solubility of n-paraffin hydrocarbons in binary solvent mixtures

Fluid Phase Equilibria, 35 (1987) 217-236 217 Elsevier Science Publishers B.V., Amsterdam -- Printed in The Netherlands

SOLUBILITY OF n-PARAFFIN H Y D R O C A R B O N S IN BINARY SOLVENT MIXTURES

URSZULA DOMANSKA

Department of Physical Chemistry, Warsaw Technical University, 00-664 Warsaw (Poland)

(Received October 1, 1986; accepted in final form March 16, 1987)

ABSTRACT

Domafiska, U., 1987. Solubility of n-paraffin hydrocarbons in binary solvent mixtures. Fluid Phase Equilibria, 35: 217-236.

Reasonable estimates of ternary solid-liquid equilibrium can be obtained by application of the Scatchard-Hildebrand, UNIFAC and Wilson models. The solubilities of Cls, C19 n-paraffins (octadecane and nonadecane) in 20 binary solvents consisting of cyclohexane and heptane or ethanol, as well as of C20 n-paraffin (eicosane) in three binary mixed solvents of 2-propanol with cyclohexane, trichloroethylene or tetrachloroethylene have been measured by a dynamic method from 275 to 279 K. The root mean square deviations of the solubility temperatures for all measured data in nonpolar solvents vary from 0.1 to 4.0 K and depend on the equation used. The best representation was obtained with the Wilson equation utilizing temperature dependent Aij parameters. The correlation of solubility curves with hh-equation has been done.

INTRODUCTION

The prediction of equilibrium solubility behaviour of n-paraffin hydrocarbon solutes in binary mixtures of cyclohexane and heptane or ethanol by Scatchard-Hi ldebrand regular solution theory (Hildebrand et al., 1970), the universal functional group activity coefficient method, U N I F A C , and Wil- son's equation (Wilson, 1964), requires some sets of experimental data: solubilities of the n-paraffin hydrocarbons in pure cyclohexane, heptane and ethanol, VLE data for the cyclohexane + heptane and cyclohexane + ethanol systems, necessary to determine the parameters of the chosen activity coefficient model and solubilities of the high-molecular-weight hydrocarbons in the 20 binary solvent mixtures.

The Scatchard-Hi ldebrand regular solution theory has been used by Buchowski et al. (1977) and Buchowski et al. (1979a,b) to describe the solubility of nitrophenols and by Domafiska (1981) with solubility of naphthalene and by Domafiska (1986a) with solubility of eicosanoic acid in binary solvent mixtures. Subsequently, the solubility prediction of normal

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218

alkanoic acids and o-toluic acid in binary solvent mixtures was studied using the Wilson equation and group contributions theory, U N I F A C (Domahska and Hofman, 1985). Beerbower et al. (1985) tested the solubility of benzoic acid and napthalene in a variety of solvents at the temperature of 298.15 K using UNIFAC and the extended Hansen solubility parameter approach. Also, the following correlation equations were used in solid-liquid equilibria calculations: Wilson, van Laar, Redlich-Kister and UNIQUAC, NRTL (Morimi and Nakanishi, 1977; Muir and Howat, 1982; Klimenko, 1984; Carta et al., 1985; Choi et al., 1985; Domafiska and Hofman, 1986).

The results of solubility correlations of high-molecular-weight hydrocarbons in one-component solvents presented by Domafiska et al. (1987) demonstrate the Xh-solubility equation (Buchowski et al., 1980) as well as the Wilson one to be the most satisfactory.

EXPERIMENTAL

Solubilities were determined by a dynamic (synthetic) method described in full detail by Buchowski et al. (1975). Mixtures of solute and binary solvent, prepared by weighing were heated very slowly (heating rate did not exceed 2 K h-1 near the equilibrium temperature) with stirring kept inside the vessel. The temperature at which the last crystals disappeared (decline of solution dullness) was taken as the temperature of the solution-crystal equilibrium. Measurements were carried out in a wide range of solute concentrations from 0.001 to 0.87 and over a temperature range from 276 K to temperatures near the melting points of hydrocarbons. The accuracy of temperature measurements was +_ 0.05 K. Reproducibility of measurements was 0.1 K, which corresponded to a relative error in composition < 1%. All solvents were dried over 4 A Molecular Sieves (BDH) or other dehydrating agents and purified by fractional distillation. The total amount of contami- nants did not exceed 0.1% for alcohols and 0.2% for other solvents, as estimated by vapour-phase chromatography. Commercially available n-alkanes were directly used without purification. The purity of octadecane (Koch-Light Lab.), nonadecane and eicosane (Fluka AG) was chromato- graphically determined to be of 0.99, 0.99 and 0.98, respectively.

