The excess enthalpies of (carbon dioxide + n-hexane + toluene) at 573.15 K and 7.50 and 12.50 MPa

O-306 J. Chem. Thermo&namics 1989,21.

41-51

The excess enthalpies of (carbon dioxide + n-hexane + toluene) at 573.15 K and 7.50 and 12.50 MPa C. PANDO,

J. A. R. RENUNCIO,

Facultad de Quimica, Oviedo, Spain 33071 P. W. FAUX,

Universidad de Oviedo,

J. J. CHRISTENSEN,?

and

R. M.

IZATT

Department of Chemical Engineering and Chemistry, Brigham Young University, Provo, UT 84602, U.S.A. [Received 10 August 1988) The excess molar enthalpies H~{x,CO,+x,C,H,,+(l -x1 -x&H,CH,} were measured at 573.15 K and 7.50 and 12.50 MPa with an isothermal flow calorimeter. All mixines were endothermic with maximum Hk values of 7120 J mol- i and 7.50 MPa and 4300 J. r&l i at 12.50 MPa. The relation between the ternary HEs and the HEs for the three related binary mixtures is discussed. Toop’s equation was found to provide accurate predictions of ternary Hzs. Correlations methods are also discussed. Results are compared with those previously obtained for the same mixture at lower temperatures.

1. Introduction A program is underway at Brigham Young University to measure excess molar enthalpies Hk at supercritical conditions for binary mixtures of carbon dioxide and various hydrocarbons. Studies of Hi are presently being extended to ternary mixtures because of the industrial importance of multicomponent mixtures. The ternary mixture chosen for the initial study was 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. HEs have been determined in this laboratory for (carbon dioxide + n-hexane),“,2) (carbon dioxide + toluene),‘3*4) and (n-hexane c toluene),C5’ over the temperature range 308.15 to 573.15 K and pressure range 7.50 to 12.50 MPa. HEs for (carbon dioxide + n-hexane + toluene) at 308.15, 358.15, 413.15, and 470.15 K and 7.50 and 12.50 MPa have been reported.‘6-g’ The present work reports HEs for the ternary mixture at 573.15 K and 7.50 and 12.50 MPa. 7 Died 5 September 1987. By acceptance of this article, the publisher acknowledges non-exclusive royalty-free license in and to any copyright

the right of the U.S. Government covering this paper.

to retain

a

42

C. PANDO

ET AL

The Hzs for the three binaries and the ternary should provide a consistent set of values for testing techniques for correlating HE for ternary mixtures and for predicting ternary Hzs from binary Hts. Methods for correlating and predicting ternary Hzs have been examined and tested for 42 sets of ternary results from the literature.“” The equations and procedures found in that study to correlate and predict ternary Hzs best were used in this paper.

2. Experimental The high-temperature high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (11-12) All runs were made in the steady-state (fixed-composition) mode. Two high-pressure ISCO 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- ’ (4 .3 x 10e5 and 1.3 x 1O-4 mol. s-l). HEs were determined using CO, in one pump and a mixture of {xC,H,,+(l -x)C,H,CH,} in the other pump. Three mixtures having compositions 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 (CO, mole fraction) from 0 to 1. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over of results in the most of the mole-fraction range (0.2 < xi < 0.8). Cli) Reproducibility present investigation was k 1 to i2 per cent. The materials employed and the calculation of the densities used to evaluate mole fractions from flow rates, were described previously.‘g’

3. Results and discussion Excess molar enthalpies were determined for (xiC0, + x&,H,, + (1 -xi -xJC,H,CH,) at 573.15 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: {xCO,+(l-x)C,H,CH,), and (x&H,,+(l-X) (xc% +U -4WL), C,H,CH,), at the same pressures and temperature, have already been reported.(1-5’ A correlation equation”’ was used to evaluate the excess molar enthalpies of (0.25C,H,, + 0.75C,H,CH3), (0.5OC 6H 14 + 0.50C,H,CH3), and (0.75C6Hl, + 0.25C,H,CH3) which were then added to HEs for the pseudobinary [x,CO, + (1 -x1)(xC6Hl, + (1 -x)C6H5CH3)] to give HEs for the ternary mixtures. 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 = 1 Hz,ij+Hz,,. (1) iij

