Estimation of DISQUAC interchange energy parameters for 1-alkanols + benzene or + toluene mixtures

Fluid Phase Equilibria, 93 (1994) l-22 Elsevier Science B.V.

Estimation of DISQUAC interchange energy parameters for 1-alkanols + benzene, or + toluene mixtures

Juan Antonio Gonzalez *, Isaias Garcia de la Fuente, JosC Carlos Cobos and Carlos Casanova

Departamento de Fisica Aplicada II, Universidad de Valladolid, 47011 Valladolid (Spain)

(Received April 26, 1993; accepted in final form July 7, 1993)

ABSTRACT

Gonzalez, J.A., Garcia de la Fuente, I., Cobos, J.C. and Casanova, C., 1994. Estimation of DISQUAC interchange energy parameters for I-alkanols + benzene, or + toluene mixtures. Fluid Phase Equilibria, 93: l-22.

The data available in the literature on vapour-liquid equilibria (VLE), molar excess Gibbs energies (GE), molar excess enthalpies (HE), molar excess heat capacities CC,“), activity coefficients (77) and partial molar excess enthalpies (HF”) at infinite dilution of l-alkanol( 1) + benzene(2), or + toluene(2) mixtures are examined on the basis of the DISQUAC group contribution model. For a more sensitive test of DISQUAC, the azeotropes, obtained from the reduction of the original isothermal VLE data, are also examined for a number of systems.

The components in the mixtures are characterized by three types of groups of surfaces: hydroxyl (OH group), alkane (CH, or CH, groups), and aromatic (C,H, or C,H, groups in benzene or in toluene, respectively; both groups considered as different). The alkane/ aromatic and alkane/hydroxyl contact parameters are available in the literature. The parameters for the hydroxyl/benzene and hydroxyl/toluene interactions are reported in this work. The quasichemical parameters are common for the whole set of alcohols (except the first interchange coefficient of methanol, which is different from that for the remaining alcohols), and do not depend on the aromatic molecule considered. Such dependence is encountered only for the second dispersive parameters. These interchange coefficients together with the first ones increase regularly with the size of the alcohol, although, from ethanol, the former are kept the same for each pair of alcohols. The third dispersive parameters behave in an opposite way to the second ones, and are constant from 1 -dodecanol.

The model consistently describes phase equilibria and the molar excess functions. Depen- dence on temperature of C,” is well represented, even the S-shape of this quantity for the I-butanol + toluene system at high temperatures. Natural logarithms of activity coefficients at infinite dilution are reasonably well reproduced. Predictions on HF” are opposite to those

* Corresponding author.

0378-3812/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZ 0378-3812(93)02398-7

2 J.A. Gonzrilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

for mixtures of I-alkanols with n-alkanes or cyclohexane. They are surprisingly good in the case of HF”, and somewhat poorer for H3”.

Keywords: theory, excess functions, group contribution, associated.

INTRODUCTION

Mixtures of alcohol with hydrocarbons are of considerable practical interest, showing complex behaviour related to the self-association of the alcohol.

Among the group of alcohol + hydrocarbon binary solutions, the systems involving saturated hydrocarbons appear to have different characteristics from those containing unsaturated and aromatic hydrocarbons. Analysis of the thermodynamic and spectroscopic data of mixtures of alcohols with an aromatic compound as solvent has indicated the presence of an interaction between the 71 electrons and the proton of the hydroxyl group (Rowlinson, 1959) which is absent in the alcohol + paraffin mixtures. This interaction, together with the new benzene to benzene interaction, makes the excess enthalpy and entropy of mixing much more positive than those for the corresponding paraffin solutions. So, any satisfactory theoretical treatment must explain these features.

A model more commonly applied to the study of alcohol + n-alkanes mixtures is the so-called associated solution theory (Kretschmer and Wiebe, 1954; Renon and Prausnitz, 1967), which has been refined in different ways to explain the thermodynamic properties of those systems involving an unassociated active molecule as second compound (Nagata, 1973; Stokes, 1977; Nagata and Kawamura, 1979; Nagata and Tamura, 1982). In partic- ular, Nagata and Tamura have studied binary mixtures of methanol ( 1982), ethanol (1984), propanol (1985) and butanol (1987) with aromatic compounds.

Some investigators (Barker, 1952a, b; Tompa, 1953) initiated the treatment of alcoholic solutions, constructing the partition function for the arrange- ment of molecules on a lattice, when the energy of the nearest neighbour interactions depends on the relative orientations of the molecules concerned. So, Barker (1953b) obtained good agreement with the experimental data for the methanol + benzene system, and Goates et al. (1961, 1962) developed a more extensive study of this type of mixture. They used mainly HE data because these provide a more exact test of the theory than GE data, due to the more asymmetric shape of the ethalpy-composition curves.

