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The excess enthalpies of (carbon dioxide + n-hexane + toluene) at 358.15 K and 7.50 and 12.50 MPa
O-265 J. Chem. Thermodynamics 1!%8,20, 559-568
The excess enthalpies of (carbon dioxide + n-hexane + toluene) at 358.15 K and 7.50 and 12.50 MPa C. PANDO, J. A. R. RENUNCIO, Facultad de Quimica, Oviedo, Spain 33007
Universidad de Oviedo,
P. W. FAUX, J. J. CHRISTENSEN,t and R. M. IZATT Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. (Received 21 September 1987) The excess molar enthalpies Hi{x,CO, +x2C,H,,+(1 -xi -x&H&H,} were measured at 358.15 K and 7.50 and 12.50 MPa with an isothermal flow calorimeter. Results are compared with those previously obtained at 413.15 K and 7.50 MPa and 12.50 MPa and the effect of a temperature decrease on H,f, for the two isobars is discussed. Toop’s equation was found to provide accurate predictions of ternary His. Correlation methods were also examined. It was found that ternary HEs can give information about vapor and liquid equilibrium-phase compositions under certain conditions.
1. Introduction A program is under way in this laboratory to measure excess molar enthalpies Hz at supercritical conditions for (carbon dioxide + a hydrocarbon). Studies of Hi are presently being extended to ternary mixtures because of the industrial importance of multicomponent mixtures. (Carbon dioxide + n-hexane + toluene) was chosen for the initial study. This is composed of carbon dioxide (extensively used in supercritical extraction techniques), n-hexane (a representative straight-chain hydrocarbon), and toluene (a representative of aromatic compounds found in petroleum products). Hks have been determined in this laboratory for (carbon dioxide + n-hexane),(‘* ‘) (carbon dioxide + toluene),‘3’4’ and (n-hexane + toluene),(5’ over the temperature range 308.15 to 573.15 K and pressure range 7.50 to 12.50 MPa. His for (carbon dioxide + n-hexane + toluene) at 413.15 K and 7.50 and 12.50 MPa have been reported. f6) The present work reports Hzs for this ternary mixture at 358.15 K and 7.50 and 12.50 MPa. By acceptance of this article, the publisher acknowledges the right of the U.S. Government to retain a non-exclusive royalty-free license in and to any copyright covering this paper. 7 Died 5 September 1987.
560
C. PANDO ET AL.
The H$ for the three binaries and the ternary should provide a consistent set of results for testing techniques for correlating HE, for ternary mixtures and for predicting ternary H,!$ from binary HLs. Methods for correlating and predicting ternary Hzs have been examined and tested for 42 sets of ternary results.(‘) The equations and procedures found in that study which best correlate and predict ternary Hf,s were used in this paper.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (8-9) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure IX0 syringe pumps supplied at a constant rate the two fluids to be mixed. The total flow rate was between 0.0056 and 0.0139 cm3.s-l (4.3 x 10V5 and 1.3 x 10e4 mol.s-‘) for the temperature and pressures studied. Hzs were determined using CO, in one pump and in the other. Three mixtures having mole fractions WJ%4 + (1 -KA’W~ x = 0.25, 0.50, and 0.75 were used. Three complete sets of pseudobinary HE, determinations, one with each mixture, were made over the range of x1 from 0 to 1. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over most of the mole-fraction range (0.2 < x < 0.8).t8) Reproducibility of results in the present investigation was + 1 to +2 per cent. The materials employed and the calculation of the densities used to evaluate mole fractions from flow rates were described previously.@’
3. Results and discussion Excess molar enthalpies were determined for (xrC0, + x$Z,H,, + (1 -x1 -x&H,CH,} at 358.15 K and 7.50 and 12.50 MPa. The results are given in table 1. The excess molar enthalpies of the three related binary mixtures, (xC0, + (1 -x)C,H,,), {Xco, + (1 -X)c,H,cH,), and (xc,H,~ + (1 -X)c6H5cH3) under the same conditions of pressure and temperature have already been reported. (lV5) A correlation equationt5) was used to evaluate the excess molar enthalpies of (0.2sc6H14 + 0.75C,H,CH,), (0.50C6H1, + O.SOC,H,CH,), and (0.75C6H,, + 0.25C6H5CH,), which were then added to Hzs for the pseudobinary [CO2 + (xC6H14 + (1 -X&H&H,}] to give His for the ternary mixture. In a previous paper,“’ we examined methods for correlating and predicting ternary excess enthalpies. Ternary His are usually represented as a sum of a binary and a ternary contribution:
Hz = C HE,ij+HE,,. i
(1)
The binary contribution, Zi
H:{x,CO, TABLE
1. Experimental,
predicted,
Hg(J.
Xl
+x,CsH,,+(l and correlated (1 -x1 -x&H&H,}
-x1
excess molar enthalpies at 358.15 K
mol-‘)
expt
pred.
561
-x&H,CH,}
Xl
HE{x,CO,
H3(J.
x2
corr.
expt
+ x&HI4
molpred.
+
‘) corr.