The binary contribution CHZ,, is calculated from the excess enthalpies of the three binary mixtures involved. The ternary contribution Hz,, has adjustable ternary coefficients which are evaluated from ternary Hzs. When the ternary contribution is

43

H~{x,CO,+x,C,H,,+(l-x1-x,)C,H,CH,}

omitted, equation (1) is contribution is included, In this study the H~,ij function of mole fraction HE,ij/(J ’ mol-‘)

considered to be a predictive equation; when the ternary equation (1) is considered to be a correlative equation. values for the three related binaries were correlated as a using on (n, m) Pad& approximant: = XiXj

i

A,(Xi-Xj)k

C2)

k=O

where xi and xi are the mole fractions of components i and j, respectively, and A, and B, are adjustable coefficients. The performance of equation (2) in the correlation of binary excess enthalpies has been discussed elsewhere. The linear section occurring for one of the three binary mixtures (corresponding to a two-phase region) was 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 the HE,ij values for the three binary mixtures comprising the ternary. The regression method was based on the maximumlikelihood principle. The criteria to discriminate between two fittings and to select the best Pad& approximant have been discussed elsewhere.(13) The predictive equations proposed by Scatchard et u1.,(14) Toop,‘l” and Hillert”6’ were shown to provide accurate and almost coincident Hi values for ternary H,!$,s. In this study, Toop’s equation was used to predict Hzs for {xlCO, + x2C,H,, + (1 -x1 -x&H,CH,}. This equation is asymmetric with respect to the numbering of the components and is given by i

Hz/(J . mol- ‘) = x1x1

A,(2x, - l)k

k=O

x1x3

k~oA;wl-l)k i

Iii

“” k~~A;i(xz-X3)/(XZ+X3)}k

,zo w%

- 1) ‘1 +

,zo N2x,

- 1)’

+

m” I

1~oB;‘i(x,-x3)l(X,+X3)~i

B,, Bb, B’; = 1.

1 ;

(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 the two components most similar to each other should be designated as components 2 and 3, while the remaining component should be designated as component 1. Consequently, CO, was designated as component 1 for (xlCO, + x&H, + (1 -x1 -x&H,CH,}. The behavior of the related binary mixtures (14,15’ indicates that there should be at 573.15 K and 7.50 MPa a two-phase region whose boundaries are indicated in the triangular-coordinate representation of figure 1. The interval bc corresponds to the (vapor + liquid) equilibrium region for (xCO,+(l -x)C,H,CH,}. The extrapolation of (vapor + liquid) equilibria taken up to 543.15 K by Sebastian et aE.(17) that a two-phase region also indicates should be expected for

44

C. PANDO TABLE

Xl

ET AL.

1. Experimental, predicted, and correlated H~jx,CO, +x,C,H,,+(l -x, -x&H&H,}

expt

Hi/(J

mol - ‘) pred. con.

X2

p= 0.0693 0.1024 0.1657 0.1960 0.2254 0.2818 0.3352 0.3857 0.4101 0.4338 0.4794 0.5228 0.5641

0.2327 0.2244 0.2086 0.2010 0.1937 0.1796 0.1662 0.1536 0.1475 0.1416 0.1302 0.1193 0.1090

1200 1990 3690 4750 5530 6270 6580 6900 7020 7120 7100 6820 6520

1070 1570 2910 3600 4250 5410 6340 7010 6940 6930 6760 6460 6080

0.0370 0.0727 0.1073 0.1407 0.1730 0.2346 0.2639 0.2924 0.3468 0.3981 0.4465 0.4923 0.5357 0.5769

0.4815 0.4636 0.4464 0.4297 0.4135 0.3827 0.3681 0.3538 0.3266 0.3010 0.2767 0.2539 0.2321 0.2115

