J . Chem. SOC., Faraday Trans. I , 1988, 84(2), 539-550 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures The Systems formed by 2,2,4-Trimethylpentane with Hexafluorobenzene and with Hexafluorobenzene-Benzene Javier Aracil, Ramh G. Rubio,* Mercedes Caceres and Mateo Diaz Pefia Departamento de Quimica Fisica, Facultad de Quimicas, Universidad Complutense, 28040-Madrid, Spain Juan A. R. Renuncio Catedra de Quimica General, Facultad de Quimica, Universidad de Oviedo, 33007 Oviedo, Spain The excess volume of hexafluorobenzene (C6F,)-2,2,4-trimethylpentane (2,2,4-TMP) has been measured at 298.15 K as well as the vapour pressures at 298.15, 323.15 and 348.15 K. From the latter, the excess Gibbs energies have been calculated, and the excess enthalpies have been estimated through the Gibbs-Helmholtz equation.The comparison with similar data for binary systems involving benzene (C,H,), C,F,, 2,2,4-TMP and cyclohexane (c-C,H,,) shows that c-C,H,, and 2,2,4-TMP have quite different volumetric and entropic behaviours when mixed with C,F,, whilst they are almost equivalent when mixed with C,H,. Finally, the vapour pressures have been measured and the excess Gibbs energies calculated at 298.15 and 323.15 K for the ternary system C,F6-C,H,-2,2,4-TMP. Previous work on mixtures containing alkanes has shown that correlation of molecular order plays a fundamental role in their thermodynamic properties.' When the alkanes are mixed with benzene or p-xylene, it seems that order correlations between the aromatic molecules and between the aromatic molecules and chain-like molecules have to be taken into account in order to explain the qualitative trends of the excess functions.2 C,F, presents a higher degree of orientational order than C6H6,3 therefore one should expect that breaking those correlations should play a more important role in C6F,-alkane mixtures than in the C,H6-alkane mixtures.Nevertheless, the excess properties of C,F,-n-hexadecane (nC16H34) or + n-tetradecane (n-C14H30) seem to be mainly dominated by the unfavourable hydrocarbon-fluorocarbon interaction^.^ In order to obtain further information on the importance of breaking the orientational order of pure C,F, upon mixing, we have found it interesting to study the system C6F,-2,2,4-TMP, the latest being an almost globular molecule which presents no order correlations at all.Since order correlations show a strong temperature dependence,' information about mixing functions up to near the normal boiling point of the ordered substance should be of value. Recently unusual W-shape CFam us. composition curves have been found in some alkane solutions with some halogeno- hydrocarbon^.^ Saint-Victor and Patterson6 have suggested that these effects could be related to the proximity of the mixture to a UCST, a situation which is associated with high GZ values. Perfluorocarbon-hydrocarbon systems are known to show large GE values, and frequently to present liquid-liquid eq~ilibria,~ which makes them good candidates for the study of this kind of effect. The binary system C6H6-2,2,4-TMP shows positive Gg values, while C,F,-C,H, presents an S-shaped GE us.x, curve. Therefore the ternary system C,F6-C,H,-2,2,4- TMP must have high positive GE values in some regions of the concentration triangle 539540 Thermodynamics of Fluorocarbon- Hydro carbon Mixtures and negative values in other regions. If the W-shaped CE,, curves were actually related to high G: values, data for this type