p = 7.50 MPa 0.0752 0.1107 0.1450 0.1781 0.2101 0.2410 0.2709 0.2998 0.3549 0.3812 0.4067 0.4314 0.4554 0.4786 0.5012 0.5232
0.2312 0.2223 0.2138 0.2055 0.1975 0.1898 0.1823 0.1751 0.1613 0.1547 0.1483 0.1421 0.1362 0.1304 0.1247 0.1192
-33 -184 -284 -497 -716 - 1010 - 1080 - 1380 - 1620 - 1930 - 1930 - 2050 -2130 - 1980 - 1930 -1780
-23 -215 -405 -592 -778 -961 -1140 -1310 -1640 - 1790 - 1930 -2060 - 2050 - 1960 -1870 - 1770
27 -154 -341 - 533 -727 -921 -1110 -1300 -1650 - 1820 - 1970 -2100 -2100 -2010 - 1920 - 1830
0.5446 0.5653 0.6052 0.6611 0.7129 0.7453 0.7762 0.8199 0.8338 0.8864 0.9230 0.9461 0.9573 0.9683 0.9791 0.9896
0.1138 0.1087 0.0987 0.0847 0.0718 0.0637 0.0560 0.0450 0.0415 0.0284 0.0193 0.0135 0.0107 0.0079 0.0052 0.0026
-1720 -1560 - 1350 -1110 -816 -672 -448 -291 - 182 87 220 335 379 418 336 168
- 1680 - 1590 - 1410 -1140 - 880 -712 - 549 -314 -238 47 237 346 391 280 250 166
- 1730 -1640 - 1450 -1160 -884 - 707 -536 -296 -220 63 248 352 395 283 251 166
0.0789 0.1160 0.1516 0.1859 0.2189 0.2507 0.3109 0.3669 0.4193 0.4442 0.4683 0.4916 0.5142 0.5574 0.5981
0.4606 0.4420 0.4242 0.4071 0.3906 0.3747 0.3446 0.3166 0.2904 0.2779 0.2659 0.2542 0.2429 0.2213 0.2009
237 91 -290 -365 -550 - 802 -1200 - 1560 -1900 -2010 - 2030 - 1950 - 1850 - 1630 - 1410
107 -87 -283 -480 -675 - 865 - 1230 - 1550 -1820 - 1930 - 2020 - 1880 -1800 - 1620 -1440
184 -7 -210 -419 - 628 -832 - 1210 - 1550 -1810 - 1920 -2010 - 1870 - 1780 - 1590 - 1390
0.6364 0.6727 0.7069 0.7394 0.7703 0.7996 0.8274 0.8540 0.8793 0.9035 0.9266 0.9487 0.9594 0.9699 0.9801
0.1818 0.1637 0.1465 0.1303 0.1149 0.1002 0.0863 0.0730 0.0604 0.0482 0.0367 0.0256 0.0203 0.0150 0.0100
- 1210 -988 - 780 -715 -430 -291 -119 9 138 263 370 451 479 445 299
- 1250 - 1070 - 880 - 697 -516 -341 -171 -9 145 286 411 507 539 247 192
-1200 -1000 -812 - 628 - 450 - 280 -118 36 180 311 427 516 545 250 194
0.0825 0.1211 0.1935 0.2600 0.3215 0.3784 0.4054 0.4313 0.4564 0.4806 0.5039 0.5265 0.5695 0.6099 0.6477
0.6881 0.6592 0.6049 0.5550 0.5089 0.4662 0.4460 0.4265 0.4077 0.3896 0.3721 0.3551 0.3229 0.2926 0.2642
35 - 249 -573 -819 - 1060 -1260 - 1430 -1540 -1690 -1760 -1840 -1710 - 1470 - 1280 - 1050
35 - 145 - 526 -901 - 1250 -1540 -1660 -1760 -1840 -1900 -1870 -1790 -1610 - 1410 - 1220
77 -96 -465 -826 -1150 - 1420 -1540 - 1630 -1700 -1760 -1721 - 1630 - 1450 -1260 - 1070
0.6834 0.7170 0.7488 0.7789 0.8073 0.8344 0.8600 0.8844 0.9077 0.9299 0.9406 0.9510 0.9613 0.9713 0.9811
0.2375 0.2122 0.1884 0.1658 0.1445 0.1242 0.1050 0.0867 0.0692 0.0526 0.0446 0.0368 0.0290 0.0215 0.0142
-855 -640 - 527 -283 - 147 31 151 303 400 550 576 536 436 333 218
- 1010 -809 -607 -408 -215 -29 147 311 459 583 631 666 283 203 134
-876 -686 -498 -316 -139
0.0831 0.1219 0.1591
0.2292 0.2195 0.2102
135 -27 - 145
113 -12 -134
0.0704 0.0663 0.0625
-2100 - 2070 - 2080
- 2020 - 2030 -2020
- 2040 - 2050 -2040
32 193 345 482 597 641 673 287 206 135
p = 12.50 MPa 157 25 -112
0.7186 0.7346 0.7502
C. PANDO ET AL.
562
TABLE l-continued Xl 0.1946 0.2288 0.2615 0.3232 0.3802 0.4332 0.4825 0.5284 0.5714
0.5919 0.6117 0.6495
0.6851 0.7021 0.087 1 0.1275 0.2028
expt
H,f,/(J.mol-‘) pred
corr.
-250 -376 -491 -713 -939
-252 -368 -481 -698 -904
-249 -384 -513 -757 -978
-1160
-1100 - 1280 - 1450
-1180 -1360
x2
0.2014 0.1928 0.1846 0.1692 0.1550 0.1417 0.1294 0.1179 0.1072 0.1020 0.0971 0.0876 0.0787 0.0745
0.2715 0.3344 0.3923 0.4458 0.4952 0.5411 0.5838 0.6237 0.6610 0.6960
0.4565 0.4363 0.3986 0.3643 0.3328 0.3038 0.2771 0.2524 0.2294 0.2081 0.1881 0.1695 0.1520
0.0910 0.1330 0.2107 0.2811 0.3453 0.4039 0.4577 0.5073 0.5531 0.5955 0.6350 0.6718 0.7061
0.6817 0.6503 0.5920 0.5392 0.4910 0.4471 0.4067 0.3695 0.3352 0.3034 0.2738 0.2461 0.2204
-1340 -1490 -1700 -1780 -1810 -1920 -2040 -2040 242
108 - 157 -365 -555 -764 -902 -1070 -1250 -1410 -1530 -1680 -1750
160 74 -159 -404 -593 -707 -946
- 1010 -1210 -1330
- 1480 - 1570 -1600
-1610 -1690 -1750 -1870 -1960 -2000 242 122 -114 -340 -557 -763 -958 -1140
- 1310 -1460
-- 1590 -1700 -1770 172 74 -124 -323 -518 -706 -885 -1050 -1200 -1340 -1450 -1540
-1600
Xl
-1530 -1670 -1740
-1800 - 1910 -2000 -2020 245 125 -108 -333 -549 -754 -949 -1130 -1300 -1450 -1580 -1690 -1770 136 28 -175 -366 -550 -725 -892
- 1050 -1200 -1330
-1440 -1530 - 1590
x2
expt 0.7654 0.7802 0.7945 0.8354 0.8609 0.8732 0.8969 0.9083 0.9304 0.9514 0.9616
0.9715 0.9812 0.7288
0.7597 0.7888 0.8163 0.8423 0.8669 0.8903
0.9125 0.9336 0.9537 0.9729
0.9821 0.7382 0.7684 0.7967 0.8234 0.8486 0.8724 0.8949 0.9163 0.9365
0.9558 0.9651 0.9741 0.9830
H3(J.mol-‘) pred.
0.0587 0.0549 0.0514 0.0412 0.0348 0.0317 0.0258 0.0229 0.0174 0.0122 0.0096 0.0071 0.0047 0.1356 0.1201 0.1056 0.0919 0.0789 0.0665 0.0549 0.0437 0.0332 0.0231 0.0136 0.0089 0.1963 0.1731 0.1525 0.1324 0.1136 0.0957 0.0788 0.0628 0.0476 0.0332 0.0262
0.0194 0.0128
-2080 -2020 -1790 -1530
-1400 -1100 -913 -580 -398 -191 -85 -37 -1790
-1800 -1730 -1660
-1440 - 1230 -974 -663
-448 -196 -56 -38 -1610
- 1510 -1490 - 1330 -1120 -918 -675 -457 -229 -95 -53 -5
11
-2010 -1970
corr.