The characteristics of solutes and solvents are collected in Table 1.

RESULTS AND DISCUSSION

The solubility of a solid 1 in a liquid is expressed in a very general manner by eqn. (1) - l n x 1 -- AHml/R(I/T- 1 / T m l )

-ACpml/R(ln T/Tml -}- T m l / T - 1) q- in "Y1 (1)

219

o

011

I

. . . . . . ~

O Z ~

~ o ~

0

220

where xl, ]/1, AHml, ACpml, Tml, T stand for mole fraction, activity coefficient, enthalpy of fusion, solute heat capacity during the melting process, melting temperature of the solute and equilibrium temperature, respectively. If the solid-solid transition occurs before fusion, an additional term must be added to the right side of eqn. (1) (Weimer and Prausnitz, 1965; Choi and McLaughlin, 1983).

The solubility equation for temperatures below that of the phase transition must include the effect of the transition. The result for a first-order transition is

- l n x I = A H m l / R ( 1 / r - 1/Tml ) - ACpml/R(ln T/rml + T m l / r - 1)

q-AHtr l /R(1/r - 1 / r t r l ) -k In Y1 (2)

where AHtr I and Ttr 1 stand for enthalpy of transition and transition temperature of the solute, respectively.

Solid-solid phase transitions typical for odd-numbered paraffins above C 7 have been reported by numerous investigators. Rotational transitions below the melting point for C9, Cll , C13 and C15 (Finke et al., 1954), C17 (Messerly et al., 1967) and C19 (Dollhopf et al., 1981) have been observed. Also, some lower even n-alkanes, e.g. butane (Rossini et al., 1953), and higher, e.g. eicosane (Schaerer et al., 1955), undergo solid-solid phase transition before fusion. Similarly, the transition point takes place on dotriacontane and is suspected to occur in the case of octadecane (Chang et al., 1983). Such transition points were also reported for even-numbered paraffins from C22 to C2s by Craievich et al. (1985). The quantitative description of the solid-solid phase transition effects is impossible up to now for many hydrocarbons, because of lack of sufficiently accurate thermodynamic data. The phase transition temperature of nonadecane (297.1 K) has been found from solubility measurements. Characteristic liquidus curves of one-component as well as two-component solvents are shown in Fig. 1. for the nonadecane-cyclohexane + heptane system for example. The molar enthalpy of transition of the solute given by Schaerer et al. (1955) is 13.8 kJ mo1-1. No transitions have been observed during the solubility measurements of octadecane and eicosane. The values of transition temperatures of eicosane (309.4 K) reported by van Oort and White (1985) and octadecane (299.1 K) shown by Chang et al. (1983) are close to the melting temperature points of these n-paraffins, so they could not be found by solubility measurements.

Experimental solubilities of two n-alkanes, i.e. octadecane and nonadecane in pure cyclohexane, heptane, ethanol and their two-component mixtures are collected in Tables 2 and 3.

Two methods of calculating of activity coefficients were tested. One, when the activity coefficients are predicted from regular solution or UNIFAC

221

T/K

303

293

1

283

3

273 o o'.z o~ ' o16 o~

.X 1 Fig. 1. Solubility of nonadecane in cyclohexane (1), in mixed solvent system containing 39.94 mol% of heptane (2) and in heptane (3). Experimental points are matched by curves calculated from eqn. (11).

model, where the parameters come from regression of VLE data. The other one, when the activity coefficients are taken from the Gibbs excess free energy of mixing (G E) models, where parameters in binary system solute-solvent are regressed from SLE data and for binary mixed solvent from VLE data.