1180 1690 2720 3620 4400 5200 5510 5900 6210 6160 6070 5740 5430 5160

876 1390 1930 2500 3090 4170 4630 5030 5670 5940 5900 5720 5440 5110

0.0761 0.1121 0.1802 0.2124 0.2435 0.3027 0.3581 0.3844 0.4100 0.4347 0.4588 0.5047 0.5480 0.5888

0.6929 0.6659 0.6149 0.5907 0.5674 0.5230 0.4814 0.4617 0.4425 0.4240 0.4059 0.3715 0.3390 0.3084

1860 2370 3870 4330 4690 5020 5160 5180 5260 5180 5210 4970 4800 4500

1570 2110 3100 3540 3930 4440 4810 4930 4900 4880 4830 4650 4420 4160

0.0767 0.1128 0.1477 0.1813 0.2449

0.2308 0.2218 0.2131 0.2047 0.1888

713 952 1280 1550 2160

622 859 1130 1410 2010

7.50 MPa, 1720 2350 3710 4350 4930 5950 6750 7330 7220 7190 7000 6700 6340

Xl x2/x3

x2/x3

1390 2220 2910 3540 4120 5070 5440 5760 6250 6410 6310 6090 5810 5490

0.6159 0.6531 0.6885 0.7222 0.7544 0.7852 0.8146 0.8427 0.8697 0.8956 0.9204 0.9443 0.9672 0.9783

7.50 MPa, 2100 2740 3740 4140 4470 4870 5140 5220 5170 5130 5060 4880 4650 4400

p=

12.50 MPa, 688 963 1270 1590 2230

x2/x3 0.6275 0.6642 0.6989 0.7320 0.7624 0.7934 0.8219 0.8491 0.8752 0.9001 0.9239 0.9468 0.9687 0.9794 x2/x3 0.2751 0.3043 0.3598 0.4118 0.4606

HE/(J

X7

mol - ‘) pred. con.

= l/3

0.6036 0.6412 0.6772 0.7117 0.7447 0.7763 0.8066 0.8357 0.8637 0.8906 0.9165 0.9415 0.9655

p = 7.50 MPa,

p=

excess molar enthalpies at 573.15 K

0.0991 0.0897 0.0807 0.0721 0.0638 0.0559 0.0484 0.0411 0.0341 0.0273 0.0209 0.0146 0.0086

6220 5890 5510 5180 4520 4240 3700 3130 2760 2180 1710 1150 580

5670 5240 4800 4360 3910 3480 3040 2620 2200 1780 1370 973 579

5940 5530 5090 4650 4200 3740 3280 2810 2350 1950 1450 1010 595

0.1921 0.1734 0.1558 0.1389 0.1228 0.1074 0.0927 0.0786 0.0651 0.0522 0.0398 0.0279 0.0164 0.0109

4880 4540 4110 3750 3480 3010 2700 2340 1840 1600 1180 824 520 297

4760 4390 4020 3640 3270 2900 2530 2180 1820 1480 1140 804 478 317

5140 4780 4410 4030 3630 3230 2830 2420 2020 1620 1230 854 497 326

0.2794 0.2519 0.2258 0.2010 0.1774 0.1550 0.1336 0.1132 0.0936 0.0749 0.0571 0.0399 0.0235 0.0155

4210 3980 3550 3330 2980 2560 2380 2080 1710 1400 1140 786 432 304

3870 3570 3270 2960 2670 2350 2060 1770 1480 1200 921 651 386 255

4130 3840 3540 3230 2930 2590 2260 1940 1610 1290 984 685 400 261

2600 2880 3410 3850 4120

2310 2600 3110 3530 3840

2550 2850 3380 3800 4100

= 1

= 3

= l/3 0.1812 0.1739 0.1601 0.1471 0.1349

45

H;{x,CO,+X~C,H,~+(~-x1-x,)C,H,CH,} TABLE Xt

expt

HE/(J . molpred.

x2

l-continued

‘)

