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Ind. Eng. Chem. Res. 2003, 42, 4382-4388
GENERAL RESEARCH Thermodynamics of Mixtures Containing Organic Carbonates. 14. Excess Molar Gibbs Energies for 1-Hexanol + Dimethyl or Diethyl Carbonate Systems at 353.15 and 363.15 K. Comparison with ERAS Results Andrzej Sporzynski,† Monika Szurgocinska,† Urszula Domanska,† and Juan Antonio Gonza´ lez*,‡ Physical Chemistry Division, Faculty of Chemistry, Warsaw University of Technology, 00-664 Warsaw, Poland, and GETEF, Departamento de Termodina´ mica y Fı´sica Aplicada, Facultad de Ciencias, Universidad de Valladolid, 47071 Valladolid, Spain
Vapor-liquid equilibria (P-x measurements) at 353.15 and 363.15 K for 1-hexanol + dimethyl carbonate or + diethyl carbonate are determined by an ebullometric method. The data are reduced using Barker’s method. All of the systems present positive deviations from Raoult’s law. Mixtures are studied in the framework of the ERAS model assuming that 1-alkanols are the only self-associated compounds in the investigated solutions. According to the high HE (excess molar enthalpy) values of 1-alkanol + linear organic carbonate systems, the model predicts a weak cross association between the mixture components. The deviations between the experimental GE (excess molar Gibbs energy) and HE values and the ERAS results can be ascribed to the existence of strong polar interactions between carbonate molecules, not described properly by the model. 1. Introduction Organic carbonates, linear or cyclic, are widely employed in industry. They are used in the synthesis of organic compounds,1 e.g., pharmaceuticals2 and agricultural chemicals, and as solvents for many synthetic and natural resins.3 They are also important in the Li battery technology.4 Dimethyl carbonate (DMC) is used in the replacement of hazardous chemicals,5,6 as a fuel additive,7 or in the design of new refrigerants.8 In the framework of the TOM Project (Thermodynamics of Organic Mixtures),9,10 the OCO program is developed to get a better understanding of the interactions between the O (oxygen) and CO (carbonyl) groups in the same or in different molecules. Particularly, we are engaged in a systematic study of mixtures involving organic carbonates (the OCOO group). Up to now, we have reported data on vapor-liquid equilibria (VLE),11-14 liquid-liquid equilibria,15,16 HE,17,18 excess molar volumes,19,20 and solid-liquid equilibria16,21,22 of systems formed by DMC and diethyl carbonate (DEC) and alkane, benzene, toluene, CCl4, or 1-alkanol. We have also presented the characterization of the OCOO/ aliphatic, OCOO/cyclic, OCOO/aromatic, OCOO/CCl4,23-25 and OCOO/OH22 contacts in terms of DISQUAC, a purely physical model.9,10 1-Alkanol + linear organic carbonate systems have been also studied22 using the ERAS model.26 Then, we showed that, in these solutions, * To whom correspondence should be addressed. † Warsaw University of Technology. ‡ Universidad de Valladolid.
