1-decanol). (ii) Weaker dipole-dipole interactions, as consequence of the decrease of the effective dipole moment, µ j , a useful magnitude to characterize the impact of polarity on bulk properties:77,82,83 µ j (methanol) ) 1.023 > µ j (ethanol) ) 0.852 > µ j (1-butanol) ) 0.664 > µ j (1E hexanol) ) 0.580 > µ j (1-decanol) ) 0.443 (Table 6). (iii) TSm E E () Hm - Gm) values also indicate that association effects decrease with the increase of the alkanol size (Table 7). (iv) Results from the ERAS model are in agreement with these features. As an example, Figure 8 shows ERAS calculations with parameters previously determined16 for the 1-alkanol + E DPE systems. We note that the physical contribution, Hphys , to HEm increases with the alcohol size, while the chemical contribuE , decreases. tion, Hchem E E ) and X12(UV,m ) decrease when the chain length of the X12(Hm 1-alkanol is increased in systems containing DPE or DBE (Table E ) variation is different for mixtures 2). In contrast, the X12(Hm involving DME or DEE (Table 2). This merely remarks the importance of the contribution of the equation of state term (eq E . 26) to Hm On the other hand, it is possible to obtain some qualitative information about the interactions present in the studied mixtures from the observed X12(HEm) variation for DPE or DBE solutions.

Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009 Table 6. Physical Constants of Some Pure Compounds Considered in This Work: µ, Dipole Moment in the Gas Phase; µ j , Effective Dipole Moment;a ∆Hv, Molar Enthalpy of Vaporization at 298.15 K; Pint, Internal Pressure;b Dce, Cohesive Energy Densityc compoundd

µ/D

µ j

∆Hv/kJ mol-1

Pint/MPa

Dce/MPa

Dce Pint/MPa

methanol ethanol 1-propanol 1-butanol 1-hexanol 1-octanol 1-decanol DME DEE DPE DBE THF THP

1.7e 1.7g 1.7g 1.66e 1.68h 1.72h 1.71h 1.28f 1.15f 1.21f 1.18e 1.75f 1.63e

1.02 0.85 0.75 0.66 0.57 0.52 0.47 0.59 0.43 0.39 0.35 0.74 0.63

37.43f 42.31f 47.32f 52.34f 61.85f 70.98f 81.50i 18.51e 27.10e 35.69e 44.97e 31.30i 34.58i

285.6 283.4 291.6 298.1 311.6 322.2 332.8 236.7 250.7 261.1 279.3 380 348.1

857.7 678.7 596.6 542.1 473.8 432.2 312.5 230.1 235.1 241.2 249.3 352.5 326.9

572.1 395.4 305 244 162.2 110 79.7 - 6.5 - 15.5 - 19.7 - 30.9 - 27.4 - 21.1

a µ j ) [(µ2NA)/(4πε0VkBT)]1/2 where NA is Avogadro’s number; V is the molar volume, T is the system temperature, ε0 is the permittivity of the vacuum, and kB is Boltzmann’s constant. b Pint ) (∂U/∂V)T ) TRP/κT - P. c Dce ) (∆Hvap - RT)/V. d For definitions, see Table 1. e Reference 98. f Reference 93. g Reference 99. h Reference 100. i Reference 101.

E Table 7. Molar Excess Functions, Gibbs Energies, Gm , Enthalpies, E E E E Hm , and TSm () Hm - Gm ) at Equimolar Composition and T ) 298.15 K for 1-Alkanol + Organic Solvent Mixtures

system

E Gm /J mol-1

E Hm /J mol-1

E TSm /J mol-1

ethanol + n-C6 1-propanol + n-C6 1-butanol + n-C6 1-pentanol + n-C6 1-hexanol + n-C6 1-decanol + n-C6 methanol + diethylether ethanol + diethylether 1-methanol + dipropylether 1-propanol + dipropylether 1-hexanol + dipropylether 1-octanol + dipropylether methanol + dibutylether 1-propanol + dibutylether 1-butanol + dibutylether 1-hexanol + dibutylether 1-octanol + dibutylether 1-decanol + dibutylether

1374102 1295104 1140106 1041107 975109 723111 81143 681113 109048 81449 61512 52612 124447 94047 85444 72747 69647 58947

548103 533105 510106 494108 460110 386112 44163 61963 60948 74049 71051 66451 78865 88665 84065 81765 80265 82265

-826 -762 -630 -547 -515 -337 -370 -62 -481 -74 95 138 -456 -54 -14 90 106 233

When the alcohol size is increased, one can expect that η11 and η12 decrease, as interactions between 1-1 and 1-2 molecules become weaker. The same is still valid for ∆χ12/P*1 , which from eqs 5 and 6 is ∆η/η11. This means that η12 must decrease more smoothly than η11. As a matter of fact, when investigating these mixtures in terms of the ERAS model,16 we encountered that the enthalpy of hydrogen bonding between 1-alkanol and ether, ∆h*AB ) -15 kJ mol-1, is independent of the alcohol (from 1-propanol) for dipropyl or dibutylether systems. 5.1.2. Effect of Increasing the Chain Length of the Ether in Systems with a Given 1-Alkanol. In this case, Table E slightly increases, which may be explained 2 shows that UV,m considering that interactions between unlike molecules become weaker, and that the creation of these interactions are more difficult when long ethers are involved, as the oxygen atom is E ) values then more sterically hindered. The similar X12(UV,m obtained for 1-alkanol (from 1-propanol) + DPE or + DBE systems are remarkable and suggest that dispersive interactions merely differ by size effects and can be represented by the same interactional parameter. These features are confirmed by the parameters obtained when applying the ERAS model.16 So, the corresponding ∆h*AB values are (in kJ mol-1): -19.5 (methanol + DEE) < -18 (methanol + DPE) < -15 (methanol + DBE);