Xl

H,f/(J

X2

COU

0.5066 0.5498 0.5907 0.6293 0.6659 0.7005 0.7335 0.7648 0.7946

0.1233 0.1126 0.1023 0.0927 0.0835 0.0749 0.0666 0.0588 0.0513

4260 4300 4220 4080 3910 3690 3450 3110 2830

4020 4100 4070 3960 3790 3570 3300 3010 2710

4270 4320 4280 4150 3950 3710 3430 3120 2790

0.0804 0.1181 0.1890 0.2545 0.3152 0.3717 0.4242 0.4733 0.5193 0.5624 0.6030 0.6411

0.4598 0.4410 0.4055 0.3728 0.3424 0.3142 0.2879 0.2634 0.2404 0.2188 0.1985 0.1795

906 1240 1830 2400 2970 3360 3710 4010 3980 3970 3900 3800

746 1010 1570 2130 2630 3050 3360 3570 3680 3700 3640 3520

p = 12.50 MPa, 910 1220 1860 2450 2970 3390 3700 3900 3990 3990 3910 3770

0.0840 0.1232 0.1606 0.1965 0.2309 0.2638 0.3258 0.3830 0.4101 0.4361 0.4612 0.4854 0.5314 0.5743 0.6145

0.6870 0.6576 0.6295 0.6026 0.5768 0.5522 0.5056 0.4628 0.4424 0.4229 0.4041 0.3860 0.3514 0.3193 0.2891

825 1190 1470 1740 1980 2330 2780 3080 3200 3310 3510 3510 3520 3430 3290

686 985 1290 1580 1850 2100 2520 2850 2970 3070 3150 3210 3260 3240 3200

0.8230 0.8501 0.8760 0.9008 0.9245 0.9472 0.9690 0.9795 x2/x3 0.6771 0.7111 0.7433 0.7738 0.8028 0.8303 0.8565 0.8815 0.9052 0.9280 0.9497 0.9705

p = 12.50 MPa,

xz/xs

798 1130 1460 1770 2050 2310 2760 3100 3230 3330 3410 3460 3510 3480 3390

0.6522 0.6876 0.7210 0.7524 0.7822 0.8103 0.8370 0.8623 0.8864 0.9093 0.9311 0.9519 0.9718 0.9814

0.0442 0.0375 0.0310 0.0248 0.0189 0.0132 0.0078 0.0051

mol - ‘) pred. corr.

2470 2150 1800 1500 1160 794 494 320

2390 2060 1740 1410 1090 768 455 302

2460 2120 1780 1440 1100 777 458 304

3540 3290 3110 2810 2540 2220 1960 1630 1380 1010 719 419

3340 3140 2900 2640 2370 2100 1810 1520 1240 957 678 402

3570 3330 3070 2790 2490 2190 1880 1580 1280 979 689 407

3210 3060 2900 2600 2340 2110 1880 1630 1390 1120 911 643 382 244

3050 2890 2710 2500 2280 2050 1820 1570 1330 1090 840 597 356 237

3250 3070 2870 2640 2400 2150 1890 1630 1370 1110 856 605 359 238

= 1 0.1614 0.1445 0.1283 0.1131 0.0986 0.0849 0.0717 0.0592 0.0474 0.0360 0.0252 0.0148 = 3 0.2609 0.2343 0.2092 0.1857 0.1634 0.1423 0.1222 0.1033 0.0852 0.0680 0.0517 0.0361 0.0211 0.0139

(xC0, +(l -x)C6H,CH,) at 573.15 K and 7.50 MPa. Unfortunately, (vapor + liquid) equilibria for (xrC0, + x&H,, + (l-x1-x,)C,H,CH,) are not available and the shape of the two-phase region in the ternary mixture is unknown. To predict ternary Hzs, we have assumed that the boundaries of the two-phase region can be approximately represented by the straight lines ab and ac. The position of a is determined as the mean value of the CO, mole fractions at the beginning and end of the two-phase region for (carbon dioxide + n-hexane) at the most similar experimental conditions. A value for a of 0.380 was obtained from results at 470.15 K and 7.50 MPa.‘9)