the strong polar interactions between carbonate molecules are more important than the self-association of the alkanol or than the association between the alcohol and the carbonate. For this reason, ERAS predictions for HE are improved by DISQUAC. The purpose of this paper is to investigate the ability of ERAS to describe GE for 1-alkanol + linear organic carbonate mixtures. For a more complete study, we also report VLE (P-x) measurements and the corresponding GE for 1-hexanol + DMC or + DEC at 353.15 and 363.15 K. 2. Experimental Section 2.1. Materials. The origins of the chemicals (in parentheses are Chemical Abstracts registry numbers) are as follows: 1-hexanol (anhydrous; 111-27-3, Aldrich); DMC (616-38-6) and DEC (105-58-8) (anhydrous, mole fraction > 99%) were supplied by Aldrich and stored over freshly activated molecular sieves of type 4 A (Union Carbide). All compounds were checked by gas-liquid chromatography analysis, and no significant impurities were found. The purity of 1-hexanol was determined to be 99.9%. 2.2. Apparatus and Procedure. The VLE was determined by an ebulliometric method, which reports, at constant temperature, T, pressure (P) values as a function of the liquid-phase mole fraction. The ebulliometer was designed by Rogalski and Malanoswki27 and was used with some modification of taking samples to enable the sampling of the liquid to be made without disturbing the working conditions.28 Pressure stability was obtained using a buffer vessel (50 dm3). Pressure
10.1021/ie0303000 CCC: $25.00 © 2003 American Chemical Society Published on Web 08/23/2003
Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4383 Table 1. VLE for the 1-Hexanol (1) + DMC (2) System at Temperature T x1
P/kPa
y1,cal
0.0212 0.0771 0.2296 0.3525 0.4484
70.51 67.41 60.25 55.11 51.14
T ) 353.15 Ka 0.003 0.5388 0.011 0.6592 0.029 0.7852 0.041 0.8808 0.051 0.9235
x1
0.0193 0.0771 0.2253 0.3538 0.4386
98.09 93.62 83.70 75.67 70.79
T ) 363.15 Kb 0.003 0.5388 0.013 0.6553 0.033 0.7844 0.049 0.8622 0.059
P/kPa
y1,cal
46.90 40.19 31.54 23.12 17.24
0.061 0.078 0.109 0.165 0.224
63.59 55.32 42.14 31.89
0.073 0.094 0.138 0.195
The parameters of eq 1 are A1 ) 1.009; A2 ) 0.032; A3 ) 0.0727; σr(P) (eq 3) ) 0.008. b The parameters of eq 1 are A1 ) 0.872; A2 ) -0.0202; A3 ) -0.0275; σr(P) (eq 3) ) 0.004.
Table 3. Total Pressures, Pi°, Molar Volumes, VLi , and Virial Coefficients, Bii, of Pure Compounds at Temperature T compound
T/K
Pi°/kPa
1-hexanol
353.15 363.15 353.15
4.13b 7.0b 72.35c 74.75d 72.36e 100.5c 100.7e 21.26c 21.26d 21.4e 31.14c 31.21e
DMC
363.15 DEC
363.15
a
Table 2. VLE for the 1-Hexanol (1) + DEC (2) System at Temperature T x1
P/kPa
y1,cal
0.0064 0.0276 0.0770 0.1361 0.1854 0.2919
21.04 20.69 20.36 19.20 18.60 17.22
T ) 353.15 Ka 0.002 0.4274 0.009 0.4588 0.025 0.5091 0.046 0.6540 0.062 0.6951 0.098 0.7772
x1
0.0083 0.0315 0.0751 0.1341 0.1893 0.2917 0.4284
30.87 30.39 29.29 28.15 27.21 25.51 23.18
T ) 363.15 Kb 0.002 0.4971 0.010 0.5163 0.027 0.6447 0.051 0.6910 0.070 0.7608 0.111 0.8861 0.156
P/kPa
y1,cal
15.86 14.98 14.67 12.56 11.76 10.23
0.142 0.152 0.169 0.231 0.256 0.323
22.01 21.64 18.69 17.30 15.59 11.50
0.182 0.189 0.259 0.294 0.359 0.546
a The parameters of eq 1 are A ) 0.599; A ) 0.0195; A ) 1 2 3 -0.1254; σr(P) (eq 3) ) 0.008. b The parameters of eq 1 are A1 ) 0.529; A2 ) -0.0382; A3 ) -0.0894; A4 ) 0.2327; σr(P) (eq 3) ) 0.004.
