Ind. Eng. Chem. Res. 1987,26, 1153-1162 the smaller increase caused by CH4 are adverse, while the pressure decreases caused by the acid gases, especially SOz, are beneficial. Additional conclusions are suggested by the modeling efforts: 1. Swelling factors can be adequately estimated for COz sources contaminated with small levels of Nz, CHI, HzS, or SOz by using either a generalized P-V-T correlation designed for pure C 0 2 or a simple equation of state. Swelling factors predided by the Simon-Graue correlation were usually closer to the measured values; however, extension of the Mulliken-Sandler approach to the PengRobinson equation of state was more successful when SOz was present and less sensitive to the chemical nature of the crude oil. 2. The simple equation of state gave unsatisfactory predictions of bubble-point pressure but adequately estimated sample volumes a t the bubble point except for mixtures of the'more paraffinic oil containing SOz.
Acknowledgment The research summarized in this report was supported by funds from the US Department of Energy. Summer salary support for Dr. Monger was provided by the Exxon Education Foundation Faculty Assistance Program. Some of the experiments were performed a t the US DOE Morgantown Energy Technology Center in Morgantown, WV.
1153
T = temperature V = vapor phase V = volume Registry NO.C H ~74-82-8; , coz,124-38-9;N, 17778-880;soz, 7446-09-5;HZS, 7783-06-4.
Literature Cited Bierlein, J. A,; Kay, W. B. Znd. Eng. Chem. 1953,45,618. Caubet, F. Comp. Red. 1900,130,828. Graue, D.J.; Zana, E. J. Pet. Technol. 1981,33,1312. Grigg, R. B.; Lingane, P. J. Presented a t the 58th Annual Fall Technical Conference of the Society of Petroleum Engineers, San Francisco, CA, Oct 1983;paper SPE 11960. Holm, L. W. J . Pet. Technol. 1982,34, 2739. Holm, L.W.;Josendal, V. A. J . Pet. Technol. 1974,16, 1427. Kesler, M. G.; Lee, B. I. Hydrocarbon Process. 1976,55(3), 153. Metcalfe, R. S. SOC.Pet. Eng. J . 1982,22,219. Metcalfe, R. S.;Yarborough, L. SOC.Pet. Eng. J. 1979, 19,242. Mulliken, C. A.; Sandler, S. I. Znd. Eng. Chem. Process Des. Deu. 1980,19, 709. Orr, F. M.; Yu, A. D.; Lien, C. L. SOC.Pet. Eng. J . 1981,21, 480. Peng, D.;Robinson, D. B. Znd. Eng. Chem. Fundam. 1976,15,59. Peterson, A. V. Pet. Eng. 1978,50,40. Reamer, H. H.; Sage, B. H. J. Chem. Eng. Data 1963,8,508. Sayegh, S. G.; Najman, J.; Hlavacek, B. Presented a t the 32nd Annual Technical Meeting of the Petroleum Society of the Canadisn Institute of Mining and Metallurgy, Calgary, Alberta, May 1981; paper 81-32-14. Shoolery, J. N.; Budde, W. L. Anal. Chem. 1976,48, 1458. Simon, R.; Graue, D. J. J. Pet. Technol. 1965,13,102. Watson, K. M.; Nelson, E. F.; Murphy, G. B. Znd. Eng. Chem. 1935,
27,1460.
Nomenclature L = liquid phase P = pressure
Received for review January 22, 1985 Accepted November 11, 1986
Solid-Liquid Phase Relations of Some Normal Long-chain Fatty Acids in Selected Organic One- and Two-Component Solvents Urszula Domafiska Department of Physical Chemistry, Warsaw Technical University, 00664 Warsaw, Poland
Solubilities of octadecanoic acid and docosanoic acid were determined from 290 to 340 K in several pure solvents a n d in several binary solvent mixtures. T h e effects of temperature changes on the observed solubilities were in close agreement with the general principles of thermodynamics, using the Wilson equation t o represent the activities in the solutions. Use of the Scatchard-Hildebrand regular-solution theory was less successful, even though the chemical association of the acids was allowed for. A knowledge of the solubility characteristics of longchain fatty acids in organic solvents is important to fats and oil technology and research. Extensive solubility data have already been published (Singleton, 1960),but new processes with two-component solvents require these data to be constantly supplemented. Ralston and Hoerr (1942, 1945),Hoerr and Ralston (1944),and Hoerr e t al. (1946) have measured the solubility of stearic acid in more than 20 solvents of different chemical properties. Preckshot and Nouri (1957) has dealt with halogen derivatives of hydrocarbons, whereas Kolb (1959)has used various hydrocarbons a t low temperatures. Harris et al. (1968) has worked with N,N-dimethylformamide, and N,N-dimethylacetamide. Bailey et al. (1969)have made comprehensive investigations of the solubility of octadecanoic acid and docosanoic acid based on the literature data and
their own measurements. The literature data concern solubilities of these two acids in a series of more than 50 one- and two-component solvents (Brandreth and Johnson, 1971). However, the discrepancy of solubility measurements, obtained by various investigators, is observed, due to the differences ih purity of used components, to .be the best solubility of stearic acid in chloroform, N,N-dimethylacetamide, and N,N-dimethylformamide. According to the literature data, aliphatic halogen derivatives, especially asymmetric compounds with a great number of chlorine or fluorine atoms in molecules, appear to be the best solvents at a temperature range of 290-300 K. Pure alcohols are not attractive solvents, but the increment of the solubility of acids with an increase in the chain length of alcohol molecules (C&) is observed. The azeotropic mixtures of alcohols with halogen derivatives of hydro-
0888-5885/8712626-1153$01.50/0 0 1987 American Chemical Society
1154 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987