of ternary system might be helpful in understanding their relationship. Experimental Excess volumes were measured using a continuous dilution dilatometer, and vapour pressures were measured by the static method. The techniques were the same as those used previ~usly,~ thus only the experimental uncertainties will be quoted here. The precision of the vapour pressure was f 8 Pa and in the excess volume was f 2 x cm3 mol-l. In both techniques the temperature was controlled to within f 5 mK, and the mole fraction was known to within & 1 x The temperature scale agrees with the IPTS-68 within f0.02 K.C,F, and C,H, were the same as used in a previous work;4 the 2,2,4-TMP was Philips- Petroleum, Research Grade, with a minimum purity of 99.9% in mole fraction. Its density at 298.15 K was 0.68769, which compares favourably with the recommended value of 0.6878.8 The refractive index of 2,2,4-TMP at 303.15 K was n, = 1.391 49, while the literature value is n, = 1.391 45.9 Results and Discussion The Binary System Table 1 shows the V z data for the C6F,-2,2,4-TMP system at 298.15 K. The excess properties of the binary system have been fitted to an (m/n) Pade approximant m Z"/X,( 1 -xl) = c A,(2x1 - l)# c Bj(2X, - 1)j (1) i - 0 ! j I o where zE is either V: or GE/RT, x, is the mole fraction of C,F,, and A, and Bj are adjustable parameters with Bo = 1.A regression method based on the maximum likelihood principle has been used to obtain the parameters of eqn ( 1).l0 These are given in table 1 for V: together with their estimated uncertainties, the standard deviations of the variables, the estimated variance of the fit and the residuals of the variables Axl and AV:. Fig. 1 shows the VE results for c,F6-2,2,4-TMP and C,H6-2,2,4-TMP at the same temperature." It can be observed that in the system with C,F, the VE curve has a maximum which is almost three times that of the system with C,H,. This is an expected result since fluorocarbon-hydrocarbon interactions are quite unfavourable,' C,F, is more ordered than C6H6,3 and both breaking correlations of molecular order and unfavourable interactions give rise to positive contributions to V;.l2 Table 2 shows the experimental pT-x, values for the C6F,-2,2,4-TMP system at 298.15,323.15 and 348.15 K.The thermodynamic consistency of the data has been tested following a version of Barker's method described previously,13 assuming that the composition dependence of G:/RT is described by eqn (1). Table 2 gives the smoothing coefficients and their uncertainties, the values of the residuals of the variables, Axl and Ap, the activity coefficients, y1 and yz, the G: values and their estimated uncertainties, AG:, calculated from the variance-covariance matrix of the parameters of eqn (1).Fig. 2 shows the three G t curves as well as the corresponding curve for the C&,- 2,2,4-TMP system at 298.15 K. One can easily understand the fact that GE for the C6F,-2,2,4-TMP system is larger than that for C6H,-2,2,4-TMP, considering the positive contribution to G: of the unfavourable fluorocarbon-hydrocarbon interactions and the high degree of enthalpic-entropic compensation of the order contribution^.'