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Excess molar enthalpies and excess molar volumes of {xCO2 + (1 − x)C2H6} up to 308.4 K and 11.0 MPa
Excess molar enthalpies and excess molar volumes of {xCO,+(l -x)C,H,} up to 308.4 K and 11.0 MPa C. J. WORMALD”
AND
J. M. EYEARS
School uf’ Chemistry, Universit~~ qf’ Bristol. Bristol BS8 ITS. U.K. i Received 9 March
1987; in ,fincd,form 10 Ju(I, 1987)
Measurements of the excess molar enthalpy Hk and excess molar volume 12 for ivCOz +( I -Y)C,H,) are described. The measurements cover the range 248.1 to 308.4 K at pressures from 4.0 to It .O MPa. The uncertainty of the His is + 2 per cent, and of the V:s is +_4 per cent. The Patel-Teja equation of state reproduces all the main features of H:(x) and Vi(x). and tits the measurements better than expected. Agreement with results from other laboratories is within the combined experimental uncertainties.
1. Introduction Excess molar enthalpies Hi of several mixtures of (carbon dioxide + a hydrocarbon) made using a flow-mixing calorimeter have been reported by Pando YI ~1.“’ Measurements of Hk{xCO,+( 1-x)C,H,) were made at 7.58 MPa and at the temperatures 293.15, 308.15, and 323.15 K. ‘l’ For the same mixture Wallis ef ~1.‘~’used a batch calorimeter to make liquid-phase measurements at 217.0 and 230.0 K and at the saturation pressureof the mixture. Lesnevskaya et a1.‘3’reported enthalpies of mixing of (carbon dioxide + ethane)(g) from 298 to 319 K at pressures up to 1.5 MPa. Using a computer-controlled flow-mixing calorimeter connected in serieswith a vibrating-tube densimeter we have made extensive measurementsof Hli, and V,” for :.xCO, +( 1-x)C,H,) in both subcritical and supercritical regions at temperatures between 248.1 and 308.4 K, at pressures up to 11.OMPa. A phase diagram showing the regions studied is shown in figure 1. For CO,, T, is 304.2I K and p is 7.38 MPa;(4) for C,H,, T, is 305.33 K and pc is 4.87 MPa.‘5) The critical locus ‘of the mixture has been studied by several workers.‘h-8’ T,(x = 0.5) is (1420.5) K below the mean of the pure-component T,s. (Liquid + vapour) equilibrium measurements show‘9’ that the mixture has a positive azeotrope with a maximum at x = 0.62 and 223 K, and at x = 0.75 and 283 K. The locus of the aLeotrope is shown by the broken line in figure I. Temperature and pressure * To whom
correspondence
0021-9614/88,'030323+09
should
%02.00/O
be addressed (’ 108X Academic
Press Limited
324
C. J. WORMALD I
0
AND
I
J. M. EYEARS I
0
1
1
I
0
IO0 0
X-
+
6-
’ in the critical region. --~-. The upper FIGURE 1. The phase diagram for /xCO,+(l -.x)C,H,, curve is the vapour pressure of carbon dioxide and the lower curve is the vapour pressure of ethane. The curves terminate at the critical points of the pure fluids where they are joined by the (p, 7) projection of the critical locus; - - -, locus of the azeotrope, reference 9. P,(x), T,(x) measurements: 0, references 6; A. references 7 and 8; 0. conditions at which Hi and V, measurements listed in table I were made: +, conditions at which Hi measurements of reference I were made.
conditions at which our H:(x) and V,“(x) measurementswere made are indicated by circles. So that we could compare our results with those of Pando et al.“’ (marked by crossesin figure 1) we made measurementsat 308.4 K at 7.5 MPa, just above p, for COz. To explore the behaviour of the excessfunctions in the supercritical region close to the critical temperatures of the pure components we made measurementsat 300.1. 306.4, and 308.4 K at pressuresfrom 4.0 to 11.OMPa.