The most widely used group contribution model to describe any mixture involving alkanols is the UNIFAC method (Fredenslund et al., 1975). Some improvements have been proposed to report more accurate predictions of

J.A. Gonzhlez et al. /Fluid Phase Equilibria 93 (1994) l-22 3

HE. The modified UNIFAC (Larsen, 1986) yields a fairly good representation of this quantity using a reasonable dependence on temperature for the interaction parameters.

As part of a systematic study, we have applied the DISQUAC model (dispersive-quasichemical group contribution method, Kehiaian, 1983, 1985) to report a complete characterization of the alkanol/aliphatic (Gonza- lez et al., 1990, 1991a, b), alkanol/alkanol (Gonzalez et al., 1992), and alkanol/cyclohexane (Gonzalez et al., 1993b) interactions, together with an extensive comparison between DISQUAC calculations and experimental data.

Usually the model gives a good representation of the equilibrium data - vapour-liquid, liquid-liquid and solid-liquid (Gonzalez et al., 1991b, 1993b, c) - as well as of the HE or Cp” data (Gonzalez et al., 1991b), the latter quantity being rather difficult to reproduce for any theoretical model (Kehiaian, 1983).

The limitations of DISQUAC are related to the shape of the HE and liquid-liquid equilibrium curves close to the critical points. In both cases, the calculated curves are not as flat as the experimental ones (Kehiaian, 1985). This behaviour is observed, e.g. in mixtures of methanol with n-alkanes (Gonzalez et al., 1991a) or cyclohexane (Gonzalez et al., 1993b).

However, the most important limitations seem to be related to the predictions of partial molar quantities at infinite dilution, and mainly to HF,“’ (Gonzalez et al., 1991b: 1993b).

The purpose of this paper is to continue the study on mixtures of I-alkanol with an organic solvent, reporting the interaction parameters for the alkanol/aromatic contacts. Previously, systems containing ethanol or methanol and aromatic compounds have been treated by us (Gonzalez et al., 1990, 1991a) using mean values for the interaction parameters of the alkane/aromatic contacts (Kehiaian et al., 1978). Currently, we are consid- ering the variation of these parameters with the chain length of the n-alkane, and distinguishing between the aromatic groups in benzene or toluene molecules (Ait-Kaci, 1982).

REDUCTION OF VAPOUR-LIQUID EQUILIBRIA DATA FROM THE LITERATURE

For the systems under study, I-alkanols + aromatic compound mixtures, a careful search of experimental data was carried out. Most of the data considered in this work are summarized in Tables 1 and 5-9. Coordinates of azeotropes for this type of mixture are not usually given in the literature, so we have reduced, for a number of systems, the experimental isothermal P-x data to obtain these coordinates. The four- or five-parameter Redlich-

4

TABLE 1

J.A. Gonzcilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

Comparison of experimental (exp) coordinates of azeotropes: pressure (P,), temperature (Z’,) and mole fraction (x,,) for 1-alkanol( 1) + benzene(2) or + toluene(2) mixtures with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the I-alkanol.)

m T,,(K) P,(kPa) XlaZ Source of data

Exp Calc Exp Calc

I-Akanol + benzene mixtures 1 298.15 24.502 24.626

313.15 48.807 48.923 2 298.15 16.643 16.675

0.539 a 0.548 Hwang and Robinson, 1977 0.5856 0.5790 Oracz and Kolasinska, 1987 0.312 a 0.319 Smith and Robinson, 1970

313.15 33.363 33.276 3 298.15 13.001 13.320

313.15 25.996 26.030

I-Alkanol + toluene mixtures 1 318.15 46.556 46.240 2 303.15 12.310 a 12.460

333.15 51.043 a 51.446 3 313.15 11.352 11.424 4 313.15 8.464 8.538 5 383.15 99.630 100.02

0.3585 0.3664 Oracz and Kolasinska, 1987 0.08 a 0.106 Hwang and Robinson, 1977 0.1250 0.1290 Oracz and Kolasinska, 1987

0.867 0.882 Nagata, 1988 0.6962 a 0.6881 Van Ness and Abbott, 0.7620 a 0.7871 Van Ness and Abbott, 0.4142 0.4165 Oracz and Kolasinska, 0.1489 0.1422 Oracz and Kolasinska, 0.0328 0.0559 Sadler et al., 1971

1977 1977 1987 1987

a Values taken directly from literature; the remaining experimental values are obtained from the reduction of literature data.

Kister equation was used to represent the molar excess Gibbs energy. The coefficients were determined by regression through minimization of the sum of deviations in total pressure, P, all points being weighted equally. Vapour phase imperfection was accounted for in terms of the second virial coefficients, calculated by the Hayden-O’Connell (1975) method. Our results are listed in Table 1.