carbons seem to be very good due to the enhanced solubility effects called synergistic effects. The studies of synergistic effects in solid-liquid equilibrium in binary solvent systems have already been carried out and reported in the literature (Gordon and Scott, 1952; Buchowski et al., 1979; Domaiiska, 1980, 1981). The occurrence of synergistic effect can be predicted on the basis of the Scatchard-Hildebrand theory (Hildebrand et al., 1970). However, in cases of polar solutes and polar solvents, the solubility parameters describing appropriate interactions, according to Barton (1975), must be considered. Thus, a binary mixture of nonpolar solvents is liable to exhibit a synergistic effect with respect to a solute if the solubility parameter of the latter has a value intermediate between the values of solubility parameters of solvents constituting the mixture. To date it has been established that synergistic effects can be observed in binary solvents exhibiting GE > 0. Additionally, the solubility of the studied solute in pure solvents must be comparable. The synergistic effect of fatty acids solubility was presented by Brandreth and Johnson (1971),Domaiiska and Hofman (1985), and Domaiiska (1986). The solubility of solids in liquids generally is expressed by
When a h phase transition takes place in the solid phase, a correction term, Q, given by expression 2, must be added to eq 1, giving eq 3 where T , and Tb specify the temper-
ACPm1(
R
l1 )
ln-+--1
~ ; i
+ Q + l n . r l (3)
ature range over which the transition takes place. CpBin eq 2 is the base line of the specific heat during the phase transition; Ah? and ASltr in eq 2 stand for the overall contribution of enthalpy and entropy changes caused by the specific heat anomaly from the beginning to the end of the transition. First, it was cited by Choi and McLaughlin (1983). By using eq 1 or 3, one can evaluate the solubility data (xlvs. T ) , assuming that other physical constants in the equations are known. In the simplest case, when such information, unfortunately, is not available, eq 4 is frequently applied. In eq 4, x1 and y1 are mole fraction
and the activity coefficient of the solute in the liquid phase, respectively, T,, is the temperature of fusion, and AHm1 is the enthalpy of fusion. Application of eq 4 to a given system requires an assumption as to the functional beand yl(T,x). In the simplest case (AHml havior of mm1(T') # f ( T ) and y1 = l ) , the well-known Schroder equation, describing ideal solubility, is obtained. Generally, suitable functional relationships between activity coefficients and
temperature or composition are obtained by means of a search procedure. In nonpolar solvents, where a positive deviation from ideality is observed, the Scatchard-Hildebrand equation is applicable (Hildebrand et al., 1970). The Wilson equation was used by Morimi and Nakanishi (1977), Muir and Howat (1982), and Domadska and Hofman (1985). Other existing correlation equations adapted from VLE can also be utilized: these include the Redlich-Kister, van Laar, and UNIQUAC equations. The SLE calculations using two of the most elaborate group contribution methods, ASOG (Hoshino et al., 1977) and UNIFAC (Gmehling et al., 1978; Domakka and Hofman, 1985), had already been published. In this paper the solubility studies of octadecanoic (c18) and docosanoic (C2J acids in pure and binary solvent systems are reported and the applicability of Wilson, Redlich-Kister, van Laar, and Ah solubility equations to the correlation of the solid-liquid equilibrium is discussed.
Experimental Work Solubilities were determined by a dynamic (synthetic) method which was described in the paper of Buchowski et al. (1975). The measurements were carried out in a temperature range of 290-340 K and in a solute concentration range of x1 = 0.003-0.50. Accuracy,of the temperature measurements was 0.05 K. Reproducibility of measurements was 0.1 K which corresponded to a relative error of composition smaller than 19'0. All solvents were dried over 4A molecular sieves (BDH) and then purified by distillation, tetralin, and triethyl phosphate by distillation under vacuum. The total amount of contaminants did not exceed 0.1 9'0 for the alcohols and 0.2% for the other solvents as estimated from vapor-phase chromatography. The acids used (Fluka, AG) were recrystallized twice from ethanol and distilled under reduced pressure. The melting points were 342.55 K for C18and 354.65 K for Czz. In the calculations, the following values were applied: enthalpy of fusion AHml = 61.209 kJ.mol-' (Schaake et al., 1982) for and AHml = 76.400 kJ-mol-' for CZ2;temperature of melting Tml= 342.49 K (c18),Tml= 353.80 K (C22);transition temperature T,, = 327.15 K (&) (Stenhagen and Sydow, 1953). The values for docosanoic acid were obtained by linear extrapolation of measured values for even-numbered normal alkanoic acids derived by Schaake et al. (1982). Results and Discussion Experimental results in one-component solvents and in most of the two-component solvents are shown in Figures 1-10. Solubilities of octadecanoic acid and of docosanoic acid in one-component solvents are listed in Tables I and 11, respectively, and of both of the acids in binary solvent systems in Table 111. Solubilities in mixed solvent systems, cyclohexane with heptane, ethanol, and 2-propanol, were presented in a preceding paper (Domabska and Hofman, 1985). The measured solubilities of the solutes in all solvents are lower than the calculated values for an ideal solubility, and they show positive deviations from ideal-solution behavior (yl > l). Various solvents were tested in order to state the influence of the molecular size of the solvent and its electron-donor properties on the solubility of acids. Moreover, mixture solvents revealing synergistic effect of solubility were investigated. Triethyl phosphate, as an electron-donor compound of a great value of dielectric constant, is a very good solvent (Figure 1). Probably intermolecular hydrogen bonding, occurring even in the crystallographic structure of acids, is rapture due to the
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1155
330
f
290
'
1
1
I
!
I
280
0.2
01
0.3 X i
Figure 1. Solubility of octadecanoic acid in acetone (11, methyl isobutyl ketone (2), cyclohexanone (3), tetralin (4), benzene (5), and triethyl phosphate (6) (lines are calculated from eq 5). 0.3
0.2
0.1
XI
Figure 3. Solubility of docosanoic acid in 2-propanol (l), l,l,l-trichloroethane (21, trichloroethylene (3), and mixed solvent system trichloroethylene
a
0 0.1
0.2
0.3
+ 47.77 mol % 2-propanol ( 4 ) .