-1340 -1210 -976 -824 -536 -298 -202 -125 -66
-2020 -1990 -1940 -1600 -1350 -1210 -977 -825 -536 -298 -202 -125 -66
-1810 -1810 -1760 -1600 -1400 - 1220
-1800 -1760 -1600 -1400 - 1220
- 1930 -1600
-957 -686 -433 -226
-81 -37
-1810
-956 -685 -433 -226 -81 -37
-1620 -1630 -1530 -1420 -1250
-1610 -1620 -1530 -1410 -1240
-1040
-1040
-804 -562 -340
-802 -561 -340
-160
-160
-92 -42
-92 -42 -9
-9
In this study, the Hz,ij values for the three related binaries were calculated as a function of mole fraction using an (n, m) Padt approximant. Hz,ij is given by HE,, ij/(J. mol- ‘) = XiXj
2 A,(xi-xj)’
B,,= 1,
(2)
k=O
where xi and xj are the mole fractions of components i and j, respectively, and Ak and B[ are the parameters. The performance of equation (2) in the correlation of binary excess enthalpies has been discussed elsewhere.(‘) The linear sections
H:{x,CO,
+x,C,H,,+(l
563
-x1 -x,&H&H,}
TABLE 2. Description of Padt approximants (equation 2) and standard deviations s for representation of binary Hz values at 358.15 K Binary mixture xCO,+(l
-x)&H,,
xC0, + (1 -x)&H&H,
xC,H,,+(l-x)C,H,CH,
PIMPa
n, m
7.50 7.50 12.50 7.50 7.50 12.50 12.50 7.50 12.50
3, 2 1. 2
2, 2, 3, 1 1, 2 1, 2 1. 2 1, 0 1, 0
x interval 0.520 > x 0.520 < x O x 0.420 < x 0.800 > x 0.800 < x O
> 0.950 < 0.950 > < > <
0.970 0.970 0.950 0.950
s 58 53 22 22 6 15 17 7 8
occurring in two of the three binary mixtures (corresponding to a two-phase region) were correlated using a (1,2) Pad& approximant, equation (2). The term xixj counterbalances the second-degree polynomial of the denominator resulting in a first-degree polynomial in the composition variable. Table 2 summarizes the equations used to represent H$j for the three binary mixtures comprising the ternary mixture involved in this study. The regression method used was based on the maximum-likelihood principle. The criteria to discriminate between two fittings and to select the best Pad6 approximant has been discussed elsewhere.(“) The predictive equations proposed by Scatchard et aZ,(’ ‘) Toop,” ‘) and Hillert” ‘I were shown to provide accurate and almost coincident HE values for ternary Hf,s. In this study, Toop’s equation was used to predict Hf, for {xlCO, + x&HI4 + (1 -xl -x&H&H,}. This equation is asymmetric with respect to the numbering of the components and is given by H3(J.
x
mol-‘)
kgo
4(2x1
= x1x2 - Ilk (3)
The selection of which component is to be designated as component 1 is critical while components 2 and 3 may be interchanged. It has been shown”) that component 1 should be the most dissimilar component of the mixture. Consequently, carbon dioxide was designated as component 1 for {xlC02 + x&H, + (1 -xl-x&H&H,}. The behavior of the related binary mixtures (14, “) indicates that there should be at 358.15 K and 7.50 MPa a two-phase region for (carbon dioxide + n-hexane) and (carbon dioxide + toluene) and at 358.15 K and 12.50 MPa a two-phase region only for (carbon dioxide + toluene). The boundaries of these regions are indicated in the triangular coordinate representation of figure 1. The intervals ef and gh
564
C. PANDO ET AL.
(4
(b)
FIGURE 1. Representation on triangular coordinates of the three series of Hz determinations (dotted lines represent the path of the approximately 30 points for each series covering the range of x, from 0 to 1) and the boundaries of the two-phase region for (x,CO, + x&HI4 + (1 -x,-x&H&H,J at 358.15 K and (a), 7.50 MPa; and (b), 12.50 MPa.
correspond to the (vapor + liquid) equilibrium regions for (X0, + (1 -x)&H,,} and (xCOz + (1 -x)C,H,CH,). Unfortunately, (vapor + liquid) equilibrium results for {xlCO, + x zC 6H 14 + (1 -x1 -x,)C,H,CH,} are not available and the shapes of the lines connecting e and g, and f and h, respectively, at 7.50 MPa, and the curved line connecting h and g at 12.50 MPa, are unknown. To predict ternary I%!$, we have assumed that these boundaries can be represented approximately by the straight lines fh and eg at 7.50 MPa, and by the straight lines eh and eg at 12.50 MPa. In the latter case, the position of e (x1 = 0.735) is determined as the mean value of the carbon-dioxide mole fractions at the beginning and ending of the two-phase region for (carbon dioxide + n-hexane) at 358.15 K and 7.50 MPa. A similar position for e (x1 = 0.739) is obtained if the two-phase region considered is that at the same pressure, p = 12.50 MPa and at a higher temperature, T = 413.15 K.(@ The predicted values of H~{x,CO, + x,C,H,, + (1 -x1 -x,)CsH,CH,) are given in table 1; the standard deviations between experimental and predicted values are given in table 3. The ratio between the standard deviation and the maximum
TABLE 3. Standard deviations s between experimental values of ternary excess enthalpies for {x1 CO, + + (1 -x1 -x2)C,H,CH3} and values correlated from equation (1) using Toop’s equation for x&H,, the binary contribution and one of several equations for the ternary contribution Equation for HL.T None References 17, 18 Reference 19 Equation (4)
Number of ternary coefficients 0 3 6 4 7 2 4 5 6
p=7SOMPa 95 82 70 75 74 75 75 73 69
’
p = 12.50 MPa 67 66 63 65 60 66 65 61 62
H~{x,CO,+x,C,H,,+(l-x,-x,)C,H,CH,}
565
absolute value of Hfj, was found to be 4 per cent or less. The accuracy of the predictions can be considered satisfactory, especially if we take into account the values of the standard deviations for some of the correlations of,the binary values involved and the variations observed in ternary I&. Figure 2 shows plots of HE against x1 for the three series of determinations performed at each pressure. The full lines represent predicted values of Hz. These plots show that variations of ternary iY:s with x1 for each series are similar to those observed for (xC0, + (1 -x)C,H,,} and (xC0, + (1 -x)&H&H,} at 358.15 K and 7.50 and 12.50 MPa. The values of the minima are intermediate between the minimum value for (xC0, + (l-x)C,H,,} (-1800 J.mol-’ at 7.50 MPa and - 1420 J.mol-’ at 12.50 MPa) and the minimum value for (xC0, + (l-x)C,H,CH,} (-2310 J.mol-’ at 7.50 MPa and -2240 J.mol-’ at 12.50 MPa). Something similar happens with the values of the maxima in the three series of determinations. {x&H,, + (1 -x)&H&H,) shows moderately endothermic mixing (maximum values are 480 J. mol- ’ at 7.50 MPa and
1 0.6 0.8 Xl FIGURE 2. Plot of If: against x,, for {xIC02 + x&H,, + (1 -x1 -x&HSCH,} at 358.15 K and (a), x2/x3 = l/3; (b), xzh = 1; and (c), x*/x3 = 3 as a function of pressure; 0, 7.50 MPa; and A, 12.50 MPa; -. predicted from equation (3). 0
0.2
0.4
566
C. PANDO
ET AL.