ESTIMATION OF THE INTERACTION PARAMETERS

The molecules under study, i.e. I-alkanols and aromatic compounds, are regarded as possessing three types of surface: (1) type a (CH3 or CH2 groups in I-alkanols and toluene) ; (2) type h (OH group in 1-alkanols) ; (3) type b (CsH6 group in benzene) or type p (C6H5 group in toluene).

The equations used to calculate GE and HE are the same as used previously (Gonzalez et al., 1991b). The temperature dependence of the interaction parameters is expressed in terms of the dispersive (DIS) or

J.A. Gonzcilez et al. / Fluid Phase Equilibria 93 (1994) l-22 5

quasichemical (QUAC) interchange coefficients Cz,:’ and C$,y*” where s, t = a, b, p or h, and I = 1 (Gibbs energy), 1 = 2 (enthalpy), and I = 3 (heat capacity). For the QUAC part, the coordination number used is z = 4.

The geometrical parameters: relative volumes, ri, total surfaces, qi, and surface fractions a$i (s = a, h), for the alkanols investigated in this work have been calculated on the basis of the group volumes and surfaces recommended by Bondi ( 1968), taking arbitrarily the volume and surface of methane as unity. The relative molecular volume of an OH group is roH = 0.46963, and the relative area q oH = 0.50345. For the aromatic compounds the geometrical parameters are listed elsewhere (Kehiaian et al., 1978).

The general procedure used by us in the fitting of any set of interaction parameters has been described in detail elsewhere (Gonzalez et al., 1991 b, 1992).

The three types of surface generate three pairs of contacts: (a, s), (a, h), and (s, h), with s = b or p.

(i) The non-polar alkanelaromatic (a, b) or (a, p) interactions are represented by dispersive parameters (Table 2; Ait-Kaci, 1982; data taken from Soriano et al., 1989). We note the relative constancy of CnDd,: and the slight increase of C,“d,: with the size of the n-alkane. Such an increase is explained in terms of the Patterson effect (Kehiaian, 1985). Owing to the size of the OH group, we have taken as homomorph to the I-alkanol under consider- ation the n-alkane with one more CH2 group.

The variation of CgT (Z = 1,2) with the length of the n-alkane has not been reported in the literature, so mean values have been considered as in other applications (Kehiaian et al., 1991; Gonzalez et al., 1993a). We proceeded similarly in our previous study on the ethanol or methanol + aromatic component systems (Gonzalez et al., 1990, 1991a).

TABLE 2

Dispersive interchange coefficients C,“b,s (n) (I = 1, Gibbs energy; I = 2, enthalpy) for contact (a, b) a (type a, aliphatic; type b, C,H6, benzene); n is the number of heavy atoms, C and 0, in the l-alcohol.

I n

I8 9 11 13 15 17 19

1 0.251 0.251 0.258 0.264 0.274 0.284 0.294 2 0.560 0.562 0.570 0.576 0.579 0.582 0.585

a For the contact (a, p), type p, C,HS (phenyl group in toluene), mean values are used: CEs = 0.332; C;;; = 0.570.

6 J.A. Gonzcilez et al. / Fluid Phase Equilibria 93 (1994) l-22

There, the following mean values of the interchange coefficients were used: c gff = 0.2598 and CnS,Z D1S = 0.5623 (S = b,p) (Kehiaian et al., 1978).

(ii) The polar alkane/alkanol (a, h) interactions are represented by the dispersive and quasichemical parameters reported previously (Gonzalez et al., 1990, 1991a, b) (Table 3). For the dispersive coefficients: CF;h increases regularly with the size of the n-alkanol. The opposite behaviour is encountered for C$$, which is constant from I-dodecanol; Cz:S, decreases as far as propanol, and then increases regularly. For the quasichemical coefficients C%lAC and CsAc are constant, and C$yAc varies in a similar way to the maximum of the HE for 1-alkanol + n-alkane mixtures. When solid-liquid equilibrium data are considered, it is shown that Cz:s and C,Dz are constant from I-octadecanol (Gonzalez et al., 1993~).

(iii) The polar aromatic/alkanol (b, h) and (p, h) interactions are also described by dispersive and quasichemical interchange coefficients (Table 4).

In our previous works on mixtures containing ethanol or methanol and benzene or toluene (Gonzalez et al., 1990, 1991a), these parameters were obtained using experimental data for systems involving benzene, and kept the same, independently of the aromatic compound. Proceeding in this way, the experimental values for mixtures containing toluene are larger than the

TABLE 3

Interchange coefficients, dispersive Cz:y and quasichemical CsyAC (1= 1, Gibbs energy; I = 2, enthalpy; 1 = 3, heat capacity) for the contacts between aliphatic (type a, CH3 or CH, in n-alkane, toluene or I-alkanol) and hydroxyl groups (type h, OH in 1-alkanol). The coordination number used for the QUAC part is z = 4. (m is the number of carbon atoms in the I-alkanol.)

