FLOIDPN[ EQUILIBRIA

ELSEVIER Fluid Phase Equilibria 113 (1995) 127-138

VLE for cryogenic methyl fluoride + nitrous oxide + xenon at 182.33 K

I.M.A. Fonseca, L.Q. Lobo *

Departamento de Engenharia Qulmica, Universidade de Coimbra, 3000 Coimbra, Portugal

Received 22 November 1994; accepted 25 June 1995

Abstract

An apparatus for accurate VLE measurements on ternary cryogenic systems is briefly described. It is a modified version of that introduced and developed by Staveley and co-workers for binary mixtures. The apparatus was tested against published results for CH 3F + Xe and N20 + Xe, at 182.33 K, the agreement being much satisfactory for both systems. The mixture CH3F + N20 + Xe at the same temperature was selected for the first measurements on a ternary system carried out using the modified experimental arrangement, the operation of which is also summarized. VLE results for 61 ternary points are presented together with the evaluation of the excess molar Gibbs free energy G E for the liquid mixture at that temperature. No ternary azeotrope has been found. G E for the three component liquid mixture is not an additive function of the G~ for its constituent binary mixtures. For the equimolar (ternary) mixture G~/3 = (500 -4- 6) J mol -~ , at 182.33 K.

Keywords: Experiments; Method; Data; VLE low pressure; Ternary; Cryogenic liquids; Non-electrolytes; Polar; Non-polar

I. Introduction

In the 1950s Staveley and co-workers (Mathot et al., 1956) reported on an apparatus specially designed for the experimental study of some of the excess thermodynamic functions of binary mixtures of condensed gases. It could be used to measure the total vapour pressure of mixtures of known overall composition (and hence of their excess molar Gibbs energy GE), the dew-point pressure, the volume change on mixing (i.e. the excess molar volume vE), and the virial coefficients of the gaseous phase at the temperatures of the other measurements. Improved versions of the original model have been used later for G E (or VLE) and V E measurements only (Davies et al., 1967). Apparatuses similar to that developed in Oxford were assembled in Lisbon by Calado and his group (Calado et al., 1980), and in Coimbra by ourselves (Fonseca and Lobo, 1989). The measurements usually cover the entire composition range, and the deviations associated with the G E values obtained

* Corresponding author.

0378-3812/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved SSDI 0378-3812(95)02810-2

128 LM.A. Fonseca, L.Q Lobo / Fluid Phase Equilibria 113 (1995) 127-138

through this technique in the cryogenic region have been assessed (Duncan and Hiza, 1972) as being one order of magnitude smaller than those attached to other low-temperature techniques used previously. By combining the results so obtained with the measurements made in low-temperature heat of mixing precision calorimeters (Lewis et al., 1975, Lewis and Staveley, 1975) highly accurate values of the four primary excess thermodynamic functions: G E, H E, S E and V E have been obtained for a considerable number of binary cryogenic systems. Since the mixtures experimentally studied in this way along the years were selected in a systematic manner so as to involve components of simple, rigid molecules for which the intermolecular potential functions are known with sufficient accuracy, they have been widely used as model systems to test theories of liquid mixtures.

In what ternary systems are concerned the situation is much different. With few exceptions the experimental results reported in the literature either contemplate ternary liquid mixtures whose component molecules are large enough for their intermolecular potential parameters to remain ill-defined, or the measurements made lack the accuracy needed to test most theories. For this reason calculations on ternary systems have been commonly approached by considering that the correspond- ing excess thermodynamic functions are simple additive functions of those of their respective constituent binary mixtures. Alternatively, if terms arising from three-component interactions are not left out from the models, then the experimental information to test their estimated contribution has not been available in general.