2. Experimental The apparatus was the same as that used for (xCO,+(l -x)C,H,CH,j.“O’ The flow-mixing calorimeter was fitted with both a heater and a Peltier-cooling device. Mixture leaving the calorimeter passedthrough a heat-exchange coil before entering the vibrating-tube densimeter. The carbon dioxide was 99.99 moles per cent CO,. The ethane used was (0.9940C,H, + O.O035C,H, + O.O025C,H,). The materials were used without further purification. The pure components were stored as liquids in cylindrical vesselsmaintained at (253.2f0.1) K. The liquids were displaced from the vessels by mercury pumped from similar cylinders, and this in turn was displaced by water from metering pumps. The molar flow rate and the composition of the mixture were calculated from the flow rate of water entering the metering pumps, the density of the liquefied gasesat 253.2 K, and the pressure chosen for the experiment. Densities of carbon dioxide were taken from reference 4 and densities of ethane from reference 11. All measurements were made by scanning the mole fraction x at a chosen temperature and pressure under computer control. Scans were begun by passing pure carbon dioxide through the apparatus, and were completed
HE AND
V; OF
(.X0,+(1
-.v)C,H,;
325
by passing pure ethane. Runs on the pure components were used to calibrate the densimeter and to check the calibration of the Peltier device. The fluid bath containing the calorimeter and the densimeter was controlled to + 10 mK. Fluid leaving the densimeter was pumped into a receiver back-pressured with nitrogen controlled to k2 kPa. Small fluctuations in temperature, pressure, and flow rate caused corresponding fluctuations in the output from the calorimeter and densimeter. These were reduced by using the computer to sample the output at 10 s intervals and to average the signal. The uncertainty on the HLs is +2 per cent. As V,Es were obtained from measurements of the density of the pure components and the mixture, the uncertainty is correspondingly greater, and is estimated to be Ifr4 per cent. Occasionally, excessive noise in the signal resulted in the standard deviation of the calculated Hzs and Vzs being unacceptably large; such runs were rejected by the computer.
3. Results and discussion Results of Hi and V,” measurements are listed in table I and plotted in figures 3 and 3. Unbroken lines were drawn with a flexicurve. For guidance as to what H:s and 1/,Es might be expected, and to assist comparison with other work, we used the Patel-Teja”” (PT) equation of state. It was shown previously”3’ that the PT equation is a better fit to saturated liquid and vapour densities than other recent cubic equations of state. The fit, however, is far from perfect; one would not expect the equation simultaneously to fit both Hz and V,” measurements, nor would one expect it to fit either Hz or V,” over anything but a small range of temperature or pressure. The method for the calculation of the enthalpy was given previously.“3’ To obtain the parameters u, b. and c for the mixture the l-fluid combining rules were used. a=x2u,a,+x(l-.u)(l-k,z)(a,a,+u,a~)”’+(l-~~)2~,aZ~
(1)
where a = {l +F(ro))(l
- T,““)‘.
(3)
an d F(o) = 0.480 + 1.574~ - 0.176~‘. where Q is the acentric factor. Parameter
(3)
h was obtained from
b = xb, +(I -x)h,.