1 1.35 1.60 2 1.84 0.81 3 2.55 0.18 4 3.00 0.40 5 3.95 0.71 6 5.30 1.10 7 6.52 a 2.04 8 8.16 a 2.90

10 12.80 5.00 12 19.20 7.40 = 14 27.00 9.80 * 16 36.00 12.20 a 18 45.70 14.70 a 20 45.70 14.70 a

-9.10 12.20 -9.10 12.20

- 15.50 12.20 - 15.50 12.20 - 21.50 12.20 - 21.50 12.20 - 27.50 12.20 - 27.50 12.20 - 33.50 12.20 -39.50 = 12.20 -39.50 = 12.20 - 39.50 a 12.20 - 39.50 a 12.20 - 39.50 a 12.20

8.10 71.10 12.20 71.10 15.20 71.10 15.20 71.10 15.00 71.10 14.40 71.10 13.75 71.10 13.20 71.10 12.00 71.10 12.00 a 71.10 12.00 a 71.10 12.00 = 71.10 12.00 = 71.10 12.00 a 71.10

a Estimated values.

J.A. Gonzhlez et al. /Fluid Phase Equilibria 93 (1994) l-22 7

TABLE 4

Interchange coefficients, dispersive C.5:; and quasichemical CsyAC (1= 1, Gibbs energy; I= 2, enthalpy; I= 3, heat capacity) for contacts (s, h), s = b, p (type b, C6H,; type p, C,HS; type h, OH in I-alkanols). The coordination number used for the QUAC part is z = 4

I-Alkanol , CES CDIS

bh.2 CD’S

ph.1 CD’S

ph.2

Methanol 1.15 -1.15 1.20 -0.95 -9.10 10.30 16.70 21.20 Ethanol 1.84 - 2.60 1.90 -2.25 -9.10 8.90 16.70 21.20 Propanol 2.45 -2.60 2.45 -2.25 - 14.00 8.90 16.70 21.20 Butanol 2.90 -2.35 2.90 -1.90 - 14.00 8.90 16.70 21.20 Pentanol 3.55 a -2.35 3.55 -1.90 - 20.00 8.90 16.70 21.20 Hexanol 5.20 a -2.10 5.20 = -1.55 a - 20.00 8.90 16.70 21.20 Qctanol 8.16 a -1.85 a 8.16 a -1.20 a -26.00 a 8.90 16.70 21.20 Decanol 12.80 = -1.60 12.80 a -0.85 = -32.00 a 8.90 16.70 21.20 Dodecanol 19.20 a -1.35 a 19.20 = -0.50 a -38.00 a 8.90 16.70 21.20 Tetradecanol 27.00 a -1.10 a 27.00 = -0.15 = -38.00 a 8.90 16.70 21.20 Hexadecanol 36.00 = -0.85 a 36.00 a 0.10 a -38.00 a 8.90 16.70 21.20

a Guessed values.

calculated ones. This shows that the interaction parameters of the alkanol/ aromatic contacts do not compensate sufficiently for the decrease of the aromatic surface in a mixture when benzene molecules are substituted by others of toluene. So, in the present paper, we have distinguished between alkanol/benzene and alkanol/toluene contacts. The same approach was applied to the study of organic carbonates + aromatic compounds (Kehiaian et al., 1991; Gonzalez et al., 1993a). However, while the carbonate/aromatic contacts were supposed to be merely dispersive, a quasichemical contribution is also needed for the interactions under study to obtain a good representation of the excess functions. This is probably due to the special nature of 1-alkanols, because, up to now, the quasichemical coefficients for those contacts studied involving an aromatic group have been shown to be zero. This is the case of, for example, the haloalkanes/benzene contacts (Garcia- Lisbona et al., 1989; Garcia-Vicente et al., 1989; Soriano et al., 1989).

In Table 4 we note that C$!s (s = b, p; I= 1,2) increases regularly with the size of the I-alkanol, although from ethanol the second dispersive parameters are kept the same for each pair of I-alkanols, and that Cz:F varies similarly to Cz:i or Cgtz (c, &Hi2 group in cyclohexane). The

CEAC (s = b,p; 1 = 1, 2, 3) coefficients are constant for the whole set of I-alkanols, independently of the aromatic group considered. The only exception is found for C$yAC of methanol.

Finally, some comments relating to the fitting of the C$$ and C$$*’ coefficients are needed. They were obtained as in other cases by using HE

8 J.A. Gonzcilez et al. 1 Fluid Phase Equilibria 93 (1994) 1-22

data from only one source (Van Ness and Abbott, 1976) and at the same temperatures 308.15 and 3 18.15 K. In this way, we report comparable values for these coefficients. Moreover, although CgTs (s = b, p) depends strongly on the size of the alkane (Kehiaian, 1985), values are not available in the literature and have been taken to equal zero. So, the C$:g coefficients were calculated on the basis of this deficiency and therefore represent an average of the true Cg:f and Cafe coefficients.

