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Liquid-liquid equilibrium in binary polar aromatic + hydrocarbon systems
Fluid Phase Equilibria, 59 (1990) 291-308
291
Elsevier Science Publishers B.V., Amsterdam
LIQUID-LIQUID EQUILIBRIUM IN BINARY POLAR AROMATIC + HYDROCARBON SYSTEMS Andrzej KSI@CZAK
and Jerzy Jan KOSIlkKI
Department of Chemistry, Technical University, 00-664 Warsaw (Poland)
(Received July 26, 1989; accepted in final form March 28, 1990)
ABSTRACT Ksiqkczak, A. and Kosihski, J.J., 1990. Liquid-liquid equilibrium in binary polar aromatic+ hydrocarbon systems. Fluid Phase Equilibria, 59: 291-308. The liquid-liquid coexistence curves for the systems: 4-chlorophenol+ hexadecane, 2methoxyphenol + hexadecane and phenol + hexadecane have been determined by measuring the temperature of disappearance of turbulence. The literature and our data have been represented on the basis of the scaling theory: The analysis of the critical point indicates that the mean value of the mean association number of phenol in various hydrocarbons is equal to 3.11, confirming that the privileged structure of phenol associates is a trimer. The mean value of the mean association number, X, of polar compounds not forming intermolecular hydrogen bonds in various hydrocarbons is equal to 2.06 and confirms that the privileged structure of associates is a dimer. The obtained outcomes bear out previous results of the analyses of solid-liquid and solid-liquid-vapour equilibrium data for the same or similar systems. The prediction of the liquid-liquid equilibrium critical point composition has been proposed on the basis of the previously determined relationships between the association and the structure of polar aromatic compounds.
INTRODUCTION
In a previous paper (Ksi$czak, 1983) a mechanism of dissolution of polar compounds in hydrocarbons has been proposed. The dissolution process consists of transferring the associates existing in the solid phase into the solution. The ideal solubility related to a X-mer existing in the solid phase was called the pseudoideal solubility. Solubility data of various binary systems can be represented by the pseudoideal solubility equation on the basis of X-ray studies of solid solutes. A saturated solution can be treated as a pseudobinary mixture consisting of X-mers and solvent molecules, where X is the mean association number of the solute. In a more recent paper (Ksi$xzak and Kosifrski, 1988a) it was 0378-3812/90/$03.50
0 1990 - Elsevier Science Publishers B.V.
292
demonstrated that as the number of adjustable parameters increases, the equation becomes more flexible, but the fitted values of parameters frequently lose the physical meaning attributed to them and cannot be used to predict other properties of the investigated system. The regular solution theory (Hildebrand and Scott, 1950) has been used to describe the nonspecific interactions in the pseudobinary solution considering the minimal number of adjustable parameters, i.e. only one parameter. The resulting solubility equation has been used to represent the solid-liquid equilibrium (Ksi@czak, 1986a, b) and the vapour pressure of the solvent along the solid-liquid-vapour equilibrium line (Ksi+zak and Kosihski, 1988a, b) . The obtained values of the mean association number, h, were consistent with the association number of the associated species detected in the solid phases of the solute. Aromatic carboxylic acids exist in the solid phase mainly as cyclic dimers (Pimentel and McClellan, 1960). The mean association number in saturated solution of carboxylic acids is close to 2, which is in agreement with the dissolution model. The mean association number of phenols with a small steric hindrance around the hydroxyl group is close to 3 in saturated solutions and is consistent with the existence of trimers in the metastable solid phase. Para-substituted phenols such as 4-chlorophenol or 4-methylphenol consist of tetramers in the solid phase. The mean association number of 4-chlorophenol in solutions with saturated alkanes, calculated from the solid-liquid-vapour equilibrium data, is close to 4 (Ksi@czak, 1986a). An increase of steric hindrance around the hydroxyl group decreases the ability of phenols to form higher associates. The mean association number of 2-tert-butyl-4-methylphenol, calculated from the solid-liquid-vapour equilibrium data (Ksi$czak and Kosihski, 1988a, b), is close to 2, which suggests the existence of dimers in the saturated solution. A large steric hindrance around the hydroxyl group precludes the formation of hydrogenbonded associates. The analysis of solid-liquid-vapour equilibrium data of 2,6-di-tert-butyl-4-methylphenol + hydrocarbon systems (Ksi@czak and Kosihski, 1988b) demonstrates that this phenol does not associate. Similar results have been obtained from isothermal vapour-liquid equilibrium data analysis for 2,6-di-tert-butylphenol (Ksi$czak et al., 1990). The analysis of solid-liquid-vapour equilibrium data performed by Ksi@czak (1986b) suggests that aromatic compounds with a large dipole moment which do not form intermolecular hydrogen bonds, such as 2-nitrophenol or 4-nitrotoluene, dimerize as a result of dipole-dipole interactions. Association of these compounds has also been investigated by studying the vapour pressure of pure liquids (Ksi@czak and Kosihski, 1990). The presented conclusions concerning the association of polar aromatic compounds can be used to predict solid-liquid equilibrium on the basis of pure component properties
293
without fitting any parameters from binary data (Ksi@czak and Anderko, 1987). The goal of this paper is to analyse liquid-liquid equilibrium data, especially the composition of the solution in the critical point, in order to confirm the existence of associated species of the same kind as detected by analysing solid-liquid-vapour equilibrium data reported previously. Liquid-liquid coexistence curves were determined for binary systems: 4chlorophenol + hexadecane, 2-methoxyphenol + hexadecane and phenol + hexadecane. The mean association numbers in the critical point have also been calculated from binary liquid-liquid equilibrium data reported in the literature for polar aromatic + hydrocarbon systems. EXPERIMENTAL
2-methoxyphenol (Fluka, pract.) and 4chlorophenol (Koch-Light, pure) were purified by repeated sublimations. The purities, determined by cryoscopy using a UNIPAN d.s.c. type 605 were 99.98% and 99.94% respectively. The purity of phenol (Chemipan, Warsaw) determined by gas chromatography was 99.95%. Hexadecane (Reachim) was purified by repeated distillation. The chromatographically determined purity was 99.9% and the refractive index was n(D,25OC) = 1.43253, while Timmermans (1950) reported n(D,25” C) = 1.4325. The liquid-liquid coexistence curves were determined by measuring the temperature of disappearance of turbulence. The sample, the concentration of which was determined by weighing, was placed in the thermostat. The turbulence disappearance temperature was determined during a very slow temperature increase to within an accuracy of about 0.1 K. Mole fractions of phenol xA and the turbulence disappearance temperatures, T, are reported in Table 1. THE MEAN ASSOCIATION CRITICAL POINT
NUMBER
AND THE LIQUID-LIQUID
EQUILIBRIA
Classical thermodynamics does not represent correctly the properties of physical systems in the vicinity of the critical point (Sir@ and Van Hook, 1987). The properties of systems in this region can be represented by the scaling theory (Levelt Sengers et al., 1983). The coexistence curve of two phases can be represented by the equation 1s1 - s2 1 = B
exp( j3t)
(1)
where t=l-T/T,
(4
294 TABLE 1 Liquid-Liquid coexistence curve data XA
T W>
4-Chlorophenol + hexadecane 0.186 320.20 0.233 328.85 0.275 335.15 0.316 340.25 0.354 344.40 0.430 351.45 0.442 352.00 0.565 357.90 0.568 357.95 0.592 358.40 0.637 359.35 0.653 359.45 0.670 359.50 0.698 359.60 0.728 359.60 0.750 359.70 0.753 359.75 0.779 359.65 0.819 358.40 0.873 353.80 0.895 349.90 0.898 348.65 0.931 336.35 0.936 332.85 0.955 316.65 BMSD =
AT” system -0.318 0.275 0.290 0.038 - 0.117 0.107 - 0.214 - 0.229 - 0.260 - 0.356 - 0.006 - 0.008 - 0.018 0.054 0.060 0.209 0.271 0.385 0.111 - 0.112 0.071 - 0.439 0.316 - 0.064 - 0.048 0.217
2-Methoxyphenol + hexadecane system 0.1593 0.2768 0.3562 0.4382
295.65 312.05 321.95 329.65
0.114 - 0.389 0.207 0.168
0.5281 0.6123 0.6869 0.7443 0.8454 0.9310 0.9768
335.65 338.95 340.35 340.55 339.65 329.95 304.65 BMSD=
0.010 - 0.165 - 0.037 0.014 0.082 - 0.012 0.001 0.157
xA
AT”
T 0-9
Phenol + hexadecane system 0.227 327.50 0.257 331.45 335.55 0.293 342.15 0.344 0.383 345.25 350.15 0.448 353.95 0.502 355.95 0.538 356.15 0.540 0.584 357.85 359.10 0.622 0.671 360.10 360.40 0.704 0.720 360.60 360.73 0.754 0.759 360.70 0.781 360.70 360.80 0.786 0.809 360.70 0.831 360.45 360.40 0.832 359.75 0.853 0.857 359.50 0.871 358.85 357.05 0.891
- 0.184 - 0.057 - 0.242 0.854 0.194 - 0.296 - 0.125 - 0.107 - 0.007 - 0.218 -0.182 - 0.159 - 0.172 - 0.042 0.051 0.021 0.033 0.143 0.154 0.193 0.162 0.104 0.016 0.104 0.000
0.906 0.917
354.90 352.75
- 0.109 -0.115
0.935 0.950 0.962 0.972
347.40 339.75 330.50 318.45
- 0.053 - 0.118 0.242 - 0.089
BMSD =
0.209
295
s is a measure of composition of the given phase, r, is a critical temperature and p = 0.326 is the critical exponent (Sengers and Levelt Sengers, 1986). The scaling theory predicts only the critical exponent values. The critical point (xc and T,) must be determined experimentally. On the basis of the scaling theory with the Wegner correction the two-liquid coexistence curve can be represented by the equation x=x,+AlItI+A,ItI’-~+AgItIl-a+w+f(B1ItIP+B*It(B+W)/2