0 0.4
0.5
XI
Figure 2. Solubility of octadecanoic acid in 2-propanol (l), tetra-
+
chloroethylene 92.16 mol % 2-propanol (21, tetrachloroethylene (3), trichloroethylene (4), and trichloroethylene + 48.40 mol % 2propanol (5).
existence of strong basic oxygen atoms in triethyl phosphate molecules. Ketones, as aprotonic solvents containing heteroatoms of great basicity, have been taken also into the investigations. It is found, however, that the solubility of stearic acid in ketones is lower than in triethyl phosphate (see Figure 1-solubility in cyclohexanone is larger than in methyl isobutyl ketone and larger than in acetone). At higher temperatures (>330K), hydrocarbons seem to
300
0.05
0.10
0.15
0.M
0.25
0.30
x,
Figure 4. Solubility of docosanoic acid in butyl acetate (2) + ethanol (1)mixed solvent system containing 49.66 mol % ethanol (3).
be better solvents than ketones. Cyclohexane and cyclohexanone have similar dissolving power, probably due to the comparable size of molecules, but because of the possibility of their forming hydrogen bonds with a solute, cyclohexanone is a little better solvent. I t seems that the donor-electron effect and molecular dimensions, especially in the case of long-chain compounds,
1156 Ind. Eng. Chem. Res., Vol. 26, No. 6,1987
I
I
1 300 005
0.10
0.15
0.20
0.25
0.30
0.35
X1
Figure 5. Solubility of docosanoic acid in cyclohexane (2) + butyl acetate (1) mixed solvent system containing 45.78 mol % butyl acetate (3).
Figure 7. Solubility of octadecanoic acid in cyclohexane (1) + 2propanol (4) mixed solvent system containing 39.63 mol % (2) and 61.60 mol % (3) 2-propanol.
0.2
0.1
0.3
X1
Figure 6. Solubility of octadecanoic acid in cyclohexane (1)+ ethanol (4) mixed solvent system containing 42.00 mol % (2) and 69.03 mol % ethanol (3).
ought to be taken into consideration in the selection of solvents. Greater solubility than in cyclohexane is observed in trichloroethylene, l,l,l-trichloroethane, and tetrachloroethylene and the lowest one in ethanol (see Figure 1). Early studies on the solid-liquid equilibrium have led to the formulation by Buchowski et al. (1980) the Ah solubility equation In [ l
+ X ( 1 - x , ) / x , ] ~=~ xh(T1- Tm1-l)
(5)
where X and h are the equation parameters, which are either adjusted to the solubility data or estimated in a different way. Parameter X may be considered as a measure of nonideality of saturation solution d In (1 - ug)
=
(
In ul
xlYB )T
= 1 - XBYB
(6)
where u1 and u2 are the activities of solute and solvent, respectively. Parameter X for ideal associated systems
2901
I 0.1
I
02
I 03
X1
Figure 8. Solubility of docosanoic acid in cyclohexane (1) + ethanol (4) mixed solvent system containing 39.80 mol % (2) and 60.01 mol % (3) ethanol.
corresponds to the mean association number, i.e., to the mean number of monomolecules per multimer. The parameter h is defined as
hR = AHml + HE/xl
(7)
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1157 Table I. Solubility Measurements of Octadecanoic Acid in Different One-Component Solventsa acetone
T,K
benzene Xl
0.2386 0.1761 0.1246 0.89183-01 0.63283-01 0.43743-01 0.30593-01 0.20803-01 0.14233-01 0.9633-02 0.6583-02 0.4503-02 ethanol
327.15 324.35 321.55 319.15 316.75 314.15 311.65 308.85 305.15 301.65 298.65 295.15
cyclohexane
T,K
XI
T,K
X1
T,K
X1
323.15 313.15 303.15 293.15 283.15
0.285 0.123 0.33E-01 0.703-02 0.103-02
320.70 316.35 313.45 311.15 308.95 306.55 303.65 300.25 298.65 296.65
0.2731 0.1839 0.1399 0.1070 0.82583-01 0.52263-01 0.35073-01 0.20543-01 0.14163-01 0.8753-02
324.85 313.15 309.55 306.55 301.65 298.65 294.85
0.263 0.913-01 0.61E-01 0.42E-01 0.233-01 0.16E-01 0.123-01
heptane
T,K
Xl
T,K
314.95 313.05 311.55 310.65 307.25 305.95 302.55 300.35 298.15
0.2603-01 0.2053-01 0.1843-01 0.1693-01 0.1333-01 0.1193-01 0.773-02 0.573-02 0.373-02
334.05 330.65 324.45 319.95 318.35 315.65 315.25 312.35 309.35 307.25 304.95 302.45 297.95
,
cyclohexanone
tetrachloroethylene
methyl isobutyl ketone X1
0.5798 0.4211 0.2511 0.1434 0.1248 0.84033-01 0.79093-01 0.51623-01 0.34993-01 0.22743-01 0.16103-01 0.10803-01 0.5153-02 tetralin
T,K 325.85 320.25 317.00 314.15 311.05 307.95 305.05 303.15 301.85 287.75
*l
0.263 0.147 0.104 0.753-01 0.533-01 0.353-01 0.263-01 0.21E-01 0.19E-01 0.5E-02
trichloroethylene
2-propanol
T,K
X1
335.45 0.5139 333.25 0.4183 327.65 0.2747 323.95 0.2115 320.05 0.1541 317.05 0.1157 312.55 0.73123-01 308.45 0.45973-01 305.45 0.32363-01 302.15 0.22403-01 299.95 0.17403-01 296.75 0.11883-01 290.95 0.6333-02 triethyl phosphate
T,K
X1
T,K
x1
T,K
X1
T,K
XI
325.55 321.95 317.15 312.95 309.15 305.95 302.45 299.25 296.45 293.65 291.45 289.05
0.3600 0.2820 0.1989 0.1416 0.99643-01 0.71693-01 0.48263-01 0.32373-01 0.21853-01 0.14793-01 0.9983-02 0.6643-02
333.95 325.65 323.40 320.65 318.80 316.55 313.35 311.25 308.45 302.15 299.25 297.15 296.55 295.15 294.15
0.595 0.371 0.265 0.206 0.169 0.136 0.943-01 0.71E-01 0.583-01 0.31E-01 0.153-01 0.103-01 0.83-02 0.73-02 0.53-02
320.55 314.45 309.65 306.35 301.35 297.25 293.65 290.85 287.85 285.05 281.65
0.2660 0.1795 0.1285 0.97673-01 0.61263-01 0.38973-01 0.25383-01 0.16623-01 0.1070E-01 0.7103-02 0.4203-02
311.75 305.10 300.90 294.85 292.65
0.240 0.138 0.883-01 0.48E-01 0.353-01
OThe notation in this and other tables of 3-01 means the value X10-‘.