46

C. PANDO

TABLE

2. Description

of Pad&

pJMPa

n, m

A0

7.50 12.50

2, 0 2, 1

14420 11035

7.50 7.50 12.50

2, 2 1, 2 1. 2

30240 35940 17229

7.50 12.50

1, 0 1, 0

ET AL.

approximants (n. m), equation (2), correlation of binary HE at 573.15 K A,

A,

4

and

B2

standard

deviations

s for

Interval

s

O
47 49

{xCO,+(l-x)GH,,j - 5825.6 11450

1683.0 -91.019

0.87714

{xCO,+(l -x&H&H,} 41736 17571 1.9027 35764 0.85465 13309 0.26027 {xC,H,,+(l

1450.3 1779.3

1.7457 0.36921 0.66864

0.4O
70 230 62

-x)C,H,CH,)

536.46 25.07

O
13 7

The predicted values of HE(x,CO, + x2C,H,, + (1 -x1--xJC,H,CH,} are given in table 1, and the standard deviations for the predictions are given in table 3. The ratio between the standard deviation and the maximum absolute value of Hz was found to be 7 and 4 per cent for predictions made at 7.50 and 12.50 MPa, respectively. The accuracy of the predictions can be considered satisfactory, especially if we take into account the standard deviations for some of the correlations of the binary results involved and the temperature and pressures at which measurements were made. The fact that at 573.15 K and 7.50 MPa toluene is very close to its critical point seems to be related to the higher standard deviations obtained for predictions at that temperature and pressure. The ratio between the standard deviation and the maximum absolute value of HE was found to be 4 per cent or less for predictions made at 358.15, 413.15, and 470.15 K, and 5 per cent for predictions made at 308.15 K.(6-9) Figure 2 shows plots of ternary HE against x1 for the three different values of x for {xC,H,, + (1 - x)C,H,CH,}. The solid lines represent predicted values of Hz.

b C6H14

FIGURE 1. Representation path of the approximately boundaries of the two-phase 7.50 MPa.

C&&H3

on triangular coordinates of the three series of HE determinations (, . t. the 30 points for each series covering the range of x1 from 0 to 1) and the region for {x,CO, + x&H,, + (1 -x1 -x&,H,CH,) at 573.15 K and

47

H~{x,CO,+x,C,H,,+(l-x1-x,)C,H,CH,)

TABLE 3. Standard deviations s for correlation of excess enthalpies for {xrCO, + x,&H,, + (1 -x1 -x2)C,H,CH3} using equation (1). Toop’s equation was used for the binary contribution term and several equations were used for the ternary contribution term Number of ternary coefficients

Equation for HE,,/(J mol-‘) none Van Ness and his colleagues’z2.23’

s

p = 7.50 MPa

p = 12.50 MPa

500 300 260 290 290 300 300 290 240

190 44

0 3 6 4 7 2

Kratochvila er ~1.“~’ Equation (4)

4 5 6

0

0.2

0.4

0.6

0.8

43 43 43 45 43 40 42

1

FIGURE 2. Plot of Hz against x1, for {xrCO, + x 2C 6H r4 + (1 -x1 -x$Z,H,CH,} at 573.15 K and = l/3; (b), x2/x3 = 1; (c) X&S = 3; as a function of pressure: 0, 7.50 MPa; and A, 12.50 MPa; ~, predicted from equation (3).

(a), xz/x3

48

C. PANDO

ETAL.