^ Similar curves have been found for the systems with n-C16H34 and with n-C14H30;4 however, it is not clear why the difference of the maxima of G: for the systems withJ. Aracil et al. 54 1 Table 1. Experimental excess volume data, their deviations from the smoothed values, and smoothing coefficients and standard deviations for system x,(C,F,)-( 1 - x,) (2,2,4-trimethyl- pentane) at 298.15 K x1 V3cm3 mol-' A V z / lo-, cm3 mol-' x, V3cm3 mol-I A V z / low3 cm3 mol-' 0.0724 0.1374 0.2023 0.2794 0.31 17 0.4082 0.4809 0.5377 0.5585 0.3386 0.6086 0.8313 1.9724 1.1402 1.2955 1.3650 1.3777 1.3716 1.4 6.5 - 0.5 -11.3 - 2.8 8.8 2.7 0.5 I .8 0.581 1 0.6375 0.6516 0.6791 0.7019 0.7 139 0.7382 0.7683 1.3661 1.3131 1.2970 1.2469 1.2074 1.1750 1.1261 1.0417 - 3.5 -2.5 -5.1 1.6 - 1.7 5.4 - 1.8 2.3 A , = 5.5004+0.0091; A, = 0.5735k0.0377; A, = 0.1502+0.0617; A , = 0.0878+0.140; o(x) c loe5; o(V3cm3 mol-') = 4.6 x lop3.2'/' / / \ \. \ 0 0.2 0.6 0.6 0.8 1 X Fig. 1. Excess volumes of the C,F,-2,2,4-TMP (---.- ) and C,H,-2,2,4-TMP (- ) systems at 298.15 K. 2,2,4-TMP is only ca. 80 J mol-', while for the corresponding systems with n-C16H34, at the same temperature, that difference is more than 500 J m01-l.~ An unrealistically large free volume contribution' would be necessary to account for such differences. The HE values have been estimated from the temperature dependence of GE.Both the Gibbs-Helmholtz equation and the procedure developed by Munsch have been used. l5542 Thermodynamics of Fluorocarbon- Hydro carbon Mixtures Table 2. Experimental and calculated variables from vapour pressure data, their deviations from smoothed values, and smoothing coefficients and standard deviations for system xl(C,F,) 41- x l ) (2,2,4-trimethylpentane) at 298.15, 323.1 5 and 358.15 K x, lo6 Ax, p/kPa Ap/Pa GZ/J mol-l AGg/J mol-' Y 1 Y 2 0 0.1114 0.1202 0.2099 0.2984 0.3816 0.4059 0.4496 0.466 1 0.4927 0.5088 0.5500 0.5606 0.603 1 0.6436 0.6887 0.731 1 0.7618 0.7962 1 .o 0 0.1114 0.1202 0.2099 0.2984 0.3816 0.4059 0.4496 0.466 1 0.4927 0.5088 0.5500 0.5606 0.603 1 0.6436 0.6887 0.73 1 1 0.7618 0.7962 1 .o 0 0 0 0 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 -1 -1 0 - 1 0 1 0 0 0 0 1 0 1 -1 -1 0 6.578 8.260 8.370 9.229 9.881 10.372 10.505 10.717 10.794 10.906 10.973 11.125 11.161 11.299 1 1.408 11.516 1 1.594 1 1.638 1 1.667 1 1.269 19.533 23.490 23.755 26.161 28.093 29.616 30.0 16 30.678 30.917 3 1.297 31.500 32.006 32.131 32.592 32.999 33.374 33.708 33.901 33.995 34.099 0 5 -5 -1 0 5 0 0 -3 -1 -3 0 1 -1 3 - 1 -1 -2 3 0 0 -4 -4 -3 7 8 5 10 7 -9 -2 -3 -6 -6 - 19 -6 - 25 -21 72 0 298.15 K" 0 200 213 327 407 457 467 48 1 484 488 489 488 487 479 465 442 41 3 387 353 0 323.15 Kb 0 153 163 257 326 372 381 394 398 402 403 403 402 395 383 364 339 316 287 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 2.3530 1.8598 1.8322 1.6076 1.4553 1.3496 1.3234 1.2806 1.2657 1.2428 1.2297 1.1980 1.1903 1.1610 1.1353 1.1089 1.0860 1.0706 1.0547 1 .oooo 1.7808 1 S743 1.5607 1.4390 1.3425 1.2676 1.248 1 1.2153 1.2037 1.1856 1.1752 1.1499 1.1437 1.1201 1.0995 1.0785 1.0607 1.0490 1.037 1 1 .oooo 1 .0000 1.0133 1.0153 1.0416 1.0774 1.1200 1.1343 1.1625 1.1741 1.1939 1.2068 1.2427 1.2527 1.2969 1.3460 1.4109 1.4848 1.5484 1.6328 2.7948 1 .ow0 1.007 1 1.0083 1.0245 1.049 1 1.0805 1.0915 1.1134 1.1225 1.1382 1.1484 1.1769 1.1848 1.2197 1.2578 1.3072 1.3615 1.4067 1.4643 2.0742J.Aracil et al. 543 Table 2. (cont.) x, lo5 Ax, p/kPa Ap/Pa G:/J mol-' AGZ/J mol-' Y1 Y 2 0 0.1091 0.2077 0.2967 0.3803 0.4485 0.4583 0.4908 0.4979 0.5485 0.5599 0.6019 0.6467 0.6879 0.7305 0.7524 0.7960 1 .o 0 3 -1 -4 -2 -2 10 -3 0 -1 0 0 0 0 1 -1 -1 0 48.252 56.936 62.859 67.320 70.999 73.678 74.124 75.207 75.472 77.155 77.524 78.797 80.046 8 1.099 82.090 82.525 83.354 84.750 348.15 K" 0 0 -11 140 