7425

-16.3 (ethanol + DEE or + DPE) < -15 (ethanol + DBE); while for the remaining solutions, it is -15 kJ mol-1. Moreover, the physical interaction parameter can be assumed to be independent of the ether (DPE or DBE) in mixtures with the longer 1-alkanols (from 1-hexanol). E Finally, we note that σr(Hm ) is higher for solutions of DBE mixed with 1-alkanol (* methanol) (Table 2). This may be due to the fact that the larger aliphatic surface of the ether leads to stronger orientational effects, as the resulting mixture is more E ) similar to 1-alkanol + n-alkane systems. The very large σr(Hm value for the methanol + DEE mixture may be due to experimental inaccuracies, as it does not fit in this scheme. E value for 1-propanol + DEE, obtained Similarly, the high UV,m E 55 , needs confirmation. from a large and negative Vm 5.1.3. Temperature Effects. Such effects can be examined from the σr(HEm) results obtained for 1-alkanol + DME mixtures E ) values at 323.15 K (Table 2, Figures 2 and 5). The low σr(Hm for systems with 1-propanol or 1-butanol reveal that the behavior of these solutions is not far from random mixing. That is, association effects decrease with the increase of temperature. E curves for 1-propanol or 1-butanol The nearly symmetric Hm mixtures also support this statement (Figure 2). 5.2. 1-Alkanol + Linear Cyclic Ether Mixtures. 5.2.1. Effect of Replacing a Linear Monoether by an Isomeric Cyclic Monoether in Mixtures with a Given E (linear 1-Alkanol: Cyclization Effect. Here, we note that Hm E monoether) < Hm(cyclic monoether) (Table 2). That is, cyclic monoethers are more active compounds when breaking the E values of systems alcohol self-association. The higher Hm involving THF or THP may be mainly ascribed to stronger dipolar interactions between molecules of such ethers, consequence of their higher µ j values: µ j (DEE) ) 0.431 < µ j (THF) ) E 0.741; µ j (DPE) ) 0.395 < µ j (THP) ) 0.629 (Table 6). The Hm values of heptane solutions support this conclusion. For example, E E (diethylether)84 ) 405 < Hm (THF)85 ) 791 J mol-1, or Hm E E (DPE)86 ) 204 < Hm (THP)85 ) 598 J mol-1. Hm E E (linear monoether) < Vm (cyclic monoether) Similarly, Vm (Table 3), which may be explained in terms of the mentioned E dipolar interactions. Nevertheless, the low Vm values of cyclic ether solutions contrast with their rather high excess enthalpies,

Figure 8. Physical, HEphys, and chemical, HEchem, contributions to HEm at 298.15 K and equimolar composition vs n, the number of C atoms in the alcohol, for 1-alkanol (1) + oxaalkane (2) mixtures: (b), dipropylether; (9), tetrahydropyran. Calculations developed using parameters previously determined.4,16

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which underlines that these are also structured mixtures, and E from the lead, in many cases, to small contributions to Hm equation of state term. Larger differences between HEm and UEV,m are encountered for methanol systems. From the comparison with 1-alkanol + linear monoether mixtures, those including cyclic ethers also differ by (i) symmetrical HEm curves for systems containing longer 1-alkanols E values; e,g., for the ethanol + (Figure 1 and 3); (ii) lower Cp,m tetrahydrofuran system, this magnitude is87 2.96 J mol-1 K-1; E E 46 values. So, for the same solution, Gm (iii) increased TSm ) E 85 E -1 -1 385 J mol , Hm ) 791 J mol , and TSm ) 406 J mol-1, which is much higher than the value of the ethanol + diethylether mixture, -62 J mol-1 (Table 7). All of this remarks that the cyclization effect leads to a strengthening of dipolar interactions and to a weakening of association effects. The Flory E ) and ∆i values which are lower for model provides σr(Hm systems with cyclic ethers (Tables 2 and 4 and Figure 4), indicating that, as average, orientational effects are weaker in this type of solution. E E and Hchem contributions to Finally, Figure 8 compares Hphys E Hm obtained from the ERAS model for 1-alkanol + THP or + E is much larger for DPE systems.4,16 It is noteworthy that Hphys the THP solutions, particularly for mixtures with the longer 1-alkanols, which explains the large deviations between experimental and ERAS results for such systems. For example, for E ) ) 0.336, much higher the 1-hexanol + THP system,68 σr(Hm than the Flory result (Table 2). 5.2.2. Effect of Increasing the Chain Length of the E 1-Alkanol in Systems with a Given Cyclic Ether. Both Hm E and Vm functions increase under this condition (Table 2), and the same occurs for THF or THP + alkane mixtures.15,85,88,89 Moreover, the HEm curves are nearly symmetrical for the mixtures containing the longer 1-alkanols (Figures 1 and 3). It is possible to state that dipolar interactions become more important when the size of the alcohol is increased. This may be due to (i) a E from the dipolar interactions between larger contribution to Hm ether molecules or (ii) a weakening of association effects, as previously shown, in such a way that interactions between unlike molecules are stronger for methanol or ethanol systems. Note that the HEm (or UEV,m) increase from methanol to ethanol, or from ethanol to 1-propanol, is steeper than those involving longer 1-alkanols (Table 2). Therefore, orientational effects become weaker when the alcohol size is increased, which is supported E ) and ∆i (i ) 1, 2) values (Tables 2 by the corresponding σr(Hm and 4). It is remarkable that mixtures containing alcohols, say from 1-hexanol, show a behavior close to random mixing (Figures 1, 3, and 5). E E ) and X12(UV,m ) with the Regarding the dependence of X12(Hm alcohol size, it is similar to those of mixtures containing homomorphic linear monoethers. As previously, the lower E ) value obtained for the methanol + THF system X12(Hm E from the underlines the importance of the contribution to Hm equation of state term. Similar considerations to those stated for ∆η/η11 of 1-alkanol + dipropyl or + dibutylether mixtures are here valid. So, in terms of the ERAS model, ∆h*AB is essentially independent (see below) of the alcohol for THF or THP systems4 (-18.5 kJ mol-1). For the methanol + THF mixture, ∆h*AB ) -19.5 kJ mol-1, indicating that interactions between unlike molecules are stronger in this case.4 5.2.3. Effect of Increasing the Size of the Cyclic Ether in Systems with a Given 1-Alkanol. We note that, except for E E (THF) ≈ Hm (THP) (Table methanol systems (see above), Hm E 2), and the same occurs for UV,m due to the rather low VEm values