Owing to the intrinsic qualities of the technique introduced by Staveley we thought it would be worth to try and extend it to the study of ternary cryogenic liquid mixtures. In this paper we report on a modified version of the GE/v z apparatus for ternary mixtures, and on the experimental results obtained for the vapour-liquid equilibrium of CHaF(1)+N20(2)+Xe(3) , at 182.33 K. This particular system was chosen for two main reasons. Firstly, because one of its three constituent binaries (CHaF + Xe) had been recently investigated in our laboratory using the unmodified version of the apparatus (Fonseca and Lobo, 1989); the binary (N20 + Xe) having been extensively measured in Staveley's laboratory some years ago (Machado et al., 1980). Secondly, because this ternary system involves as components species whose molecules are almost pure-dipoles (CH3F: /x = 1.85 X 10-18 esu; Q = 0.04 × 10 -26 esu), almost pure-quadrupoles (N20: /~ = 0.16 × 10 -18 esu; Q = 3.8 × 10 -26

esu)(Gray and Gubbins, 1984), and non-polar, spherical molecules (Xe). Molecular shape and polarity have been shown to be essential in studying the thermodynamic behaviour of liquid mixtures using modern statistical theories of solutions; in this context the ternary system on which we report here may help in testing such theories.

As far as we are aware the technique described in this work has not been used previously in the study of any other ternary cryogenic system.

2. Experimental

The apparatus and the technique used to measure the total vapour pressure of binary liquified gas mixtures have been already described in detail (Fonseca and Lobo, 1989). However, to extend them both to the measurement of ternary systems some changes had to be made. In what the glass apparatus is concerned an additional calibrated gas storage globe of (2337.2 _ 0.2) cm 3 capacity (C in Fig. 1) was included, as well as two thick-walled bulbs (G and K, in Fig. 1) of (0.51 +0.02) and (0.33 + 0.02) cm 3 capacity, respectively, to help in preparing the ternary mixtures to be studied. One starts an experiment by condensing measured amounts of the third, usually more volatile component,

I.M.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138 129

,°v,cuu-i I ,5, D GI ~ ,

,,: I l . . . . . . . . . . .

L to storage or vacuum

~ J

Fig. 1. Ternary G E and V E apparatus. A, B and C, calibrated storage globes; D,G and K, small thick-walled glass bulbs; E, Boyle manometer; F, quartz-spiral gauge; H, mercury compressor with fiducial marks h' and h"; I, gas pipette with fiducial marks i' and i"; J, mercury reservoir; L, glass globe for transfer gas (He); M and P, mercury manometers; N, pyknometer assembly; O, glass trap for cryostat substance; 1 to 21, stopcocks. The heavier line represents thick-walled capilary glass.

in bulbs G and K where they are to remain while measurements are taken on the binary mixture of the other two components, which is prepared first in the way previously reported (Fonseca and Lobo, 1989). After the equilibrium vapour pressure measurements on the binary mixture have been taken, stopcock 3 (Fig. 1) is opened, and by lowering the level of liquid nitrogen refrigerant surrounding bulb G the measured amount of the third component contained in it is allowed to mix with the binary mixture in the equilibrium vessel N. Prior to starting the measurements of the vapour pressure of the ternary mixture it is necessary to ensure that both phases are homogeneous and in true equilibrium with each other. This is accomplished in much the same way as that described for binary mixtures (Fonseca and Lobo, 1989), although it takes longer (about two hours). After the cryostat substance (in the intermediate vessel surrounding pyknometer N) is adjusted to its triple-point the vapour pressure of the ternary mixture should remain constant within a few parts in 10 4 o v e r a period of at least 30 minutes during which readings are taken every minute with the calibrated quartz-spiral manometer F (Texas Instruments, model 145-01, capsule type 811). When these measurements are over the (measured) amount of the third component in bulb K is added to the previous mixture (by opening stopcock 2), and the process is repeated for a second ternary mixture, richer in the third component. In this way one binary (A) and two ternary (B and C) experimental points are obtained in each run, as schematically shown in Fig. 2. One such complete run takes about 10 hours. In the modified version of the apparatus the main features of the original one are retained, namely: (i) the remarkable constancy in temperature (which is essential in static VLE cells) that can be achieved by surrounding the liquid sample with a highly purified substance melting at its own triple-point; (ii) the small amounts of substance needed in each experiment (less than 1 c m 3 of any of the component liquids); (iii) the much smaller amount of substance in the vapour phase than in the equilibrium liquid; (iv) the small uncertainties attached to the measured and the derived thermodynamic quantities. With the new arrangement of the apparatus the uncertainties in these quantities for ternary systems (as compared