3 230 19 288 13 324 14 342 - 67 343 18 347 1 348 6 348 -1 347 -2 342 0 332 -2 317 - 12 297 13 284 6 255 0 0 0 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 0 1.6843 1.4609 1.3363 1.2579 1.2019 1.1646 1.1597 1.1443 1.1410 1.1191 1.1145 1.0980 1.0817 1.0676 1.0539 1.0473 1.0348 1 .oooo 1 .oooo 1.0078 1.0247 1.0457 1.0703 1.0944 1.0982 1.1 116 1.1 147 1.1387 1.1446 1.1684 1.1979 1.2299 1.2692 1.2925 1.3468 1.91 18 a A, = 0.7896+0.0003; B, = -0.0772k0.0009; B, = -0.1550+0.0019; a@) = 2Pa; a(x,) = 1 x lop6.A, = 0.5997+0.0009; B, = -0.1095+0.0038; B, = -0.0690+_0.0073; a@) = 19Pa; 18Pa; a(xl) = 3 x lop5. ~(x,) = 5 x ' A, = 0.48 12 & 0.004; B, = - 0.0902 f 0.0024; B, = - 0.1676 f 0.0043; a($) = 500 L 00 - I I E 2 300 W E u 2 oc 1 oc I I I I Fig. 2. Excess Gibbs energy of the C,F,-2,2,4-TMP system at 298.15 K (- ), 323.15K (----), 348.15 K (-*--- ) and of the C,H,-2,2,4-TMP system at 298.15 K (---------).544 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures Table 3. Maximum values excess properties for C6F6--hydocarbon systems at 298.15 K cosolvent G:/J mol-1 H:/J mo1-l TSZ/J mol-l V3cm3 mol-1 C,F,-cosolvent 2,2,4-TMP 489 1740 1252 I .37 c-C,H,,~ 776 1517 74 1 2.57 678 - 2.13 2.19 n-C16H34 624 - - - n-C14H30 C,H,-cosolvent 2,2,4-TMP * 409 990 58 1 c-C6H12 383 420 800 n-C14H30 23 I 1260 1030 n-C16H34 127 1400 1272 0.5 0.65 1.10 1.17 a At 303.15 K.Table 4. Characteristic parameters of the pure substances for the Flory-Prigogine-Patterson model at 298. I5 K substance p*/J v*/cm3 mol-' P / K P C6F6 635 87 4361 1.332 2,2,4-TMP 372 129 4728 1.287 628 69 4709 1.292 4720 1.291 c-C6H12 540 84 C6H6 From the disagreement between both methods we estimate an uncertainty of 18 % in Hg. The HE curves are symmetric around x, = 0.5, and the calculated values at that composition are 1740, 1300 and 920 J mol-1 at 298.15,323.15 and 348.15 K, respectively. Most the work done in discussing order effects in mixtures is based on the use of a globular molecule which acts as an order breaker.1*2114 Probably the most frequently used order-breakers have been c-C,H,, and 2,2,4-TMP. The existing work seems to indicate that methyl and methylene groups can be considered as equivalent in mixtures of alkanes with c-C6H12, CCl, or C,&.1'2 Since both C6Fe3 and C6H6' present some degree of orientational order, it is worth comparing the behaviour of their binary systems with C-C6H12 and 2,2,4-TMP. Table 3 shows the equimolar excess functions for these systems, and it can be observed that in the systems with C,F, they are larger than in those with C6H,.In order to discuss these values in terms of the usual energetic, free volume and order contributions,' the characteristic parameters of the pure components for the Prigogine-Flory-Patterson theory16 at 298.15 K are shown in table 4.As it can be seen, the most important differences between 2,2,4-TMP and C-C6H12 lie in their p* values. The so-called p* effect," if noticeable for these systems, would give a larger positive VE contribution for the 2,2,4-TMP system than for that with c-C6H12; however, the fact that Vg is very similar for the corresponding systems with C,H, seems to indicate that this effect is not important in this case since C6F6 and C,$6 have almost the same p* values. Moreover, the free-volume contribution (negative for VE and HE)l must be larger for the systems with C6F6 according to the reduced volume D values in table 4. The difference in interactions between the components