The Scatchard-Hildebrand equation (Hildebrand et al., 1970) was used to predict the solute activity coefficients (eqn. (3)) of the nonpolar systems investigated

R T In ~1 = V l ~ 2 ( ~ l - 3 2 ) 2 (3)

The solubility parameter of two-component solvent is expressed by eqn. (4)

32 = (¢&3 A + q~B3,)/(q~A + ~ , ) (4)

where V 1 is the molar volume of the solute q~2, q'A, q'B are volume fractions of the pure solvent or mixed compounds of solvents A and B, and 31, 32 are solubility parameters of the solute and solvent, respectively. The appropriate data of liquid molar volumes and solubility parameters given by Maffiolo et al. (1972) and Barton (1975) for solute and solvents are listed in Table 1. Assuming that (31 -32 ) and V 1 do not depend on temperature, the activity

222

T A B L E 2

Solubility measurementsofoctadecaneinbinarysolvents

X 1 T(K) X 1 T(K)

Cyclohexane 0.7188 297.50 0.7044 297.05 0.6053 295.35 0.5755 294.80 0.4792 292.60 0.4448 290.95 0.4107 290.35 0.3505 287.20 0.3485 288.35 0.2645 284.35 0.3151 287.00 0.2137 281.45 0.2840 285.65

0.2447 283.80 Cyclohexane+ 20.02mo1% heptane 0.2091 282.05 0.7059 297.35 0.5714 294.40 Cyclohexane+ 79.25mo1% heptane 0.4615 291.75 0.7391 297.65 0.3636 288.15 0.5862 294.55 0.2791 283.70 0.5152 293.05 0.2222 281.70 0.4474 291.45 0.1905 279.65 0.3953 289.90 0.1644 278.28 0.3333 287.55 0.1463 276.75 0.2982 286.20 0.1333 275.65 0.2576 284.60

0.2237 282.75 Cyclohexane+ 39.94mo1% heptane 0.1954 281.10 0.8214 299.10 0.6389 295.90 Heptane 0.5227 293.05 0.7333 297.65 0.4600 291.50 0.6471 296.40 0.3833 288.95 0.5238 293.65 0.3286 287.00 0.4583 291.90 0.2875 285.30 0.3929 290.15 0.2421 283.25 0.3143 287.60 0.2170 281.75 0.2245 283.70 0.1855 279.80 0.1833 281.40

0.1507 279.00 Cyclohexane + 49.98mo1% heptane 0.1236 276.90 0.8750 300.35 0.8000 298.70 Cyclohexane+ 20.03mol%mol% ethanol 0.6667 296.65 0.6970 297.75 0.6087 295.20 0.6053 295.95 0.5185 293.25 0.5257 294.15 0.4516 291.50 0.4423 292.60 0.3684 288.80 0.3710 290.10 0.3111 286.50 0.3239 288.85 0.2692 284.70 0.2805 286.95 0.2258 282.90 0.2447 285.50 0.1918 280.60 0.2054 283.45

0.1716 281.50 Cyclohexane + 60.00 mol% heptane 0.8214 299.35

TABLE 2 (continued)

223

x I T(K) x I T(K)

Cyclohexane+40.04mol% ethanol 0.1275 294.15 0.6286 297.45 0.1171 291.15 0.4783 295.25 0.1102 289.05 0.4231 294.05 0.1024 286.25 0.3438 291.95 0.0956 283.85 0.2895 290.05 0.0884 282.75 0.2472 288.15 0.0828 282.30 0.2115 286.85 0.1930 286.00 Cyclohexane+ 80.01mo1% ethanol 0.1705 284.65 0.0854 299.25 0.1429 283.05 0.0817 297.70

0.0702 293.80 0.0651 292.15 0.0584 289.80 0.0545 287.90 0.0502 284.95 0.0453 282.90

Cyclohexane + 49.99 mol% ethanol 0.2055 299.35 0.1948 298.25 0.1852 296.90 0.1724 295.50 0.1648 293.95 0.1546 292.35 0.1456 290.55 0.1389 288.95 0.1282 286.45 0.1163 283.20

Cyclohexane+ 59.02mo1% ethanol 0.1494 299.25 0.1398 297.45 0.1327 295.75

Ethanol 0.0162 299.45 0.0122 297.95 0.0093 296.20 0.0072 294.35 0.0058 292.60 0.0047 291.013 0.0038 289.25 0.0032 287.70 0.0025 285.75 0.0018 283.05

coefficients as a function of solute mole fraction (xl) and temperature (T) were obtained from eqn. (3). The root mean square deviation of temperature defined by eqn. (5) was used as a measure of the goodness of solubility curve prediction

where T/ca and T~ are, respectively, the calculated and experimental temperatures of the i th point. The results of solubility calculations by means of Scatchard-Hildebrand equation are presented in Table 4 in the form of the root mean square deviations OSH. The prediction of n-paraffins solubility in nonpolar solvents, i.e. cyclohexane, heptane and mixtures of them, is satisfactory (OSH = 0.6--2.0 K). Unfortunately, it is not possible to use the