130 LM.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 12 7-138

2

1 3

Fig. 2. Paths to obtain one binary (A) + two ternary (B and C) experimental points in one run.

with those for binary mixtures) become as shown in Tables 1 and 2, respectively. The method to derive the errors attached to the calculated G E values is reported elsewhere (Fonseca and Lobo,

1994b). Cyl inder gases were used as the sources of the pure substances either to prepare the mixtures or for

the cryostat. Methyl f luoride was a Matheson product of mole fraction purity better than 0.990, while nitrous oxide and xenon were both f rom Air Liquide with purities stated as better than 0.9999 and 0.9995, respectively. As usual, each of these substances was further purified by fractionation in the laboratory low-temperature distillation column, the middle fraction being used in the experiments. The final purity o f the samples was confirmed by the constancy of the triple point pressure during

Table 1 Uncertainties in the experimentally measured quantities for binary and ternary mixtures, at 182.33 K

Experimental Uncertainty

quantity ~ Binary mixtures Ternary mixtures

T / K 10 -3 10 -3 P/Pa 10 100 X i 5× 10 -4 5× 10 - 4

X i is the overall (global) mole fraction of component i in the system.

Table 2 Uncertainty in G E for binary and ternary mixtures

Uncertainties in the experimental quantities a

Uncertainty in G E (J moi- t)

Binary mixtures Ternary mixtures

AP = 100 Pa 0.5 1 Ax i = 5 × 10 -4 0.5 1 Ay i = 5 × 10 -4 0.5 3

a AP is the uncertainty in the experimental equilibrium pressure; Ax i and Ay i are the uncertainties in the mole fractions of component i in the liquid and in the vapour, respectively.

LM.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138

Table 3 Triple-point pressures Pt of the substances used

131

Substance P t /kPa

This work Literature Ref.

CH 3F 0.400 ± 0.005 0.379 + 0.003 N20 87.875 ± 0.012 87.895 ± 0.007

87.865 +_ 0.012 Xe 81.680 + 0.012 81.608 + 0.008

81.675 + 0.011

Fonseca and Lobo, 1989 Fonseca and Lobo, 1989 Staveley et al., 1981 Fonseca and Lobo, 1989 Staveley et al., 1981

melting, as measured with a wide-bore standard mercury manometer. The triple-point pressures Pt so obtained are compared in Table 3 with values taken from the literature.

All the measurements for the binary and ternary mixtures reported in this work were made using dinitrogen oxide melting at its own triple-point as the cryostatic medium (T t = 182.33 K; cf. Staveley et al., 1981).

To evaluate G E from the raw experimental data some ancillary values were needed, the sources of which will be summarized briefly. Allowance was made for the nonideality of the vapours but since the pressures involved were always low only-second virial coefficients B were considered. These were taken from the compilation of Dymond and Smith (1980) and fitted to the equation,

2

B/Vc= E biTr -i ( l ) i=0

where V c is the critical volume, T r = T/T~ is the reduced temperature, and b i are parameters. The cross second virial coefficients Bij were assumed to be the arithmetic means of the values for the pure components. The molar volumes Vmi of the pure components in the liquid state at 182.33 K, which are also needed in the calculation o f 'G E, were taken as: Vm~ 1 = 37.513 cm 3 mol-1 for methyl fluoride (Fonseca and Lobo, 1989), Vm*2 = 35.487 cm 3 mo1-1 and Vm. 3 = 46.453 cm 3 mol- l for dinitrogen oxide and xenon, respectively (Machado et al., 1980). Throughout this paper methyl fluoride is designated as component 1, dinitrogen oxide as component 2, and xenon as component 3. Tempera- tures have been converted into ITS-90 using standard methods (Lobo and Staveley, 1979; McGlashan, 1990).

3. Results and discussion

The three binary mixtures involving C H 3 F , N 2 0 , and Xe as components can be studied as liquids at 182.33 K over their complete composition ranges. Independent measurements provide accurate VLE results at that temperature for the pairs CH3F + Xe (Fonseca and Lobo, 1989) and N20 + Xe (Machado et al., 1980). For this reason these two systems have been used to test the performance of the modified version of the apparatus on which we are reporting in the present work.