where HE is the enthalpy of mixing. The value of hR should be close to the melting enthalpy of the solute, when the enthalpy of mixing, HE, is close to zero. Equation 5 has been led out on the basis of the Gibbs-Duhem equation for the two-component and three-phase systems being in equilibrium. In the case of ternary systems, the binary mixed solvent is considered to be equivalent to the onecomponent solvent. Equation 5 describes well experimental data for many systems, as was shown by Domadska et al. (1982) and Domadska (1986). For example, in the graph (Figure l ) , experimental points are matched with curves calculated from eq 5 for optimum values of X and h parameters, found by the Rosenbrock numerical method (Rosenbrock, 1960) for octadecanoic acid in a few onecomponent solvents. Values of the coefficients, X and h for binary systems, and of the root mean square deviation of temperature, uxh,defined by expression 8, are listed in Table IV. u
= [5(T,“”‘- T,)Z/(n- 1)]”2
(8)
r=l
Values of the root mean square deviations for one-component solvents are from 0.25 to 1.77 K. Taking into
consideration that the binary solvent system makes one compound, the calculations were derived also for ternary systems. The results are collected in Tables V and VI. The root mean square deviations in the most tested systems were smaller than 2 K. In the literature it was shown, from measurements of a freezing point depression, that fatty acids form dimers in cyclohexane and benzene (Broughton, 1934; Ralston and Hoerr, 1942). The distribution of fatty acids between organic solvents and aqueous solutions and dielectric measurements also suggests the dimerization of the fatty acids in organic solvents (Pohl et al., 1941; Maryott et al., 1949; Loveluck, 1960; Goodman, 1958; Kojima and Tanaka, 1970; Singh, 1968; Fuks and Tichonow, 1976; Kowalska, 1977; Sliwiok and Kowalska, 1977; Madec and Marechal, 1978). However, the extent of dimerization depends on the nature of the solvent, of the solute concentration, and of the temperature. It was concluded by Murata et al. (1978) that the order of solvents in the extent of the dimer formation is cyclohexane > benzene > ethyl methyl ketone. Considering that the solutions of acids in many undertested solvents are the ideal associated systems, one should expect the value of parameter X to be close to the mean
1158 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table 11. Solubility Measurements of Docosanoic Acid in Different One-Component Solvents butyl acetate
cyclohexane
T,K
XI
338.75 335.85 333.15 329.65 326.75 324.25 321.15 318.15 312.25 308.95
0.2798 0.1991 0.1365 0.8973-01 0.6003-01 0.4023-01 0.2733-01 0.1843-01 0.1263-01 0.873-02
T,K
ethanol
T,K
XI
340.45 0.3606 0.2716 336.75 333.15 0.1961 0.1431 329.55 0.9963-01 326.35 0.6763-01 323.25 0.4633-01 320.15 0.3153-01 316.95 0.2103-01 314.35 0.142E-01 312.65 0.9603-02 310.75 0.4853-02 308.95 0.1363-02 300.35 0.833-03 298.45 0.523-03 296.15 l,l,l-trichloroethane
2-propanol
XI
342.15 0.2986 337.15 0.1644 334.85 0.1198 0.8003-01 332.75 0.5033-01 329.75 327.45 0.3393-01 0.2273-01 325.65 0.1513-01 323.45 321.15 0.102E-01 0.6803-02 318.25 314.25 0.4603-02 0.2123-02 308.15 0.1103-02 303.25 0.693-03 299.75 0.473-03 297.25 trichloroethylene
T, K
XI
T,K
XI
T, K
XI
341.15 339.25 335.75 333.15 330.65 327.65 324.95 321.75 318.75 315.95 313.15 309.35 305.25 301.35 297.85 294.95
0.2829 0.2341 0.1624 0.1154 0.80193-01 0.53983-01 0.36143-01 0.23353-01 0.15703-01 0.10383-01 0.6873-02 0.4703-02 0.2823-02 0.1923-02 0.1243-02 0.793-03
338.75 332.25 327.35 323.95 319.75 315.85 313.95 311.95 309.75
0.3302 0.2202 0.1407 0.1037 0.73443-01 0.50443-01 0.35393-01 0.17593-01 0.13063-01
338.95 336.05 330.95 326.65 321.75 317.95 314.25 311.05 308.35 305.65 303.55 301.25
0.3422 0.2868 0.2029 0.1537 0.1048 0.7233-01 0.491E-01 0.3283-01 0.2193-01 0.1463-01 0.983-02 0.663-02
1
I
I
I
'
290 01
03
07
09
XI
Figure 10. Solubility of octadecanoic acid in cyclohexane (l), cyclohexane !
I
I
Figure 9. Solubility of docosanoic acid in cyclohexane (1) + 2propanol (4) mixed solvent system containing 40.82 mol 70 (2) and 60.09 mol % (3) 2-propanol.
association number x = Cini/Cni= 2 for dimers. In all systems, the values of parameter X were from 0.35 (C18 in ethanol) to 3.01 (CISin heptane) and 7.93 (CI8 in cyclo-
+ 39.99 mol % heptane (2), and heptane (3).