224

TABLE 3

Solubility measurements of nonadecane in binary solvents

x 1 T (K) x 1 T (K)

Cyclohexane Cyclohexane+ 60.00mo1% heptane 0.7500 301.75 0.8400 302.25 0.6000 297.00 0.7000 299.30 0.5534 295.65 0.5675 295.70 0.4575 292.80 0.4773 293.50 0.3588 289.65 0.3889 290.85 0.2899 286.65 0.3281 288.85 0.2330 283.95 0.2763 286.60 0.2012 282.25 0.2386 283.95

0.2020 282.85 Cyclohexane+ 20.02mo1% heptane 0.1810 281.35 0.7083 300.35 0.5152 294.55 Cyclohexane+ 79.25mo1% heptane 0.4146 291.50 0.8000 301.55 0.3617 289.75 0.6667 298.20 0.2982 287.25 0.5556 295.25 0.2576 285.50 0.4767 293.35 0.2125 283.70 0.3922 291.00 0.1977 281.91 0.3390 289.10 0.1771 280.80 0.2899 287.15 0.1700 279.85 0.2353 283.65

0.1980 282.60 Cyclohexane+39.94mol%heptane 0.1695 280.60 0.7917 302.25 0.6129 296.85 Heptane 0.5135 294.15 0.7857 302.30 0.4043 291.10 0.6111 296.95 0.3519 289.30 0.4783 293.70 0.2879 286.85 0.3929 290.95 0.2468 284.90 0.3143 288.70 0.2021 282.55 0.2558 286.55 0.1624 279.90 0.2200 284.25 0.1407 278.20 0.1897 282.45

0.1642 280.95 Cyclohexane+49.98mol% heptane 0.1447 279.50 0.8519 302.45 0.1294 278.25 0.7419 300.10 0.5897 296.45 Cyclohexane+ 20.03mo1% ethanol 0.4894 293.75 0.7222 300.70 0.4035 291.30 0.6500 299.15 0.3433 289.00 0.56.52 296.90 0.2840 286.75 0.5098 295.35 0.2371 283.40 0.4483 294.15 0.2035 282.65 0.3880 292.40 0.1769 280.90 0.3377 290.90

TABLE 3 (continued)

X 1 T (K) x 1 T (K)

0.2857 288.45 0.0899 290.00 0.2342 286.25 0.0816 286.75 0.1615 281.90 0.0755 283.70

0.0708 282.70 Cyclohexane+40.04mol% ethanol 0.0684 282.15 0.6271 299.45 0.0571 280.80 0.6066 299.15 0.5692 298.70 Cyclohexane+ 80.01mo1% ethanol 0.4805 296.45 0.4253 295.35 0.3663 293.75 0.3162 292.35 0.2761 290.95 0.1979 287.45 0.1418 284.65

0.0568 302.85 0.0540 301.50 0.0493 298.50 0.0450 295.05 0.0416 291.80 0.0384 288.55 0.0356 287.15 0.0329 286

Cyclohexane+49.99mol% ethanol 0.0299 285.85 0.1667 300.85 0.0238 284.15 0.1538 298.95 0.1429 296.75 Ethanol 0.1333 294.65 0.0115 303.85 0.1250 292.25 0.0083 300.85 0.1176 290.35 0.0062 297.25 0.1149 288.55 0.0051 295.60 0.1053 286.00 0.0041 293.75 0.1000 283.90 0.0035 292.45 0.0909 281.90 0.0030 290.95

0.0025 289.95 Cyclohexane+ 59.02mo1% ethanol 0.0022 288.70 0.1250 301.55 0.0019 287.40 0.1127 298.60 0.0016 286.00 0.1053 296.10 0.0014 284.80 0.0976 292.95 0.0011 282.70

225

226

TABLE 4

Values of the root mean square deviation a of temperature obtained Hildebrand (aSH), UNIFAC (Ou) , Wilson (Ow) and Xh-equation

for the Scatchard-

x o b OSI_ I (K) o U (K) o w (K) oxh (K)