RESULTS AND DISCUSSION

Tables 1 and 5-9 and Figs. l-9 show numerical and graphical compari- sons, respectively, between experimental data and DISQUAC predictions. As usually, the model yields fairly well the dependence on concentration of the VLE data (Table 1, Fig. 3) and of the excess functions (Figs. l-2 and 4-9). So, with the coordination number used (z = 4) DISQUAC reproduces the typically unsymmetrical curves of HE (Figs. 4-7). It should be considered as a success that the dependence on temperature of the bulk properties is also well represented by the model. So, GE increases with temperature, and at sufficiently high temperatures starts to decrease (Table 5). The same behaviour is found for CpE (Table 7). The model describes fairly well the

Fig. 1. Comparison of theory with experiment for the molar excess Gibbs energy GE at 298.15 K of 1-alkanols( 1) + benzene(2). Lines, predicted values; points, experimental results (Brown et al., 1969): 0, (methanol); 0, (ethanol); A, (propanol); 0, (butanol).

J.A. Gonzblez et al. 1 Fluid Phase Equilibria 93 (1994) 1-22 9

TABLE 5

Molar excess Gibbs energies GE (T; x, = 0.5) for I-alkanol( 1) + benzene(2), or + toluene(2) mixtures at various temperatures, T (K), and equimolar composition. Coniparison of experimental results (exp) with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the 1-alkanol.)

m T W) GE (J/mol) Source of data

EXP Calc

1 -Alkanol + benzene mixtures

1 298.15

308.15

313.15

318.15

2 298.15

308.15

313.15

318.15

298.15

308.15

313.15

318.15

328.15

338.15

348.15

298.15

308.15

313.15

318.15

328.15

338.15

6 303.15

1 -Alkanol + toluene mixtures 1 313.15

318.15

2 303.15 313.15

333.15

3 313.15

4 313.15

5 303.15

343.15 383.15

1241

1260 a

1280

1282

1300

1100

1110 a

1076

1120

1126

1120

1007

1000 a

1000

944

1001

1000

961

969

902

920 a

920

906

870

910

854

834

866

1362 =

1380

1179 1197 =

1187

1203 1069 a

965 a

876 a

821 696

1267

1287

1296

1303

1117

1127

1130

1131

1007

1007

1006

1002 993

979

961

916

910

905

899

883 864

793

1358

1366

1198

1207

1208

1085

990

873

827 731

Hwang and Robinson, 1977

Brown et al., 1969

Brown et al., 1969

Oracz and Kolasinska, 1987

Brown et al., 1969


Brown et al., 1969

Smith and Robinson, 1970 Brown et al., 1969


Brown et al., 1969


Brown et al., 1969

Brown et al., 1969

Strubl et al., 1975


Brown et al., 1969

Strnbl et al., 1975

Strubl et al., 1975

Fu and Lu, 1966

Brown et al., 1969

Brown et al., 1969


Dohnal et al., 1979

Brown et al., 1969

Dohnal et al., 1979

Dohnal et al., 1979

Myers and Clever, 1970


Nagata, 1988

Van Ness and Abbott, 1977


Van Ness and Abbott, 1977

Van Ness and Abbott, 1977 Oracz and Kolasinska, 1987


Sadler et al., 1971

Sadler et al., 1971 Sadler et al., 1971

a System used in the estimation of the interchange coefficients.

10

TABLE 6

J.A. Gonzblez et al. 1 Fluid Phase Equilibria 93 (1994) I-22

Molar excess enthalpies HE (T; x1 = 0.3) for 1-alkanol( 1) + benzene(2), or + toluene(2) mixtures at various temperatures, T (K), and xr = 0.3. Comparison of experimental results (exp) with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the I-alkanol.)

m T (K) HE (J/mol) Source of data

Bxp Calc

I-Alkanol + benzene mixtures 1 293.15

298.15

308.15

318.15

298.15

308.15

318.15

298.15

308.15

318.15

298.15

308.15

318.15

298.15 308.15 318.15 298.15

298.15

653 664 722 713 = 714 700 838 836 a 820 962 a 968 940 869 a 904 870

1020 a 1000 1175 = 1140 1042 a 1040 1194 a 1170 1343 a 1330 1124 a 1090 1261 = 1260 1414 a 1370 1147 a 1274 a 1401 a 1185 a 1141 b 1060 b 1130 b