(3)
where f= - 1 for x < x, and f= 1 for x > xc, a = 0.11 is the critical exponent and w = 0.5 is the Wegner exponent. Equation (3) was fitted to liquid-liquid equilibrium data in the range of applicability of the scaling theory (Ewing et al., 1988) and also in a broader range of temperature (Luszczyk and Stryjek, 1984). The number of terms in eqn. (3) taken into consideration depends on the temperature range and on the asymmetry of the miscibility gap. Equation (3) has been used in this work to determine the temperature and the composition of the solution in the critical point (T, and x,) from experimental coexistence curves. The position of the critical point is related to the structure of the solution -in the case of investigated systems mainly to the structure of associated species. Assuming, analogously to the solid-liquid equilibria studies (Ksi@czak, 1983, 1986a, b), that the solution along the saturation line can be treated as a pseudobinary mixture consisting of solute X-mer and solvent molecules, the mole fraction of the X-mer is equal to the sum of mole fractions of the monomer and all associates and can be expressed as
x = x/[ x
+ X(1 - x)]
Assuming, also as previously, that non-specific interactions of the X-mer and solvent molecules can be taken into account by the regular solution theory (Hildebrand and Scott, 1950) the activity of the X-mer solute in the mixture can be expressed by a simple equation: G = X exp( XV,D*(l - @)*/RT)
(5)
where @=
xv,/(xv,
+ (1 - x)&J)
(6)
and D is the difference between the modified solubility parameter of the solute (Ksi@czak and Moorthi, 1985) and the solubility parameter of the solvent, and V,, V, are the van der Waals molar volumes of the solute and solvent (Bondi, 1968). Assuming that, to an approximation, the mean association number of the solute, A, does not depend on composition at a given temperature, the
296
activity coefficient of the solute is given by In a = (ln ;)/A = (In x)/h
+ VAD2(1 - @)‘/RT
(7)
The criteria of the existence of the critical point (Prausnitz et al., 1986) applied to the pseudobinary solution model defined by eqn. (7) lead to eqns. (8) and (9) as shown by (Ksigczak, 1981): x,=hVrJ[(X-
l)v,+AVA+
T, = 2D2V;V;x,(1
(h2V;+
- x,)[x,X(l
V;-xV*VJ’2]
- x,)]/(x,VA
(8)
+ (1 - XJV,)’
(9)
For h = 1 eqns. (8) and (9) give the well-known equations describing the critical point of the regular solution model (Hildebrand and Scott, 1950). The various models of association can be applied to the liquid-liquid critical point. If the non-specific interactions can be represented by the regular solution model the activity coefficient of the solute can be expressed as a sum of two independent terms: In yA = In yIhem+ VAD2(l - @)2/RT
(IO)
chemis the activity coefficient of the associated compound resulting where yA from the assumed association model, not taking into account the non-specific interactions effect. In this case, x, is a solution of the equation [3V* - 2V, - 2( V* - VJX] (1 + x d In yihem/dx)x -[V,+(&-
d2 In yihem/dx2) = 0
I/,)x1(1-x2
T, = 2~~v37;x~(l-
x,)/(x,&,
+ (1 - x,)V,)~,‘(~
(II)
+ x d m yihem/dx) 02)
For the Mecke-Kempter YAthem =
2(K+ 1)/(2Kx
For the monomer-i-mer
association model (Kempter and Mecke, 1940)
+ 1 + [4KX(l -x)
+ l]r’*)
(13)
model
chem=S/S~ ?A
(14)
where s is the solution of the equation K[i-x(i-l)]x’-lsi+s-l=O
(15)
and so is the solution of the equation Ksd + so - 1 = 0
06)
297
If K tends to infinity, X, tends, for the Mecke-Kempter
model, to
XC= &AT/, + 5A (17) and T, tends to infinity. In the case of the monomer-i-mer association models, if K goes to infinity the mean association number, A, goes to the limiting values X = i. The critical parameters (x, and q) can be calculated from eqns. (8) and (9). RESULTS AND DISCUSSION
Experimental liquid-liquid equilibrium data have been represented using eqn. (3). It was assumed that A, = 0 and six parameters, T,, xc, A,, A,, B,
TABLE 2 Liquid-liquid
equilibrium data used in this work
No.
System
No. of points
Source
1 2 3 4 5 6 7 8 9 10 11 12
25 11 31 16 9 10 a 8” 9a 10 a 12 a 21 16
This work This work This work Gmehling (1982) Campetti and de1 Gross0 (1913) Vondracek (1937) Vondracek (1937) Vondracek (1937) Vondrficek (1937) Vondracek (1937) Ksi@czak (1981) b Ksi$czak (1981) b
13 14 15 16 17 18
CChlorophenol + hexadecane 2-Methoxyphenol + hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,6-Dimethoxyphenol + cyclohexane ZNitrophenol + eicosane 2-Nitrophenol + hexadecane 2-Nitrophenol + decane 2-Nitrophenol + hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane
Ksi#czak and Jodzewicz (1981) Ksi@czak and Jodzewicz (1981) Ksi@czak and Jodzewicz (1981) Ksigczak and Jodzewicz (1981) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977)
19 20 21 22 23 24 25
ZNitrotoluene 2-Nitrotoluene ZNitrotoluene 2-Nitrotoluene Nitrobenzene Nitrobenzene Nitrobenzene
15 8 9 9 lC lC lC lC 1’ 1’ lC 22 1’
+ nonane + heptane + hexane + pentane + heptane + hexane + pentane
a Any points deleted. b Appendix B. ’ Critical point only.
Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Dega-Dalkowska (1980) Snyder and Eckert (1973) Sada et al. (1977)
b b b b
298 TABLE 3 Parameters of eqn. (3) giving the best fit of the turbulence-disappearance temperature No.
T, 6)
xc
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 24
359.5460 340.5359 360.6786 336.5491 321.7110 325.5805 326.1606 329.7667 329.6248 341.5106 361.7713 347.9217 344.5920 334.6305 320.7311 315.9934 293.1510
0.706374 0.746595 0.756597 0.616663 0.571700 0.492496 0.492585 0.448685 0.406706 0.435426 0.340233 0.366231 0.795612 0.765021 0.634121 0.499912 0.446026
3.034029 2.006988 3.264029 - 1.082646 1.740738 - 3.282876 24.009904 - 7.483945 - 1.912502 2.926570 - 1.719126 - 1.773174 - 6.654817 1.246488 4.460081 30.658959 2.642828
A2
-
3.370477 2.666791 3.860512 0.087110 1.852002 2.068155 - 17.009854 5.629329 1.453208 - 2.410240 1.729005 1.948828 3.691445 - 2.253259 - 3.762900 - 19.196594 - 1.997348
4
1.564859 1.430666 1.426372 1.662264 1.682077 1.692430 0.960659 1.609474 1.403624 1.204361 1.806703 1.947575 1.105134 1.382777 1.567547 1.334920 1.652866
AT
B2
-
-
-
0.040829 0.451082 0.601583 0.388953 0.186947 0.364167 4.715504 0.135302 0.801566 0.762687 0.753103 0.721616 0.924163 0.107431 0.333095 2.290054 0.498471
0.22 0.16 0.21 0.16 0.40 0.18 0.29 0.41 0.17 0.50 0.16 0.27 0.16 0.03 0.02 0.04 0.16
and B,, have been fitted to minimize the root of the mean square deviation dT of the calculated and measured temperatures of equilibrium:
I
l/2
dT = c ( rcalc - ~exP)2,‘i’V i
(18)
where N is the number of experimental points and the summation is performed over all experimental points. The data sets used in the calculations are collected in Table 2. The obtained parameters of eqn. (3) and the resulting deviations, AT, are presented in Table 3. For some data sets, the experimental points giving a difference between calculated and reported equilibrium temperatures much greater than others have not been taken into account (see footnotes in Table 2). In the case of Vondracek’s (1937) data the points marked as metastable with respect to solid-liquid equilibrium have been removed. For the systems investigated earlier in our laboratory, the original data have been presented in Table 1A (analogous to Table 1) because these data were presented in the form of figures only (Ksi@czak, 1981; Ksi@czak and Jodzewicz, 1981). To illustrate the obtained representation of the experimental data by the deviations calculated equilibrium temperatures, Tcalc, AT = TCdc_
i-P
(19)
299 TABLE 1A Liquid-liquid
coexistence curve data
xA
T (K)
AT”
3-Methoxyphenol + cyclohexane system (Ksi+zak, 1981) - 0.084 0.082 347.66 0.157 0.096 350.76 - 0.112 0.118 353.96 0.140 0.147 357.36 - 0.080 0.197 360.11 - 0.060 0.217 360.76 - 0.204 0.263 361.36 - 0.121 0.272 361.51 - 0.023 0.295 361.71 - 0.092 0.304 361.66 0.039 0.332 361.81 0.090 0.356 361.86 0.124 0.385 361.86 - 0.004 0.413 361.61 0.166 0.455 361.31 0.092 0.495 360.31 0.171 0.544 358.36 0.035 354.26 - 0.493 347.51 0.290 337.36 - 0.031 309.26 RMSD = 0.163 2-Nitrophenol + eicosane system (Ksi@czak and Jodzewicz, 1981) - 0.325 0.516 330.65 0.075 0.560 334.55 0.177 0.616 338.75 0.086 0.652 340.95 - 0.121 0.724 343.85 0.029 0.761 344.55 - 0.042 0.791 344.55 - 0.041 0.805 344.55 - 0.027 0.817 344.55 0.027 0.831 344.55 0.055 0.846 344.45 - 0.029 0.883 343.55 0.017 0.913 342.05 0.442 0.930 340.95 0.000 0.965 324.75 RMSD = 0.157
xA
AT”
T 6)
2,6-Dimethoxyphenol + cyclohexane system (Ksi.$czak, 1981) 319.51 - 0.223 0.0468 323.86 0.320 0.0557 341.46 - 0.399 0.141 342.51 0.051 0.147 344.76 0.056 0.176 346.91 0.178 0.223 347.81 0.096 0.282 347.96 0.084 0.314 348.11 0.189 0.351 347.96 0.043 0.391 347.81 0.029 0.443 347.51 - 0.042 0.472 346.66 0.064 0.528 344.96 - 0.758 0.558 339.56 0.387 0.671 326.66 - 0.076 0.775 RMSD = 0.267
0.600 0.655 0.717 0.806
2-Nitrophenol + hexadecane system (Ksi+kak and Jodzewicz, 1981) 319.15 - 0.010 0.427 324.15 0.025 0.480 329.65 - 0.026 0.557 333.55 0.007 0.649 334.65 0.060 0.728 334.55 - 0.060 0.794 333.15 0.004 0.870 327.25 - 0.000 0.914 RMSD =
0.033
300 TABLE 1A (continued) XA
T(K)
ATa
2-Nitrophenol + decane system (Ksiqkczak and Jodzewicz, 1981) - 0.003 316.75 0.422 0.010 318.65 0.466 - 0.009 320.05 0.522 - 0.014 320.55 0.565 0.022 320.75 0.616 0.029 320.75 0.661 - 0.044 320.55 0.695 0.010 319.95 0.739 - 0.001 316.25 0.812 RMSD= 0.021
XA
T W)
AT”
2-Nitrophenol + hexane system (Ksigczak and Jodzewicz, 1981) 0.024 313.25 0.320 - 0.084 314.05 0.340 0.079 314.95 0.365 -0.012 315.55 0.405 0.014 315.85 0.435 - 0.038 315.95 0.518 0.029 315.65 0.567 - 0.026 314.05 0.625 0.013 312.75 0.665 RMSD = 0.044
a AT=F-T.