measurements were made with a mercury manometer equipped with a cathetometer with a resolution of (0.01 mm, which gives an accuracy of the vapor-pressure measurements to be better than (0.03 kPa. Vaporpressure measurements were corrected according to the standard method.29 The temperature was measured using a calibrated platinum resistance thermometer (1220 by Frontec Pajala AB, Sweden), with an accuracy of (0.01 K. All of the measurements were conducted in a purified argon atmosphere. The composition of the liquid was determined by a precision refractometer (Carl Zeiss, Jena), with an accuracy of (0.000 01 at 298.15 ( 0.01 K. A calibration curve was made for each mixture, and the accuracy of the composition determination was better than (0.0005 in mole fraction. 2.3. Results and Data Reduction. The experimental P-x1 data at 353.15 and 363.15 K are listed in Tables 1 and 2. No data have been found in the literature for comparison. The P-x1 measurements were reduced using Barker’s method30 to obtain values of y1 (mole fraction in the vapor phase) and γi, the activity coefficient of component i in the liquid state. To this end, it was assumed that GE is represented by an equation of the Redlich-Kister type: k
GE/RT ) x1(1 - x1)
∑ Am(2x1 - 1)m m)0
(1)
353.15
VLi / mol-1)
(cm3
Biia/ (cm3 mol-1) -2730 -2335 -989
133.15b 134.75b 88d 90f
-923
133d
-1702
135f
-1573
a B /(cm3 mol-1) ) -1195 (T ) 353.15 K); -1112 (T ) 363.15 12 K) for 1-hexanol + DMC; B12/(cm3 mol-1) ) -1564 (T ) 353.15 K); -1448 (T ) 363.15 K) for 1-hexanol + DEC. b Reference 41. c This work. d Reference 42; e Reference 43. f Extrapolated using data from ref 42.
Table 4. Boiling Temperatures, Tb, at 101.325 kPa, Critical Temperatures, Tc, Pressures, Pc, Mean Radii of Gyration, RD, and Dipole Moments, µ, in the Vapor Phase of 1-Hexanol and Linear Organic Carbonates compound
Tb/K
Tc/K
Pc/K
RD/A
µ/D
1-hexanol DMC DEC
430.2a 363.6b 400a
610a 547c 577c
34.6a 43.4c 34.2c
3.87d 2.98d 3.78d
1.55a 0.87e 0.90a
a Reference 44. b Reference 45. c Calculated using Joback’s method.45 d Calculated from parachor values.45 e Reference 46.
The parameters in eq 1 were determined by minimizing the sum of squares between the measured and calculated pressures, with all of the points equally weighted. Calculated pressures are obtained from
Pcalc )
[
x1γ1P1° exp
]
-(B11 - VL1 )(P - P1°) - Pδ12y22 + RT
[
x2γ2P2° exp
]
-(B22 - VL2 )(P - P2°) - Pδ12y12 (2) RT
where Pi° is the vapor pressure and VLi the saturated liquid volume of the pure component i at temperature T. The second virial coefficients are denoted by Bij, and δ12 ) 2B12 - B11 - B12. Equation 2 is valid assuming that the vapor phase of the mixture, as well as the vapor in equilibrium with the pure components, is described by the volume-explicit virial equation terminated after the second virial coefficient; VLi is constant over the pressure range considered, the liquid partial molar volume of each component is invariant with composition, and the standard states for γi are the pure components at the same T and P as those of the mixtures. The values of the second virial coefficients and saturated liquid volumes used in the calculations are given in Table 3. Second virial coefficients were determined from the Hayden-O’Connell method.31 The constants needed for their determination are given in Table 4. For 1-hexanol, the association parameter used was 1.55. The solvation parameters between alcohol and carbonates were neglected. Parameters of eq 1 together with the relative standard deviation in P from the corresponding adjustement,
4384 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 Table 5. ERAS Parametersa for Pure Compounds at Temperature T compound
T/K
Vi/(cm3 mol-1)
Vi*/(cm3 mol-1)
Pi*/(J cm-3)
Ki
∆hi*/(kJ mol-1)
∆vi*/(cm3 mol-1)
methanol ethanol 1-propanol 1-pentanol 1-hexanol
313.15 313.15 313.15 298.15 298.15 353.15 363.15 313.15 353.15 363.15 353.15 363.15
41.12 59.66 76.29 108.69 125.19 133.15b 134.75b 86.48 88b 90b 133b 135b
34.23 47.26. 61.49 89.76 103.52 105.68 106.3 65.54 63.5 64.13 97.45 97.81
420.7 392.6 385.63 411.0 431.1 401.1 397.1 693.1 669.3 657.4 565.9 556.3
607 317 121.3 153 120 24.6 19.6 0 0 0 0 0
-25.1 -25.1 -25.1 -25.1 -25.1 -25.1 -25.1 0 0 0 0 0
-5.6 -5.6 -5.6 -5.6 -5.6 -5.6 -5.6 0 0 0 0 0
DMC DEC
a V , molar volume; V *, reduction parameter for volume; P *, reduction parameter for pressure; K , equilibrium constant; ∆h *, association i i i i i enthalpy; ∆vi*, association volume. The reduction parameters were determined from P-V-T data reported in refs 35, 44, and 47-49 and using eqs 8-10. b See Table 3.