The largely positive values of HE obtained are a consequence of mixing low-density supercritical carbon dioxide (T, = 304.21 K, p, = 7.38 MPa) with high-density fluid n-hexane (T, = 507.40 K, pc = 2.97 MPa), and near-critical liquid toluene (T, = 593.95 K, pc = 4.22 MPa). The enthalpy effects are bigger at 573.15 K and 7.50 MPa where toluene is closer to its critical point. For the same reasons described above, (xC0, +(l -x)C,H,,} at 573.15 K shows very endothermic mixing with maxima of 3770 J. mol-’ at 7.50 MPa and 2800 J. mol-’ at 12.50 MPa, and (xCO,+(l -x)C,H,CH,) at 573.15 K shows extremely endothermic mixing with maxima of 8060 J. mole1 at 7.50 MPa and 4450 J. mol- ’ at 12.50 MPa. The third binary (xC,H,, + (1 - x)C,H,CH,} shows moderately endothermic mixing with maxima of 380 J. mol- ’ at 7.50 MPa and 460 J. mol- ’ at 12.50 MPa. The contribution of (XC 6H 14 + (1 -x)C,H,CH,) to the ternary HE is small and positive. As was already observed at the other temperatures studied,‘6-9’ the magnitudes and mole-fraction dependences of the ternary Hgs are determined mostly by the contributions to the ternary Hz of the two binary mixtures which include carbon dioxide. Ternary Hzs lie between the His for and (xC0, + (1 -x)C&H,CH,}. When x2/x3 = l/3, ternary {XC02 + (1 -x)C,H,,) mixtures are richer in toluene and show the most endothermic mixing, as shown in figure 2(a). When x2/x3 = 3, figure 2(c), ternary mixtures are richer in n-hexane and show the least endothermic mixing. When x2/x3 = 1, figure 2(b), ternary Hzs are intermediate between the other two series. + (1 -x1 - x2)C6H,CH,} were correlated using H&CO, + x&H,, equation (1). Equation (3), used to predict HE, was used to evaluate the binary contribution term xHz,ij. In a previous paper, the equations used in the literature to represent the ternary contribution term Hz,, with varying numbers of adjustable ternary coefficients were reviewed and tested, and a partial differential approximant for representing HE,, was proposed. (lo) This approximant is the ternary equivalent of a Pad6 approximant and is given by Hg,,/(J .mol-‘)

= x1x2x3

~~oA,(xl-x3)“+I~l~;(x,-x3)‘+

where A,, A;, Anr, B,, B;, and B,, are the adjustable coefficients. Each approximant is represented indicating the values adopted by nl, n2, m,, and m2 as (n,, nz, m,, mz). The (1, 0, 0,O) approximant has two ternary coefficients, the (1, 1, 0,O) has four, both the (1, 1, 1,0) and the (1, l,O, 1) have five, and both the (2, l,O, 0) and the (1,2,0,0) have six. Table 3 gives the standard deviations for various correlations of HE using several different equations to evaluate HE,,. The regression method was based on the maximum-likelihood principle. (13) As was expected, the standard deviations are lowered by the addition of a ternary contribution term with a few adjustable

49

H~{x,COZ+x,C,H,,+(l-x1-x&H&H,} TABLE equation

4. Ternary coefficients for correlation of Hi{x,CO, (1) using Toop’s equation for the binary contribution for the ternary contribution

PIMPa 7.50 12.50

n,. n2, ml, m, 2, 2,

1, 0, 0 1,030

A0 16163 9189.4

A,

+ x2C,H,, + (1 -x1 -x,)C,H,CH,} by term and equation (4) with six coefficients term