Octadecane-cyclohexane + heptane 0.0 1.22 1.45 0.38 0.35 0.2002 2.06 1.69 0.62 0.45 0.3994 1.37 1.25 0.61 0.15 0.4998 1.06 1.31 0.74 0.28 0.6000 0.97 1.42 0.73 0.18 0.7925 1.33 1.24 0.29 0.10 1.0 1.52 1.92 0.11 0.12

Octadecane-cyclohexane + ethanol 0.2003 2.07 1.32 0.32 0.4004 1.82 2.45 0.18 0.4999 12.28 4.62 3.17 0.5902 6.91 4.75 3.67 0.8001 5.21 4.71 4.62 1.0 4.39 0.70 0.76

Nonadecane-cyclohexane + heptane 0.0 1.29 3.27 0.75 0.09 0.2002 1.63 4.06 0.54 0.40 0.3994 1.39 3.62 0.49 0.46 0.4998 0.91 2.90 0.44 0.34 0.6000 0.95 3.02 0.36 0.30 0.7925 0.60 2.75 0.43 0.34 1.0 0.87 3.79 0.56 0.48

Nonadecane-cyclohexane + ethanol 0.2003 3.38 1.21 0.23 0.4004 2.89 1.92 0.14 0.4999 10.57 5.14 3.48 0.5902 8.99 5.64 3.52 0.8001 6.09 5.13 3.74 1.0 8.13 1.49 2.65

n ca l a o 1 = [~i=l(T~ -Ti)/n]l/2, where Ti TM and T, are calculated and experimental values of solubility temperature, n is the number of experimental points. b X O is the mole fraction of the second named component in the solute-free mixed solvent.

Scatchard-Hildebrand equation for the description of the cyclohexane + ethanol systems studied, since it has been derived for nonpolar systems.

The solute activity coefficients were also obtained using the UNIFAC model and the solubilities were predicted through solution of eqn. (1) for octadecane and eqn. (2) for nonadecane with respect to T, for each experimental composition (xl). The parameters derived previously by Gmehling et

227

al. (1982) were used in the calculations. The calculated temperatures were not accurate, as evidenced by the values of the root mean square deviation obtained, which were in the range from Ou = 1.2 to 12.3 K (see Table 4). The highest discrepancy was observed for the octadecane and nonadecane in cyclohexane + ethanol solvent systems containing 50 mol% of ethanol. The low accuracy of the group contributions model, when applied to the polar systems can be rationalized on the basis of the assumptions of that method. In the UNIFAC model all interactions are treated in the same manner, while the existence of hydrogen bonding in the solvent systems discussed is evident. The accuracy of the description of the solubilities of n-paraffins in pure and binary nonpolar solvent systems, i.e. cyclohexane + heptane is significantly better than in polar systems and the values of deviations are from 1.2 to 4.0 K. Generally, the prediction of high-molecular-weight hydrocarbons solubility by U N I F A C model is worse than by means of other methods under study, but considerably better than that obtained with monocarboxylic acids by Domafiska and Hofman (1985).

Only in one nonpolar system, i.e. octadecane-cyclohexane + heptane, the root mean square deviations did not exceed the value of 2 K (from solubility studies conducted by a dynamic method, o = 2 K is taken as a criterion of maximum allowable deviation from observed solubility). Apparently, UNI- FAC cannot satisfactorily reproduce the solubility results for more polar solutes like benzoic acids, naphthols (Domafiska, 1985) and their analogues. As the interaction energy parameters for groups such as - O H ( C A r ) , - C O O H ( C A r ) are not currently found in the U N I F A C tables, the application of U N I F A C to polar systems must await development of new parameters.

The use of Wilson's equation to represent the activity coefficient of a solute in mixed solvent systems ought to show a marked improvement over regular solution theory and U N I F A C method, especially for systems exhibit- ing a significant deviation from ideal behaviour.