656

716

847

995

869

1042

1227

1029

1180

1335

1123

1269

1416

1135 1269 1402 1191 1093

943

Battler and Rowley, 1985 Scatchard et al., 1952 Battler and Rowley, 1985 Van Ness and Abbott, 1976 Vesley et al., 1974 Brown et al., 1969 Battler and Rowley, 1985 Van Ness and Abbott, 1976 Brown et al., 1969 Van Ness and Abbott, 1976 Vesely et al., 1974 Brown et al., 1969 Van Ness and Abbott, 1976 Smith and Robinson, 1970 Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Brown et al., 1969 Van Ness and Abbott, Van Ness and Abbott, Van Ness and Abbott, Hsu and Clever, 1975 Hsu and Clever, 1975 Brown et al., 1969 Brown et al., 1969

1976

1976

1976

1976

1976

1976

1976

1976

1976 1976 1976

J.A. Gonz6lez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

TABLE 6 (continued)

m T(K) HE (J/mol) Source of data

Exp Calc

11

1 -Alkanol + toluene mixtures 1 298.15 708 a 710 Van Ness and Abbott, 1976

308.15 854 843 Van Ness and Abbott, 1976 318.15 993 995 Van Ness and Abbott, 1976

2 298.15 821 a 849 Van Ness and Abbott, 1976 308.15 988 1024 Van Ness and Abbott, 1976 318.15 1155 1214 Van Ness and Abbott, 1976 333.15 1395 1525 Van Ness and Abbott, 1976

3 298.15 979 a 942 Van Ness and Abbott, 1976 308.15 1135 1099 Van Ness and Abbott, 1976 318.15 1304 1267 Van Ness and Abbott, 1976



a System used in the estimation of the interchange coefficients. b x, = 0.5.

Fig. 2. Comparison of theory with experiment for the molar excess Gibbs energy GE at 313.15 K of I-alkanols( 1) + toluene( 2). Lines, predicted values; points, experimental results (Oracz and Kolasinska, 1987): 0, (methanol); 0, (ethanol); A, (propanol); 0, (butanol).

12 J.A. Gonzdlez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

TABLE 7

Molar excess heat capacities C,” (T; x,) for 1-alkanol( 1) + benzene(2), or + toluene(2) mixtures at various temperatures, T (K), and composition x1. Comparison of experimental results (exp) with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the 1-alkanol.)

m T(K) C,” (J/mol K)

Exp Calc

Source of data

1 -Alkanol + benzene mixtures 3” 298.15

303.15 308.15 313.15

I-Alkanol + toluene mixtures 2b 273.15

288.15 298.15 308.15

4” 298.15 323.15 348.15 368.15

14.2 14.2 Recko, 1968 15.2 14.7 Recko, 1968 15.5 15.0 Recko, 1968 15.2 15.1 Recko, 1968

11.1 11.6 Hwa and Ziegler, 1966 13.6 14.6 Hwa and Ziegler, 1966 15.1 16.7 Hwa and Ziegler, 1966 16.4 18.7 Hwa and Ziegler, 1966 15.7 13.7 Cobos et al., 1991 16.3 15.8 Cobos et al., 1991 13.9 13.6 Cobos et al., 1991 9.8 6.2 Cobos et al., 1991

= x, = 0.5012. by, = 0.4505. cxl = 0.5.

negative region which appears, e.g. in the I-butanol + toluene mixture, at low alcohol concentrations when the temperature increases (Fig. 9). So, DISQUAC can represent the change in the translational, rotational and vibrational degrees of freedom with temperature (Mrazek and Van Ness, 1961), and in consequence, the strong non-ideality which explains the negative region mentioned above, and which results from the self-association of the alcohol in both the pure liquid and the mixture (Cobos et al., 1991).

DISQUAC predictions on In yy (Table 8) are similar to those found with 1-alkanols + n-alkanes or cyclohexane mixtures; In y? is fairly well represented; somewhat large positive differences Aln 7;” = In y ;” (talc) - In y r (exp) are encountered. At least a part of these differences is due to the results given by the model for 1-alkanol + n-alkane systems.

In mixtures with n-alkanes or cyclohexane, the results for the partial molar enthalpies at infinite dilution are opposite to those given by DIS- QUAC for the systems under study. At present, the model yields a surprisingly good description of HF”, and a poorer one for HF” (Table 9). This

J.A. Gonzhlez et al. /Fluid Phase Equilibria 93 (1994) l-22

TABLE 8

13

Natural logarithms of the activity coefficients at infinite dilution In yp” in I-alkanol( 1) + benzene(2), or + toluene(2) mixtures at various temperatures, T (K). Comparison of experimental results (exp) with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the I-alkanol.)

m T(R) lny? Lny? Source of data

Exp Calc Exp Calc

1 -Alkanol -+- benzene mixtures 1 298.15 2.96 a 3.74 2 298.15 2.80 a 3.06

2.53 b 313.15 2.56 a 2.71

3 298.15 2.49 a 2.96 308.15 2.38 ’ 2.72 318.15 2.20 c 2.49 338.15 1.86 c 2.07

4 318.15 2.01 c 2.62 328.15 1.84 = 2.39 338.15 1.67 ’ 1.96

6 303.15 2.45 d 2.67 12 308.15 2.61

326.15 2.24 333.15 2.12

14 317.95 2.53 338.25 2.18 348.95 2.03

16 333.15 2.42 393.15 1.88 453.15 2.18

1 -Alkanol + toluene mixtures 1 308.6 3.56

318.5 3.33 337.0 2.92

2 308.15 2.95 h 3.10 2.82 ’