gives rise to positive contributions to VE, 7's: and H z , in accordance with the differences between the excess functions of the systems with C6F6 and those with C6H6.Nevertheless, whilst TSE andJ . Aracil et al. 545 1.0 0 -1.0 d 5 -2.0 -3.0 -4.0 I i 0 0 2 0 4 0 6 0 8 1 X 1 0 -1.5 LL----+ 02 O L 0.6 0.8 X Fig. 3. (a) Excess number of neighbour molecules around a C,F, (or C,H,) molecule as defined in eqn (2), T = 298.15 K. C,F,-n-C,,H3, (- ) ; C,F,-n-C,,H,, (---) ; C6F,-2,2,4-TMP Bars indicate the estimated uncertainty. (b) Excess number of neighbour molecules around an alkane molecule as defined in eqn (2). Symbols as in (a). (-.-. ); C6H6-n-C1,H30 (- ); C,H,-n-C,,H,, (---); C6H,-2,2,4-TMP (-.-a- 1 HE are larger for the system C6F,-2,2,4-TMP than for C,F,-c-C,H,,, the opposite holds for Vg.We can conclude that 2,2,4-TMP and c-C,H,, show quite different volumetric and entropic behaviours when mixed with C,F,, while their behaviour is much more similar when mixed with other hydrocarbons like C,H,. However, from the energetic point of view the differences are not so important (recall that HZ for C6F,-2,2,4-TMP has an 18 % uncertainty). For the sake of completeness we have included in table 3 the maxima of GE and V: curves for the systems n-C16H34 and n-C14H3,, with C,F, or C6H6e4 Whether the differences found between the systems with 2,2,4-TMP and c-C,H,, are due to the different behaviour of methyl and methylene groups, or to the ring shape of c-C,H,, cannot be discussed with the present data. Experiments involving other octane isomers with different methyl to methylene ratios and methylcyclohexanes would be helpful in order to clarify this point.Further insight into the behaviour of these systems can be obtained from the so-called Kirkwood-Buff integrals. l8 These can be calculated from experimental data, the main contributions coming from the GE and V z ~a1ues.l~ This is interesting since these magnitudes show the most important differences in the systems discussed above. From the Kirkwood-Buff integrals one can calculate the quantity (2) N " ANj = x j v l 0 krj(r)-gjj(r)]4nr2drul P Q\ Table 5. Liquid phase compositions, xi, vapour pressures, p, vapour phase compositions, ys, activity coefficients, yi, excess Gibbs energy, G:, calculated from the PDA for the C,F6-C,H,-2,2,4-TMP system (residuals of the variables are also shown) y3 GE/J mol-' xl 105Ax1 x2 105Ax, p/kPa Ap/kPa y1 Y2 Y1 Y 2 0.6810 0.5969 0.5322 0.4810 0.4392 0.4045 0.3763 0.3472 0.0954 0.0764 0.0630 0.05 17 0.043 1 0.0360 0.0301 0.4174 0.3418 0.2878 0.2477 0.1985 0.1456 0.1042 0.0832 0.2754 0.1917 0.1421 0.1 120 0.0921 0.0762 0.0650 -1 -4 3 0.1 -4 6 ' 2 0.2 -4 -0.1 11 -0.8 -1 1 -3 2 12 16 - 0.8 4 26 28 6 20 0.2 0.3 - 16 6 12 6 0.1448 -1 0.2504 -2 0.3317 1 0.3959 -0.1 0.4485 2 0.4919 12 0.5274 1 0.5639 -0.1 0.21 14 8 0.3688 0 0.4796 11 0.5731 -0.4 0.6440 0.3 0.7025 0.3 0.7514 7 0.1061 -1 0.2680 -13 0.3838 -21 0.4695 6 0.5749 -16 0.6883 -17 0.7769 5 0.8218 0.1 0.3231 -20 0.5289 6 0.6508 -4 0.7247 1 0.7736 -0.2 0.8126 -0.7 0.8403 5 298.15 K 11.955 -0.193 12.018 -0.006 12.099 0.075 12.197 0.079 12.336 0.005 12.450 - 0.065 12.563 -0.120 12.705 -0.181 10.515 -0.172 11.827 0.069 12.608 0.034 13.120 -0.075 13.429 -0.188 13.611 -0.272 13.692 -0.316 11.317 0.057 11.829 0.015 12.192 0.145 12.478 0.272 12.871 0.332 13.228 0.283 13.365 0.177 13.386 0.096 12.572 -0.399 13.232 -0.172 13.492 0.088 13.549 -0.047 13.545 -0.036 13.524 -0.048 13.483 -0.053 0.6010 