of these systems. This may be ascribed to a compensation between the larger positive contribution to HEm from the stronger interactions between ether molecules in THF solutions and the more negative contribution related to the higher number of new OH-O interactions created consequence of the less steric hindrance of the oxygen atom placed in THF. The latter effect together with structural effects (size differences between E E mixtures components) may explain that Vm (THF) < Vm (THP) (Table 3). The replacement of THF by THP does not change essentially the orientational effects in mixtures with the longer 1-alkanols, which show a behavior close to random mixing. The stronger orientational effects are encountered in the methanol + THF system. 5.3. Kirkwood-Buff Integrals. The previous findings are supported by the results obtained from the Kirkwood-Buff formalism (Table 5). For 1-alkanol + n-alkane mixtures, the G11 curves show a very high maximum al low concentrations of the alcohol.90 So, for the 1-butanol + heptane system at 313.15 K, the maximum of G11 is ≈8000 cm3 mol-1 at x1 ≈ 0.15. When in mixtures with a given 1-alkanol, the alkane is replaced by a linear monoether, decreased G11 values are obtained due to the formation of new alcohol-ether interactions (Table 5). The larger G11values are encountered for these systems at lower mole fractions of the alcohol, which confirms the important role of the alcohol self-association (Figures 6 and 7). The local mole factions, x11, also show that there is an excess of molecules of alcohol around a central one of the same type (Table 5). This is in agreement with the results obtained from the Flory theory. Note that this model overestimates the interactions between unlike molecules in the region of low alcohol concentration, as the E X12 values obtained from Hm data in that region are larger E than the value calculated using the corresponding Hm measurement at equimolar composition. On the other hand, G11 decreases in mixtures with a given linear monoether, when the 1-alkanol size is increased (Table 5). The larger differences between values of the local mole fractions and the bulk compositions are found for those systems including the shorter alcohols, i.e., orientational effects are more important in such solutions. The increase of the ether size in mixtures with a given 1-alkanol leads to increasing values of G11, |G12|, and of the xij - xi differences (Table 5) and, therefore, to stronger orientational effects in systems involving ethers with larger aliphatic surfaces. So, the Gij integrals indicate that the weaker orientational effects are encountered for the methanol + DEE system and confirm E that the very large σr(Hm ) value obtained for this solution using the Flory theory is due, at least in part, to experimental inaccuracies. The replacement of a linear by a cyclic monoether yields lower G11 and |G12| values and also smaller xij - xi differences (Table 5, Figure 7). Particularly, the 1-propanol + THF mixture is close to random mixing. Similar results have been previously reported in the literature for this mixture34 and have been found for other systems of polar/associated compounds which also show a random mixing behavior, e.g., 1-alkanol + amide.41,91,92 Finally, Table 5 also shows that the temperature increase leads to lower G11 and |G12| values and to weaker orientational effects. A result is also obtained from the Flory theory.