Wilson's equation for the excess Gibbs free energy of a n component mixture is given by eqn. (6)

G E / R T = - x a In x j A i j (6) i=1 [ j = l

where

A,j = (Vj/V~) e x p [ - (gij - g . ) / R T ] (7)

where V~ is the molar volume of pure i component in the liquid phase and g i j is the molar energy of interaction between the i and j components. The

228

TABLE 5

The parameters obtained by the Wilson equation a in binary solute-solvent systems

S y s t e m g12 - g l l g12 - g22 (J mo1-1) (J mo1-1)

Octadecane + cyclohexane - 1072.64 1004.00 ethanol 5310.02 61780.48 heptane - 3652.75 4821.77

Nonadecane + • cyclohexane - 653.59 611.46 ethanol 5918.66 63 694.81 heptane - 315.08 292.73

Given by eqn. (8) and eqn. (1) or (2).

resulting expression for the activity coefficient of the '1' component can be expressed by eqn. (8)

In 7x = 1 - In X j A l j -- x iAi l / E xjAij ( 8 ) i = l j = l

Recommended values of the solvent-solvent binary interaction parameters Aij are given for cyclohexane + heptane system by Nagata (1973) and for cyclohexane + ethanol system by Hirata et al. (1975) from VLE data. Since in the case of saturated solutions of hydrocarbons the Wilson parameters are not available, they have been obtained by fitting of solubility curves of the solute in one-component solvent. Their values are collected in Table 5. In the previous paper of Domafiska et al. (1987) three versions of Wilson equation were tested (i.e. Ai j ~ flT)," (gij - gii) ~ f lT) and (g~_i - gii) = a , j / T, aij--/:f(T)) to the description of n-paraffin solubilities and the simplest temperature dependence of parameters Aij (i.e. ( g i j - gi~):.-/:fiT)) gave the lowest values of the root mean square deviations. In this paper the same version of the Wilson equation with Aij parameters dependent on temperature (i.e. ( gii - gi~) ~ f ( T ) ) has been applied.

The parameters were fitted by the optimization technique (not for ethanol). The objective function was as follows

n

F(A12, A21) = E wa-2[ In xli 'Yli(T, Xli, A12, A 2 1 ) - l n ali] 2 (9) i = 1

where In al, is an 'experimental ' value of the logarithm of solute activity taken as the right side of eqn. (1) for octadecane and eqn. (2) for nonadecane, wi is the weight of experimental point, Aa2, A21 are two adjustable parameters of the Wilson equation, i denotes the i th experimental point and

229

n the number of experimental data. The weights were calculated by means of the error propagation formula

); ( 3 In xl~, 1 w/2 = 3 In x?h • (AT/) 2 + • (Ax~i) 2 (10) 3 T =r, 3xa xl=xl,

where AT and Ax~ are the estimated errors of T and Xl, respectively. According to the above formulation, the objective function is consistent

with the Maximum Likelihood Principle, provided that the first-order ap- proximation (eqn. (10)) is valid.

The experimental errors of temperature and solute mole fraction were fixed for all cases and set to: AT= 0.2, Ax I = 0.001. The results of the solubility prediction in ternary systems are presented in the form of root mean square deviations o w in Table 4. It is noted that a good description has been obtained for one-component solvents and for the inactive solvent system cyclohexane + heptane. All deviations are in the range o w from 0.11 to 0.75 K and get worse in the polar cyclohexane + ethanol binary solvent system (o w is from 0.70 to 5.64 K). The Wilson approach is deficient in polar systems, probably because it does not take into consideration specific interactions (electron-donor, electron-acceptor characteristics of complex organic molecules and hydrogen bonding) in ternary systems. Anyway, the success of the n-paraffin hydrocarbons solubility predictions was increased by use of the Wilson equation; 80% of the solubilities being predicted with root mean square deviations o w < 2 K. Only seven of 25 solvents under study showed the root square deviations aboVe 2 K, but the strongly polar solvents with - 50 mol% of alcohol were still not well represented with this method. Typical solid-liquid phase predictions in polar systems are presented in Fig. 2 for octadecane-cyclohexane + ethanol system, which shows the comparisons between the calculated by Wilson equation and experimental results.

In many previous papers (Domafiska et al., 1982; Domahska, 1986a,b) a good description of experimental curves has been achieved using the Xh- solubility equation

ln[1 + X(1 - x1)/Xl] = )kh( T - 1 - T~n? ) (11)

where X and h are the equation parameters, which are either adjusted to the solubility data or estimated in a different way. In the case of ternary systems, the binary mixed solvent is considered to be equivalent to the one-component solvent, so the root mean square deviations OXh given by eqn. (5) are calculated as for binary systems. Parameters X and h of eqn. (11), found by Rosenbrock's numerical method (Rosenbrock, 1960) for octadecane and nonadecane are collected in Table 6, while the results of deviations are listed in Table 4.