500 J .mol-’ at 12.50 MPa) and its contribution to each series of ternary Hi determinations is positive and relatively small. Figure 2 also allows us to make some inferences concerning the phase diagram of (xlCO, +x&H,, + (1 -x, -x$Z,H,CH,}. The fact that Hji, varies linearly with x1 at 7.50 MPa indicates that vapor- and liquid-phase compositions can be determined as the x coordinates of the intersection of the extrapolated straight lines and the curves describing Hz. The good agreement between experimental and predicted values of Hz indicates that the assumption of linearity for the boundaries fh and eg is valid. Predicted values of HE, vary almost linearly with x1. Departures from linearity are due to the relatively small contribution of (n-hexane + toluene). On the other hand figure 2 shows that when pressure is increased to 12.50 MPa, only the series corresponding to mixtures richer in toluene, figure 2(a), seems to exhibit a linear section. These results are a consequence of the fact that at 358.15 K and 12.50 MPa (carbon dioxide + toluene) is the only binary mixture exhibiting a two-phase region. On the other hand, these results also indicate that, as could already have been expected, e should be located in the interior of the (b) triangle of figure 1. The shape of the phase boundary could be estimated from calorimetric measurements if more series of Hi determinations were made but this would require considerable time and effort. Thus, the excess enthalpies taken at 358.15 K and 7.50 MPa provide information concerning (vapor + liquid) equilibrium for {x,CO, + x,C,H,, + (1 -x1 -x&H,CH,} whereas no definitive conclusions can be adopted from the examination of results at 358.15 K and 12.50 MPa. The comparison of figure 2 of this study and a similar figure from our previous study@’ at 413.15 K allows us to examine the effect on the Hz against x1 of a temperature decrease for two isobars. Since both (carbon dioxide + n-hexane) and (carbon dioxide + toluene) have critical loci passing through a maximum, the situation for the ternary mixture is similar to that reported previously for binary mixtures containing carbon dioxide. For Hfi, against x1 as the temperature decreases, the minimum becomes larger and the maximum becomes smaller. This effect has been discussed thoroughly for (carbon dioxide f toluene) by Morrison et Al. H%,CO,
+ (1 -x1 - x&,H,CH,) were correlated using + x&H,, equation (1). The equation used to predict Hz, equation (3), was used to evaluate the binary contribution term Xi, jHz, ij. In a previous paper, the equations used in the literature to represent the ternary contribution HE,, with varying numbers of adjustable ternary coefficients were reviewed and tested, and a partial differential approximant for representing Hz,T was proposed.‘7’ This approximant is the ternary equivalent of a Pad& approximant and is given by
fE.T J . mol-i
=
“r. 4,(x,- .‘c$f ,gl AI(x,- ~3)’+ .rl ,zl 4,(x,- XJYXZ - ~3)’ --,
x1x2x3
1+ 2 B,(x, -x,)"+ II=1
'E, B,(x,-x3)'+
2 n=11=1
% B"&-X3)n(X2-X3)'
(4)
567
H:{x,CO,+x,C,H,,+(l-x1-x,)C,H,CH,J
TABLE 4. Ternary coefficients for correlation of Hk{x,CO, + x zC 6H 14 + (1 -XI-xzG%CH,~ by equation (1) using Toop’s equation for the binary contribution and equation (4) with six coefficients for the ternary contribution
PIMPa
Oh,n2,4, m2)
A0
A,
7.50 12.50
(1, TO, 0) (1, 2, 0, 0)
175.37 219.49
-3711.9 204.89
A2 ~__ A3 ___. 20414 4190.5
5968.9 - 25040
A4____~~ A5 16985 14902
46646 -49618
where A,, A,, A,,*, B,, I?, and B,* are the parameters. Each approximant is represented by indicating the values adopted by n,, n2, m,, and m2 as (n,, n2, m,, mJ. The (1, 0, 0,O) approximant has two ternary coefficients, the (1, 1, 0,O) has four of them, the (1, 1, 1,0) and the (1, 1, 0, 1) have five coefficients each, and the (2, 1, 0,O) and (1,2,0,0) have six coefficients each. Table 3 gives the standard deviations between experimental and correlated values of Hk using several different equations to evaluate #&The regression method used is based on the maximum-likelihood principle.“‘) As was expected, the
FIGURE 3. Representation on triangular coordinates of the correlated HE{x,CO, (1 -x1 -x&,HsCH,} at 358.15 K and (a), 7.50 MPa; and (b). 12.50 MPa.
+ x&H,,
+
568
C. PANDO ET AL
standard deviations between experimental and predicted values of Hfi, are lowered by the addition of a ternary contribution term with a few adjustable coefficients. Table 4 gives the ternary coefficients when equation (4) with six coefficients is used to represent I-I:. T and table 1 gives the correlated values of Hk. A representation on triangular coordinates of the correlation obtained is shown in figure 3. As has been noted already, (6, 7, this correlation procedure has been shown to lead to lower standard deviations for other ternary mixtures showing a similar combination of endothermic and exothermic mixing but without a two-phase region. Additional difficulties are introduced in the study of (carbon dioxide + n-hexane + toluene) by the existence of a two-phase region and the lack of (vapor + liquid) equilibrium results for the ternary mixture. However, it is noteworthy that these difficulties did not prevent us from obtaining accurate predictions of ternary H$ in this study. This work was partially funded by U.S. Department of Energy Grant No. DE-FG02-85ER13443, Cooperative Research Grant in Basic Sciences No. CCB8402019 between Spain and the United States, and by the Donors of the Petroleum Research Fund administered by the American Chemical Society. We appreciate the aid given to us in collecting the results by G. Anderson and P. R. Harding. REFERENCES I. Christensen, J. J.; Walker, T. A. C.; Schofield, R. S.; Faux, P. W.; Harding. P. R.: Izatt, R. M. J. Chem. Thermodynamics 1984, 16, 445. 2. Christensen, J. J.; Zebolsky, D. M.: Izatt, R. M. J. Chem. Thermodynamics 1985, 17, 183. 3. Pando. C.; Renuncio. J. A. R.; Schofield, R. S.; Izatt, R. M.; Christensen, J. J. J. C&m. Thermodynamics
1983, 15, 747.
4. Christensen, J. J.; Zebolsky. D. M.; Izatt, R. M. J. Chem. Thermodynamics 1985, 17, I. 5. hUX. P. W.; Christensen, J. J.; Izatt, R. M. J. Chem. Thermodynamics 1987, 19, 757. 6. Faux, P. W.; Christensen, J. J.: Izatt. R. M.; Pando, C.; Renuncio, J. A. R. J. Chem. Thermodynamics
1988, 20, 503.
7. Pando, C.: Renuncio. J. A. R.; Calzon, J. A. G.; Christensen, J. J.; Izatt, R. M. J. Solution Chemistry
1987, 16, 503.
8. Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1984, 73, 117. 9. Christensen, J. J.; Hansen, L. D.; Izatt. R. M.; Eatough, D. J.; Hart,
R. M. Reil. Sci. Instrum.
1981,
52. 1226.