6. Conclusions Binary mixtures of 1-alkanols with linear or cyclic monoethers have been studied using the Flory model and the Kirkwood-Buff formalism. Both theories provide consistent results. Systems involving linear monoethers are characterized by orientational effects related to the self-association of the alcohol, in such way that the mentioned effects decrease when the size of the alcohol is increased in solutions with a given ether. Orientational effects become more relevant when the chain length of the linear monether mixed with a fixed 1-alkanol increases. Dispersive interactions merely differ by size effects for solutions of 1-alkanol (from 1-propanol) and DPE or DBE. Systems with cyclic monoethers are characterized by a strengthening of dipolar interactions and a weakening of association effects. As result, orientational effects are weaker in this type of solutions. It is remarkable that mixtures with the longer 1-alkanols (from 1-hexanol) show a behavior close to random mixing. A behavior close to random mixing is also observed when the temperature increase, as in the case of 1-propanol or 1-butanol + diethylether systems. Acknowledgment The authors gratefully acknowledge the financial support received from the Consejerıá de Educacioń y Cultura of Junta de Castilla y Leoń, under Projects VA075A07 and VA052A09, and from the Ministerio de Educacioń y Ciencia, under the Project FIS2007-61833. Literature Cited (1) (a) Kehiaian, H. V. Group contribution methods for liquid mixtures: a critical review. Fluid Phase Equilib. 1983, 13, 243. (b) Kehiaian, H. V. Thermodynamics of binary liquid organic mixtures. Pure Appl. Chem. 1985, 57, 15. (2) Guggenheim, E. A. Mixtures; Oxford University Press: Oxford, 1952. (3) Delcros, S.; Quint, J. R.; Grolier, J.-P. E.; Kehiaian, H. V. DISQUAC calculation of thermodynamic properties of ether + 1-alkanol systems. Comparison with UNIFAC calculation. Fluid Phase Equilib. 1995, 113, 1. (4) Gonza´lez, J. A.; Mozo, I.; Garcıá de la Fuente, I.; Cobos, J. C.; Durov, V. A. Thermodynamics of 1-alkanol + cyclic ether molecules. Fluid Phase Equilib. 2006, 245, 168. (5) Gmehling, J.; Li, J.; Schiller, M. A modified UNIFAC model. 2. Present parameter matrix and results for different thermodynamic properties. Ind. Eng. Chem. Res. 1993, 32, 178. (6) Heintz, A. A new theoretical approach for predicting excess properties of alkanol/alkane mixtures. Ber. Bunsen-Ges. Phys. Chem. 1985, 89, 172. (7) Kretschmer, C. B.; Wiebe, R. Thermodynamics of alcoholhydrocarbon mixtures. J. Chem. Phys. 1954, 22, 1697. (8) Renon, H.; Prausnitz, J. M. On the thermodynamics of alcoholhydrocarbon solutions. Chem. Eng. Sci. 1967, 22, 299; errata p 1891. (9) Treszczanowicz, A.; Kehiaian, H. V. Excess enthalpy and excess entropy of athermal associated mixtures of type A+Ai+B. Bull. Acad. Pol. Sci. 1968, 171. (10) Flory, P. J. Statistical thermodynamics of liquid mixtures. J. Am. Chem. Soc. 1965, 87, 1833. (11) Garriga, R.; Pe´rez, P.; Gracia, M. Vapour pressures at eight temperatures of mixtures of di-n-propylether + ethanol or + 1-butanol. Thermodynamic description of mixtures of di-n-propylether + alkanol according to the ERAS model. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1466. (12) Garriga, R.; Martıńez, S.; Pe´rez, P.; Gracia, M. Vapour pressures at several temperatures between 288.15 and 323.15 K of di-n-propylether with 1-hexanol or 1-octanol. Application of the ERAS model. Fluid Phase Equilib. 1998, 147, 195. (13) Kammerer, K.; Lichtenthaler, R. N. Excess properties of binary alkanol-ether mixtures and the application of the ERAS model. Thermochim. Acta 1998, 310, 61. (14) Rezanova, E. N.; Kammerer, K.; Lichtenthaler, R. N. Excess properties of binary 1-alkanol + diisopropyl ether (DIPE) or + dibutyl ether