are reported in Tables 1 and lA, together with the experimental data. The obtained representation of data is good and the resulting deviations, AT, can be treated as a measure of random error of experimental data. The mean association number in the critical point The mean association numbers in the critical point have been calculated for the pseudobinary solution model using eqn. (8), and for classical association models: the Mecke-Kempter model, monomer-dimer, monomer-trimer, monomer-tetramer and monomer-hexamer association models, by calculating the association constant K by solving eqn. (11). The van der Waals molar volumes of components have been used, analogously to the solubility equation (Ksi@czak, 1986a). These values have been calculated from group contributions given by Bondi (1968) consistent with UNIFAC group sizes (Fredenslund et al., 1977). In the systems investigated in this work, with hexadecane as a solvent, the van der Waals molar volume of the solvent is several times greater than that of the monomer of the solute, and close to the van der Waals molar volume of the associated species. It enables us to suppose that the effects of different sizes of species in the solution, not taken properly into account in the regular solution theory (Hildebrand and Scott, 1950), are not important in the analysis of the properties of the pseudobinary solution of the associated solute and solvent. The results of the mean association number calculations, performed on the basis of the fitted (see Table 3) or experimental x, values are presented in Table 4. The values of the mean association number, X, in the critical
301 TABLE 4 The mean association number in the critical point in various association models No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a b ’ d
System CChlorophenol + hexadecane 2-Methoxyphenol + hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,6-Dimethoxyphenol + cyclohexane 2-Nitrophenol + eicosane 2-Nitrophenol + hexadecane 2-Nitrophenol + decane 2-Nitrophenol f hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane 2-Nitrotoluene + nonane 2-Nitrotoluene + heptane 2-Nitrotoluene + hexane 2-Nitrotoluene + pentane Nitrobenzene + heptane Nitrobenzene + hexane Nitrobenzene + pentane
Const. h”
MK b
l-2”
l-3”
l-4”
l-6 ’
3.38f0.34
-
d
-
3.08
2.79
1.74 f 0.20
1.76
1.66
1.55
1.54
1.63
3.28 f 0.36 3.30 f 0.33 2.56 f 0.24 3.90f0.55 2.25 f 0.22 3.88f0.62 3.42 f 0.59 2.29 f 0.27 4.74 f 1.45
-
-
-
2.42 -
2.86 3.14 2.53 3.90 2.47 3.90 3.57 2.64
2.52 3.09 2.69 4.09 2.76 4.24 4.05 3.02 5.25
1.22f0.13
-
1.40
1.72
1.98
2.38
2.OOf0.28 1.48 f 0.20
1.87 1.40
1.38
1.70 1.33
1.62 1.35
1.62 1.45
1.42f 0.12 1.04f0.08 2.54 f 0.25
1.87 -
1.38 1.10 -
1.44 1.32 2.35
1.54 1.53 2.20
1.74 1.83 2.19
2.83f0.27
-
-
2.75
2.53
2.49
2.18 f0.20 2.16f0.24 1.80f0.20 1.75 f 0.22 2.80* 0.33 2.23 f 0.25 2.57 f 0.39
-
1.83 1.82 -
2.21 2.32 2.08 2.13 2.82 2.36 2.69
2.34 2.53 2.32 2.43 2.96 2.57 2.98
2.60 2.90 2.72 2.89 3.27 2.93 3.48
-
2.51 2.32 -
Model given in eqn. (7). Mecke-Kempter association model, see eqn. (13). Monomer-i-mer association models, i = 2,3,4,6, see eqns. (14)-(16). A value of x, is out of the range acceptable for the given model.
points in a pseudobinary solution model (column 3), the Mecke-Kempter continuous association model (column 4), and the monomer-dimer (column 5), monomer-trimer (column 6), monomer-tetramer (column 7) and monomer-hexamer (column 8) association models are given for systems investigated in this work and found in the literature. The number of the specific
302
monomer-i-mer association models used is limited by the structures of associates observed in the solid phases of solutes (Ksi@czak, 1983). The lack of numerical values denotes that the given model cannot explain the observed value of the critical point composition x,. The errors of determining the critical point have not been taken into account in the calculations. Only for the pseudobinary solution model (with constant h) is the error of determining the mean association number, X, in the critical point reported. This results from the conventionally used estimate of the error in x, equal to 0.01 and the calculated values of the derivative dX/dx,. For the 4-chlorophenol + hexadecane system the mean association number h = 3.38 + 0.34 has been obtained in the pseudobinary solution model. In previous papers (Ksi$czak, 1986a, Ksi@czak and Anderko, 1987) the solid-liquid-vapour equilibrium data for the 4-chlorophenol + cyclohexane system was interpreted assuming that the mean association number, X, along the saturation line is equal to or close to 4. Tetramers of 4-chlorophenol’were detected in the metastable solid phase, /?, of this compound (Perrin and Michel, 1973). These results are consistent, especially taking into account the error of determining the value of x,. The position of the critical point cannot be justified using the Mecke-Kempter continuous association model or monomer-dimer and monomer-trimer association models. For the 2-methoxyphenol + hexadecane system, in all models used, values of the mean association number h = 2 have been obtained. This result agrees well with the solid-liquid equilibrium data analysis performed previously by Ksi@czak (1986b) for 2-methoxyphenol + cyclohexane systems, where a value of X = 2.11 was obtained. The analysis of the pure liquid vapour pressure data (Ksigczak and Kosinski, 1990) suggests that this compound forms intermolecular hydrogen bonds. A cyclic dimer, tith two hydrogen bonds between hydroxyl and methoxy groups, is probably formed. For the phenol + hexadecane system values of the mean association number A = 3 have been obtained, fully consistent with the results of the solid-liquid equilibrium data analysis for the systems: phenol + 4bromotoluene (Ksi@czak, 1983), + hexane, + heptane (Ksigczak, 1986a, Ksi@czak and Anderko, 1987), + pentane, + 2-methylbutane, + 2-methylpentane, + methylcyclohexane, and + decane (Ksi@czak and Anderko, 1987). For these systems a good representation of solid-liquid equilibrium data was obtained assuming X = 3. For the liquid-liquid systems: phenol + pentane, phenol + 2methylbutane, phenol + hexane, phenol + 2-methylpentane, phenol + heptane (Vondracek, 1937), phenol + octane (Campetti and de1 Grosso, 1913) and phenol + decane (Gmehling, 1982) mean association numbers between 2 and 4 have been obtained, also consistent with the previously published results. For systems containing phenol the position of the critical
303
point cannot be explained using the Mecke-Kempter continuous association model. For the 3-methoxyphenol + cyclohexane system (Ksi@czak, 1981) values of the mean association number X = 5 have been obtained. If the estimated uncertainty of these results (about 1.5) is taken into account, they suggest the formation of higher associates (hexamers?). For the system 2,6-dimethoxyphenol + cyclohexane (Ksi$czak, 1981) the mean association number X = 1.22 in the pseudobinary solution model suggests a weak association, similar to that observed in the 2,6-dimethylpheno1 + cyclohexane system (Ksiqiczak and Kosinslci, 1988a). In a molecule of 2,6-dimethoxyphenol two o&ho-substituents bring about a steric hindrance around the hydroxyl group, impeding association (as in 2,6_dimethylphenol), and additionally can form an intramolecular hydrogen bond with the hydroxyl group. This explains the weak autoassociation. For the sequence of systems: 2nitrophenol+ eicosane, + hexadecane, + decane and + hexane, values of the mean association number X between 1 and 2 have been obtained. It was previously shown (Ksigczak, 1986b, Ksi@czak and Anderko, 1987), that 2nitrophenol dimerizes as a result of dipole-dipole interactions, and the hydroxyl group is bonded in the intramolecular hydrogen bond. This fact is confirmed by the analysis of pure liquid vapour pressure data (Ksi@czak and Kosinski, 1990). For 4nitrotoluene and nitrobenzene solutions, values of the mean association number X between 1.75 and 2.83 have been obtained, confirming the existence of the association of nitroaromatic compounds as a result of dipole-dipole interactions. Prediction of the liquid-liquid equilibrium critical point composition In the models discussed, the composition of the solution in the liquidliquid critical point depends on specific interactions, leading to association, and on (van der Waals) molar volumes of components, but does not depend on the parameter D describing the effects of non-specific intermolecular interactions. These models enable us to predict x, on the basis of information about the structure of associates arising from X-ray studies of solid solutes or from the analysis of the solid-liquid(-vapour) equilibrium data. In the solution in an inert solvent such as hydrocarbon, the effect of the specific interactions of the solute molecules on the deviations of the properties of the solution from ideality is stronger than in the solution in a more active solvent. In the case of specific monomer-i-mer association models the mean association number, A, in concentrated solutions of a strong autoassociated solute in an inert solvent is close to the limiting value X = i. This approximation can be used to predict x,.