3.1. The binary system CH3F(1) + Xe(3)

The equilibrium pressure P has been measured for nine binary mixtures of methyl fluoride and xenon, covering the entire composition range at 182.33 K. The experimental results, which are shown

132 I.M.A. Fonseca, L, Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138

Table 4 Vapour pressure P and excess molar Gibbs free energy G E for CHaF(1)+Xe(3) , at 182.33 K a

xl Yl P (kPa) Rp (kPa) G E (J mol-1)

0.0000 0.0000 247.913 - 0 0.1024 0.0978 254. 884 0.393 279.4 0.1963 0.1280 252.325 0.185 457.5 0.3402 0.1477 246.693 - 0.022 617.1 0.4008 0.1541 243.620 - 0.262 648.4 0.5278 0.1688 235.027 - 0.063 656.1 0.5313 0.1688 234.647 - 0.701 654.8 0.6440 0.1864 222.818 0.411 599.5 0.7328 0.2084 206,620 0.037 511.1 0.8590 0.2738 165,822 - 0,053 320.0 1 . 0 0 0 0 1 . 0 0 0 0 48.163 - 0

a xl and Yl are the mole fractions of methyl fluoride in the liquid and in the vapour, respectively. Rp -- P - Pcalc, are the pressure residuals.

in Table 4 and in Fig. 3, have been reduced using Barker's method (Barker, 1953) assuming a three,term Redlich-Kister equation for the excess molar Gibbs free energy G~ of the binary mixture:

GE/(RT) = x i xj[ aij + Bij (x i - xj) + Cij ( x i - xj)2], (i = 1;j = 3) (2)

The values obtained for the parameters are A13 = 1.7470 + 0.0018; B13 = -0 .1467 + 0.0039; and Cl3 = 0.1957 + 0.0081. For the equimolar mixture GE3(x~ = 0.5) = (657.4 + 0.7) J mo1-1 The agreement with the results obtained in the unmodified version of the apparatus (Fonseca and Lobo, 1989) is excellent. This is particularly reassuring having in mind that CH3F + Xe is a markedly nonideal mixture forming an azeotrope at x I = 0.09 and P = 255 kPa, as observed in both studies.

60O

, 0o

g

20O

0 J I i

o.o o'., ' oi, o'., ' ,.o Xl

Fig. 3. Excess molar Gibbs free energy of the system CH 3F(1)+ Xe(3), at 182.33 K, plotted against the liquid mole fraction x I. The line represents G ~ values from Eq. (1). The symbols represent experimental values: 0 , this work; A, Fonseca and Lobo, 1989.

I.M.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138

Table 5 Vapour pressure P and excess molar Gibbs free energy G E for N20(2)+Xe(3), at 182.33 K a

133

x2 Y2 P (kPa) Rp (kPa) G E (J mol-1)

0.0000 0.0000 247.913 - 0 0.2191 0.1702 245.624 -0.788 303.5 0.3705 0.2335 237.475 0.047 423.5 0.4853 0.2712 230.096 1.604 465.7 0.5935 0.3111 217.249 - 0.423 447.3 0.7197 0.3664 199.554 - 0.515 381.6 0.8270 0.4438 175.853 0.004 277.8 1.0000 1.0000 87.875 - 0

a x2 and Y2 are the mole fractions of nitrous oxide in the liquid and in the vapour, respectively. R o = P - Pcalc, are the pressure residuals.

3.2. The binary system N20(2) + Xe(3)

For the binary system of dinitrogen oxide and xenon at 182.33 K only six mixtures have been investigated in this work, spanning the interval from x 2 --- 0.2 to x 2 - 0.8. The experimental results, which have been treated in much the same way as that used for CH aF + Xe, are listed in Table 5. The parameters in the Redl ich-Kis te r Eq. (2), with i = 2 and j = 3, are: A23 = 1 . 2 1 2 6 + 0.0148;

B23 = 0.0715 + 0.0194; C23 = 0.0506 + 0.0221. For the equimolar binary mixture GE3(x2 = 0.5)----(458.5 + 5.6) J mo1-1. The comparat ively

higher value of the uncertainty attached to GE3 is due to the small number of experimental points measured for this system. Even so, comparison with the results reported by Machado et al. (1980), obtained in the Oxford apparatus, is quite satisfactory as shown in Fig. 4. The agreement is also good for the coordinates of the azeotrope ( x 2 = 0.09; P = 248 kPa).