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(DBE) mixtures and the application of the extended real associated solution model. J. Chem. Eng. Data 1999, 44, 1235. (15) Keller, M.; Schnabel, S.; Heintz, A. Thermodynamics of the ternary mixture propan-1-ol + tetrahydrofuran + n-heptane at 298.15 K. Experimental results and ERAS model calculations of GE, HE and VE. Fluid Phase Equilib. 1995, 110, 231. (16) Gonza´lez, J. A.; Mozo, I.; Garcıá de la Fuente, I.; Cobos, J. C. Thermodynamics of (1-alkanol + linear monoether) systems. J. Chem. Thermodyn., 2008, 40, 1495. (17) Mohren, S.; Heintz, A. Excess properties of propan-1-ol + polyether and propan-1-ol + polyamine mixtures. Experimental results of HE and VE and application of a multiple cross-association theory based on the ERAS model. Fluid Phase Equilib. 1997, 133, 247. (18) Riesco, N.; Gonza´lez, J. A.; Villa, S.; Garcıá de la Fuente, I.; Cobos, J. C. Thermodynamics of organic mixtures containing amines. III. Molar excess volumes at 298.15 K for tripropylamine + n-alkane systems. Application of the Flory theory to N, N, N-trialkylamine + n-alkane systems. Phys. Chem. Liq. 2003, 41, 309. (19) Wang, L.; Benson, G. C.; Lu, B.C.-Y. Excess molar enthalpies of methyl tert-butyl ether + n-hexane + (n-decane or n-dodecane) ternary mixtures at 298.15 K. Thermochim. Acta 1993, 213, 83. (20) Benson, G. C.; Pflug, H. D. Molar excess volumes of binary systems of normal alcohols at 25 °C. J. Chem. Eng. Data 1970, 15, 382. (21) Riesco, N.; Villa, S.; Gonza´lez, J. A.; Garcıá de la Fuente, I.; Cobos, J. C. Thermodynamic properties of n-alkoxyethanols + organic solvent mixtures. XIII. Application of the Flory theory to 2-methoxyethanol + n-alkoxyethanols systems. Thermochim. Acta 2000, 362, 89. (22) Benson, G. C.; Halpin, C. J. Ultrasonic speeds and isentropic compressibilities of binary mixtures of n-octane with each of hexane isomers at 298.15 K. Can. J. Chem. 1987, 65, 322. (23) Aicart, E.; Menduinã, C.; Arenosa, R. L.; Tardajos, G. Correlation of the Prigogine-Flory theory with isothermal compressibility and excess enthalpy data for cyclohexane + alkane mixtures. J. Solution Chem. 1984, 13, 443. (24) Aicart, E.; Menduinã, C.; Arenosa, R. L.; Tardajos, G. Correlation of the Prigogine-Flory theory with isothermal compressibility and excess enthalpy data for benzene + n-alkane mixtures. J. Solution Chem. 1983, 12, 703. (25) Letcher, T. M.; Spiteri, W. L. The excess volumes of some mixtures of a cycloalkane and an n-alkane. J. Chem. Thermodyn. 1979, 11, 435. (26) Battacharyya, S. N.; Patterson, D. Excess heat capacities of cyclohexane + alkane systems and orientational order of n-alkanes. J. Phys. Chem. 1979, 83, 2979. (27) Letcher, T. M. Excess volumes of (benzene + a cycloalkane) and of (benzene + an n-alkane) at two temperatures. J. Chem. Thermodyn. 1984, 16, 805. (28) Tardajos, G.; Aicart, E.; Costas, M.; Patterson, D. Liquid structure and second-order mixing functions for benzene, toluene and p-xylene with n-alkanes. J. Chem. Soc., Faraday Trans. 1 1986, 82, 2977. (29) Gonza´lez, J. A.; Mozo, I.; Garcıá de la Fuente, I.; Cobos, J. C.; Riesco, N. Thermodynamics of mixtures containing alkoxyethanols XXVII. Predictions of isobaric thermal expansion coefficients, compressibilities and speeds of sound from the Flory theory. Thermochim. Acta 2008, 476, 20. (30) Gonza´lez, J. A.; Riesco, N.; Mozo, I.; Garcıá de la Fuente, I.; Cobos, J. C. Thermodynamics of mixtures containing alkoxyethanols XXI. Application of the Flory theory to the study of orientational effects in systems with dibutyl ether or 1-butanol. Ind. Eng. Chem. Res. 2007, 46, 1350. (31) Kirkwood, J. G.; Buff, F. P. The statistical mechanical theory of solutions. 1. J. Chem. Phys. 1951, 19, 774. (32) Ben-Naim, A. Inversion of the Kirkwood-Buff theory of solutions: application to the water-ethanol system. J. Chem. Phys. 1977, 67, 4884. (33) Matteoli, E.; Lepori, L. Solute-solute interactions in water. II. An analysis through the Kirkwood-Buff integrals for 14 organic solutes. J. Chem. Phys. 1984, 80, 2856. (34) Marcus, Y. Preferential solvation in mixed solvents. 13. Mixtures of tetrahydrofuran with organic solvents: Kirkwood-Buff integrals and volume-corrected preferential solvation parameters. J. Solution Chem. 2006, 35, 251. (35) Abe, A.; Flory, P. J. The thermodynamic properties of mixtures of small, nonpolar molecules. J. Am. Chem. Soc. 1965, 87, 1838. (36) Flory, P. J.; Orwoll, R. A.; Vrij, A. Statistical thermodynamics of chain molecular liquids. I. An equation of state for normal paraffin hydrocarbons. J. Am. Chem. Soc. 1964, 86, 3507. (37) Flory, P. J.; Orwoll, R. A.; Vrij, A. Statistical thermodynamics of chain molecular liquids. II. Liquid mixtures of normal paraffin hydrocarbons. J. Am. Chem. Soc. 1964, 86, 3515. (38) Orwoll, R. A.; Flory, P. J. Thermodynamic properties of binary mixtures of n-alkanes. J. Am. Chem. Soc. 1967, 89, 6822.