10. Rubio, R. G.; Renuncio, J. A. R.; Diaz Petia, M. Fluid Phase Equilibria 1983, 12, 217. Il. Scatchard, G.; Ticknor, L. B.; Goates, J. R.; McCartney, E. R. J. Am. Chem. Sac. 1952, 74, 3721. 12. Toop, G. W. Trans. TMS-AIME 1%5, 233, 850. 13. Hillert, M. Calphod 1980, 4. 1. 14. Li. Y.-H.; Dillard, K. H.; Robinson, R. L. J. Chem. Eng. Data 1981, 26, 53. 15. Ng, H.-J.; Robinson, D. B. J. Chem. Eng. Dafa 1978, 23, 325. 16. Morrison, G.; Levelt Sengers, J. M. H.; Chang, R. F.; Christensen, J. J. Supercritical Fluid Technol0g.v. Penninger, J. M. L. ef al.: editors. Elsevier: Amsterdam. 1985. 17. Morris, J. W.; Mulvey, P. J.; Abott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403. 18. Shatas, J. P.; Abott, M. M.; Van Ness, H. C. J. Chem. Etig. D&u 1975,20, 406. 19. Kratochvila. J.; Cibulka, I.: Holub, R. Collect. Czech. Chem. Commun. 1980, 45, 3241.
The excess enthalpies of (carbon dioxide + n-hexane + toluene) at 358.15 K and 7.50 and 12.50 MPa C. PANDO, J. A. R. RENUNCIO, Facultad de Quimica, Oviedo, Spain 33007
Universidad de Oviedo,
P. W. FAUX, J. J. CHRISTENSEN,t and R. M. IZATT Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. (Received 21 September 1987) The excess molar enthalpies Hi{x,CO, +x2C,H,,+(1 -xi -x&H&H,} were measured at 358.15 K and 7.50 and 12.50 MPa with an isothermal flow calorimeter. Results are compared with those previously obtained at 413.15 K and 7.50 MPa and 12.50 MPa and the effect of a temperature decrease on H,f, for the two isobars is discussed. Toop’s equation was found to provide accurate predictions of ternary His. Correlation methods were also examined. It was found that ternary HEs can give information about vapor and liquid equilibrium-phase compositions under certain conditions.
1. Introduction A program is under way in this laboratory to measure excess molar enthalpies Hz at supercritical conditions for (carbon dioxide + a hydrocarbon). Studies of Hi are presently being extended to ternary mixtures because of the industrial importance of multicomponent mixtures. (Carbon dioxide + n-hexane + toluene) was chosen for the initial study. This is composed of carbon dioxide (extensively used in supercritical extraction techniques), n-hexane (a representative straight-chain hydrocarbon), and toluene (a representative of aromatic compounds found in petroleum products). Hks have been determined in this laboratory for (carbon dioxide + n-hexane),(‘* ‘) (carbon dioxide + toluene),‘3’4’ and (n-hexane + toluene),(5’ over the temperature range 308.15 to 573.15 K and pressure range 7.50 to 12.50 MPa. His for (carbon dioxide + n-hexane + toluene) at 413.15 K and 7.50 and 12.50 MPa have been reported. f6) The present work reports Hzs for this ternary mixture at 358.15 K and 7.50 and 12.50 MPa. By acceptance of this article, the publisher acknowledges the right of the U.S. Government to retain a non-exclusive royalty-free license in and to any copyright covering this paper. 7 Died 5 September 1987.
560
C. PANDO ET AL.
The H$ for the three binaries and the ternary should provide a consistent set of results for testing techniques for correlating HE, for ternary mixtures and for predicting ternary H,!$ from binary HLs. Methods for correlating and predicting ternary Hzs have been examined and tested for 42 sets of ternary results.(‘) The equations and procedures found in that study which best correlate and predict ternary Hf,s were used in this paper.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (8-9) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure IX0 syringe pumps supplied at a constant rate the two fluids to be mixed. The total flow rate was between 0.0056 and 0.0139 cm3.s-l (4.3 x 10V5 and 1.3 x 10e4 mol.s-‘) for the temperature and pressures studied. Hzs were determined using CO, in one pump and in the other. Three mixtures having mole fractions WJ%4 + (1 -KA’W~ x = 0.25, 0.50, and 0.75 were used. Three complete sets of pseudobinary HE, determinations, one with each mixture, were made over the range of x1 from 0 to 1. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over most of the mole-fraction range (0.2 < x < 0.8).t8) Reproducibility of results in the present investigation was + 1 to +2 per cent. The materials employed and the calculation of the densities used to evaluate mole fractions from flow rates were described previously.@’
3. Results and discussion Excess molar enthalpies were determined for (xrC0, + x$Z,H,, + (1 -x1 -x&H,CH,} at 358.15 K and 7.50 and 12.50 MPa. The results are given in table 1. The excess molar enthalpies of the three related binary mixtures, (xC0, + (1 -x)C,H,,), {Xco, + (1 -X)c,H,cH,), and (xc,H,~ + (1 -X)c6H5cH3) under the same conditions of pressure and temperature have already been reported. (lV5) A correlation equationt5) was used to evaluate the excess molar enthalpies of (0.2sc6H14 + 0.75C,H,CH,), (0.50C6H1, + O.SOC,H,CH,), and (0.75C6H,, + 0.25C6H5CH,), which were then added to Hzs for the pseudobinary [CO2 + (xC6H14 + (1 -X&H&H,}] to give His for the ternary mixture. In a previous paper,“’ we examined methods for correlating and predicting ternary excess enthalpies. Ternary His are usually represented as a sum of a binary and a ternary contribution:
Hz = C HE,ij+HE,,. i
(1)
The binary contribution, Zi
H:{x,CO, TABLE
1. Experimental,
predicted,
Hg(J.
Xl
+x,CsH,,+(l and correlated (1 -x1 -x&H&H,}
-x1
excess molar enthalpies at 358.15 K
mol-‘)
expt
pred.
561
-x&H,CH,}
Xl
HE{x,CO,
H3(J.
x2
corr.
expt
+ x&HI4
molpred.