hexane) (see Table IV). In order to obtain the physical meaning of the X parameter, it must be calculated from the vapor pressures in saturated systems or from the thermodynamic data, describing the association of the acid as presented in the earlier work of DomaAska et al. (1982). The parameter h numerically calculated from eq 5 has different values in comparison with the enthalpy of melting (see eq 7). This can be seen especially in the case of small
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1159 Table 111. Solubilitv Measurements of Octadecanoic Acid and Docosanoic Acid in Binary Solvent Systems ~~~~
Cl8
~
+
Cl8
+
+
C22 + butyl acetate
czz +
CZ2+ cyclohexane + 45.78 mol 3' % butyl acetate
trichloroethylene 48.40 mol % 2-propanol
T,K
T,K
X1
T,K
Xl
T,K
XI
T,K
Xl
321.15 315.15 309.75 303.55 298.25 293.35 289.05 284.15 279.95
0.2762 0.1980 0.1477 0.1041 0.7393-01 0.5133-01 0.3523-01 0.2463-01 0.1673-01
338.15 334.05 330.25 327.75 325.55 322.35 319.65 314.15 310.05 306.05
0.2646 0.1771 0.1195 0.8793-01 0.6273-01 0.4373-01 0.3023-01 0.205E-01 0.1393-01 0.933-02
340.15 335.65 330.55 325.95 322.65 319.75 316.85 315.15 313.15 311.25 309.65
0.3694 0.2565 0.1681 0.1170 0.8463-01 0.6063-01 0.4273-01 0.2913-01 0.2013-01 0.1383-01 0.863-02
337.05 332.55 327.95 322.65 317.55 312.35 308.15 303.45 298.95 294.75
0.2981 0.2279 0.1737 0.1276 0.9293-01 0.6293-01 0.4483-01 0.3083-01 0.2103-01 0.1413-01
+
327.35 323.25 319.75 315.65 312.15 308.55 304.75 301.15 297.45 293.65 289.75 285.85 284.45
Xl
0.3315 0.2492 0.1951 0.1391 0.1050 0.7453-01 0.5063~01 0.3433-01 0.2363-01 0.1593-01 0.1063-01 0.723-02 0.603-02
+ 49.66 mol % eth a n o1
trichloroethylene 47.77 mol % 2-propanol
+
tetrachloroethylene 92.16 mol % 2-propanol
Table IV. Results of Calculations Based on Equation 5 and Scatchard-Hildebrand, Wilson, Redlich-Kister, and van Laar Equations in One-Component Solvents ea 5
acetone benzene cyclohexane cyclohexanone ethanol heptane methyl isobutyl ketone 2-propanol tetrachloroethylene tetralin trichloroethylene triethyl phosphate
1.29 4.88 7.93 1.61 0.35 3.01 1.11 1.09 2.94 3.33 3.16 5.46
9.66 2.77 1.84 6.57 28.97 4.79 9.14 9.11 3.70 3.90 3.44 1.83
0.73 1.17 0.74 0.49 0.82 0.49 0.97 0.69 1.00 1.13 0.85 0.25
10.05 12.30 6.79 2.21 86.98 5.01 9.63 24.91 4.28 7.76 3.74 4.32
8.53 9.45 10.15 15.35 131.70 12.54 6.95 44.65 13.06 9.70 16.42 7.26
2.89 4.29 0.52 0.66 1.54 1.22 0.33 1.77 1.29 1.93 22.93 2.23
2.28 3.43 0.52 0.58 1.35 0.97 0.32 1.60 0.71 1.59 5.65 2.54
3.81 8.46 3.11 1.58 1.60 3.96 1.08 2.31 4.52 4.51 4.86 0.48
2.42 3.06 1.16 0.53 2.57 1.37 0.35 1.80 5.57 1.60 4.91 1.73
butyl acetate cyclohexane ethanol 2-propanol l,l,l-trichloroethane trichloroethylene
1.34 4.26 1.08 1.06 2.70 2.13
9.60 3.73 13.83 12.35 4.66 5.23
2. Docosanoic Acid 1.20 7.94 6.45 1.49 10.20 9.63 1.48 89.00 134.00 0.97 32.98 60.06 3.19 11.61 1.77 1.59 3.19 15.86
0.74 5.21 2.54 2.04 1.08 1.07
0.81 4.61 1.75 1.54 3.29 2.93
0.83 7.67 5.58 3.55 2.70 2.57
0.74 2.55 3.17 2.19 1.55 2.75
Table V. Results of Calcu-Ations Based on Equations 5 and 10 for Azeotropic Binary Solvent Systems ea 5 solvent system tetrachloroethylene + 92.16 mol 70 2-propanol trichloroethylene + 48.40 mol % 2-propanol butyl acetate + 49.66 mol % ethanol cyclohexane 45.78 mol % butyl acetate trichloroethylene 47.77 mol % 2-propanol
+
+
1. Octadecanoic Acid 1.31 6.87 0.95 6.39
0.39 0.78
25.96 15.60
47.08 30.47
2. Docosanoic Acid 1.06 10.44 4.66 2.89 8.72 0.80
1.00 1.53 0.77
1.08 4.26 17.30
15.51 10.59 30.70
solubilities, e.g., Cls in ethanol. The values of enthalpy parameters, 10-3h, are from 1.83 K (CISin triethyl phosphate) to 28.97 K (Cls in ethanol), when the enthalpies of melting are 1 0 - 3 ~ m , R -=1 7.36 K for Cl8 and 10-3AHm1R-' = 9.19 K for CZZ. The xh solubility equation eq 5 can be tested as a prediction equation if the excess of enthalpy of mixing in a saturated solution is known. The binary solvents studied (except cyclohexane + heptane system) were found to exhibit a synergistic effect on solubility. A n inherent property of these solvents is that a t particular composition their power of dissolution becomes much higher than that of their individual components. Synergistic effects occur in halogen derivatives + alcohols systems (see Figure 2 and 3), in esters + alcohols systems (see Figure 4),cyclohexane + esters systems (see
Figure 5), and cyclohexane + alcohols systems as it is exemplified in Figures 6-9. The biggest enhancement of solubility was attained in the cyclohexane + 2-propanol system and the trichloroethylene + 2-propanol system. The prediction of a synergistic effect for a given system follows from the Hildebrand's theory of regular solutions (Hildebrand et al., 1970) according to the condition 6 A .e 61 .e 6B (9) The values of solute solubility parameters and molar volume are 61 = 8.75 ~ a l ' / ~ . c m and - ~ / ~Vl = 327.64 ~m~~mo1-l - ~ / ~V , = 395.2 cm3.mo1-' for Cl8 and 6, = 8.60 ~ a l ' / ~ . c m and for CZ2. They were calculated on the basis of the work of Konstam and Feairheller (1970) and Murata et al. (1978). Solubility parameters for solvents, according to Barton (1975) and Hansen (1969), were taken. From the values
1160 Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 Table VI. Standard Deviations from the Description by Eauations 5 and 10 acid
xRoo
Cis
0.1005 0.2001 0.3999 0.4977 0.5975 0.7998
eq 5 10-3h, K u f i , K 1. Cyclohexane-Heptane 5.40 1.85 2.05 2.74 4.44 0.84 2.41 0.83 5.03 2.44 5.25 0.83 4.56 1.47 2.94 2.91 4.85 1.33
0.2000 0.2990 0.4200 0.5020 0.6903 0.8010 0.8990
C22
X
UHS,
K
UHS',
K
4.51 5.27 4.16 5.33 6.08 5.83
9.18 9.48 8.90 8.88 9.89 9.92
2. Cyclohexane-Ethanol 1.39 1.02 7.05 7.24 1.23 0.94 7.10 1.22 0.91 0.44 0.82 7.66 9.57 0.44 0.75 11.31 1.40 0.67 0.80 0.80 10.53
1.61 2.29 4.04 6.30 8.58 19.98 27.01
10.56 12.88 13.59 18.06 19.62 35.66 41.50
0.1666 0.5710 0.6160 0.7638
3. Cyclohexane-2-Propanol 0.80 7.95 0.39 1.80 3.91 0.21 3.27 2.51 1.18 1.40 5.60 1.15
1.79 11.15 13.39 15.29
11.93 20.71 23.11 32.35
0.2003 0.3980 0.4976 0.6001 0.8000
1. Cyclohexane-Ethanol 1.07 1.28 6.97 1.15 7.42 1.47 1.66 1.56 6.23 0.94 9.34 1.48 10.18 0.89 1.03
3.48 6.81 8.48 12.63 32.30
15.73 20.90 23.55 28.10 54.43
0.2025 0.4082 0.4979 0.6009 0.8002
2. Cyclohexane-2-Propanol 0.35 17.58 3.15 1.08 8.17 0.95 0.50 14.65 3.42 0.61 13.18 2.25 0.96 10.45 1.37
4.99 4.04 6.70 7.97 17.34
17.32 17.53 20.87 22.79 37.00
" x B 0 = mole fractions of the second named component in the solute-free mixed solvent.