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(39) Marcus, Y. Preferential solvation in mixed solvents. X. Completely miscible aqueous co-solvent binary mixtures at 298.15 K. Monatsh. Chem. 2001, 132, 1387. (40) Zielkiewicz, J. Solvation of DMF in the N, N-dimethylformamide + alcohol + water mixtures investigated by means of the Kirkwood-Buff integrals. J. Phys. Chem. 1995, 99, 4787. (41) Zielkiewicz, J. Preferential solvation in (amide + alcohol) binary mixtures. Part 1. The N-methylpyrrolidinone + ethanol mixture at T ) 313.15 K: thermodynamic results and molecular dynamic calculation. Phys. Chem. Chem. Phys. 2003, 5, 1619. (42) Zielkiewicz, J. Solvation of amide group by water and alcohols investigated using the Kirkwood-Buff theory of solutions. J. Chem. Soc., Faraday Trans. 1998, 94, 1713. (43) Srivastava, R.; Smith, B. D. Total-pressure vapor-liquid equilibrium data for binary systems of diethylamine with acetone, acetonitrile, and methanol. J. Chem. Eng. Data 1985, 30, 308. (44) Lepori, L.; Matteoli, E.; Bernazzani, L.; Ceccanti, N.; Conti, G.; Gianni, P.; Mollica, V.; Tine´, M. R. Isothermal vapour/liquid equilibria of binary mixtures with dibutyl ether at 298.15 K. Phys. Chem. Chem. Phys. 2002, 2, 4837. (45) Arm, H.; Bankay, D.; Schaller, R.; Walti, M. Untersuchungen uber das verhalten organischer mischphasen - dampfdrucke thermodynamische mischungsfunktionen und brechungsindizes der binaren systeme tetrahydrofuran-diathylather und methanol-tetrahydrofuran bei 25 degrees. HelV. Chim. Acta 1966, 49, 2598. (46) Lepori, L.; Matteoli, E. Excess Gibbs energies of the ternary system ethanol + tetrahydrofuran + cyclohexane at 298.15 K. Fluid Phase Equilib. 1997, 134, 113. (47) Mozo, I. unpublished results, personal communication. (48) Garriga, R.; Sańchez, F.; Pe´rez, P.; Gracia, M. Vapour pressures at eight temperatures between 278.15 and 323.15 K and excess enthalpies and volumes at T ) 298.15 K of (n-propylether + methanol). J. Chem. Thermodyn. 1997, 29, 649. (49) Garriga, R.; Sańchez, F.; Pe´rez, P.; Gracia, M. Isothermal vapourliquid equilibrium at eight temperatures and excess functions at 298.15 K of di-n-propylether with 1-propanol or 2-propanol. Fluid Phase Equilib. 1998, 138, 131. (50) Canosa, J.; Rodrı´guez, A.; Tojo, J. Binary mixture properties of diethyl ether with alcohols and alkanes from 288.15 to 298.15 K. Fluid Phase Equilib. 1999, 156, 57. (51) Inãrrea, I.; Valero, J.; Pe´rez, P.; Gracia, M.; Gutie´rrez Losa, C. HmE and VEm of some (butanone or dipropylether + an alkanol) mixtures. J. Chem. Thermodyn., 1988, 20, 193. (52) Serna, A.; Garcıá de la Fuente, I.; Gonza´lez, J. A.; Cobos, J. C.; Casanova, C. Excess molar volumes of 1-alcohol + aliphatic monoethers at 298.15 K. Fluid Phase Equilib., 1995, 110, 361. (53) Mozo, I.; Garcıá de la Fuente, I.; Gonza´lez, J. A.; Cobos, J. C. Densities, excess molar volumes, speeds of sounds at (293.15, 298.15 and 303.15) K and isentropic compressibilities at 298.15 K for 1-butanol, 1-pentanol or 1-hexanol + dibutylether systems. J. Chem. Eng. Data 2008, 53, 857. (54) Lepori, L.; Matteoli, E. Excess volumes of the ternary system ethanol + tetrahydrofuran + cyclohexane at 298.15 K. Fluid Phase Equilib. 1998, 145, 69. (55) Savaroglu, G.; Tasagal, D.; Aral, E. Excess molar isentropic compressibilities, excess molar volumes, and excess sound speeds of the 1-propanol + diethyl ether + 1-octanol ternary mixture and constituent binary mixtures at 298.15 K. J. Solution Chem. 2007, 28, 245. (56) Amigo, A.; Bravo, R.; Pintos, M. Excess volumes of binary mixtures containing cyclic ethers + alkanols at 298.15 K. J. Chem. Eng. Data 1993, 38, 141. (57) Parveen, S.; Shukla, D.; Singh, S.; Singh, K. P.; Gupta, M.; Shukla, J. P. Ultrasonic velocity, density, viscosity and their excess parameters of the binary mixtures of tetrahydrofuran with methanol and o-cresol at varying temperaturas. Appl. Acoustics 2009, 70, 507. (58) Zielkiewicz, J. Preferential solvation of N-methylformamide N,Ndimethylformamide and N-methylacetamide by water and alcohols in the binary and ternary mixtures. Phys. Chem. Chem. Phys. 2000, 2, 2925. (59) Marcus, Y. Preferential solvation in mixed solvents. 14. Mixtures of 1,4-dioxane with organic solvents: Kirkwood-Buff integrals and volumecorrected preferential solvation parameters. J. Mol. Liq. 2006, 128, 115. (60) Allen, G.; Chai, Z.; Chong, C. L.; Higgins, J. S.; Tripathi, J. Thermodynamics of oligomeric binary mixtures of polyethylene glycol and polypropylene glycol methylethers. Polymer 1984, 25, 239. (61) Howell, P. J.; Skillerne de Bristowe, B. J.; Stubley, D. Enthalpies of mixing of carbon tetrachloride with some methyl-substituted benzenes. Part III.Analysis of the results by use of Flory’s theory of liquid mixtures. J. Chem. Soc. A 1971, 397.