304 TABLE 5 Prediction of the composition of the solution in the critical point on the basis of the analysis of the solid-liquid-vapour binary systems and X-ray studies No. 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
System 4Chlorophenol+ hexadecane 2_Methoxyphenol+ hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,dDimethoxyphenol + cyclohexane 2-Nitrophenol + eicosane 2-Nitrophenol -I hexadecane 2-Nitrophenol + decane 2-Nitrophenol + hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane 2-Nitrotoluene + nonane 2-Nitrotoluene + heptane 2-Nitrotoluene+ hexane 2-Nitrotoluene + pentane Nitrobenzene + heptane Nitrobenzene -I-hexane Nitrobenzene + pentane
xc
a
0.706 0.747 0.757 0.617 0.572 0.492 0.493 0.449 0.407 0.435 0.340 0.366 0.796 0.765 0.634 0.500 0.710 0.680 0.520 0.440 0.410 0.360 0.473 0.446 0.383
ib
x,(A=i)”
x,HSd
4 2 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0.690
0.802 0.785 0.832 0.736 0.676 0.636 0.587 0.587 0.528 0.528 0.458 0.387 0.831 0.789 0.671 0.505 0.784 0.771 0.611 0.527 0.475 0.415 0.588 0.537 0.476
0.734 0.765 0.626 0.555 0.513 0.467 0.467 0.415 0.415 0.359 0.327 0.796 0.740 0.594 0.427 0.734 0.716 0.529 0.447 0.401 0.350 0.505 0.456 0.402
a For systems 1-16 and 24, calculated from experimental data (see Table 3); for systems 17-23 and 25, experimental value. b Associated species detected on solid-liquid equilibrium line or in the solid phase. ’ Predicted using eqn. (8), A = i. d Predicted using eqn. (8), h = 1.
The prediction of x, for the systems discussed is presented in Table 5. The limiting values of the mean association number, A, taken from X-ray studies (Ksir+.ak, 1983) or the analysis of the solid-liquid(-vapour) equilibrium data (Ksi@czak, 1986a, b) are presented in column 4. In column 5, x, predicted from these A values are given. They can be compared with the x, values obtained from experimental data or from the literature (column 3) and with the x, values predicted on the basis of the classical regular solution theory (Hildebrand and Scott, 1950) (A = 1) (column 6).
305 CONCLUSION
The analysis of the mean association number, A, in the liquid-liquid critical point confirms the results concerning association of polar aromatic compounds in hydrocarbon solutions, obtained previously from analysis of solid-liquid and solid-liquid-vapour equilibrium data. The mean value of the mean association number, A, of phenol in various hydrocarbons is equal to 3.11 and confirms that the privileged structure of phenol associates is a trimer. The mean value of the mean association number, A, of polar compounds not forming intermolecular hydrogen bonds in various hydrocarbons is equal to 2.06 and confirms that the privileged structure of associates is a dimer. The presented results agree well with the results of previous analyses, although the effects of different molecular size and shape are not fully recognized by the models used and the uncertainty of determining the x, values cannot be disregarded for some systems for which the number of experimental points is small and comparable with the number of adjusted parameters. The models of solution used in this work enable us to determine the composition of the solution in the critical point without paying attention to the value of parameter D describing the contribution of non-specific interaction. This fact makes it possible to determine if a given model can describe X, in a solution and to verify the parameters of association. The values of x, determined from the liquid-liquid equilibrium experimental data for the solutions of phenol in hydrocarbons cannot be analysed on the basis of either the Mecke-Kempter continuous association model or the monomerdimer association model. In addition, in the case of the 4nitrotoluene and nitrobenzene solutions the Mecke-Kempter continuous association model cannot be applied to represent x,. These results additionally suggest the specific association of these compounds. LIST OF SYMBOLS a
-
:. B’ Bi
D
dT
activity of the associated compound activity of the A-mer, see eqn. (5) parameter in eqn. (3) constant in eqn. (1) parameter in eqn. (3) difference between the modified solubility parameter of the solute (Ksi+zak and Moor&i, 1985) and the solubility parameter of the solvent root mean square deviation, see eqn. (18)
306
K
association constant number of experimental points N n (D,25 OC) refractive index R gas constant s see eqn. (15) see eqn. (16) so composition of the phase in equilibrium, i = 1, 2 si T turbulence disappearance temperature see eqn. (2) t critical temperature of liquid-liquid equilibrium T, temperature deviation, see eqn. (19) AT calculated turbulence disappearance temperature in point i experimental turbulence disappearance temperature in point i van der Waals molar volume of the associated compound van der Waals molar volume of the solvent Wegner exponent, w = 0.5 mole fraction h-mer mole fraction, see eqn. (4) x mole fraction of the associated compound XA mole fraction of the associated compound in the critical point xc of liquid-liquid equilibrium Greek letters
y%~In YA
A @
critical exponent, (Y= 0.11 critical exponent, /? = 0.326 activity coefficient of the associated compound contribution to the activity coefficient due to an association model mean association number volume fraction of the associated compound
ACKNOWLEDGEMENTS
The authors express their sincere thanks to Professor A. Bylicki for suggestions and discussions. The work reported here was sponsored by the Polish Academy of Sciences within the framework of Project 01.16. REFERENCES Bondi, A., 1968. Physical Properties of Molecular Crystals, Liquids and Glasses. Wiley, New York.
307 Campetti, A. and de1 Grosso, C., 1913. Sull’equilibrio di coppie di liquidi parzialmente miscibili. Nuovo Cimento, 6: 379-417. Dega-Dalkowska, A., 1980. Critical exponent fi for systems: nitrobenzene-n-hexane and nitrobenzene-n-heptane. Acta Phys. Polon. A, 58: 31-36. Ewing, M.B., Johnson, K.A. and McGlashan, M.L., 1988. The (liquid + liquid) critical state of (cyclohexane + methanol). IV. (T, x)~ coexistence curve and the slope of the critical line. J. Chem. Thermodyn., 20: 49-62. Fredenslund, A., Gmehling, J. and Rasmussen, P., 1977. Vapor-Liquid Equilibria using UNIFAC. Elsevier, Amsterdam. Gmehling, J., 1982. Phase equilibria in binary systems formed by phenol with benzene, n-octane and n-decane. J. Chem. Eng. Data, 27: 371-373. Hildebrand, J.H. and Scott, R.L., 1950. The Solubility of Nonelectrolytes, 3rd edn. Reinhold, New York. Kempter, H. and Mecke, R., 1940. Spectroscopic determination of association equilibrium. Z. Phys. Chem., Teil B, 46: 229-241. Ksi@czak, A., 1981. Liquid-liquid and liquid-crystal equilibria of some phenols in hydrocarbons. Pol. J. Chem., 55: 911-916. Ksi@czak, A., 1983. Solid-liquid equilibrium and the hydrogen bond in crystals. Fluid Phase Equilibria, 15: l-9. Ksi@czak, A., 1986a. The effect of auto-association on solid-liquid equilibrium. Fluid Phase Equilibria, 28: 39-56. Ksi@czak, A., 1986b. Solid-liquid equilibrium and the structure of solution of highly polar aromatic compounds. Fluid Phase Equilibria, 28: 57-72. Ksi@czak, A. and Anderko, A., 1987. Prediction of solid-liquid equilibria on the basis of pure compound properties. Fluid Phase Equilibria, 35: 127-151. Ksi@czak, A. and Jodzewicz, W., 1981. Liquid-liquid and liquid-solid equilibria of 2nitrophenol in hydrocarbons. Pol. J. Chem., 55: 1889-1981. Ksi@czak, A. and Kosihski, J.J., 1988a. Solid-liquid-vapour equilibrium of binary systems. Fluid Phase Equihbria, 42: 241-259. Ksi@zak, A. and Kosihski, J.J., 1988b. Vapour pressure of binary, three-phase (S-L-V) systems and solubility. Fluid Phase Equilibria, 44: 211-236. Ksigczak, A. and Kosihski, J.J., 1990. Vapour pressure and association of phenols. Fluid Phase Equilibria, 55: 17-37. Ksigczak, A. and Moorthi, K., 1985. Prediction of thermodynamic properties of alkylphenol + hydrocarbon binary systems on the basis of pure liquid properties. Fluid Phase Equilibria, 23: 153-164. Ksi$czak, A., Kosif~ski, J.J. and Moorthi, K., 1990. Vapour-liquid equilibrium of dialkylphenols in cyclohexane. Fluid Phase Equilibria, 57: 173-190. Levelt Sengers, G., Morrison, J.M.H. and Chang, R.F., 1983. Critical behavior in fluids and fluids mixtures. Fluid Phase Equilibria, 14: 19-44. Luszczyk, M. and Stryjek, R., 1984. Mutual solubility of C,-hydrocarbons-/3-methoxypropionitrile systems. Bull. Pol. Acad. Sci., Chem., 32: 371-377. Perrin, M. and Michel, P., 1973. Polymorphisme du p-chlorophenol. II. Structure cristalline a basse temperature de la forme mttastable (forme /I). Acta Crystallogr. Sect. B, 29: 258-263. Pimentel, G.C. and McClellan, A.L., 1960. The Hydrogen Bond. Freeman, San Francisco, CA. Prausnitz, J.M., Lichtenthaler, R.N. and Gomes de Azevedo, E., 1986. Molecular Thermodynamics of Fluid-Phase Equilibria, 2nd edn. Prentice-Ha& Englewood Cliffs, NJ.