230

T/K

31}1]

290

280

2 3 o ~

5

V A

s •

j j ! •

j s ~ $ 1 ~ / & i S p J I s °

o t / / s / / ® p s

o / i i @ • •

, , , / S ; / / " V A S / i X

ol / / / /7" /

3

' ' ' 0'/,. ' ' 0.1 0.2 0.3 0.5 0 .6 0.7 X .

Fig. 2. Prediction of octadecane solubility in cyclohexane (7), in ethanol (1) and mixture containing 80.01 mol% (2), 59.02 mol% (3), 49.99 mol% (4), 40.04 mol% (5) and 20.03 mol% (6) of ethanol. Lines are calculated by the Wilson equation for parameters given by Nagata (1973) (solid lines) and by Hirata (1975) (dashed lines).

The correlation by ?,h-equation is satisfactory especially in cyclohexane + heptane binary solvent mixtures, where the root mean square deviations oxh are in the range from 0.10 to 0.48 K and become worse in cyclohexane + ethanol mixtures (OXh is from 0.14 to 4.62 K). The results of the fit are presented in Fig. 1 for nonadecane in cyclohexane + heptane mixed solvent system.

The phenomenon of enhanced solubility in binary solvent systems, known as the synergistic effect has been observed by Domaflska (1986a) with eicosanoic acid in cyclohexane + alcohols mixed solvents and in the case of 5-methyl-2-ni t rophenol (Buchowski et al., 1979b) as well as naphthalene

T A B L E 6

Parameters of the Xh-equat ion a for oc tadecane and n o n a d e c a n e

231

X O b O c t a d e c a n e

X h x l 0 -3 (K)

N o n a d e c a n e

h h X l 0 -3 (K)

Cyclohexane + hep tane 0.0 0.71 7.74 1.19 5.60 0.2002 0.79 7.38 1.08 5.95 0.3994 0.74 7.66 1.21 5.61 0.4998 0.70 8.04 1.19 5.61 0.6000 0.67 8.25 1.23 5.61 0.7925 0.80 7.67 1.28 5.48 1.0 0.83 7.98 1.22 5.83

Cyclohexane + e thanol 0.2003 0.73 8.87 1.01 6.83 0.4004 0.54 12.43 1.06 8.10 0.4999 0.10 x 10 - l ° 48.33 0.12 x 10 -7 44.36 0.5902 0.23 x 10 - l ° 59.85 0.93 x 10 -11 58.71 0.8001 1.39 x 10 -8 122.35 0.14 x 10 -8 171.89 1.0 0.26 x 10 -2 1541.4 0.16 x 10 -3 2465

a Xh is the solubil i ty equat ion given by eqn. (11). b x o is the mole f ract ion of the second n a m e d c o m p o n e n t in the solute-free mixed solvent.

(Domaflska, 1981) in hexane + alcohols binary solvents. It has also been noticed with 2-acetyl-l-naphthol(1-hydroxy-2-acetylnaphthalene) solubility in cyclohexane + alcohols and hexane + alcohols solvents (Domafiska, 1985). Thus, the solvents systems mentioned above revealing the enhanced solubility phenomenon include a variety of solids such as compounds with stable intramolecular hydrogen bond (5-methyl-2-nitrophenol, 2-acetyl-l-naphthol) in polar solvents, their structural nonpolar isomers (naphthalene, phenantrene) and compounds forming stable complexes (cyclic dimers of alkanoic acids).

From the analysis of solubility parameters collected in Table 1 it follows that the ternary hydrocarbon-cyclohexane + ethanol system should reveal the increased solubility, but it did not, probably due to the very small solubility of hydrocarbons in pure ethanol and thus the large difference in solubilities of hydrocarbons in pure solvents (cyclohexane, ethanol).