(62) Park, S.-J.; Han, K.-J.; Gmehling, J. Vapor-liquid equilibria for binary systems aof dimethyl ether (DME) with C1-C4 alkanol-1-ols at 323.15 K and liquid-liquid equilibria for ternary system DME + methanol + water at 313.15 K. J. Chem. Eng. Data 2007, 52, 230. (63) Villamanãń, M. A.; Casanova, C.; Roux, A. H.; Grolier, J.-P. E. Calorimetric investigation of the interactions between oxygen and hydroxyl groups in (alcohol + ether) at 298.15. J. Chem. Thermodyn. 1982, 14, 251. (64) Pintos, M.; Bravo, R.; Paz Andrade, M. I.; Pe´rez Villar, V. Excess enthalpies of (n-alkanol + dipropylether), (n-alkanol + 1,2-diethoxyethane), and (n-alkanol + 2-ethoxyethanol) at 298.15 K. J Chem. Thermodyn. 1982, 14, 951. (65) Mozo, I.; Garcıá de la Fuente, I.; Gonza´lez, J. A.; Cobos, J. C. Molar excess enthalpies at 298.15 K for 1-alkanol + dibutylether systems. J. Chem. Thermodyn., in press. (66) Letcher, T. M.; Govender, P. U. Excess molar enthalpies of an alkanol + a cyclic ether at 298.15. J. Chem. Eng. Data 1995, 40, 1097. (67) Pin˜eiro, A.; Olvera, A.; Garcıá-Miaja, G.; Costas, M. Excess molar enthalpies of tetrahydrofuran or diisopropyl ether + 1-alkanols at 298.15 K using a newly designated flow mixing cell for isothermal microcalorimeter. J. Chem. Eng. Data 2001, 46, 1274. (68) Alonso, V.; Calvo, E.; Bravo, R.; Pintos, M.; Amigo, A. Thermodynamic properties of tetrahydropyran + 1-alkanol mixtures. J. Chem. Eng. Data 1994, 39, 926. (69) Miranda, Y.; Pin˜eiro, A.; Brocos, P. Thermodynamics of mixing tetrahydropyran with 1-alkanols and excess enthalpies of homomorphyrelated systems. J. Chem. Eng. Data. 2007, 52, 429. (70) Cha´vez, H.; Pin˜eiro, A.; Brocos, P. Thermodynamics of mixing tetrahydrofuran with 1-alkanols and excess enthalpies of homomorphyrelated systems. J. Chem. Eng. Data 2007, 52, 2298. (71) Villamanãń, M. A.; Casanova, C.; Roux-Desgranges, G.; Grolier, J.-P. E. Thermochemical behaviour of mixtures of n-alcohol + aliphatic ether: heat capacities and volumes at 298.15 K. Thermochim. Acta 1982, 52, 279. (72) Paraskevopoulos, G. C.; Missen, R. W. Thermodynamic properties of solutions of alcohols and carbon tetrachloride. 1. Free energies and volumes of mixing. Trans. Faraday Soc. 1962, 58, 869. (73) Benson, G. C.; Kiyohara, O. Thermodynamic properties of some cycloalkane-cycloalkanol systems at 298.15 K. 4. Excess volumes. J. Chem. Eng. Data 1976, 21, 362. (74) Treszczanowicz, A. J.; Kiyohara, O.; Benson, G. C. Interpretation of the excess volume in alcohol and saturated-hydrocarbon binary-systems. Bull. Acad. Pol. Sci., Ser. Sci. Chim. 1981, XXIX, 103. (75) Treszczanowicz, A. J.; Benson, G. C. Excess volumes for n-alkanols + n-alkanes. II. Binary mixtures of n-pentanol, n-hexanol, n-octanol, and n-decanol + n-heptane. J. Chem. Thermodyn. 1978, 10, 967. (76) Treszczanowicz, A. J.; Benson, G. C. Excess volumes for n-alkanols + n-alkanes. I. Binary mixtures of methanol, ethanol, n-propanol, and n-butanol + n-heptane. J. Chem. Thermodyn. 1977, 9, 1189. (77) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworths: London, 1982. (78) Kalali, H.; Kohler, F.; Svejda, P. Excess properties of binary mixtures of 2,2,4-trimethylpentane with one polar component. Fluid Phase Equilib. 1985, 20, 75. (79) Ivanov, E. V.; Abrosimov, V. K. Relationship between the internal pressure and cohesive energy density of a liquid nonelectrolyte. Consequence of application of Dack’s concept. J. Struct. Chem. 2005, 46, 856. (80) Bagley, E. B.; Nelson, T. P.; Barlow, J. W.; Chen, S.-A. Internal pressure and liquid-state energies. Ind. Eng. Chem. Fundam. 1970, 9, 92. (81) Dack, M. R. J. Solvent structure. The use of internal pressure and cohesive energy density to examine contributions to solvent-solvent interactions. Aust. J. Chem. 1975, 28, 1643. (82) Gonza´lez, J. A.; Garcıá de la Fuente, I.; Cobos, J. C. Thermodynamics of mixtures with strongly negative deviations from Raoult’s Law: Part 4. Application of the DISQUAC model to mixtures of 1-alkanols with primary or secondary linear amines. Comparison with Dortmund UNIFAC and ERAS results. Fluid Phase Equilib. 2000, 168, 31. (83) Wilhelm, E. Thermodynamics of solutions: selected aspects. Thermochim. Acta 1990, 162, 43. (84) Marongiu, B.; Dernini, S.; Lepori, L.; Matteoli, E.; Kehiaian, H. V. Thermodynamics of binary mixtures containing ethers or acetals. 1. Excess enthalpies of linear ethers or acetals + heptane or + cyclohexane mixtures. J. Chem. Eng. Data 1988, 33, 118. (85) Inglese, A.; Wilhelm, E.; Grolier, J.-P. E.; Kehiaian, H. V. Thermodynamics of binary mixtures containing cyclic ethers. I. Excess enthalpies of oxolane, 1,3-dioxolane, 1,3-dioxane and 1,4-dioxane with n-alkanes. J. Chem. Thermodyn. 1980, 12, 217. (86) Kimura, F.; D’Arcy, P. J.; Benson, G. C. Excess enthalpies and heat capacities for (di-n-propylether + heptane). J. Chem. Thermodyn. 1983, 6, 511.