Sada, E., Takahashi, K. and Hamada, M., 1977. Viscosity of nitrobenzene-n-pentane and nitrobenzene-n-heptane systems. J. Chem. Eng. Data, 22: 279-282. Sengers, J.V. and Levelt Sengers, J.M.H., 1986. Thermodynamic behavior of fluid near the critical point. Ann. Rev. Phys. Chem., 37: 189-222. Singh, R.R. and Van Hook, W.A., 1987. Comments on classical and nonclassical representations of critical demixing in liquid-liquid binary solutions. J. Chem. Phys., 87: 6088-6096. Sliwinska-Bartkowiak, M., 1977. Wykladnik krytyczny /3 dla roztworow o-nitrotoluenu w w@owodorach alifatycznych. Poznah. Tow. Przyj. Nauk, Wydzial Mat. Przyr., Pr. Kom. Mat. Przyr., Fiz. Dielektr. Radiospektrosk., 9: 39-51. Snyder, R.B. and Eckert, C.A., 1973. Effect of third component on liquid-liquid critical point. J. Chem. Eng. Data, 18: 282-285. Timmermans, J., 1950. Physico-Chemical Constants of Pure Organic Compounds. Elsevier, New York. Vondracek, R., 1937. On binary systems of phenol with some hydrocarbons. Collect. Czech. Chem. Commun., 2: 168-175.
291
Elsevier Science Publishers B.V., Amsterdam
LIQUID-LIQUID EQUILIBRIUM IN BINARY POLAR AROMATIC + HYDROCARBON SYSTEMS Andrzej KSI@CZAK
and Jerzy Jan KOSIlkKI
Department of Chemistry, Technical University, 00-664 Warsaw (Poland)
(Received July 26, 1989; accepted in final form March 28, 1990)
ABSTRACT Ksiqkczak, A. and Kosihski, J.J., 1990. Liquid-liquid equilibrium in binary polar aromatic+ hydrocarbon systems. Fluid Phase Equilibria, 59: 291-308. The liquid-liquid coexistence curves for the systems: 4-chlorophenol+ hexadecane, 2methoxyphenol + hexadecane and phenol + hexadecane have been determined by measuring the temperature of disappearance of turbulence. The literature and our data have been represented on the basis of the scaling theory: The analysis of the critical point indicates that the mean value of the mean association number of phenol in various hydrocarbons is equal to 3.11, confirming that the privileged structure of phenol associates is a trimer. The mean value of the mean association number, X, of polar compounds not forming intermolecular hydrogen bonds in various hydrocarbons is equal to 2.06 and confirms that the privileged structure of associates is a dimer. The obtained outcomes bear out previous results of the analyses of solid-liquid and solid-liquid-vapour equilibrium data for the same or similar systems. The prediction of the liquid-liquid equilibrium critical point composition has been proposed on the basis of the previously determined relationships between the association and the structure of polar aromatic compounds.
INTRODUCTION
In a previous paper (Ksi$czak, 1983) a mechanism of dissolution of polar compounds in hydrocarbons has been proposed. The dissolution process consists of transferring the associates existing in the solid phase into the solution. The ideal solubility related to a X-mer existing in the solid phase was called the pseudoideal solubility. Solubility data of various binary systems can be represented by the pseudoideal solubility equation on the basis of X-ray studies of solid solutes. A saturated solution can be treated as a pseudobinary mixture consisting of X-mers and solvent molecules, where X is the mean association number of the solute. In a more recent paper (Ksi$xzak and Kosifrski, 1988a) it was 0378-3812/90/$03.50
0 1990 - Elsevier Science Publishers B.V.
292
demonstrated that as the number of adjustable parameters increases, the equation becomes more flexible, but the fitted values of parameters frequently lose the physical meaning attributed to them and cannot be used to predict other properties of the investigated system. The regular solution theory (Hildebrand and Scott, 1950) has been used to describe the nonspecific interactions in the pseudobinary solution considering the minimal number of adjustable parameters, i.e. only one parameter. The resulting solubility equation has been used to represent the solid-liquid equilibrium (Ksi@czak, 1986a, b) and the vapour pressure of the solvent along the solid-liquid-vapour equilibrium line (Ksi+zak and Kosihski, 1988a, b) . The obtained values of the mean association number, h, were consistent with the association number of the associated species detected in the solid phases of the solute. Aromatic carboxylic acids exist in the solid phase mainly as cyclic dimers (Pimentel and McClellan, 1960). The mean association number in saturated solution of carboxylic acids is close to 2, which is in agreement with the dissolution model. The mean association number of phenols with a small steric hindrance around the hydroxyl group is close to 3 in saturated solutions and is consistent with the existence of trimers in the metastable solid phase. Para-substituted phenols such as 4-chlorophenol or 4-methylphenol consist of tetramers in the solid phase. The mean association number of 4-chlorophenol in solutions with saturated alkanes, calculated from the solid-liquid-vapour equilibrium data, is close to 4 (Ksi@czak, 1986a). An increase of steric hindrance around the hydroxyl group decreases the ability of phenols to form higher associates. The mean association number of 2-tert-butyl-4-methylphenol, calculated from the solid-liquid-vapour equilibrium data (Ksi$czak and Kosihski, 1988a, b), is close to 2, which suggests the existence of dimers in the saturated solution. A large steric hindrance around the hydroxyl group precludes the formation of hydrogenbonded associates. The analysis of solid-liquid-vapour equilibrium data of 2,6-di-tert-butyl-4-methylphenol + hydrocarbon systems (Ksi@czak and Kosihski, 1988b) demonstrates that this phenol does not associate. Similar results have been obtained from isothermal vapour-liquid equilibrium data analysis for 2,6-di-tert-butylphenol (Ksi$czak et al., 1990). The analysis of solid-liquid-vapour equilibrium data performed by Ksi@czak (1986b) suggests that aromatic compounds with a large dipole moment which do not form intermolecular hydrogen bonds, such as 2-nitrophenol or 4-nitrotoluene, dimerize as a result of dipole-dipole interactions. Association of these compounds has also been investigated by studying the vapour pressure of pure liquids (Ksi@czak and Kosihski, 1990). The presented conclusions concerning the association of polar aromatic compounds can be used to predict solid-liquid equilibrium on the basis of pure component properties
293
without fitting any parameters from binary data (Ksi@czak and Anderko, 1987). The goal of this paper is to analyse liquid-liquid equilibrium data, especially the composition of the solution in the critical point, in order to confirm the existence of associated species of the same kind as detected by analysing solid-liquid-vapour equilibrium data reported previously. Liquid-liquid coexistence curves were determined for binary systems: 4chlorophenol + hexadecane, 2-methoxyphenol + hexadecane and phenol + hexadecane. The mean association numbers in the critical point have also been calculated from binary liquid-liquid equilibrium data reported in the literature for polar aromatic + hydrocarbon systems. EXPERIMENTAL
2-methoxyphenol (Fluka, pract.) and 4chlorophenol (Koch-Light, pure) were purified by repeated sublimations. The purities, determined by cryoscopy using a UNIPAN d.s.c. type 605 were 99.98% and 99.94% respectively. The purity of phenol (Chemipan, Warsaw) determined by gas chromatography was 99.95%. Hexadecane (Reachim) was purified by repeated distillation. The chromatographically determined purity was 99.9% and the refractive index was n(D,25OC) = 1.43253, while Timmermans (1950) reported n(D,25” C) = 1.4325. The liquid-liquid coexistence curves were determined by measuring the temperature of disappearance of turbulence. The sample, the concentration of which was determined by weighing, was placed in the thermostat. The turbulence disappearance temperature was determined during a very slow temperature increase to within an accuracy of about 0.1 K. Mole fractions of phenol xA and the turbulence disappearance temperatures, T, are reported in Table 1. THE MEAN ASSOCIATION CRITICAL POINT