The synergistic effect of solubility has also been found in the ternary systems of aliphatic acids with azeotropic mixtures of halogen derivatives of hydrocarbons and alcohols (Domafiska, 1986a). Azeotropic mixtures were taken into consideration because of their general utilization in the industry due to the convenience of the regeneration by distillation. Searching for

232

TABLE 7

Solubility measurements of eicosane in different azeotropic mixtures of binary solvents

x 1 T (K) x I T (K)

Cyclohexane+ 39.62mo1% 2-propanol 0.3988 301.55 0.5372 0.3285 299.95 0.2851 0.2924 298.65 0.1877 0.2486 296.95 0.1132 0.1881 293.95 0.0586 0.1468 291.65 0.0385 0.1218 289.65 0.0232 0.1056 288.15 0.0148 0.0753 285.35 0.0095 0.0475 282.25 0.0350 278.45

Tetrachloroethylene+ 92.17mo1% 2-propanol 0.4106 306.85 0.2723 305.65 0.1591 304.55 0.0748 302.75 0.0315 299.85 0.0149 295.75 0.0097 292.15 0.0072 290.05 0.0063 288.75 0.0047 286.55 0.0027 282.35 0.0020 279.75

Trichloroethylene + 48.37 mol% 2-propanol 306.00 301.20 298.15 295.35 290.15 287.15 283.35 280.15 276.80

azeotropic solvent mixtures giving the synergistic effect is then the main tendency in investigations.

To test the use of azeotropic mixtures in solubility of n-paraff in hydrocarbons the following systems have been investigated: eicosane (C20)-cyclohexane + 2-propanol, e icosane- te t rachloroethylene + 2-propanol and eicosane- t r ichloroethylene + 2-propanol. The results are collected in Table 7. Solubility measurements of eicosane in pure solvents were discussed in the first paper of this study (Domafiska et al., 1987). The synergistic effect of solubility is not observed in the systems ment ioned above.

CONCLUSIONS

This paper represents the second test of the predict ion of solubility in binary solvent mixtures by applicat ion of the Wilson equat ion and the

233

U N I F A C method. In an earlier study (Domafiska and Hofman, 1985) the solubility of normal alkanoic acids as well as o-toluic acid in binary solvents consisting of a common component (cyclohexane) and various components (heptane, methanol, ethanol, 2-propanol and 1-butanol) has been predicted by these two methods. The results of prediction obtained with the Wilson equation were better than with the U N I F A C method, especially in binary solvent systems containing more than 60 mol% of alcohol and in pure alcohol, but they were not fully satisfactory with some systems under study.

In the present work, the description of n-paraffin hydrocarbons solubility was better than in the case of the acids mentioned above. The application of the UNIFAC model was less satisfactory than the Wilson procedure.

The mathematical description of n-paraffin solubility in nonpolar systems (cyclohexane + heptane) is much better than in polar systems (cyclohexane + alcohols). The description of solubility in cyclohexane + alcohols mixed solvents becomes better when the synergistic effect was observed, as was shown in an earlier study by Domaflska (1986a), which was related to the interaction parameters gij - gi~ of a couple of pure binary solvents (G E >> 0).

Unfortunately, none of investigated binary solvent systems consisting of a hydrocarbon of a halogenhydrocarbon with an alcohol was found to exhibit the enhanced solubility effect due to the small solubility of n-paraffin hydrocarbons in pure alcohols.

Good results of correlation by means of Xh-equation were also obtained as in the first paper of this study (Domaflska et al., 1987).

ACKNOWLEDGEMENTS

The author gratefully acknowledges the financial support received from the Institute of Low Temperatures and Structural Researches, Polish Academy of Sciences, within the framework of the Project 01.12 entitled 'Structure, phase transitions and properties of molecular systems and con- densed phases'.

LIST OF SYMBOLS

al m l

AHml AHtr 1 h

activity of the solute difference between heat capacities of the solute in the solid and liquid states molar energy of interaction between i and j excess Gibbs free energy molar enthalpy of fusion of the solute molar enthalpy of transition of the solute parameter of eqn. (11)

234

n R T AT rcal

Tml rtrx Vl

X1 x o

Ax 1 W

number of experimental points universal gas constant experimental equilibrium temperature estimated error of temperature calculated equilibrium temperature melting point temperature of the pure solute transition point temperature of the pure solute molar volume of the solute molar volumes of pure liquid components i and j mole fraction of the solute mole fraction of the second named component in the solute free mixed solvent estimated error of the solute mole fraction weight of experimental point

Greek letters

(~1, 82' (~A' (~B

'/'2, q'a, '/'B

Aij

o

activity coefficient of the solute solubility parameter of the solute and of one-component or binary solvent mixed of solvent A and B volume fraction of the pure solvent or mixed compounds of solvents A and B parameter of the Wilson eqn. parameter of eqn. (11) root mean square deviation of temperature

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solubility of n-paraffin hydrocarbons in binary solvent mixtures

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