+
‘) corr.
p = 7.50 MPa 0.0752 0.1107 0.1450 0.1781 0.2101 0.2410 0.2709 0.2998 0.3549 0.3812 0.4067 0.4314 0.4554 0.4786 0.5012 0.5232
0.2312 0.2223 0.2138 0.2055 0.1975 0.1898 0.1823 0.1751 0.1613 0.1547 0.1483 0.1421 0.1362 0.1304 0.1247 0.1192
-33 -184 -284 -497 -716 - 1010 - 1080 - 1380 - 1620 - 1930 - 1930 - 2050 -2130 - 1980 - 1930 -1780
-23 -215 -405 -592 -778 -961 -1140 -1310 -1640 - 1790 - 1930 -2060 - 2050 - 1960 -1870 - 1770
27 -154 -341 - 533 -727 -921 -1110 -1300 -1650 - 1820 - 1970 -2100 -2100 -2010 - 1920 - 1830
0.5446 0.5653 0.6052 0.6611 0.7129 0.7453 0.7762 0.8199 0.8338 0.8864 0.9230 0.9461 0.9573 0.9683 0.9791 0.9896
0.1138 0.1087 0.0987 0.0847 0.0718 0.0637 0.0560 0.0450 0.0415 0.0284 0.0193 0.0135 0.0107 0.0079 0.0052 0.0026
-1720 -1560 - 1350 -1110 -816 -672 -448 -291 - 182 87 220 335 379 418 336 168
- 1680 - 1590 - 1410 -1140 - 880 -712 - 549 -314 -238 47 237 346 391 280 250 166
- 1730 -1640 - 1450 -1160 -884 - 707 -536 -296 -220 63 248 352 395 283 251 166
0.0789 0.1160 0.1516 0.1859 0.2189 0.2507 0.3109 0.3669 0.4193 0.4442 0.4683 0.4916 0.5142 0.5574 0.5981
0.4606 0.4420 0.4242 0.4071 0.3906 0.3747 0.3446 0.3166 0.2904 0.2779 0.2659 0.2542 0.2429 0.2213 0.2009
237 91 -290 -365 -550 - 802 -1200 - 1560 -1900 -2010 - 2030 - 1950 - 1850 - 1630 - 1410
107 -87 -283 -480 -675 - 865 - 1230 - 1550 -1820 - 1930 - 2020 - 1880 -1800 - 1620 -1440
184 -7 -210 -419 - 628 -832 - 1210 - 1550 -1810 - 1920 -2010 - 1870 - 1780 - 1590 - 1390
0.6364 0.6727 0.7069 0.7394 0.7703 0.7996 0.8274 0.8540 0.8793 0.9035 0.9266 0.9487 0.9594 0.9699 0.9801
0.1818 0.1637 0.1465 0.1303 0.1149 0.1002 0.0863 0.0730 0.0604 0.0482 0.0367 0.0256 0.0203 0.0150 0.0100
- 1210 -988 - 780 -715 -430 -291 -119 9 138 263 370 451 479 445 299
- 1250 - 1070 - 880 - 697 -516 -341 -171 -9 145 286 411 507 539 247 192
-1200 -1000 -812 - 628 - 450 - 280 -118 36 180 311 427 516 545 250 194
0.0825 0.1211 0.1935 0.2600 0.3215 0.3784 0.4054 0.4313 0.4564 0.4806 0.5039 0.5265 0.5695 0.6099 0.6477
0.6881 0.6592 0.6049 0.5550 0.5089 0.4662 0.4460 0.4265 0.4077 0.3896 0.3721 0.3551 0.3229 0.2926 0.2642
35 - 249 -573 -819 - 1060 -1260 - 1430 -1540 -1690 -1760 -1840 -1710 - 1470 - 1280 - 1050
35 - 145 - 526 -901 - 1250 -1540 -1660 -1760 -1840 -1900 -1870 -1790 -1610 - 1410 - 1220
77 -96 -465 -826 -1150 - 1420 -1540 - 1630 -1700 -1760 -1721 - 1630 - 1450 -1260 - 1070
0.6834 0.7170 0.7488 0.7789 0.8073 0.8344 0.8600 0.8844 0.9077 0.9299 0.9406 0.9510 0.9613 0.9713 0.9811
0.2375 0.2122 0.1884 0.1658 0.1445 0.1242 0.1050 0.0867 0.0692 0.0526 0.0446 0.0368 0.0290 0.0215 0.0142
-855 -640 - 527 -283 - 147 31 151 303 400 550 576 536 436 333 218
- 1010 -809 -607 -408 -215 -29 147 311 459 583 631 666 283 203 134
-876 -686 -498 -316 -139
0.0831 0.1219 0.1591
0.2292 0.2195 0.2102
135 -27 - 145
113 -12 -134
0.0704 0.0663 0.0625
-2100 - 2070 - 2080
- 2020 - 2030 -2020
- 2040 - 2050 -2040
32 193 345 482 597 641 673 287 206 135
p = 12.50 MPa 157 25 -112
0.7186 0.7346 0.7502
C. PANDO ET AL.
562
TABLE l-continued Xl 0.1946 0.2288 0.2615 0.3232 0.3802 0.4332 0.4825 0.5284 0.5714
0.5919 0.6117 0.6495
0.6851 0.7021 0.087 1 0.1275 0.2028
expt
H,f,/(J.mol-‘) pred
corr.
-250 -376 -491 -713 -939
-252 -368 -481 -698 -904
-249 -384 -513 -757 -978
-1160
-1100 - 1280 - 1450
-1180 -1360
x2
0.2014 0.1928 0.1846 0.1692 0.1550 0.1417 0.1294 0.1179 0.1072 0.1020 0.0971 0.0876 0.0787 0.0745
0.2715 0.3344 0.3923 0.4458 0.4952 0.5411 0.5838 0.6237 0.6610 0.6960
0.4565 0.4363 0.3986 0.3643 0.3328 0.3038 0.2771 0.2524 0.2294 0.2081 0.1881 0.1695 0.1520
0.0910 0.1330 0.2107 0.2811 0.3453 0.4039 0.4577 0.5073 0.5531 0.5955 0.6350 0.6718 0.7061
0.6817 0.6503 0.5920 0.5392 0.4910 0.4471 0.4067 0.3695 0.3352 0.3034 0.2738 0.2461 0.2204
-1340 -1490 -1700 -1780 -1810 -1920 -2040 -2040 242
108 - 157 -365 -555 -764 -902 -1070 -1250 -1410 -1530 -1680 -1750
160 74 -159 -404 -593 -707 -946
- 1010 -1210 -1330
- 1480 - 1570 -1600
-1610 -1690 -1750 -1870 -1960 -2000 242 122 -114 -340 -557 -763 -958 -1140
- 1310 -1460
-- 1590 -1700 -1770 172 74 -124 -323 -518 -706 -885 -1050 -1200 -1340 -1450 -1540
-1600
Xl
-1530 -1670 -1740
-1800 - 1910 -2000 -2020 245 125 -108 -333 -549 -754 -949 -1130 -1300 -1450 -1580 -1690 -1770 136 28 -175 -366 -550 -725 -892
- 1050 -1200 -1330
-1440 -1530 - 1590
x2
expt 0.7654 0.7802 0.7945 0.8354 0.8609 0.8732 0.8969 0.9083 0.9304 0.9514 0.9616
0.9715 0.9812 0.7288
0.7597 0.7888 0.8163 0.8423 0.8669 0.8903
0.9125 0.9336 0.9537 0.9729
0.9821 0.7382 0.7684 0.7967 0.8234 0.8486 0.8724 0.8949 0.9163 0.9365
0.9558 0.9651 0.9741 0.9830
H3(J.mol-‘) pred.