318.15 2.53 i 2.76 333.15 2.30 h 2.44

4 349.5 1.89 359.5 1.70 389.9 1.24

12 315.95 2.55 326.15 2.35 333.15 2.23

14 329.25 2.36

1.87 2.00 Endler et al., 1985 1.49 1.63 Endler et al., 1985 1.50 Smith and Robinson, 1970 1.45 1.59 Endler et al., 1985 1.19 1.36 Endler et al., 1985 1.33 1.33 Dohnal et al., 1979 1.29 1.29 Dohnal et al., 1979 1.21 1.20 Dohnal et al., 1979 1.09 1.13 Dohnal et al., 1979 1.04 1.08 Dohnal et al., 1979 0.99 0.99 Dohnal et al., 1979 1.73 0.91 Myers and Clever, 1970 0.73 e 0.51 Alessi et al., 1982 0.58 e 0.47 Alessi et al., 1982 0.54 = 0.45 Alessi et al., 1982 0.24 = 0.41 Alessi et al., 1982 0.36 e 0.38 Alessi et al., 1982 0.28 e 0.36 Alessi et al., 1982 0.14 f 0.33 Turek et al., 1979

-0.01 f 0.25 Turek et al., 1979 -0.05 f 0.32 Turek et al., 1979

2.27 g 2.22 2.24 g 2.19 2.19 8 2.13 1.87 1.83 1.76 1.72 1.79 1.62 1.73 1.03 g 1.12 0.96 g 1.07 0.82 g 0.94 0.44 e 0.65 0.39 e 0.63 0.37 = 0.62 0.24 e 0.46

Trampe and Eckert, 1990 Trampe and Eckert, 1990 Trampe and Eckert, 1990 Van Ness and Abbott, 1977 Van Ness et al., 1967 Van Ness et al., 1967 Van Ness and Abbott, 1977 Trampe and Eckert, 1990 Trampe and Eckert, 1990 Trampe and Eckert, 1990 Alessi et al., 1982 Alessi et al., 1982 Alessi et al., 1982 Alessi et al., 1982

14 J.A. Gonzrilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

TABLE 8 (continued)

m T(K) lny? lny,” Source of data

Exp Calc Exp Calc

16

338.25 2.21 0.20 e 0.53 Alessi et al., 1982 348.95 2.06 0.12 e 0.52 Alessi et al., 1982 393.15 1.77 0.03 f 0.40 Turek et al., 1979 453.15 1.93 Of 0.46 Turek et al., 1979

a Obtained by inert gas stripping method. b From a Redlich-Kister equation with four coefficients. c From Wilson’s equation. d From Rayleigh light scattering data. e Obtained by gas-liquid chromatography using the retention time method. f Obtained by gas-liquid chromatography corrected for vapour-phase nonideality. g Obtained by differential ebulliometry. h P-x data extrapolated to xi = 0. ’ P-x-y data extrapolated to x, = 0.

TABLE 9

Partial molar excess enthalpies of 1-alkanol( 1) + benzene(2), or + toluene(2) mixtures at infinite dilution HF.“, and at various temperatures T(K). Comparison of experimental results (exp) with values calculated (talc) using the coefficients from Tables 2-4. (m is the number of carbon atoms in the 1-alkanol.)

m T(K) HF” (J/mol) HT” (J/mol) Source of data

Exp Calc Exp Calc

1 -Alkanol + benzene mixtures 1 298.15 15731 18703 2 283.15 15800 16747

298.15 15750 17507 298.15 15886 318.15 15700 18289

3 298.15 17084 18202 4 298.15 18016 18736 5 298.15 18035 18893

I-Alkanol + toluene mixtures 1 298.15 16503 17100

323.15 19453 2 298.15 16662 17258 3 298.15 19813 17975 4 298.15 17595 18278

350 19488 5 298.15 17012 18199

1507

1560 1573

2110 2289 2441

1794 1811 Mrazek and Van Ness, 1961 2860 2814 Trampe and Eckert, 1991 1507 1749 Mrazek and Van Ness, 1961 1944 2285 Mrazek and Van Ness, 1961 2001 2561 Mrazek and Van Ness, 1961 7600 4760 Trampe and Eckert, 1990 1973 2428 Mrazek and Van Ness, 1961

1574 1038 1734

2869 2561 2882 2827

Mrazek and Van Ness, 1961 Stokes and Burfitt, 1973 Stokes and Burfitt, 1973 Mrazek and Van Ness, 1961 Stokes and Burfitt, 1973 Mrazek and Van Ness, 1961 Mrazek and Van Ness, 1961 Mrazek and Van Ness, 1961

J.A. Gonzcilez et al. / Fluid Phase Equilibria 93 (1994) I-22

3

15

Fig. 3. Comparison of theory with experiment for the isothermal vapour-liquid equilibrium diagram for I-butanol( 1) + toluene(2) at 313.15 K. Total pressure, P, versus x, or y, , the mole fractions of I-butanol in the liquid and vapour phases, respectively. Lines, predicted values; points, experimental results (Oracz and Kolasinska, 1987).