NUMBER
AND THE LIQUID-LIQUID
EQUILIBRIA
Classical thermodynamics does not represent correctly the properties of physical systems in the vicinity of the critical point (Sir@ and Van Hook, 1987). The properties of systems in this region can be represented by the scaling theory (Levelt Sengers et al., 1983). The coexistence curve of two phases can be represented by the equation 1s1 - s2 1 = B
exp( j3t)
(1)
where t=l-T/T,
(4
294 TABLE 1 Liquid-Liquid coexistence curve data XA
T W>
4-Chlorophenol + hexadecane 0.186 320.20 0.233 328.85 0.275 335.15 0.316 340.25 0.354 344.40 0.430 351.45 0.442 352.00 0.565 357.90 0.568 357.95 0.592 358.40 0.637 359.35 0.653 359.45 0.670 359.50 0.698 359.60 0.728 359.60 0.750 359.70 0.753 359.75 0.779 359.65 0.819 358.40 0.873 353.80 0.895 349.90 0.898 348.65 0.931 336.35 0.936 332.85 0.955 316.65 BMSD =
AT” system -0.318 0.275 0.290 0.038 - 0.117 0.107 - 0.214 - 0.229 - 0.260 - 0.356 - 0.006 - 0.008 - 0.018 0.054 0.060 0.209 0.271 0.385 0.111 - 0.112 0.071 - 0.439 0.316 - 0.064 - 0.048 0.217
2-Methoxyphenol + hexadecane system 0.1593 0.2768 0.3562 0.4382
295.65 312.05 321.95 329.65
0.114 - 0.389 0.207 0.168
0.5281 0.6123 0.6869 0.7443 0.8454 0.9310 0.9768
335.65 338.95 340.35 340.55 339.65 329.95 304.65 BMSD=
0.010 - 0.165 - 0.037 0.014 0.082 - 0.012 0.001 0.157
xA
AT”
T 0-9
Phenol + hexadecane system 0.227 327.50 0.257 331.45 335.55 0.293 342.15 0.344 0.383 345.25 350.15 0.448 353.95 0.502 355.95 0.538 356.15 0.540 0.584 357.85 359.10 0.622 0.671 360.10 360.40 0.704 0.720 360.60 360.73 0.754 0.759 360.70 0.781 360.70 360.80 0.786 0.809 360.70 0.831 360.45 360.40 0.832 359.75 0.853 0.857 359.50 0.871 358.85 357.05 0.891
- 0.184 - 0.057 - 0.242 0.854 0.194 - 0.296 - 0.125 - 0.107 - 0.007 - 0.218 -0.182 - 0.159 - 0.172 - 0.042 0.051 0.021 0.033 0.143 0.154 0.193 0.162 0.104 0.016 0.104 0.000
0.906 0.917
354.90 352.75
- 0.109 -0.115
0.935 0.950 0.962 0.972
347.40 339.75 330.50 318.45
- 0.053 - 0.118 0.242 - 0.089
BMSD =
0.209
295
s is a measure of composition of the given phase, r, is a critical temperature and p = 0.326 is the critical exponent (Sengers and Levelt Sengers, 1986). The scaling theory predicts only the critical exponent values. The critical point (xc and T,) must be determined experimentally. On the basis of the scaling theory with the Wegner correction the two-liquid coexistence curve can be represented by the equation x=x,+AlItI+A,ItI’-~+AgItIl-a+w+f(B1ItIP+B*It(B+W)/2
(3)
where f= - 1 for x < x, and f= 1 for x > xc, a = 0.11 is the critical exponent and w = 0.5 is the Wegner exponent. Equation (3) was fitted to liquid-liquid equilibrium data in the range of applicability of the scaling theory (Ewing et al., 1988) and also in a broader range of temperature (Luszczyk and Stryjek, 1984). The number of terms in eqn. (3) taken into consideration depends on the temperature range and on the asymmetry of the miscibility gap. Equation (3) has been used in this work to determine the temperature and the composition of the solution in the critical point (T, and x,) from experimental coexistence curves. The position of the critical point is related to the structure of the solution -in the case of investigated systems mainly to the structure of associated species. Assuming, analogously to the solid-liquid equilibria studies (Ksi@czak, 1983, 1986a, b), that the solution along the saturation line can be treated as a pseudobinary mixture consisting of solute X-mer and solvent molecules, the mole fraction of the X-mer is equal to the sum of mole fractions of the monomer and all associates and can be expressed as
x = x/[ x
+ X(1 - x)]
Assuming, also as previously, that non-specific interactions of the X-mer and solvent molecules can be taken into account by the regular solution theory (Hildebrand and Scott, 1950) the activity of the X-mer solute in the mixture can be expressed by a simple equation: G = X exp( XV,D*(l - @)*/RT)
(5)
where @=
xv,/(xv,
+ (1 - x)&J)
(6)
and D is the difference between the modified solubility parameter of the solute (Ksi@czak and Moorthi, 1985) and the solubility parameter of the solvent, and V,, V, are the van der Waals molar volumes of the solute and solvent (Bondi, 1968). Assuming that, to an approximation, the mean association number of the solute, A, does not depend on composition at a given temperature, the
296
activity coefficient of the solute is given by In a = (ln ;)/A = (In x)/h
+ VAD2(1 - @)‘/RT
(7)
The criteria of the existence of the critical point (Prausnitz et al., 1986) applied to the pseudobinary solution model defined by eqn. (7) lead to eqns. (8) and (9) as shown by (Ksigczak, 1981): x,=hVrJ[(X-
l)v,+AVA+
T, = 2D2V;V;x,(1
(h2V;+
- x,)[x,X(l
V;-xV*VJ’2]
- x,)]/(x,VA
(8)
+ (1 - XJV,)’
(9)
For h = 1 eqns. (8) and (9) give the well-known equations describing the critical point of the regular solution model (Hildebrand and Scott, 1950). The various models of association can be applied to the liquid-liquid critical point. If the non-specific interactions can be represented by the regular solution model the activity coefficient of the solute can be expressed as a sum of two independent terms: In yA = In yIhem+ VAD2(l - @)2/RT
(IO)
chemis the activity coefficient of the associated compound resulting where yA from the assumed association model, not taking into account the non-specific interactions effect. In this case, x, is a solution of the equation [3V* - 2V, - 2( V* - VJX] (1 + x d In yihem/dx)x -[V,+(&-
d2 In yihem/dx2) = 0
I/,)x1(1-x2
T, = 2~~v37;x~(l-
x,)/(x,&,
+ (1 - x,)V,)~,‘(~
(II)
+ x d m yihem/dx) 02)
For the Mecke-Kempter YAthem =
2(K+ 1)/(2Kx
For the monomer-i-mer
association model (Kempter and Mecke, 1940)
+ 1 + [4KX(l -x)
+ l]r’*)
(13)
model
chem=S/S~ ?A
(14)
where s is the solution of the equation K[i-x(i-l)]x’-lsi+s-l=O
(15)
and so is the solution of the equation Ksd + so - 1 = 0
06)
297
If K tends to infinity, X, tends, for the Mecke-Kempter
model, to
XC= &AT/, + 5A (17) and T, tends to infinity. In the case of the monomer-i-mer association models, if K goes to infinity the mean association number, A, goes to the limiting values X = i. The critical parameters (x, and q) can be calculated from eqns. (8) and (9). RESULTS AND DISCUSSION
Experimental liquid-liquid equilibrium data have been represented using eqn. (3). It was assumed that A, = 0 and six parameters, T,, xc, A,, A,, B,
TABLE 2 Liquid-liquid
equilibrium data used in this work
No.
System
No. of points
Source
1 2 3 4 5 6 7 8 9 10 11 12
25 11 31 16 9 10 a 8” 9a 10 a 12 a 21 16
This work This work This work Gmehling (1982) Campetti and de1 Gross0 (1913) Vondracek (1937) Vondracek (1937) Vondracek (1937) Vondrficek (1937) Vondracek (1937) Ksi@czak (1981) b Ksi$czak (1981) b
13 14 15 16 17 18
CChlorophenol + hexadecane 2-Methoxyphenol + hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,6-Dimethoxyphenol + cyclohexane ZNitrophenol + eicosane 2-Nitrophenol + hexadecane 2-Nitrophenol + decane 2-Nitrophenol + hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane
Ksi#czak and Jodzewicz (1981) Ksi@czak and Jodzewicz (1981) Ksi@czak and Jodzewicz (1981) Ksigczak and Jodzewicz (1981) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977)
19 20 21 22 23 24 25
ZNitrotoluene 2-Nitrotoluene ZNitrotoluene 2-Nitrotoluene Nitrobenzene Nitrobenzene Nitrobenzene
15 8 9 9 lC lC lC lC 1’ 1’ lC 22 1’
+ nonane + heptane + hexane + pentane + heptane + hexane + pentane
a Any points deleted. b Appendix B. ’ Critical point only.
Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Sliwihska-Bartkowiak (1977) Dega-Dalkowska (1980) Snyder and Eckert (1973) Sada et al. (1977)
b b b b
298 TABLE 3 Parameters of eqn. (3) giving the best fit of the turbulence-disappearance temperature No.
T, 6)
xc
4
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 24
359.5460 340.5359 360.6786 336.5491 321.7110 325.5805 326.1606 329.7667 329.6248 341.5106 361.7713 347.9217 344.5920 334.6305 320.7311 315.9934 293.1510
0.706374 0.746595 0.756597 0.616663 0.571700 0.492496 0.492585 0.448685 0.406706 0.435426 0.340233 0.366231 0.795612 0.765021 0.634121 0.499912 0.446026
3.034029 2.006988 3.264029 - 1.082646 1.740738 - 3.282876 24.009904 - 7.483945 - 1.912502 2.926570 - 1.719126 - 1.773174 - 6.654817 1.246488 4.460081 30.658959 2.642828
A2
-
3.370477 2.666791 3.860512 0.087110 1.852002 2.068155 - 17.009854 5.629329 1.453208 - 2.410240 1.729005 1.948828 3.691445 - 2.253259 - 3.762900 - 19.196594 - 1.997348
4
1.564859 1.430666 1.426372 1.662264 1.682077 1.692430 0.960659 1.609474 1.403624 1.204361 1.806703 1.947575 1.105134 1.382777 1.567547 1.334920 1.652866
AT
B2
-
-
-
0.040829 0.451082 0.601583 0.388953 0.186947 0.364167 4.715504 0.135302 0.801566 0.762687 0.753103 0.721616 0.924163 0.107431 0.333095 2.290054 0.498471
0.22 0.16 0.21 0.16 0.40 0.18 0.29 0.41 0.17 0.50 0.16 0.27 0.16 0.03 0.02 0.04 0.16
and B,, have been fitted to minimize the root of the mean square deviation dT of the calculated and measured temperatures of equilibrium:
I
l/2
dT = c ( rcalc - ~exP)2,‘i’V i
(18)
where N is the number of experimental points and the summation is performed over all experimental points. The data sets used in the calculations are collected in Table 2. The obtained parameters of eqn. (3) and the resulting deviations, AT, are presented in Table 3. For some data sets, the experimental points giving a difference between calculated and reported equilibrium temperatures much greater than others have not been taken into account (see footnotes in Table 2). In the case of Vondracek’s (1937) data the points marked as metastable with respect to solid-liquid equilibrium have been removed. For the systems investigated earlier in our laboratory, the original data have been presented in Table 1A (analogous to Table 1) because these data were presented in the form of figures only (Ksi@czak, 1981; Ksi@czak and Jodzewicz, 1981). To illustrate the obtained representation of the experimental data by the deviations calculated equilibrium temperatures, Tcalc, AT = TCdc_
i-P
(19)
299 TABLE 1A Liquid-liquid
coexistence curve data
xA
T (K)
AT”
3-Methoxyphenol + cyclohexane system (Ksi+zak, 1981) - 0.084 0.082 347.66 0.157 0.096 350.76 - 0.112 0.118 353.96 0.140 0.147 357.36 - 0.080 0.197 360.11 - 0.060 0.217 360.76 - 0.204 0.263 361.36 - 0.121 0.272 361.51 - 0.023 0.295 361.71 - 0.092 0.304 361.66 0.039 0.332 361.81 0.090 0.356 361.86 0.124 0.385 361.86 - 0.004 0.413 361.61 0.166 0.455 361.31 0.092 0.495 360.31 0.171 0.544 358.36 0.035 354.26 - 0.493 347.51 0.290 337.36 - 0.031 309.26 RMSD = 0.163 2-Nitrophenol + eicosane system (Ksi@czak and Jodzewicz, 1981) - 0.325 0.516 330.65 0.075 0.560 334.55 0.177 0.616 338.75 0.086 0.652 340.95 - 0.121 0.724 343.85 0.029 0.761 344.55 - 0.042 0.791 344.55 - 0.041 0.805 344.55 - 0.027 0.817 344.55 0.027 0.831 344.55 0.055 0.846 344.45 - 0.029 0.883 343.55 0.017 0.913 342.05 0.442 0.930 340.95 0.000 0.965 324.75 RMSD = 0.157
xA
AT”
T 6)
2,6-Dimethoxyphenol + cyclohexane system (Ksi.$czak, 1981) 319.51 - 0.223 0.0468 323.86 0.320 0.0557 341.46 - 0.399 0.141 342.51 0.051 0.147 344.76 0.056 0.176 346.91 0.178 0.223 347.81 0.096 0.282 347.96 0.084 0.314 348.11 0.189 0.351 347.96 0.043 0.391 347.81 0.029 0.443 347.51 - 0.042 0.472 346.66 0.064 0.528 344.96 - 0.758 0.558 339.56 0.387 0.671 326.66 - 0.076 0.775 RMSD = 0.267
0.600 0.655 0.717 0.806
2-Nitrophenol + hexadecane system (Ksi+kak and Jodzewicz, 1981) 319.15 - 0.010 0.427 324.15 0.025 0.480 329.65 - 0.026 0.557 333.55 0.007 0.649 334.65 0.060 0.728 334.55 - 0.060 0.794 333.15 0.004 0.870 327.25 - 0.000 0.914 RMSD =
0.033
300 TABLE 1A (continued) XA
T(K)
ATa
2-Nitrophenol + decane system (Ksiqkczak and Jodzewicz, 1981) - 0.003 316.75 0.422 0.010 318.65 0.466 - 0.009 320.05 0.522 - 0.014 320.55 0.565 0.022 320.75 0.616 0.029 320.75 0.661 - 0.044 320.55 0.695 0.010 319.95 0.739 - 0.001 316.25 0.812 RMSD= 0.021
XA
T W)
AT”
2-Nitrophenol + hexane system (Ksigczak and Jodzewicz, 1981) 0.024 313.25 0.320 - 0.084 314.05 0.340 0.079 314.95 0.365 -0.012 315.55 0.405 0.014 315.85 0.435 - 0.038 315.95 0.518 0.029 315.65 0.567 - 0.026 314.05 0.625 0.013 312.75 0.665 RMSD = 0.044
a AT=F-T.
are reported in Tables 1 and lA, together with the experimental data. The obtained representation of data is good and the resulting deviations, AT, can be treated as a measure of random error of experimental data. The mean association number in the critical point The mean association numbers in the critical point have been calculated for the pseudobinary solution model using eqn. (8), and for classical association models: the Mecke-Kempter model, monomer-dimer, monomer-trimer, monomer-tetramer and monomer-hexamer association models, by calculating the association constant K by solving eqn. (11). The van der Waals molar volumes of components have been used, analogously to the solubility equation (Ksi@czak, 1986a). These values have been calculated from group contributions given by Bondi (1968) consistent with UNIFAC group sizes (Fredenslund et al., 1977). In the systems investigated in this work, with hexadecane as a solvent, the van der Waals molar volume of the solvent is several times greater than that of the monomer of the solute, and close to the van der Waals molar volume of the associated species. It enables us to suppose that the effects of different sizes of species in the solution, not taken properly into account in the regular solution theory (Hildebrand and Scott, 1950), are not important in the analysis of the properties of the pseudobinary solution of the associated solute and solvent. The results of the mean association number calculations, performed on the basis of the fitted (see Table 3) or experimental x, values are presented in Table 4. The values of the mean association number, X, in the critical
301 TABLE 4 The mean association number in the critical point in various association models No.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 a b ’ d
System CChlorophenol + hexadecane 2-Methoxyphenol + hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,6-Dimethoxyphenol + cyclohexane 2-Nitrophenol + eicosane 2-Nitrophenol + hexadecane 2-Nitrophenol + decane 2-Nitrophenol f hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane 2-Nitrotoluene + nonane 2-Nitrotoluene + heptane 2-Nitrotoluene + hexane 2-Nitrotoluene + pentane Nitrobenzene + heptane Nitrobenzene + hexane Nitrobenzene + pentane
Const. h”
MK b
l-2”
l-3”
l-4”
l-6 ’
3.38f0.34
-
d
-
3.08
2.79
1.74 f 0.20
1.76
1.66
1.55
1.54
1.63
3.28 f 0.36 3.30 f 0.33 2.56 f 0.24 3.90f0.55 2.25 f 0.22 3.88f0.62 3.42 f 0.59 2.29 f 0.27 4.74 f 1.45
-
-
-
2.42 -
2.86 3.14 2.53 3.90 2.47 3.90 3.57 2.64
2.52 3.09 2.69 4.09 2.76 4.24 4.05 3.02 5.25
1.22f0.13
-
1.40
1.72
1.98
2.38
2.OOf0.28 1.48 f 0.20
1.87 1.40
1.38
1.70 1.33
1.62 1.35
1.62 1.45
1.42f 0.12 1.04f0.08 2.54 f 0.25
1.87 -
1.38 1.10 -
1.44 1.32 2.35
1.54 1.53 2.20
1.74 1.83 2.19
2.83f0.27
-
-
2.75
2.53
2.49
2.18 f0.20 2.16f0.24 1.80f0.20 1.75 f 0.22 2.80* 0.33 2.23 f 0.25 2.57 f 0.39
-
1.83 1.82 -
2.21 2.32 2.08 2.13 2.82 2.36 2.69
2.34 2.53 2.32 2.43 2.96 2.57 2.98
2.60 2.90 2.72 2.89 3.27 2.93 3.48
-
2.51 2.32 -
Model given in eqn. (7). Mecke-Kempter association model, see eqn. (13). Monomer-i-mer association models, i = 2,3,4,6, see eqns. (14)-(16). A value of x, is out of the range acceptable for the given model.