0.0587 0.0549 0.0514 0.0412 0.0348 0.0317 0.0258 0.0229 0.0174 0.0122 0.0096 0.0071 0.0047 0.1356 0.1201 0.1056 0.0919 0.0789 0.0665 0.0549 0.0437 0.0332 0.0231 0.0136 0.0089 0.1963 0.1731 0.1525 0.1324 0.1136 0.0957 0.0788 0.0628 0.0476 0.0332 0.0262
0.0194 0.0128
-2080 -2020 -1790 -1530
-1400 -1100 -913 -580 -398 -191 -85 -37 -1790
-1800 -1730 -1660
-1440 - 1230 -974 -663
-448 -196 -56 -38 -1610
- 1510 -1490 - 1330 -1120 -918 -675 -457 -229 -95 -53 -5
11
-2010 -1970
corr.
-1340 -1210 -976 -824 -536 -298 -202 -125 -66
-2020 -1990 -1940 -1600 -1350 -1210 -977 -825 -536 -298 -202 -125 -66
-1810 -1810 -1760 -1600 -1400 - 1220
-1800 -1760 -1600 -1400 - 1220
- 1930 -1600
-957 -686 -433 -226
-81 -37
-1810
-956 -685 -433 -226 -81 -37
-1620 -1630 -1530 -1420 -1250
-1610 -1620 -1530 -1410 -1240
-1040
-1040
-804 -562 -340
-802 -561 -340
-160
-160
-92 -42
-92 -42 -9
-9
In this study, the Hz,ij values for the three related binaries were calculated as a function of mole fraction using an (n, m) Padt approximant. Hz,ij is given by HE,, ij/(J. mol- ‘) = XiXj
2 A,(xi-xj)’
B,,= 1,
(2)
k=O
where xi and xj are the mole fractions of components i and j, respectively, and Ak and B[ are the parameters. The performance of equation (2) in the correlation of binary excess enthalpies has been discussed elsewhere.(‘) The linear sections
H:{x,CO,
+x,C,H,,+(l
563
-x1 -x,&H&H,}
TABLE 2. Description of Padt approximants (equation 2) and standard deviations s for representation of binary Hz values at 358.15 K Binary mixture xCO,+(l
-x)&H,,
xC0, + (1 -x)&H&H,
xC,H,,+(l-x)C,H,CH,
PIMPa
n, m
7.50 7.50 12.50 7.50 7.50 12.50 12.50 7.50 12.50
3, 2 1. 2
2, 2, 3, 1 1, 2 1, 2 1. 2 1, 0 1, 0
x interval 0.520 > x 0.520 < x O
> 0.950 < 0.950 > < > <
0.970 0.970 0.950 0.950
s 58 53 22 22 6 15 17 7 8
occurring in two of the three binary mixtures (corresponding to a two-phase region) were correlated using a (1,2) Pad& approximant, equation (2). The term xixj counterbalances the second-degree polynomial of the denominator resulting in a first-degree polynomial in the composition variable. Table 2 summarizes the equations used to represent H$j for the three binary mixtures comprising the ternary mixture involved in this study. The regression method used was based on the maximum-likelihood principle. The criteria to discriminate between two fittings and to select the best Pad6 approximant has been discussed elsewhere.(“) The predictive equations proposed by Scatchard et aZ,(’ ‘) Toop,” ‘) and Hillert” ‘I were shown to provide accurate and almost coincident HE values for ternary Hf,s. In this study, Toop’s equation was used to predict Hf, for {xlCO, + x&HI4 + (1 -xl -x&H&H,}. This equation is asymmetric with respect to the numbering of the components and is given by H3(J.
x
mol-‘)
kgo
4(2x1
= x1x2 - Ilk (3)
The selection of which component is to be designated as component 1 is critical while components 2 and 3 may be interchanged. It has been shown”) that component 1 should be the most dissimilar component of the mixture. Consequently, carbon dioxide was designated as component 1 for {xlC02 + x&H, + (1 -xl-x&H&H,}. The behavior of the related binary mixtures (14, “) indicates that there should be at 358.15 K and 7.50 MPa a two-phase region for (carbon dioxide + n-hexane) and (carbon dioxide + toluene) and at 358.15 K and 12.50 MPa a two-phase region only for (carbon dioxide + toluene). The boundaries of these regions are indicated in the triangular coordinate representation of figure 1. The intervals ef and gh
564
C. PANDO ET AL.
(4
(b)
FIGURE 1. Representation on triangular coordinates of the three series of Hz determinations (dotted lines represent the path of the approximately 30 points for each series covering the range of x, from 0 to 1) and the boundaries of the two-phase region for (x,CO, + x&HI4 + (1 -x,-x&H&H,J at 358.15 K and (a), 7.50 MPa; and (b), 12.50 MPa.
correspond to the (vapor + liquid) equilibrium regions for (X0, + (1 -x)&H,,} and (xCOz + (1 -x)C,H,CH,). Unfortunately, (vapor + liquid) equilibrium results for {xlCO, + x zC 6H 14 + (1 -x1 -x,)C,H,CH,} are not available and the shapes of the lines connecting e and g, and f and h, respectively, at 7.50 MPa, and the curved line connecting h and g at 12.50 MPa, are unknown. To predict ternary I%!$, we have assumed that these boundaries can be represented approximately by the straight lines fh and eg at 7.50 MPa, and by the straight lines eh and eg at 12.50 MPa. In the latter case, the position of e (x1 = 0.735) is determined as the mean value of the carbon-dioxide mole fractions at the beginning and ending of the two-phase region for (carbon dioxide + n-hexane) at 358.15 K and 7.50 MPa. A similar position for e (x1 = 0.739) is obtained if the two-phase region considered is that at the same pressure, p = 12.50 MPa and at a higher temperature, T = 413.15 K.(@ The predicted values of H~{x,CO, + x,C,H,, + (1 -x1 -x,)CsH,CH,) are given in table 1; the standard deviations between experimental and predicted values are given in table 3. The ratio between the standard deviation and the maximum
TABLE 3. Standard deviations s between experimental values of ternary excess enthalpies for {x1 CO, + + (1 -x1 -x2)C,H,CH3} and values correlated from equation (1) using Toop’s equation for x&H,, the binary contribution and one of several equations for the ternary contribution Equation for HL.T None References 17, 18 Reference 19 Equation (4)
Number of ternary coefficients 0 3 6 4 7 2 4 5 6
p=7SOMPa 95 82 70 75 74 75 75 73 69
’
p = 12.50 MPa 67 66 63 65 60 66 65 61 62
H~{x,CO,+x,C,H,,+(l-x,-x,)C,H,CH,}
565
absolute value of Hfj, was found to be 4 per cent or less. The accuracy of the predictions can be considered satisfactory, especially if we take into account the values of the standard deviations for some of the correlations of,the binary values involved and the variations observed in ternary I&. Figure 2 shows plots of HE against x1 for the three series of determinations performed at each pressure. The full lines represent predicted values of Hz. These plots show that variations of ternary iY:s with x1 for each series are similar to those observed for (xC0, + (1 -x)C,H,,} and (xC0, + (1 -x)&H&H,} at 358.15 K and 7.50 and 12.50 MPa. The values of the minima are intermediate between the minimum value for (xC0, + (l-x)C,H,,} (-1800 J.mol-’ at 7.50 MPa and - 1420 J.mol-’ at 12.50 MPa) and the minimum value for (xC0, + (l-x)C,H,CH,} (-2310 J.mol-’ at 7.50 MPa and -2240 J.mol-’ at 12.50 MPa). Something similar happens with the values of the maxima in the three series of determinations. {x&H,, + (1 -x)&H&H,) shows moderately endothermic mixing (maximum values are 480 J. mol- ’ at 7.50 MPa and
1 0.6 0.8 Xl FIGURE 2. Plot of If: against x,, for {xIC02 + x&H,, + (1 -x1 -x&HSCH,} at 358.15 K and (a), x2/x3 = l/3; (b), xzh = 1; and (c), x*/x3 = 3 as a function of pressure; 0, 7.50 MPa; and A, 12.50 MPa; -. predicted from equation (3). 0
0.2
0.4
566
C. PANDO
ET AL.