5OO

400

200

100

0 J I I t I I. I n. t 0.0 0,2 0.4 0 6 0 8 1.0

X2

Fig. 4. Excess molar Gibbs free energy of the system N20(2)+ Xe(3), at 182.33 K, plotted against the liquid mole fraction x 2. The line represents G ~ values from Eq. (1). The symbols represent experimental values: O, this work; A, Machado et al., 1980.

134 LM.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138

Table 6 Vapour pressure P and excess molar Gibbs free energy G E for CHaF(1)+N20(2)+Xe(3), at 182.33 K a

Xj X 2 Yl Y2 P (kPa) Rp (kPa) G E (J mol- i )

0.0384 0.5604 0.0144 0.2911 214.712 -2.111 447 0.0530 0.7719 0.0195 0.4175 172.137 -2.687 274 0.0809 0.7710 0.0302 0.4346 164.623 -0.977 261 0.0870 0.1788 0.0580 0.1192 246.046 0.664 421 0.0882 0.8421 0.0396 0.5760 131.774 -0.098 155 0.0893 0,3220 0.0410 0.1856 235.044 -0.216 486 0.0957 0.0823 0.0736 0.0606 251.293 0.773 356 0,1113 0.7302 0.0402 0.4078 168.164 -0.250 288 0.1222 0.8037 0.0530 0.5470 133.005 -0.157 169 0.1371 0.4527 0.0487 0.2321 217.918 -0.375 494 0.1398 0.6944 0.0493 0.3859 168.414 - 1.730 290 0.1452 0.5989 0.0483 0.3086 192.561 -0.912 395 0.1527 0.2211 0.0715 0.1261 240.144 0.866 517 0.1612 0.1878 0.0784 0.1084 241,634 0.379 511 0.1678 0.2961 0.0675 0.1581 232,444 0.374 533 0.1696 0.6749 0.0598 0.3825 166.652 0.288 299 0.1735 0.4786 0.0581 0.2416 209.996 -0.048 476 0.1742 0.1035 0.0966 0.0625 246.839 0.412 490 0.1790 0.3891 0.0635 0.1985 223.028 1.524 527 0.1877 0.7484 0.0822 0.5404 126.130 0.206 166 0.2115 0.1639 0.0947 0.0894 240.758 0.333 546 0.2135 0.6342 0.0745 0.3638 164.276 -0.298 296 0.2341 0.0712 0.1168 0.0396 246.123 0.036 540 0.2354 0.7007 0.1017 0.5135 124.166 -0.517 162 0.2433 0.2520 0.0904 0.1277 231.536 0.904 563 0.2550 0.6006 0.0890 0.3513 159.983 - 1.189 281 0.2583 0.3907 0.0840 0.1940 212.247 0.838 503 0.2712 0.5107 0.0877 0.2703 184.393 0.212 385 0.2850 0.1232 0.1160 0.0624 240.001 0.287 587 0.3089 0.1580 0.1151 0.0774 235.288 0.219 591 0.3095 0.3295 0.0996 0.1610 216.187 2.323 531 0.3137 0.3976 0.0989 0.1991 202.333 1.457 470 0.3168 0.1796 0.1137 0.0872 232.696 -0.542 582 0.3360 0.5096 0.1140 0.2945 165.494 1.303 323 0.3552 0.0801 0.1342 0.0381 238.890 -0.468 615 0.3712 0.5640 0.1580 0.4274 123.076 1.038 187 0.4084 0.1917 0.1303 0.0890 222.063 0.265 568 0.4148 0.1794 0.1326 0.0828 222.820 0.014 572 0.4189 0.4265 0.1409 0.2461 165.387 1.431 329 0.4631 0.4722 0.1984 0.3649 121.874 1.852 196 0.4661 0.0806 0.1507 0.0355 229.905 -0.873 614 0.4667 0.0791 0.1509 0.0348 229.650 - 1.239 612 0.4734 0.3765 0.1596 0.2186 160.831 - 1.173 301 0.4784 0.2202 0.1457 0.1041 206.471 0.407 502 0.4974 0.3291 0.1618 0.1814 170.480 -0.471 342 0.5146 0.2537 0,1585 0.1270 189.218 -0.490 422 0.5475 0.1116 0.1641 0.0495 215.279 -0.526 551 0.5528 0.2333 0,1713 0.1183 185.960 0.778 414