of solubility parameters, it appears that condition 9 is satisfied only in cyclohexane + alcohol and ester + alcohol systems. However, the great synergistic effects are observed in the chlorocarbons + alcohols systems. The synergistic effect doesn't appear in the case of a large content of alcohol in an azeotropic solvent mixture (C18 - tetrachloroethylene + 92.16 mol % 2-propanol-see Figure 2). Azeotropic mixtures (see Table V) were taken
into consideration because of the general utilization in industry due to the convenience of the regeneration by the distillation process. Searching for azeotropic solvent mixtures giving the synergistic effect is the main tendency in investigations. The solubility of octadecanoic acid in azeotropic mixtures of binary solvent systems have been measured by Brandreth and Johnson (1971). In this work, mixtures of freons with alcohols, ketones, and chlorocarbons were tested. All solvent mixtures were positive homoazeotropes. In a cyclohexane + heptane system, the solubility values are intermediate between the values obtained for pure solvents, as shown in Figure 10. This is consistent with Scatchard-Hildebrand theory. Unfortunately, it is not possible to use Scatchard-Hildebrand's eq 10 for the description of the systems studied, since it has been derived for nonpolar systems.
Assuming that ( 6 , - 6,) # f(T),the activity coefficients as a function of x1 and T were obtained. This way the solubility could be predicted throughout the solution of eq 3 for C18and eq 4 for CZ2(no data for ACp, Ah?, ASP, Tw)for each experimental composition, x,. The root mean square deviations, oHS, according to formula 8 have been determined (see Tables IV-VI). The deviations are especially high in pure alcohol systems and alcohol-rich systems. Furthermore, the root mean square deviations are not satisfied even in inert cyclohexane + heptane mixed solvent systems. If a saturated solution of an alkanoic acid in a nonpolar solvent contains primarily dimers, the nominal mole fraction in eq 3 and 4 should be replaced by the effective mole fraction, xl' = x1/(2 - xl), and AHmlshould be the enthalpy of fusion of the dimer, AHml' = 2AHm1. The results of such a description are collected in Tables IV-VI (the root mean square deviation, oHs2). The accuracy of the description of the solubilities in pure and binary solvents systems with this assumption is considerably worse, even in cyclohexane + heptane systems. The correlation equations of Wilson, Redlich-Kister, and van Laar in binary systems were also tested. The calculations with the Wilson equation (Wilson, 1964) were carried out in the version presented earlier for the description of the solid-liquid equilibrium by Morimi
Table VII. Parameters for the Wilson. Redlich-Kister. and van Laar Eauations for Binary Systems Acid (l)-Solvent (B) Wilson 2 Wilson 1
van Laar
AI
AR
1.3815 2.7875 2.9280 2.1697 1.0537 2.0625 1.8125 1.4473 2.9586 2.4656 0.4054 0.2558
0.6040 -0.1083 -0.5064 0.2185 -0.0756 0.3815 0.3195 0.6147 -0.1633 0.0564 -0.3020 -1.2932
-0.7331 -0.8311 -1.3321 -0.6129 -2.1649 -0.8130 -0.7521 -0.2035 -0.2787 -0.7929 -0.1396 -1.0323
1.5604 1.8417 2.1966 1.1496 1.8584 1.8195 1.2432 0.9489 -0.5076 1.6165 -0.1705 -0.5565
1.9681 2.7748 1.7570 1.7635 3.4090 3.5399
2. Docosanoic Acid 5.9127 -1.8529 8.4346 -2.8255 7.8008 -1.5521 6.0670 -1.5521 -0.4815 0.3943 -1.3430 0.9248
0.1902 -0.0616 0.4553 0.4379 -0.2998 -0.3387
-0.8307 -0.6273 -1.1230 -0.7731 -0.4253 -0.1965
1.2052 1.7913 1.9834 1.4467 5370 -0.1906
A i l R
liRl
acetone benzene cyclohexane cyclohexanone ethanol heptane methyl isobutyl ketone 2-propanol tetrachloroethylene tetralin trichloroethylene triethyl phosphate
0.1529 0.0357 0.0225 0.1041 0.1148 0.0523 0.1268 0.2463 0.0604 0.0524 13.783 3.9158 0.1136 0.0561 0.0572 0.1066 0.0303 0.0540
butyl acetate cyclohexane ethanol 2-propanol l,l,l-trichloroethane trichloroethylene
Redlich-Kister
- g1y g l B - gBB, kJ.molkJ.mol-' 1. Octadecanoic Acid 4.9303 -0.8437 9.1305 -2.6745 10.4480 -2.7781 5.9951 -2.0420 4.5349 0.8311 7.7956 -1.9128 -5.3364 -1.5476 3.5075 -0.9089 8.3083 -2.8772 8.0692 -2.3941 -0.5623 -0.0874 -3.0033 2.1874
glB
solvent
A,
AR
0.4657 0.0835 0.0791 0.1617 -0.151E+ll 0.2477 0.2851 0.3713 0.9283 0.1254 0.212E+10 -0.259E+11 0.2337 0.0588 0.3579 0.3229 0.8346 -0.7259
Ind. Eng. Chem. Res., Vol. 26, No. 6, 1987 1161 and Nakanishi (1977) and by Muir and Howat (1982), assuming the independence of parameters, Ajj, on temperature (the root mean square deviation, awl). In the second version, the temperature dependence of parameters, Aij, for Vi = Vj and (gij - gii) # f(V,according to formula 11, was applied (the root mean square deviation, aw2), hij= V j / Vi exp[-(gjj
- gii)/RT]
(11)
where Vi is the molar volume of the pure “in component in the liquid phase and gjj is the molar energy of interaction between the ith and j t h components. Therefore, the activity coefficient can be expressed as
in halogen derivatives of hydrocarbons + alcohols and cyclohexane + alcohols systems, including 2-propanol. 2. The application of the corrections for the existence of dimers in solid-liquid equilibrium calculations doesn’t improve the mathematical description of a solubility phenomena by the Scatchard-Hildebrand equation in the case of polar systems. 3. The solubility data in binary systems are correlated well in the following order by the Ah solubility equations of Wilson (W2), van Laar, and Redlich-Kister.