500 J .mol-’ at 12.50 MPa) and its contribution to each series of ternary Hi determinations is positive and relatively small. Figure 2 also allows us to make some inferences concerning the phase diagram of (xlCO, +x&H,, + (1 -x, -x$Z,H,CH,}. The fact that Hji, varies linearly with x1 at 7.50 MPa indicates that vapor- and liquid-phase compositions can be determined as the x coordinates of the intersection of the extrapolated straight lines and the curves describing Hz. The good agreement between experimental and predicted values of Hz indicates that the assumption of linearity for the boundaries fh and eg is valid. Predicted values of HE, vary almost linearly with x1. Departures from linearity are due to the relatively small contribution of (n-hexane + toluene). On the other hand figure 2 shows that when pressure is increased to 12.50 MPa, only the series corresponding to mixtures richer in toluene, figure 2(a), seems to exhibit a linear section. These results are a consequence of the fact that at 358.15 K and 12.50 MPa (carbon dioxide + toluene) is the only binary mixture exhibiting a two-phase region. On the other hand, these results also indicate that, as could already have been expected, e should be located in the interior of the (b) triangle of figure 1. The shape of the phase boundary could be estimated from calorimetric measurements if more series of Hi determinations were made but this would require considerable time and effort. Thus, the excess enthalpies taken at 358.15 K and 7.50 MPa provide information concerning (vapor + liquid) equilibrium for {x,CO, + x,C,H,, + (1 -x1 -x&H,CH,} whereas no definitive conclusions can be adopted from the examination of results at 358.15 K and 12.50 MPa. The comparison of figure 2 of this study and a similar figure from our previous study@’ at 413.15 K allows us to examine the effect on the Hz against x1 of a temperature decrease for two isobars. Since both (carbon dioxide + n-hexane) and (carbon dioxide + toluene) have critical loci passing through a maximum, the situation for the ternary mixture is similar to that reported previously for binary mixtures containing carbon dioxide. For Hfi, against x1 as the temperature decreases, the minimum becomes larger and the maximum becomes smaller. This effect has been discussed thoroughly for (carbon dioxide f toluene) by Morrison et Al. H%,CO,
+ (1 -x1 - x&,H,CH,) were correlated using + x&H,, equation (1). The equation used to predict Hz, equation (3), was used to evaluate the binary contribution term Xi, jHz, ij. In a previous paper, the equations used in the literature to represent the ternary contribution HE,, with varying numbers of adjustable ternary coefficients were reviewed and tested, and a partial differential approximant for representing Hz,T was proposed.‘7’ This approximant is the ternary equivalent of a Pad& approximant and is given by
fE.T J . mol-i
=
“r. 4,(x,- .‘c$f ,gl AI(x,- ~3)’+ .rl ,zl 4,(x,- XJYXZ - ~3)’ --,
x1x2x3
1+ 2 B,(x, -x,)"+ II=1
'E, B,(x,-x3)'+
2 n=11=1
% B"&-X3)n(X2-X3)'
(4)
567
H:{x,CO,+x,C,H,,+(l-x1-x,)C,H,CH,J
TABLE 4. Ternary coefficients for correlation of Hk{x,CO, + x zC 6H 14 + (1 -XI-xzG%CH,~ by equation (1) using Toop’s equation for the binary contribution and equation (4) with six coefficients for the ternary contribution
PIMPa
Oh,n2,4, m2)
A0
A,
7.50 12.50
(1, TO, 0) (1, 2, 0, 0)
175.37 219.49
-3711.9 204.89
A2 ~__ A3 ___. 20414 4190.5
5968.9 - 25040
A4____~~ A5 16985 14902
46646 -49618
where A,, A,, A,,*, B,, I?, and B,* are the parameters. Each approximant is represented by indicating the values adopted by n,, n2, m,, and m2 as (n,, n2, m,, mJ. The (1, 0, 0,O) approximant has two ternary coefficients, the (1, 1, 0,O) has four of them, the (1, 1, 1,0) and the (1, 1, 0, 1) have five coefficients each, and the (2, 1, 0,O) and (1,2,0,0) have six coefficients each. Table 3 gives the standard deviations between experimental and correlated values of Hk using several different equations to evaluate #&The regression method used is based on the maximum-likelihood principle.“‘) As was expected, the
FIGURE 3. Representation on triangular coordinates of the correlated HE{x,CO, (1 -x1 -x&,HsCH,} at 358.15 K and (a), 7.50 MPa; and (b). 12.50 MPa.
+ x&H,,
+
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C. PANDO ET AL
standard deviations between experimental and predicted values of Hfi, are lowered by the addition of a ternary contribution term with a few adjustable coefficients. Table 4 gives the ternary coefficients when equation (4) with six coefficients is used to represent I-I:. T and table 1 gives the correlated values of Hk. A representation on triangular coordinates of the correlation obtained is shown in figure 3. As has been noted already, (6, 7, this correlation procedure has been shown to lead to lower standard deviations for other ternary mixtures showing a similar combination of endothermic and exothermic mixing but without a two-phase region. Additional difficulties are introduced in the study of (carbon dioxide + n-hexane + toluene) by the existence of a two-phase region and the lack of (vapor + liquid) equilibrium results for the ternary mixture. However, it is noteworthy that these difficulties did not prevent us from obtaining accurate predictions of ternary H$ in this study. This work was partially funded by U.S. Department of Energy Grant No. DE-FG02-85ER13443, Cooperative Research Grant in Basic Sciences No. CCB8402019 between Spain and the United States, and by the Donors of the Petroleum Research Fund administered by the American Chemical Society. We appreciate the aid given to us in collecting the results by G. Anderson and P. R. Harding. REFERENCES I. Christensen, J. J.; Walker, T. A. C.; Schofield, R. S.; Faux, P. W.; Harding. P. R.: Izatt, R. M. J. Chem. Thermodynamics 1984, 16, 445. 2. Christensen, J. J.; Zebolsky, D. M.: Izatt, R. M. J. Chem. Thermodynamics 1985, 17, 183. 3. Pando. C.; Renuncio. J. A. R.; Schofield, R. S.; Izatt, R. M.; Christensen, J. J. J. C&m. Thermodynamics
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