I.M.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138 135

Table 6 (continued)

xl x2 Yl Y2 P (kPa) Rp (kPa) G E (J tool-l)

0.5613 0.3702 0.2384 0.2841 120.255 -0.318 174 0.5626 0.2866 0.1883 0.1640 164.535 1.784 333 0.5732 0.2855 0.1949 0.1671 154.623 - 3.081 265 0.6066 0.2007 0.1900 0.1038 178.354 -0.767 377 0.6123 0.1200 0.1815 0.0552 199.312 - 2.298 469 0.6206 0.3164 0.2720 0.2512 117.273 1.070 180 0.6349 0.2410 0.2230 0.1468 148.649 -2.409 252 0.6544 0.2755 0.2776 0.2104 123.724 3.113 218 0.6901 0.1602 0.2272 0.0891 164.731 0.770 330 0.6941 0.0913 0.2080 0.0438 186.390 - 2.487 407 0.7549 0.1754 0.3205 0.1338 121.688 1.805 200 0.7617 0.0989 0.2521 0.0555 159.346 - 1.529 296 0.4154 b 0.2997 0.1280 0.1665 200.605 -0.880 465

a xi and Yi are the mole fractions of component i in the liquid and in the vapour. Rp = P - Pcalc, are the pressure residuals. b Experimental point obtained by using the technique described by Fonseca and Lobo, 1989 (in which the three components are condensed into the pyknometer directly from globes A, B, and C (Fig. 1).

3.3. The binary system CHsF(1) + N20(2)

Experimental GE2 results obtained in our laboratory for the binary mixture of methyl fluoride and dinitrogen oxide at 182,33 K were reported recently in detail (Fonseca and Lobo, 1994a). As far as we are aware no other VLE study on this system is available in the literature, a fact that precludes the use of such values in testing the performance of the apparatus on which we are reporting here. However, considering the purpose of this work, i.e., the study of VLE for the ternary system, it is convenient to recall that CH3F + N20 at the temperature considered is the less non-ideal system amongst the three binaries, with GE2(xl -- 0.5) = (48.5 + 2.2) J mol - l . Its parameters in Eq. (2) are: A12 = 0.1248 + 0.0057; B~2 = -0 .0862 + 0.0034; C12 = 0.0645 _ 0.0164.

3.4. The ternary mixture CH3F(1) + N20(2) + Xe(3)

The analysis of the 61 VLE experimental points obtained at 182.33 K for the ternary mixtures indicated in Table 6 was carried out assuming that for the three-component system G E is represented by a Redlich-Kister equation of the form:

3

GE = E E GE + GlE23 (3) i<j j= 1

where Gij E. for the binary mixtures are given by Eq. (2) with the values of the parameters stated above, and

a 231( R r ) = x l x2 x3( co - c , x l - c2 x2 ) (4) is a ternary contribution on which we have reported recently (Lobo and Fonseca, 1993). The parameters Co, c~, and c 2 have been optimized from ternary data only, by using an extension of Barker's method described elsewhere (Fonseca and Lobo, 1994b). With Co= -0.6711 + 0.0746,

1 3 6 I.M.A. Fonseca, L.Q. Lobo l Fluid Phase Equilibria 113 (1995) 127-138

~ 0 0 -

'-- 6 0 0 - O .e

~ ' 400- (,9

200" 3

0 1 2

Fig. 5. G E as a function of composition for liquid CH 3F(1)+ N20(2)+ Xe(3), at 182.33 K.

c~ =--0 .4088-1-0.1354, C 2 = --0.5585-1-0.1488 the G E dependence on the mole fractions is as shown in Fig. 5. G E is an asymmetrical function of composition with a maximum at x I = 0.48, x 2 = 0.00. For the equimolar m i x t u r e GE/3(Xl = x 2 = x 3 = 1/3) = (500 + 6) J mo1-1. Fig. 6 shows a perspective view of the P-x-y surfaces for the ternary system. No ternary azeotrope has been found. Calculated tie-lines, obtained by making P = 150 and 200 kPa (in Eqs. (2)-(5) in reference Fonseca and Lobo, 1994b) are compared in Fig. 7 with three of the nearest experimental equilibrium lines taken from Table 6. The agreement is quite satisfactory.