A2

-45377 2149.5

115420 9010.5

A; 21766 -2929.3

A 11

A 21

- 88256 - 7668.6

- 35657 28746

coefficients. Table 4 gives the ternary coefficients obtained when equation (4) with six coefficients is used to represent Hz,, and table 1 gives the correlated values of HE. The critical loci for (xC0, + (1 -x)C,H,,},(‘~) {xCO, + (1 -x)C,H,CH,},‘~‘” and the points indicating the conditions at and {xC,H,, + (1 -x)C,H,CH,},(~~’ which Hf,s were measured for {xlCO, + x,C,H,, + (l-x,+x,)C,H,CH,} are shown in figure 3. Unfortunately, critical loci for the ternary mixture are not available. The ternary locus should be a convex and smooth surface stretching from one binary locus to another. Figure 4 shows the isotherms with x2/x3 = 1 at 7.50 MPa and 12.50 MPa obtained in this and previous studies for (xlCO, + x&HI4 + (l-x1--x,)C,H,CH,}. Similar curves were obtained for the isotherms with x2/x3 = l/3 and xZ/xJ = 3. All curves of figure 4 start with a small positive value for ternary Hz at x1 = 0 which corresponds to the excess enthalpy of (xC,H,, + (1 -x)C,H,CH,} and return to zero at x1 = 1. Some of the curves have a minimum and a maximum connected by a linear section. Other curves show only a maximum or a minimum. The critical locus for a ternary mixture with a given x2/x3 should be a curve which starts at the critical point of carbon dioxide, passes through a

6-

300

I 400

I 500

600

T/K FIGURE 3. Plot of p against T for (xrC0, points, binary critical loci, and (T, p) coordinates

+ x2&H,, + (1 -x1 -xJC+H,CH,} where experimental measurements

showing were made.

critical

50

ET AL

C. PANDO

00 o"oo,p$zo"_

-40

0.2

0.4

0.6

0.8

1

FIGURE 4. Plot of Hi against x,, for {xlCO, + x&H,, + (1 -x1 -xJC6H,CH,} at x2/x3 = 1 and (a), 7.50 MPa; and (b), 12.50 MPa; as a function of temperature: 0, 308.15; 0, 358.15; 0, 413.15; A, 470.15; and 0, 573.15 K.

maximum, and ends at a point on the (n-hexane + toluene) critical locus. Thus, the behavior of each series of ternary mixtures is similar to that previously reported for (xC0, + (1 -x)hydrocarbon}. The effect of a temperature increase on the isobar has been thoroughly discussed for (xC0, + (1 -x)C,H,CH,} by Morrison et ~1.~~‘) Similar considerations can be made for the results represented in figure 4. At 308.15 K and 7.50 MPa, carbon dioxide is a low-density near-critical fluid while both n-hexane and toluene are liquids. Ternary HE values are very large and negative with a minimum of -4650 J. mol- ‘. When the temperature is increased to 358.15, 413.15, or 470.15 K, carbon dioxide becomes a low-density supercritical fluid while both n-hexane and toluene are still distant from their critical points and remain liquid. Isotherms at these temperatures show a minimum and a maximum connected by a linear section which corresponds to a two-phase region for the ternary mixture. The two-phase region is confined to the carbon-dioxide-rich region at 308.15 K, enlarges at 358.15 K to include mixtures richer in hydrocarbons, and moves away from the carbon-dioxide-rich region as the temperature further increases. At 573.15 K, n-hexane becomes a high-density fluid and toluene is a liquid very close to its critical point. Ternary HE values are very large and positive with a maximum of 7120 J.mol-‘. The isotherms at 12.50 MPa show some differences from those at 7.50 MPa. At 308.15 K and 12.50 MPa, carbon dioxide is not close to its critical point. Two liquids (n-hexane and toluene) are mixed with a high-density fluid (carbon dioxide) and ternary HE values are moderately positive. When the temperature is increased to 358.15, 413.15, or 470.15 K, the isotherms cross the two-phase region and show features similar to those observed at 7.50 MPa. At 573.15 K, carbon dioxide is a low-density fluid, n-hexane is a high-density fluid, and toluene is a liquid which is not as close to its critical point as it is at 573.15 K and 7.50 MPa. Thus, HEs are substantially less positive than those reported for the lower isobar. We may conclude that large enthalpy effects are observed for {xlCO, +