Acknowledgment I thank the Institute of Physical Chemistry, Polish Academy of Sciences, for its financial aid of the Project CPBR 3.20.62.
and the root mean square deviations, according to formula 3 for C18 and formula 4 for C22,were calculated. The results for binary systems are shown in Table IV. The constants of the Wilson equation were derived from the fitting of the solubility curves. The parameters obtained in such a manner are listed in Table VII. The introduction of a temperature dependence of parameter, Ajj, significantly improves the description of the solubility curves. In the previous paper of DomaAska and Hofman (19851, the prediction of undertested acids solubility in ternary systems was discussed using Wilson parameters for binary solvent systems (solute free) from VLE. It was compared with a method using the UNIFAC parameters for the description of solute activity coefficients. The Redlich-Kister equation is applied in the following shape:
G E / R T = x ~ x B [ A+~ A B ( x ~- XB)]
(13)
The parameters, Al and AB (see Table VII), activity coefficients, and the root mean square deviations from eq 3 (CIJ and eq 4 (C22)were calculated (aRKin Table IV). According to the van Laar equation, the excess Gibbs free energy and the activity coefficient can be expressed as
and
Similarly to the above, the parameters, Al and AB (see Table VII), and the root mean square deviations, avL (Table IV), were tested. Comparing the results shown in Table IV, one must conclude that the description by van Laar’s equation is better than by Redlich-Kister’s, except for four systems (CIS- ethanol, trichloroethylene, tetrachloroethylene, Czz - trichloroethylene). Confronting these two equations with the Wilson formula, a better description of the experimental curves is obtained, especially considering the temperature dependence of parameters, Ajj.
Conclusions The solubility study presented in this paper suggests the following results. 1. Six binary mixture solvents, revealing great synergistic effects on solubility, were presented. The biggest enhancement of the solubility of fatty acids was observed
Nomenclature Al, AB = parameters of the Redlich-Kister and the van Laar
equations al, aB = solute and solvent activities ACpmJ = difference between heat capacities of solute in the
solid and liquid states at fusion temperature g i . = molar energy of interaction between i and j components C$ = excess Gibbs free energy HE = excess enthalpy of mixing AHml = enthalpy of fusion of pure compound AHm1‘= enthalpy of fusion of dimer Ahltr = molar enthalpy change of phase transition h = parameter from eq 5 Q = correction term for the transition R = gas constant ASltr = molar entropy change of phase transition T = solid-liquid equilibrium temperature T,, = melting temperature of solute VI = molar volume of solute r,, XB = mole fraction of solute and solvent xB0 = mole fraction of the second named component in the solute-free mixed solvent Greek Symbols yl, YB = activity coefficient of the solute and solvent 6,, 6B = solubility parameter of solute and solvent Ai, = parameter of Wilson equation X = parameter from eq 5 a =
x
root mean square deviation of temperature
= mean association number
Registry No. Octadecanoic acid, 57-11-4;docosanoic acid, 112-85-6;acetone, 67-64-1;benzene, 71-43-2; cyclohexane, 110-82-7; cyclohexanone, 25512-62-3;ethanol, 64-17-5;heptane, 142-82-5; methyl isobutyl ketone, 108-10-1; 2-propanol, 67-63-0; tetrachloroethylene, 127-18-4; tetralin, 119-64-2; trichloroethylene, 79-01-6; triethyl phosphate, 78-40-0; butyl acetate, 123-86-4; l,l,l-trichloroethane, 71-55-6.
Literature Cited Bailey, A. V.; Harris, J. A,; Skau, E. L. J . Am. Oil Chem. SOC.1969, 46,583. Barton, A. F. M. Chem. Reu. 1975,75,731. Brandreth, D.A.; Johnson, R. E. J. Chem. Eng. Data 1971,16,325. Broughton, G. Trans. Faraday SOC.1934,30,367. Buchowski, H.; Domaiiska, U.; Ksiqiczak, A. Pol. J . Chem. 1979,53, 1127. Buchowski, H.; Jodzewicz, W.; MBek, R.; Ufnalski, W.; Mqczyiiski, A. Roczniki Chem. 1975,49, 1879. Buchowski, H.; Ksiqiczak, A,; Pietrzyk, S. J. Phys. Chem. 1980,84, 975. Choi, P. B.; McLaughlin, E. Ind. Eng. Chem. Fundam. 1983,22,46.