0.4546 0.3555 0.2879 0.2407 0.2078 0.1832 0.1602 0.1591 0.1 177 0.1015 0.0898 0.0805 0.07 17 0.0632 0.5253 0.3541 0,2504 0.1905 0.1354 0.0946 0.07 12 0.0606 0.2762 0.1517 0.1068 0.0862 0.0743 0.0648 0.0587 0.086 1 0.1660 0.2524 0.3355 0.4 107 0.4742 0.5264 0.5785 0.3786 0.5612 0.6328 0.6749 0.7020 0.7250 0.7486 0,1440 0.3558 0.4835 0.5624, 0.6422 0.7 160 0.7766 0.8106 0.4284 0.6039 0.68 15 0.7298 0.7640 0.7941 0.8 175 0.9034 0.7843 0.689 1 0.61 75 0.5649 0.5287 0.5012 0.4761 1.4599 1.4972 1.6546 1.8440 2.0185 2.1750 2.2973 1.2336 1.0430 0.8885 0.7948 0.7 177 0.6944 0.7319 0.778 1 1.0579 0.8571 0.8202 0.8388 0.8754 0.9191 0.9700 0.5081 0.5856 0.6899 0.7834 0.8589 0.9 138 0.9559 0.9936 1.433 1 1.3905 1.2915 1.2024 1.1409 1.0962 1.066 1 1.1302 1.1886 1.1783 1.1546 1.1171 1.0741 1.0463 1.0357 1.2695 1.1693 1.0998 1.0654 1.0467 1.0358 1.029 1 3.1076 4.5103 5.3663 5.7602 5.8591 5.7958 5.6798 5.5304 1.0262 1.0409 1.0936 1.1804 1.2794 1.3906 1.5017 1.1917 1.3544 1.5721 1.7839 2.0892 2.4436 2.6727 2.7351 1.2758 1.6470 1.9724 2.1855 2.3204 2.4005 2.4384 75 - 121 - 230 - 280 - 298 - 298 - 289 -271 322 432 484 494 476 443 40 1 456 443 440 432 408 358 296 256 47 1 477 432 38 1 337 296 264323.15 K 0.6810 - 1 0.5969 0 0.5322 -2 0.48 10 2 0.4392 0 0.4045 -0.1 0.3763 -3 0.3472 3 0.0954 2 0.0764 3 0.0630 1 0.0516 0.2 0.0431 -2 0.0360 -29 0.0301 1 0.4172 1 0.3418 -10 0.2877 -3 0.2477 -2 0.1985 2 0.1456 2 0.1042 1 0.0832 3 0.2754 3 0.1917 -6 0.1421 6 0.1120 6 0.0921 2 0.0762 -2 0.0650 -5 0.1448 0.2504 0.3317 0.3959 0.4484 0.4919 0.5274 0.5639 0.21 13 0.3688 0.4796 0.573 1 0.6441 0.7025 0.7514 0.1061 0.2679 0.3837 0.4694 0.5749 0.6883 0.7769 0.8218 0.3230 0.5288 0.6508 0.7247 0.7736 0.8126 0.8403 -1 -1 -2 2 2 1 - 5 -2 -7 -6 -2 -6 -6 2 -7 2 -2 2 -3 -2 -1 -4 6 12 -7 -4 -5 -0.1 2 0.4 34.583 0.018 34.799 - 0.122 35.020 -0.044 35.278 -0.071 35.516 0.015 35.722 0.035 35.938 0.074 29.398 0.164 33.007 0.303 35.032 0.070 36.173 - 0.027 36.3 19 - 0.250 37.03 1 - 0.434 37.41 5 - 0.477 37.596 - 0.45 1 31.249 0.266 32.576 -0.344 33.741 -0.152 34.596 - 0.03 1 35.584 0.022 36.438 0.024 36.797 0.102 36.896 0.125 32.418 0.454 34.735 0.601 36.047 0.296 36.649 0.117 36.964 -0.005 37.103 -0.048 37151 -0.064 0.72 12 0.629 1 0.5545 0.4972 0.4498 0.41 12 0.3805 0.3488 0.1556 0.1082 0.0849 0.0662 0.0525 0.0417 0.0334 0.5 157 0.3522 0.2674 0.2187 0.1699 0.1263 0.0957 0.0802 0.2737 0.1664 0.1222 0.0987 0.0839 0.0721 0.0639 0.1464 0.2705 0.3619 0.4296 0.4843 0.5284 0.5633 0.5991 0.3507 0.5257 0.6062 0.6562 0.6944 0.7299 0.7635 0.1203 0.3444 0.47 1 5 0.5486 0.6350 0.7245 0.7953 0.83 10 0.43 13 0.6 100 0.6975 0.7519 0.788 1 0.8183 0.8400 1.0556 1.0393 1.021 1 1.0070 0.991 5 0.9788 0.9688 0.9569 1.2257 1.1684 1.1497 1.1160 1.0692 1.0187 0.9733 1.0708 0.9019 0.8202 0.7833 0.7625 0.7713 0.8083 0.841 5 0.8479 0.7578 0.7585 0.7776 0.80 17 0.8288 0.8565 0.81 11 0.9104 0.9549 0.9765 0.9932 1.0042 1.0115 1.0192 1.2355 1.2396 1.1735 1.1109 1.0728 1.0504 1.0373 0.8296 1.0515 1.0738 1.064 1 1.0508 1.0396 1.0298 1.0236 1.1 127 1.0670 1.0429 1.0339 1.0284 1.0235 1.0193 1.2124 1.1267 1.0982 1.089 1 1.0890 1.0911 1.0944 1.0987 1.0730 1.0815 1.1367 1.2236 1.3090 1.3847 1.4475 1.1909 1.2649 1.3519 1.426 1 1.4982 1.5346 1.5472 1.5638 1.2732 1.457 1 1 S377 1.5613 1.5707 1.5838 1.6008 108 48 23 12 7 6 7 10 303 36 1 387 380 355 323 289 247 188 186 185 178 161 141 127 23 1 232 207 184 166 149 136548 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures Table 6.Parameters of partial