Ind. Eng. Chem. Res., Vol. 48, No. 15, 2009 (87) Conti, G.; Gianni, P.; Matteoli, E. Excess enthalpies and excess heat capacities of the ternary system ethanol + tetrahydrofuran + cyclohexane at 298.15 K. Thermochim. Acta 1994, 247, 293. (88) Inglese, A.; Grolier, J.-P. E.; Wilhelm, E. Excess volumes of mixtures of oxolane, oxane, 1,3-dioxolane, and 1,4-dioxane with n-alkanes at 298.15 K, 308.15 and 318.15 K. J. Chem. Eng. Data 1983, 28, 124. (89) Pintos, M.; Amigo, A.; Bravo, R. Effect of the alkane chaıń-length of a binary mixture containing a cyclic ether. J. Chem. Thermodyn. 1993, 25, 337. (90) Zielkiewicz, J. Kirkwood-Buff integrals in the binary and ternary mixtures containing heptane and aliphatic alcohol. J. Phys. Chem. 1995, 99, 3357. (91) Zielkiewicz, J. Preferential solvation in (amide + alcohol) binary mixtures. Part 2. The N-methylpyrrolidinone + methanol mixture at T ) 313.15 K: thermodynamic results and molecular dynamic calculation. Phys. Chem. Chem. Phys. 2003, 5, 3193. (92) Zielkiewicz, J. Preferential solvation of N-methylformamide N,Ndimethylformamide and N-methylacetamide by water and alcohols in the binary and ternary mixtures. Phys. Chem. Chem. Phys. 2000, 2, 2925. (93) Riddick, J. A.; Bunger, W. B.; Sakano T. K. Organic solVents; Weissberger, A., Ed.; Techniques of Chemistry; Wiley: New York, 1986; Vol. II. (94) Manzini, G.; Crescenzi, V. Simple, accurate method of calculation of the thermal pressure coefficient of non-polar liquids and a possible estimate of their excess volumes of mixing. G. Chim. Ital. 1974, 104, 51. (95) Mozo, I.; Garcıá de la Fuente, I.; Gonza´lez, J. A.; Cobos, J. C. Thermodynamics of mixtures containing alkoxyethanols. Part XX. Densities, excess molar volumes and isothermal compressibilities for 2-alkoxyethanol + dibutylether systems at 293.15, 298.15 and 303.15 K. J. Mol. Liq. 2006, 129, 155. (96) Giner, B.; Olivares, B.; Giner, I.; Pera, G.; Lafuente, C. Isentropic and excess isentropic compressibilities of binary mixtures containing cyclic ethers and chloroalkanes. J. Solution Chem. 2007, 36, 375. (97) Cibulka, I.; Hneskowsky, L.; Takagi, T. P-F-T data of liquids: summarization and evaluation. 3. Ethers., ketones, aldehydes, carboxylic acids, and esters. J. Chem. Eng. Data 1997, 42, 2. (98) CRC Handbook of Chemistry and Physics, 75th ed.; Lide, D. R., Ed.; CRC Press: Boca Raton, 1995. (99) Reid, R. C.; Prausnitz, J. M.; Poling, B. E. The Properties of Gases and Liquids, 4th ed.; McGraw Hill: New York, 1987. (100) McClellan, A. L. Tables of Experimental Dipole Moments; Rahara Enterprises: El Cerrito, US, 1974; Vols. 1-3.

7429

(101) Majer, V.; Svoboda, V. Enthalpies of Vaporization of Organic Compounds; Blackwell: Oxford, 1985. (102) O’Shea, S. J.; Stokes, R. H. Activity coefficients and excess partial molar enthalpies for (ethanol + hexane) from 283 to 318 K. J. Chem. Thermodyn. 1986, 18, 691. (103) Wang, L.; Benson, G. C.; Lu, B. C.-Y. Excess enthalpies of (ethanol + hexane + decane or dodecane) at the temperature 298.15 K. J. Chem. Thermodyn. 1992, 24, 1135. (104) Hwang, S.-C.; Robinson, R. L. Vapor-liquid equilibriums at 25 °C for nine alcohol-hydrocarbon binary systems. J. Chem. Eng. Data 1977, 22, 319. (105) Wang, L.; Benson, G. C.; Lu, B. C.-Y. Excess enthalpies of 1-propanol + n-hexane + n-decane or n-dodecane at 298.15 K. J. Chem. Eng. Data 1992, 37, 403. (106) Brown, I.; Fock, W.; Smith, F. The thermodynamic properties of solutions of normal and branched alcohols in benzene and n-hexane. J. Chem. Thermodyn. 1969, 1, 273. (107) Sayegh, S. G.; Ratcliff, G. A. Excess Gibbs energies of binary systems of iso-pentanol and n-pentanol with hexane isomers at 25 °C: measurement and prediction by analytical group solution model. J. Chem. Eng. Data 1976, 21, 71. (108) Gonza´lez-Posa, C.; Nuń˜ez, L.; Villar, E. Enthalpies of mixing: 1-pentanol + n-hexane, 1-pentanol + cyclohexane, 1-pentanol + n-hexane + cyclohexane at 25 °C. J. Chem. Thermodyn. 1972, 4, 275. (109) Wieczorek, S. A.; Stecki, J. Vapour pressures and thermodynamic properties of hexan-1-ol + n-hexane between 298.230 and 342.824 K. J. Chem. Thermodyn. 1978, 10, 177. (110) Kimura, F.; Benson, G. C. Excess enthalpies of binary mixtures of 1-hexanol with hexane isomers at 298.15 K. J. Chem. Eng. Data 1981, 26, 317. (111) Wieczorek, S. A. Vapour pressures and thermodynamic properties of decan-1-ol + n-hexane between 283.160 and 333.151 K. J. Chem. Thermodyn. 1979, 11, 239. (112) Kumaran, M. K.; Benson, G. C. Excess enthalpies of decan1-ol + n-pentane, + n-hexane, + n-heptane, + n-octane, + n-nonane, + n-decane, and + n-undecane at 298.15 K. J. Chem. Thermodyn. 1984, 16, 175. (113) Gordon, A. R.; Hornibrook, W. J. Liquid-vapour equilibrium for the system ethanol-diethyl-ether. Can. J. Res. 1946, 24, 263.

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