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Domaiiska, U. Le&-Czech.-Pol. Colloq. Chem. Thermodyn. Phya Org. Chem. 2nd 1980, p 92. Domaiiska, U. Pol. J . Chem. 1981,55, 1715. Domaiiska, U. Fluid Phase Equilib. 1986, 26, 201. Domadska. LJ.; Buchowski, H.; Pietrzyk. S. Pol. J . Chem. 1982, 56, 1491. Domaiiska, LJ.; Hofman, T . J . Solution Chem. 1985, 14, 531. Fuks, G. J.; Tichonow, W. P. Kolloidn. Zh. 1976, 38, 931. Gmehling, J. G.; Anderson, T. F.; Prausnitz, J. M. Znd. Eng. Chem. Fundam. 1978, 17, 269. Goodman, D. S. J . Am. Chem. SOC.1958, 80, 3887. Gordon, L. J.; Scott, R. L. J . Am. Chem. SOC.1952, 74, 4138. Hansen, Ch. M. Ind. Eng. Chem. Prod. Res., Deu. 1969,8, 2. Harris, J. A,; Bailey, A. V.; Skau, E. L. J . Am. Oil Chem. Soc. 1968, 45, 183. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions; Van Nostrand-Reinhold: New York, 1970; p 147. Hoerr, C. W.; Ralston, A. W. J . Org. Chem. 1944, 9, 329. Hoerr, C. W.; Sedgwick, R. S.; Ralston, A. W. J . Org. Chem. 1946, 11, 603. Hoshino, D.; Unno, Y.;Nagahama, K.; Hirata, M. Bull. Jpn. P e t . Inst. 1977, 19, 56. Kojima, J.: Tanaka, M. J . Inorg. Nucl. Chem. 1970, 32. 987. Kolb, D. K. Dissert. Abstr. 1959, 20, 82. Konstam, A. H.; Feairheller, W. R. AIChE J . 1970, 16, 837. Kowalska. T. Microchem. J . 1977, 22, 131.
Loveluck, G. J . Phys. Chem. 1960,64, 385. Madec, P. J.; Marechal, E. J . Mucromol. Sci. Chem., Ser. A 1978,12, 1091. Maryott, A.; Hobbs, M. E.; Gross, P. M. J . Am. Chem. Soc. 1949, 71, 1671. Morimi, J.; Nakanishi, K. Fluid Phase Equilib. 1977, 1, 153. Muir, R. F.; Howat, C. S., 111. Chem. Eng. 1982, 22, 89. Murata, Y.; Motomura, K.; Matuura, R. Mem. Fac. Sci. Kjnshu Uniu. 1978, l l c , 29. Pohl, H. A.; Hobbs, M. E.; Gross, P. M. J . Chem. P h y . 1941,9,408. Preckshot, G. W.; Nouri, F. J. J . Am. Oil Chem. Soc. 1957,34,151. Ralston, A. W.; Hoerr, C. W. J . Org. Chem. 1942, 7, 546. Ralston, A. W.; Hoerr, C. W. J . Org. Chem. 1945, 10, 170. Rosenbrock, H. H. Comput. J . 1960, 3, 175. Schaake, R. C. F.; Miltenburg, J. C.; van Kruif, C. G. J . Chem. Thermodyn. 1982, 14, 771. Singh, S. S. Ind. J . Chem. 1968, 6, 393. Singleton, W. S. In Fatty Acids; Markley, K. S., Ed.; Interscience: New York, 1960; Part I. p 609. Stenhagen, E.; Sydow, E. van Ark. Kemi. 1953, 6 , 309. Sliwiok, J.; Kowalska, T. Microchem. J . 1977, 22, 226. Wilson, G. M. J . Am. Chem. Soc. 1964, 86, 127.
Receiued for reuiew J u n e 13, 1985 Reuised manuscript received January 12, 1987 Accepted February 27, 1987
A Test for the Thermodynamic Consistency of VLE Data for the Systems Water-Formaldehyde and Methanol-Formaldehyde? Vincenzo Brandani,* Gabriele Di Giacomo, and Vittoria Mucciante Dipartimento di Chimica, Ingegneria Chimica e Materzali, Uniuersitii de' L'Aquila, 67100 L'Aquila, Zta1.y
Despite the appreciable amount of VLE data available for the binary systems, water-formaldehyde and methanol-formaldehyde, their thermodynamic consistency has never been tested systematically. In fact, there is no method available which is directly applicable and satisfactory for these systems even though it is known that there are several possible sources of systematic error that may be responsible for data of poor quality. As an example, there is the formation of small amounts of paraformaldehyde in some point of the equilibrium which still alters the equilibrium conditions. All the above considerations led us t o set u p a test t o determine the thermodynamic consistency of VLE data for the water-formaldehyde system and for the methanol-formaldehyde system. Application to most of the available data shows that the thermodynamic consistency of data for the system methanol-formaldehyde is usually better than that of data for water-formaldehyde. Our results may prove useful in selecting consistent data for model parametrization. The description of the VLE behavior of systems which contain water-formaldehyde or methanol-formaldehyde is of great importance for the design of separation processes in the chemical industry. In contrast to most other systems, strong chemical interactions have to be taken into account as well as physical forces both in the liquid phase and in the vapor phase. In the past, different authors have shown how to describe the VLE behavior of these complex mixtures, and many VLE experimental measurements have been published for the two binary systems, water-formaldehyde and methanol-formaldehyde. For an up-to-date survey of this subject, see Brandani and Di Giacomo (1985) and Maurer (1986). However, the thermodynamic consistency of these data has never been tested since the usual methods are not applicable in this case. In fact, Gmehling and Onken (1977, 1981, 19821, in their comprehensive collection of VLE data for binary and multicomponent mixtures a t moderate +Presented at t h e 8th Seminar on Applied Thermodynamics, Trieste, May 30-31, 1985.
pressures, do not give any consistency analysis for these systems. The only attempt to test thermodynamic consistency of water-formaldehyde VLE data was made by Brandani and Di Giacomo (1984) who applied the Gibbs-Konovalow theorems to two isobaric different sets of data at 100 kPa reported in the literature. It was possible to show that the set of data which does not present an "apparent" azeotrope does not follow the second Gibbs-Konovalow theorem, and therefore, it is not thermodynamically consistent. However, it was pointed out that the method could only be used as a rule of thumb, i.e., for rejecting data which are very wrong. In this paper, the consistency analysis is extended to most of the data reported in the literature for the two binary systems, water-formaldehyde and methanol-formaldehyde, by applying one differential and one integral test which are both based on the Gibbs-Duhem equation. Despite the peculiarity of the systems under consideration, which involve chemical reactions in both of the phases, it is worth noting that the results are not overly influenced by any assumption that we might make about the structure of the mixtures since a sufficient amount of
0888-5885/87/2626-1162$01.50/0 0 1987 American Chemical Society