differential ap- proximants for the ternary system xl(C6F6)-x2 (C6H6)-x3(2,2,4-TMP) 298.15 K 323.15 K uoo 0.4983 UlO UNl - 5.2794 - _ _ UOl 0.3214 16.190 - - 4 2 u21 u22 - PlO - 1.0464 POI - 1.0865 4 1 0.6426 dP)/kPa 0.172 104+,) 1 1044x2) 1 1 02a( T)/K 2 - 1.61 16 -3.8081 5.5081 0.8792 - 3.2822 - 3.1628 - 5.6578 12.652 18.659 - 0.241 6 4 0 where N / V is the number density of the mixture and gij(r) is the radial distribution function of the i-j pair.ANj is a measure of the difference between the distribution o f j molecules around an i molecule and around a j Fig. 3 shows ANl and AN2 at 298.15 K for the systems considered in this paper. The ANl values indicate that the aromatic molecules preferentially surround other aromatic molecules rather than alkane molecules. The AN, values indicate that the alkane molecules tend to surround other alkane molecules for x, > 0.5, while they tend to surround aromatic molecules for high alkane concentrations.The final distribution arises from the competition between both tendencies. It has been pointed out that n-alkanes show some degree of orientational correlations with C,H,, toluene or p-xylene.2 The values AN2 > 0 seem to indicate that those correlations contribute to stabilize the n-alkanes in the solution, whilst according to the values ANl < 0 in the same concentration interval, they seem to be unfavourable for the aromatic molecules. The curves corresponding to mixtures of 2,2,4-TMP with C,F, or with C,H, are very similar, the differences being due mainly to the differences in molar volumes between C,F, and C,H,.Also the behaviour of the systems with n-CI6H3* and n-C,,H,, are similar when mixed with C,F, (or C,H,), although there are some quantitative differences between the two pairs of curves corresponding to each aromatic molecule, confirming the tendency of fluorocarbons and hydrocarbons to segregate. ’ The Ternary System Table 5 shows the vapour-pressure data for the x~(C,F,)-~,(C,H,)-~~(~,~,~-TMP) system at 298.15 and 323.15 K. The data reduction has been carried out by a modified Barker’s method described previ~usly.~ The concentration dependence of GE for the ternary system has been described by where the GE(ij) are the excess Gibbs energies of the i-j binary systems, and GF,, is a ternary contribution.The GZ(iJ3 for the C,F,-C,H, system has been calculated from theJ . Aracil et al. 549 Fig. 4. (a) Concentration triangle for the ternary system including the G: curves of the three binary systems at 323.15 K. (b) GZ surface for the ternary system calculated from the PDA, eqn (4). The parameters of the ternary contributions are given in table 6. data of Gaw and Swinton,,, for C6H6-2,2,4-TMP it has been taken from the work of Funk and Prausnitz,22 and for C,F,-2,2,4-TMP the results in table 1 have been used. As in ref. (4) we have investigated the correlation abilities of several expressions for G,E,m but for the sake of brevity we will only report on the one which gave the best results : (4) i "' "* m1 mz j = O j ' = O 1 = 0 Z ' = O G,E,,/RTxlx2x3 = C C Ujj,z:zi C C Pll,z;z;.Eqn (4) is a partial differential approximant, PDA, in which z, = x, - x,, z, = x, - x, and Uijr, and P,l, are the adjustable parameters. Table 6 gives the values of the parameters550 Thermodynamics of Fluorocarbon-Hydrocarbon Mixtures of the optimal PDA, as well as the standard deviations of the variables, the activity coefficients, vapour-phase compositions and GE values. Fig. 4(a) shows