defined as
components but also for the mixture:
σr(P) )
{
1 N-k
]}
[
∑
Pcalc - Pexp Pexp
2 1/2
(3)
are given as footnotes in Tables 1 and 2. In eq 3, N is the number of data points and k the number of fitted parameters for each system. All of the solutions show positive deviations from Raoult’s law and do not present azeotropic behavior. 3. ERAS Model This model combines the real association solution model32 with Flory’s equation of state.33 The excess functions are split into two additive terms that arise from hydrogen-bonding effects (the so-called chemical contribution) and nonpolar van der Waals interactions including free-volume effects (the so-called physical interactions). Moreover, it is assumed that only consecutive linear association occurs between A (1-alkanol) molecules, which is described by a chemical equilibrium constant KA independent of the chain length i of the associated species, according to KA
Am + A1 {\} Am+1
(4)
Linear organic carbonates (B) are considered to be not self-associated. The cross association between A and B molecules is represented by KAB
Am + B {\} AmB
(5)
The dependence of Ki on temperature is given by the van’t Hoff relation
[
(
∆hi* 1 1 Ki ) K0 exp R T T0
)]
(6)
where ∆hi* is the enthalpy variation for reactions (4) and (5), which corresponds to the hydrogen bond energy. K0 is the association constant at temperature T0. Reactions (4) and (5) are also characterized by the volume change ∆vi* related to the formation of the linear chains. The physical contribution is derived from Flory’s equation of state,33 which holds not only for pure
P h iV hi T hi
)
V h i1/3 V h i1/3 - 1
-
1 V h iT hi
(7)
with P h i ) P/Pi*, V h i ) Vi/Vi*, and T h i ) T/Ti* being the reduced pressure, volume, and temperature, respectively. Pi*, Vi*, and Ti* are the corresponding reduction parameters. For associating molecules, the procedure to obtain the reduction parameters is somewhat different from the original one applied in Flory’s model. In ERAS, the reduction parameters of the pure compounds are calculated from P-V-T data [density (d), thermal expansion (RP), and isothermal compressibility (κT)], but they also depend on Ki, ∆hi*, and ∆vi*. The method is explained elsewhere.34 The reduction parameters for the binary mixtures are calculated using the mixing rules.34 The XAB parameter, which characterizes the difference of dispersive intermolecular interactions between molecules A and B in the solution and in the pure components, is the only adjustable parameter of the physical part of HE and VE,22. On the other hand, for VLE or liquid-liquid equilibria (LLE) calculations, a new parameter, QAB, is needed in order to characterize the entropic contribution to the difference of intermolecular interactions.35 Expressions for the chemical and physical contributions to HE, VE, or ln γi can be found elsewhere36 and will not be repeated here. To calculate the reduction parameters of pure compounds at T * 298.15 K (Table 5), the following expressions37 were used to determine the values of d (density), Rp, and γ ()Rp/κT):
d ) d0 exp(-Rp∆T)
(8)
Rp ) R0 + R02(7 + 4R0T)∆T/3
(9)
γ ) γ0 - γ0(1 + 2R0T)∆T/T
(10)
The KA, ∆hA*, and ∆vA* parameters are known from HE and VE data at 298.15 K of 1-alkanol + alkane mixtures34 (Table 5). Similarly, KAB, ∆hAB*, and ∆vAB* were determined in a previous work22 (Table 6) on the basis of data for 1-alkanol + linear organic carbonate systems. Here, the QAB values were obtained from GE data, which is the usual procedure,35 and the XAB values were calculated using the available38 HE data at T *
Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003 4385 Table 6. ERAS Parametersa for 1-Alkanol + DMC or + DEC Mixtures system
T/K
KAB
∆hAB*/(kJ mol-1)
∆vAB*/(cm3 mol-1)
XAB/(J cm-3)
QAB/(J cm-3 mol-1)
methanol + DMC ethanol + DMC 1-propanol + DMC 1-hexanol + DMC
313.15 313.15 313.15 353.15 363.15 298.15 298.15 353.15 363.15
18.9 10.4 10.4 9. 8.9 10.5 8 6.2 6.