The additivity assumption for G E (i.e., considering GIE23 = 0 in Eq. 3) leads t o GEl3 = (519 + 3) J mol-~ for the equimolar mixture which is not too far from the observed value reported above. However, not only the difference (of 19 J mo1-1) exceeds the experimental uncertainty i n GEl3, but also the frequency distribution of the pressure residuals (as shown in Fig. 8) indicates that the contribution of the ternary t e r m GlE23 cannot be neglected (cf. Lobo and Fonseca, 1993).

500-

400-

~-aoo. n

200.

,-.~Y/////////~I o

2

Fig. 6. Perspective view of the P-x-y surfaces for CH3F(1) -I- N 2 0 ( 2 ) + Xe(3), at 182.33 K.

LM.A. Fonseca, L.Q. Lobo/FluidPhase Equilibria 113 (1995) 127-138 137

3

i "° " i J ° " v ~ .

s J ~ i

' ' " ",-4 , , ' ,, ' , , a ,

. . . . ' ',_..2'.;_..2 s i i j t p i . i i ~

/ ~ . Z . - ~ - - . - , " " ~ _ / P.2OOkPa ; I ', \ . f , ' - - , , " / " / ' ! : ",, i i # i I

1 / v v v v v v v v v x 2

Fig. 7. Calculated (dotted) and experimental (full) tie-lines for the ternary system CH3F(I)+ N20(2)+ Xe(3), at 182.33 K. The full triangles ( • ) indicate the composition of the liquid phase in equilibrium with the vapour (open triangles, zx). tl is for P = 148.649 kPa; t2, for 199.312 kPa; and t3, for 202.333 kPa. The dash-dotted lines are: -.-, for 150 kPa; . . . . , for 200 kPa. O are binary azeotropes, A and B.

T h e sugges t ion m a d e by W o h l (1953) that the main ternary parameter c o could be es t imated f rom

in format ion on b inary mix tures paramete rs only, namely

c o = ~ ( Aij + Cij ) (i,j = 1 ,2 ,3) (5) i J

leads to an unaccep t ab l e f r equency dis t r ibut ion o f the pressure residuals, and to G E values far f rom

expe r im en t (e.g., GE/3 = 710 J m o l - 1 ) .

i

- 8 - 4

No, of )olnts

25-

O~

5.

I I I

R, x l O0 P (a)

No. ~ ~n ts

2 5

T

0 4 -8

-•x100 (b)

Fig. 8. Frequency distribution of the percentual pressure residuals, Ro = 100 X (P-P~a~)/P: (a), considering GEl23 = 0 in Eq. (3); (b), considering Gl23F" = x~ x 2 x3(co-C l x r c 2 x 2) in Eq. (3).

138 I.M.A. Fonseca, L.Q. Lobo / Fluid Phase Equilibria 113 (1995) 127-138

4. Conclusions

The extension to ternary mixtures of the technique introduced by Staveley for VLE measurements of binary liquified gas mixtures has been successfully accomplished, the experimental uncertainties being similar for both cases.

The ternary system CH3F + N 2 0 + Xe, which is an example of a mixture of the type dipolar + quadrupolar + nonpolar, exhibits comparat ively large positive values of the excess molar Gibbs energy G E, at 182.33 K. At this temperature G ~ is an asymmetric function of composit ion, being GEl3 = 500 J mol -1 for the equimolar mixture.

It is necessary to take into account a ternary contribution GIE23 to bring the frequency distribution of the pressure residuals closer to the Gaussian model. This is a clear indication that G E for the ternary system is not a simple additive function of the excess molar Gibbs free energies o f the constituent binary mixtures. The suggestion made by Wohl that the main ternary parameter c o in the Red l i ch - Kister G E expression could be estimated from values o f binary parameters only is not o f use for the system studied in the present work.

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