the triangle of compositions for the ternary system and the GE (ij) curves for each of the three binary systems. Fig. 4(b) shows the GZ surface of the ternary system referred to the same triangle of compositions. The main feature is a minimum placed near the C6F6 corner of the composition triangle. Similar behaviour was found by Anderson et aZ.23 in their study of the C,F,-C6H6-CS, system. However, the standard deviations in vapour pressures and compositions shown in table 6 are much larger than the experimental errors.This leads to an uncertainty in the G: values of f 10 J mol-1 at the centre of the composition triangle. Since the calculation of the AN,, eqn (2), involves derivatives of G: with respect to composition, much more precise G: data than those reported in table 5 are needed for a detailed discussion of the way the molecules are distributed in the ternary solution. References 1 S. N. Bhattacharyya, M. Costas, D. Patterson and H. V . Tra, Fluid Phase Equilibria, 1985, 20, 27; A. Heintz and R. Lichtenthaler, Angew. Chem., Int. Ed. Engl., 1982, 21, 184. 2 R. G. Rubio, C. Menduiiia, M.Diaz Peiia and J. A. R. Renuncio, J. Chem SOC., Faraday Trans. 1,1984, 80, 1425; G. Tardajos, E. Aicart, M. Costas and D. Patterson, J. Chem. SOC., Faraday Trans. I , 1986, 82, 2977. 3 M. R. Battaglia, T. I. Cox and P. A. Madden, Mol. Phys., 1979, 37, 1413; P. A. Madden, M. R. Battaglia, T. I. Cox, R. K. Pierens and J. Champion, Chem. Phys. Lett., 1980, 76, 604; E. Bartsch, H. Bertagnolly, G. Schulz and P. Chieux, Ber. Bunsenges. Phys. Chem., 1985, 89, 147. 4 J. Aracil, R. G. Rubio, M. Caceres, M. Diaz Peiia and J. A. R. Renuncio, Fluid Phase Equilibria, 1986, 31, 7 1 ; J. Aracil, R. G. Rubio, J. Nuiiez, M. Diaz Peiia and J. A. R. Renuncio, J. Chem. Thermodyn., 1987, 19, 605. 5 E. Wilhelm, Thermochim. Acta, 1985, 94, 47. 6 M. E. Saint Victor and D. Patterson, Fluid Phase Equilibria, 1987, 35, 237. 7 F. L. Swinton, in Chemical Thermodynamics. A Specialist Report, ed. M. L. McGlashan (The Chemical 8 D. Rossini, API Research Project No. 44, 1954. 9 J. A. Riddick and W. B. Bunger, in Organic Solvents. Physical Properties and Methodr of Purification Society, London 1978), vol. 2. (Wiley-Interscience, New York, 1970). 10 T. F. Anderson, D. S. Abrams and E. A. Grens, AIChE J., 1978, 24,20. I I Y-P. Handa and G. C. Benson, Fluid Phase Equilibria, 1979, 3, 185. 12 M. Barbe and D. Patterson, J. Solution Chem., 1980, 9, 753. 13 R. G. Rubio, J. A. R. Renuncio and M. Diaz Peiia, Fluid Phase Equilibria, 1983, 12, 217. 14 M. Barbe and D. Patterson, J. Phys. Chem., 1987,82, 40. 15 E. Munsch, Thermochim. Acra, 1979, 32, 151. 16 P. J. Flory, J. Am. Chzm. SOC., 1965, 87, 1833. 17 H. T. Van and D. Patterson, J. Solution Chem., 1982, 11, 793. 18 J. G. Kirkwood and F. Buff, J. Chem. Phys., 1951, 19, 774; A. Ben Naim, J. Chem. Phys., 1977, 67, 4884. 19 E. Matteoli and L. Lepori, J . Chem. Phys., 1984, 80, 2856; R. G. Rubio, M. G. Prolongo, M. Cabrerizo, M. Diaz Peiia and J. A. R. Renuncio, Fluid Phase Equilibria, 1986, 26, 1 ; R. G. Rubio, M. G. Prolongo, J. A. R. Renuncio and M. Diaz Peiia, J. Phys. Chem., 1987,91, 1177. 20 E. D. Crozier, S. P. McAlister and R. Turner, J. Chem. Phys., 1974, 61, 126. 21 W. J. Gaw and F. L. Swinton, Trans. Faraday SOC., 1968, 64, 2023. 22 E. W. Funk and J. M. Prausnitz, Znd. Eng. Chem., 1970,62, 8. 23 D. Anderson, R. J. Hill and F. L. Swinton, J. Chem. Thermodyn., 1980, 12,483. Paper 7/581; Received 1st April, 1987