-3.0 -3.0 -3.0 -3.0 -3.0 -4.0 -4.0 -4.0 -4.0
-7.5 -7.5 -7.5 -7.5 -7.5 -7.5 -7.5 -7.5 -7.5
9 24 28 29 29 17.7 21 21 21
0.015 0. -0.026 -0.07 -0.07
1-pentanol + DEC 1-hexanol + DEC
0.023 0.020
a K , association constant of 1-alkanol with carbonate;22 ∆h *, association enthalpy of 1-alkanol with carbonate;22 ∆v *, association AB AB AB volume of 1-alkanol with carbonate;22 XAB, adjustable physical parameter in the ERAS model (this work); QAB, entropic parameter needed for GE calculations (this work).
Figure 1. GE for 1-alkanol (1) + DMC (2) systems. Points, experimental results: (9) methanol,38 T ) 313.15 K; (b) 1-hexanol (this work), T ) 353.15 K. Solid lines, ERAS calculations using parameters from Tables 5 and 6. Dashed lines, DISQUAC results with interaction parameters from the literature.22
298.15 K. The XAB and QAB parameters are collected in Tables 5 and 6. The total relative molecular volumes and surfaces of the mixture compounds, needed to calculate their surface-to-volume ratios (s), were obtained additively on the basis of Bondi’s method.39 4. Discussion GE values from VLE measurements for 1-hexanol + DMC or + DEC are plotted in Figures 1-3. We note that, at a given temperature, GE (1-hexanol + DMC) > GE (1-hexanol + DEC) (Figure 3); i.e., interactions between like molecules are stronger in systems with DMC. At equimolar composition and 313.15 K, for systems with DMC,38 GE(methanol) ) 939 J mol-1, GE(ethanol) ) 953 J mol-1, and GE(1-propanol) ) 966 J mol-1. These rather constant values may be well attributed to a certain enthalpic-entropic compensation. For example, at the same conditions as above, TSE ()HE - GE) ) 604 J mol-1 for methanol + DMC38 (HE ) 1543 J mol-1) and TSE ) 1355 J mol-1 for 1-propanol + DMC38 (HE ) 2321 J mol-1). These high TSE and HE values together with the symmetrical GE and HE curves (Figures 1-4) reveal that, in the present solutions, polar interactions between carbonate molecules are more important than the self-association of the 1-alkanol or
Figure 2. GE for 1-alkanol (1) + linear organic carbonate (2) systems. Points, experimental results: (b) ethanol (1) + DMC (2),38 T ) 313.15 K; (9) 1-hexanol (1) + DEC (2) (this work), T ) 353.15 K. Solid lines, ERAS calculations using parameters from Tables 5 and 6. Dashed lines, DISQUAC results with interaction parameters from the literature.22
than the cross association between alkanol and carbonate molecules.22 In terms of ERAS, this leads to low KAB and |∆hAB*| values (Table 6). In contrast, the methanol + propylamine system, where strong interactions exist between unlike molecules, is characterized34 by KAB ) 2124 and ∆hAB* ) -46.3 kJ mol-1. On the other hand, GE and HE curves calculated using ERAS are skewed to low mole fractions of the alcohol (Figures 1-4). The observed differences with experimental results (Figures 1-4) may be ascribed to ERAS and cannot represent properly the mentioned strong dipole-dipole interactions between carbonate molecules. These interactions are better represented by DISQUAC. As a consequence, DISQUAC improves ERAS results for GE and HE (Figures 1-4). Strong dipole-dipole interactions are also present in linear organic carbonate + alkane systems. Figure 5 shows DISQUAC HE results for DMC or DEC + nheptane systems at very high temperatures. The agreement with experimental data (not used in the fitting of the interaction parameters25) is good. Azeotropic data at given temperatures are also reproduced in the correct range of pressure and composition. For example, DISQUAC predicts an azeotrope for the DMC (1) + cyclohexane (2) mixture at 346.55 K; Paz ) 106.7 kPa and x1az ) 0.622. The experimental values40 are Paz ) 101.5 kPa and x1az ) 0.621.