points in a pseudobinary solution model (column 3), the Mecke-Kempter continuous association model (column 4), and the monomer-dimer (column 5), monomer-trimer (column 6), monomer-tetramer (column 7) and monomer-hexamer (column 8) association models are given for systems investigated in this work and found in the literature. The number of the specific
302
monomer-i-mer association models used is limited by the structures of associates observed in the solid phases of solutes (Ksi@czak, 1983). The lack of numerical values denotes that the given model cannot explain the observed value of the critical point composition x,. The errors of determining the critical point have not been taken into account in the calculations. Only for the pseudobinary solution model (with constant h) is the error of determining the mean association number, X, in the critical point reported. This results from the conventionally used estimate of the error in x, equal to 0.01 and the calculated values of the derivative dX/dx,. For the 4-chlorophenol + hexadecane system the mean association number h = 3.38 + 0.34 has been obtained in the pseudobinary solution model. In previous papers (Ksi$czak, 1986a, Ksi@czak and Anderko, 1987) the solid-liquid-vapour equilibrium data for the 4-chlorophenol + cyclohexane system was interpreted assuming that the mean association number, X, along the saturation line is equal to or close to 4. Tetramers of 4-chlorophenol’were detected in the metastable solid phase, /?, of this compound (Perrin and Michel, 1973). These results are consistent, especially taking into account the error of determining the value of x,. The position of the critical point cannot be justified using the Mecke-Kempter continuous association model or monomer-dimer and monomer-trimer association models. For the 2-methoxyphenol + hexadecane system, in all models used, values of the mean association number h = 2 have been obtained. This result agrees well with the solid-liquid equilibrium data analysis performed previously by Ksi@czak (1986b) for 2-methoxyphenol + cyclohexane systems, where a value of X = 2.11 was obtained. The analysis of the pure liquid vapour pressure data (Ksigczak and Kosinski, 1990) suggests that this compound forms intermolecular hydrogen bonds. A cyclic dimer, tith two hydrogen bonds between hydroxyl and methoxy groups, is probably formed. For the phenol + hexadecane system values of the mean association number A = 3 have been obtained, fully consistent with the results of the solid-liquid equilibrium data analysis for the systems: phenol + 4bromotoluene (Ksi@czak, 1983), + hexane, + heptane (Ksigczak, 1986a, Ksi@czak and Anderko, 1987), + pentane, + 2-methylbutane, + 2-methylpentane, + methylcyclohexane, and + decane (Ksi@czak and Anderko, 1987). For these systems a good representation of solid-liquid equilibrium data was obtained assuming X = 3. For the liquid-liquid systems: phenol + pentane, phenol + 2methylbutane, phenol + hexane, phenol + 2-methylpentane, phenol + heptane (Vondracek, 1937), phenol + octane (Campetti and de1 Grosso, 1913) and phenol + decane (Gmehling, 1982) mean association numbers between 2 and 4 have been obtained, also consistent with the previously published results. For systems containing phenol the position of the critical
303
point cannot be explained using the Mecke-Kempter continuous association model. For the 3-methoxyphenol + cyclohexane system (Ksi@czak, 1981) values of the mean association number X = 5 have been obtained. If the estimated uncertainty of these results (about 1.5) is taken into account, they suggest the formation of higher associates (hexamers?). For the system 2,6-dimethoxyphenol + cyclohexane (Ksi$czak, 1981) the mean association number X = 1.22 in the pseudobinary solution model suggests a weak association, similar to that observed in the 2,6-dimethylpheno1 + cyclohexane system (Ksiqiczak and Kosinslci, 1988a). In a molecule of 2,6-dimethoxyphenol two o&ho-substituents bring about a steric hindrance around the hydroxyl group, impeding association (as in 2,6_dimethylphenol), and additionally can form an intramolecular hydrogen bond with the hydroxyl group. This explains the weak autoassociation. For the sequence of systems: 2nitrophenol+ eicosane, + hexadecane, + decane and + hexane, values of the mean association number X between 1 and 2 have been obtained. It was previously shown (Ksigczak, 1986b, Ksi@czak and Anderko, 1987), that 2nitrophenol dimerizes as a result of dipole-dipole interactions, and the hydroxyl group is bonded in the intramolecular hydrogen bond. This fact is confirmed by the analysis of pure liquid vapour pressure data (Ksi@czak and Kosinski, 1990). For 4nitrotoluene and nitrobenzene solutions, values of the mean association number X between 1.75 and 2.83 have been obtained, confirming the existence of the association of nitroaromatic compounds as a result of dipole-dipole interactions. Prediction of the liquid-liquid equilibrium critical point composition In the models discussed, the composition of the solution in the liquidliquid critical point depends on specific interactions, leading to association, and on (van der Waals) molar volumes of components, but does not depend on the parameter D describing the effects of non-specific intermolecular interactions. These models enable us to predict x, on the basis of information about the structure of associates arising from X-ray studies of solid solutes or from the analysis of the solid-liquid(-vapour) equilibrium data. In the solution in an inert solvent such as hydrocarbon, the effect of the specific interactions of the solute molecules on the deviations of the properties of the solution from ideality is stronger than in the solution in a more active solvent. In the case of specific monomer-i-mer association models the mean association number, A, in concentrated solutions of a strong autoassociated solute in an inert solvent is close to the limiting value X = i. This approximation can be used to predict x,.
304 TABLE 5 Prediction of the composition of the solution in the critical point on the basis of the analysis of the solid-liquid-vapour binary systems and X-ray studies No. 1
2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
System 4Chlorophenol+ hexadecane 2_Methoxyphenol+ hexadecane Phenol + hexadecane Phenol + decane Phenol + octane Phenol + heptane Phenol + hexane Phenol + 2-methylpentane Phenol + pentane Phenol + 2-methylbutane 3-Methoxyphenol + cyclohexane 2,dDimethoxyphenol + cyclohexane 2-Nitrophenol + eicosane 2-Nitrophenol -I hexadecane 2-Nitrophenol + decane 2-Nitrophenol + hexane 2-Nitrotoluene + heptadecane 2-Nitrotoluene + hexadecane 2-Nitrotoluene + nonane 2-Nitrotoluene + heptane 2-Nitrotoluene+ hexane 2-Nitrotoluene + pentane Nitrobenzene + heptane Nitrobenzene -I-hexane Nitrobenzene + pentane
xc
a
0.706 0.747 0.757 0.617 0.572 0.492 0.493 0.449 0.407 0.435 0.340 0.366 0.796 0.765 0.634 0.500 0.710 0.680 0.520 0.440 0.410 0.360 0.473 0.446 0.383
ib
x,(A=i)”
x,HSd
4 2 3 3 3 3 3 3 3 3 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2
0.690
0.802 0.785 0.832 0.736 0.676 0.636 0.587 0.587 0.528 0.528 0.458 0.387 0.831 0.789 0.671 0.505 0.784 0.771 0.611 0.527 0.475 0.415 0.588 0.537 0.476
0.734 0.765 0.626 0.555 0.513 0.467 0.467 0.415 0.415 0.359 0.327 0.796 0.740 0.594 0.427 0.734 0.716 0.529 0.447 0.401 0.350 0.505 0.456 0.402
a For systems 1-16 and 24, calculated from experimental data (see Table 3); for systems 17-23 and 25, experimental value. b Associated species detected on solid-liquid equilibrium line or in the solid phase. ’ Predicted using eqn. (8), A = i. d Predicted using eqn. (8), h = 1.
The prediction of x, for the systems discussed is presented in Table 5. The limiting values of the mean association number, A, taken from X-ray studies (Ksir+.ak, 1983) or the analysis of the solid-liquid(-vapour) equilibrium data (Ksi@czak, 1986a, b) are presented in column 4. In column 5, x, predicted from these A values are given. They can be compared with the x, values obtained from experimental data or from the literature (column 3) and with the x, values predicted on the basis of the classical regular solution theory (Hildebrand and Scott, 1950) (A = 1) (column 6).
305 CONCLUSION
The analysis of the mean association number, A, in the liquid-liquid critical point confirms the results concerning association of polar aromatic compounds in hydrocarbon solutions, obtained previously from analysis of solid-liquid and solid-liquid-vapour equilibrium data. The mean value of the mean association number, A, of phenol in various hydrocarbons is equal to 3.11 and confirms that the privileged structure of phenol associates is a trimer. The mean value of the mean association number, A, of polar compounds not forming intermolecular hydrogen bonds in various hydrocarbons is equal to 2.06 and confirms that the privileged structure of associates is a dimer. The presented results agree well with the results of previous analyses, although the effects of different molecular size and shape are not fully recognized by the models used and the uncertainty of determining the x, values cannot be disregarded for some systems for which the number of experimental points is small and comparable with the number of adjusted parameters. The models of solution used in this work enable us to determine the composition of the solution in the critical point without paying attention to the value of parameter D describing the contribution of non-specific interaction. This fact makes it possible to determine if a given model can describe X, in a solution and to verify the parameters of association. The values of x, determined from the liquid-liquid equilibrium experimental data for the solutions of phenol in hydrocarbons cannot be analysed on the basis of either the Mecke-Kempter continuous association model or the monomerdimer association model. In addition, in the case of the 4nitrotoluene and nitrobenzene solutions the Mecke-Kempter continuous association model cannot be applied to represent x,. These results additionally suggest the specific association of these compounds. LIST OF SYMBOLS a
-
:. B’ Bi
D
dT
activity of the associated compound activity of the A-mer, see eqn. (5) parameter in eqn. (3) constant in eqn. (1) parameter in eqn. (3) difference between the modified solubility parameter of the solute (Ksi+zak and Moor&i, 1985) and the solubility parameter of the solvent root mean square deviation, see eqn. (18)
306
K
association constant number of experimental points N n (D,25 OC) refractive index R gas constant s see eqn. (15) see eqn. (16) so composition of the phase in equilibrium, i = 1, 2 si T turbulence disappearance temperature see eqn. (2) t critical temperature of liquid-liquid equilibrium T, temperature deviation, see eqn. (19) AT calculated turbulence disappearance temperature in point i experimental turbulence disappearance temperature in point i van der Waals molar volume of the associated compound van der Waals molar volume of the solvent Wegner exponent, w = 0.5 mole fraction h-mer mole fraction, see eqn. (4) x mole fraction of the associated compound XA mole fraction of the associated compound in the critical point xc of liquid-liquid equilibrium Greek letters
y%~In YA
A @
critical exponent, (Y= 0.11 critical exponent, /? = 0.326 activity coefficient of the associated compound contribution to the activity coefficient due to an association model mean association number volume fraction of the associated compound
ACKNOWLEDGEMENTS
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