I C

Fig. 4. Comparison of theory with experiment for the molar excess enthalpy HE at different temperatures of methanol( 1) + benzene(2). Lines, predicted values; points, experimental results (Van Ness and Abbott, 1976): 0, (298.15 K); 0, (308.15 K); A, (318.15 K).

16 J.A. Gonzcilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

Fig. 5. Comparison of theory with experiment for the molar excess enthalpy HE at different temperatures of I-propanol( 1) + benzene( 2). Lines, predicted values; points, experimental results (Van Ness and Abbott, 1976): 0, (298.15 K); 0, (308.15 K); A, (318.15 K).

400

Oh 0.~ ’ 0.~ 0.8 r

1 Xl

3

Fig. 6. Comparison of theory with experiment for the molar excess enthalpy HE at different temperatures of ethanol( 1) + toluene( 2). Lines, predicted values; points, experimental results (Van Ness and Abbott, 1976): 0, (298.15 K); El, (308.15 K); A, (318.15 K).

J.A. Gonzblez et al. 1 Fluid Phase Equilibria 93 (1994) l-22 17

120(

401

Fig. 7. Comparison of theory with experiment for the molar excess enthalpy HE at ditTerent temperatures of I-butanol( 1) + toiuene(2). Lines, predicted values; points, experimental results (Van Ness and Abbott, 1976): 0, (298.15 K); 0, (308.15 K); A, (318.15 K).

0 0.0 0.2 0.4 0.6 0.8 1.0

Fig. 8. Comparison of theory with experiment for the molar excess heat capacity C,” at different temperatures of ethanol( 1) + toluene(2). Lines, predicted values; points, experimental results (Hwa and Ziegler, 1966): q (223.15 K); A, (273.15 K); 0, (298, 15 K).

18 J.A. Gonzcilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22

0.0 0.2 0.4 0.6 0.8 1 Xl

Fig. 9. Comparison of theory with experiment for the molar excess heat capacity C,” at different temperatures of I-butanol( 1) + toluene(2). Lines, predicted values; points, experimental results (Cobos et al., 1991): 0, (298.15 K); 0, (368.15 K).

is probably due to a compensation in the interaction parameters. So, because in the actual mixtures the number of groups is increased in comparison to the systems with n-alkanes, the influence of the interchange coefficients of the alkane/aromatic contacts on the prediction of partial molar quantities at infinite dilution is currently under study.

It is noteworthy that while the second dispersive interchange coefficients depend on the type of aromatic molecule, the C,D,yf coefficients (certainly many of them estimated and in need of experimental verification) in practice do not depend on the aromatic molecule (Table 4). This behaviour may be related to the values of GE and HE for the benzene + toluene mixture: the former, not found in the literature, should be close to 17 J/mol at equimolar composition and 298.15 K, on the basis of DISQUAC predictions; the latter is 68 J/mol, under the same conditions (Murakami et al., 1966). However, the observed increase in the dispersive coefficients may be attributed to the inductive effect of the alkyl groups, while there is no steric effect on the quasichemical coefficients. The inductive effect was also pointed out by Goates et al. (1962), in their application of a quasilattice theory to the mixtures under study. However, they found greater differences between the interaction parameters involving methanol and ethanol than between ethanol and any of the other alcohols. So, they distinguished mainly between methanol and the remaining alcohols.

J.A. Gonztilez et al. 1 Fluid Phase Equilibria 93 (1994) l-22 19

LIST OF SYMBOLS

C interchange coefficient

c, molar heat capacity G molar Gibbs energy H molar excess enthalpy P pressure

4 relative molecular area r relative molecular volume s contact surface

Greek letters

a molecular surface fraction

Y activity coefficient

Superscripts

DIS dispersive term E excess property QUAC quasichemical term cc property at infinite dilution

Subscripts

a, b, h, p type of contact surface: a, CH3, CH2; b, C,H,; h, OH; p, C6H5

; type of molecule (component) order of interchange coefficient: I = 1, Gibbs energy; I = 2, enthalpy; I= 3, heat capacity

s. t contact surface

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Documents

Estimation of DISQUAC interchange energy parameters for 1-alkanols + benzene or + toluene mixtures