H~{x,CO,

+x,C,H,,+(l

-xi

-x&,H,CH,}

51

+ (l-x1-x,)C,H,CH3} at 308.15, 358.15, 413.15, 470.15, and 573.15 K x&H,, and 7.50 and 12.50 MPa. These effects seem to be a consequence of the temperatures and pressures at which measurements were made. Pressures exceed the critical pressures of the three components and temperatures span the critical temperature of carbon dioxide and n-hexane and almost reach the critical temperature of toluene. An asymmetric equation which uses the binary excess enthalpies for the three-component binary mixtures has been shown to give accurate predictions of ternary HE. This seems to indicate that the binary contribution to ternary His is much more important than the ternary contribution. Correlation methods were also examined and a partial differential approximant was proposed to represent the ternary contribution to the excess enthalpy. This work was partially funded by U.S. Department of Energy Grant No. DEFG02-85ER13443, Cooperative Research Grant in Basic Sciences No. CCB8402019 between Spain and the United States, NATO Collaborative Research Grant No. SA. 5-2-05 (RG. 0035/88), and by the Donors of the Petroleum Research Fund administered by the America1 Chemical Society. We appreciate the aid given to us in collecting the results by G. Anderson and P. R. Harding. REFERENCES 1. 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.: Remmcio, J. A. R.; Schofield, R. S.; Izatt. R. M.; Christensen, J. J. J. Chem. Thermodynamics 1983, 15, 141. 4. Christensen, J. J.; Zebolsky, D. M.; Izatt, R. M. J. Chem. Thermodynamics 1985, 17, 1. 5. Faux, P. W.; Christensen, J. J.; Izatt, R. M. J. Chem. Thermodynamics 1987, 19, 757. 6. Pando, C.; Remmcio, J. A. R.; Faux. P. W.; Christensen, J. J.; Izatt, R. M. J. Chem. Thermodynamics 1988, 20, 897. 7. Pando, C.: Renuncio, J. A. R.; Faux, P. W.; Christensen, J. J.; Izatt. R. M. J. Chem. Thermodynamics 1988, 20, 559. 8. Faux, P. W.; Christensen, J. J.; Izatt, R. M.; Pando, C.; Renuncio, J. A. R. J. Chem. Thermodynamics 1988, 20, 503. 9. Faux, P. W.; Christensen, J. J.; Izatt, R. M.; Pando, C.; Renuncio, J. A. R. J. Chem. Thermodynamics 1989, 21, 1291. 10. Pando, C.; Renuncio, J. A. R.; Calzon, J. A. G.; Christensen, J. J.; Izatt, R. M. J. Solution Chemistry 1987, 16, 503. 11. Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1984, 73, 117. 12. Christensen, J. J.; Hansen, L. D.; Izatt, R. M.; Eatough, D. J.; Hart, R. M. Rev. Sci. Instrum. 1981, 52, 1226. 13. Rubio, R. G.; Remmcio, J. A. R.; Diaz Peiia, M. Fluid Phase Equilibria 1983, 12, 217. 14. Scatchard, G.: Ticknor, L. B.: Goates, J. R.; McCartney, E. R. J. Am. Chem. Sot. 1952, 74, 3721. 15. Toop, G. W. Trans. TMS-AIME 1965,233, 850. 16. Hillert, M. Calphad 1980, 4, 1. 17. Sebastian, H. M.; Simnick. J. J.; Lin, H. M.; Chao, K.-C. J. Chem. Eng. Data 1980, 25, 246. 18. Leder. F.; Irani, C. A. J. Chem. Eng. Data 1975, 20, 323. 19. Ng, H.-J.; Robinson, D. B. J. Chem. Eng. Data 1978, 23, 325. 20. Hicks, C. P.: Young, C. L. Chem. Rev. 1975, 75, 119. 21. Morrison, G.; Levelt Sengers, J. M. H.; Chang, R. F.; Christensen, J. J. Supercritical Fluid Technology. Penninger, J. M. L. et al.: editors, Elsevier: Amsterdam. 1985. 22. Morris, J. W.; Mulvey, P. J.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 403. 23. Shatas, J. P.; Abbott, M. M.; Van Ness, H. C. J. Chem. Eng. Data 1975, 20, 406. 24. Kratochvila, J.: Cibulka, I.; Holub, R. Collect. Czech. Chem. Commun. 1980, 45, 3241.