4386 Ind. Eng. Chem. Res., Vol. 42, No. 19, 2003
Figure 3. GE for 1-alkanol (1) + linear organic carbonate (2) systems. Points, experimental results: (b) 1-propanol (1) + DMC (2),38 T ) 313.15 K; (9) 1-hexanol (1) + DMC (2) (this work), T ) 363.15 K; (2) 1-hexanol (1) + DEC (2) (this work), T ) 363.15 K. Solid lines, ERAS calculations using parameters from Tables 5 and 6. Dashed lines, DISQUAC results with interaction parameters from the literature.22
Figure 4. HE for 1-alkanol (1) + DMC (2) systems at 313.15 K. Points, experimental results:38 (b) methanol; (9) ethanol; (2) 1-propanol. Solid lines, ERAS calculations using parameters from Tables 5 and 6. Dashed lines, DISQUAC results with interaction parameters from the literature.22
This is the main advantage of DISQUAC (and of any physical model): they can be applied to any type of mixture. ERAS can be used only when the thermodynamic properties of the systems are mainly determined by the self-association of one component or by cross associations between components. However, it is possible to obtain accurate information on excess molar volumes using ERAS (Figure 6). 5. Conclusions P-x measurements at 353.15 and 363.15 K for 1-hexanol + DMC or + DEC systems are reported. The deviations between the experimental GE and HE values and the ERAS results can be ascribed to the existence
Figure 5. HE for the DMC (1) or DEC (1) + n-heptane (2) mixtures. Points, experimental values:49 (b) system with DMC at T ) 363.15 K and P ) 15.48 bar; (9) system with DEC at T ) 373.15 K and P ) 14.79 bar. Solid lines, DISQUAC calculations with the interaction parameters from literature.25
Figure 6. VE for 1-alkanol (1) + DEC (2) systems at 298.15 K. Points, experimental results: (9) 1-pentanol;51 (b) 1-hexanol.52 Solid lines, ERAS calculations using parameters from Tables 5 and 6. Dashed lines, chemical, VEchem, and physical, VEphys, contributions to VE.
of strong polar interactions between carbonate molecules, not described properly by the model. Acknowledgment JAG gratefully acknowledges the financial support received from the Ministerio de Ciencia y Tecnologı´a “Programa Nacional de Procesos y Productos Quı´micos” (Project PPQ2001-1664) y Unio´n Europea (FEDER) and by the Consejerı´a de Educacio´n y Cultura de la Junta de Castilla y Leo´n (Project VA039/01) y Unio´n Europea (FSE). Literature Cited (1) Parrish, J. P.; Salvatore, R. N.; Jung, K. W. Perspectives on alkyl carbonates in organic synthesis. Tetrahedron 2000, 56, 8207-8237.
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Received for review April 9, 2003 Revised manuscript received July 14, 2003 Accepted July 15, 2003 IE0303000