(4)
and a similar expression was used to obtain c. After experimenting with different values of the adjustable parameter k,, we decided not to make it temperature dependent and chose k,, = 0.1325 which gives a reasonable fit over the whole temperature range. This is close to the value k,, = 0.128 used by Pate1 and Teja”” to fit the bubble-pressure curve. The broken lines shown in figures 2, 3. and 4 were calculated using k,, = 0.1325. The fit to the results in the subcritical region at 248.1 and 272.1 K shown in
C. J. WORMALD
326 TABLE
105
H’ m J.mol-’
153 410
671 1301
93 152 202
274 599 795
41 125 172 213 256
1. Excess molar Vm’
cm3.molm’
1.5
enthalpies
He l0J.x m J.mol-’
459 509
1465 1509
I.1 1.6
305 357 407
1113 1215 1292
137 429 792 1055 1264
3.8 3.7 4.9
299 340 425 465 508
I328 1519 1641 1655 1670
loo 152 202 254
260 547 762 901
2.1 2.9 3.7 4.0
353 403 455 506
1196 1277 1353 1381
98 197 247
218 399 474
14.2 26.3 29.3
298 400 499
511 545 522
46 95 122 134 153
8 82 128 318 449
- 7.0 - 12.6 - 16.0 - 15.0 ~ 14.3
169 199 248 299 371
754 1142 2459 2982 2912
96 148 198 290
475 752 974 1403
4.3 6.4 8.4 12.3
351 398 500 548
1602 1782 2130 2299
96 194 243 294
188 302 415 542
334 398 450 504
683 898 1078 1301
106 210
236 356
313 512
436 433
AND
Hk and excess molar
ft 103.x ~ J.moi-’
T = 248.1 K
p = 3.0 MPa
3.0 3.1
2.1 2.3 2.5 T = 272.1 K 5.2 5.6
6.6 T=27?.1K 4.6 4.3 4.4 4.8 T=3OO.lK 31.6 33.9 34.1 T = 300.1 K -9.5 12.0 42.5 68.7 73.0 T=3OO.lK 15.8 17.6 23.5 26.2 T = 306.4 K -1.2 1.3 8.1 12.3 T=
14.0 24.5
volumes
VP m cm3,molm’
T = 248.1 K
-2.0 -3.3 -3.6 -3.5
J. M. EYEARS
308.4 K 29.7 30.3
609 709
VL of [rCOL c’ E m cm3,molF’
+ (I -~ .y)CLHb
IO”!. ~J.;;;-
I
I
cm-
1 .!;,,,~~I
2.8 2.5
807 904
1048 519
2.0 0.5
2.6 2.6 2.3
706 806 903
1203 923 480
7.1 1.6 0.x
1702 1626 1595 1475 1416
6.5 6.3 5.9 5.4
796 838 870 918 959
1075 906 725 432 194
4.0 3.3 7.3 1.9 1.2
1319 1345 1285 II74
4.5 4.2 4.2 3.7
803 851 900 950
913 665 408 206
2.7 1.5 1.4 0.5
510 473 435
32.6 31.1 ‘7.8
698 749 850
398 343 219
24.8 20.3 12.2
2861 2769 248 I 2350 2147
72.6 74.8 63.9 60.8 55.5
699 747 799 848 899
I893 1615 1330 999 681
48.8 41.8 33.8 25.0 15.4
2361 2420 2429 2319
28.7 30.4 30.8 29.0
798 850 546
2040 1501 1101
‘4.5 17.1 11.4
19.1 22.7 26.0 27.1
798 850 901 952
1271 1051 809 460
25.8 ‘2.5 18.0 10.1
26.3 23.5
809 903
1514 1365
p = 10.9 MPa 505 557 655
1363 1370 1370
p = 4.5 MPa 525 597 633 673 7138 ~=11.0MPa 556 605 655 706 p=4.0MPa 548 600 650
/I = 5.5 MPa 398 413 559 598 648 p=7.5MPa 600 651 698 749
p = 7.5 MPa 555 607 660 747
1438 I523 1519 1415
p = 4.0 MPa 616 711
402 340
249 133
18.4 9.4
Hk
AND
V,” OF TABLE
]OJr
-2
If’
J mol-’
V’ 103x
cm”.&-’
Hk J molt
m
VL ’ cm3. mol
l--continurd
I
T = 308.4 K Y7 I 20 14X 171 I ox
IX11 2200 2552 2738 2964
45.8 5x.2 73.1 79.8 X7.6
208 297 321 372 374
291 I 3028 303 1 2897
YX 14x 230 243 294
317 659 I680 1998
4.2 -3.2 19.4 20.0 31.6
374 424 473 519 519
2156 2160 2201 2008 2016
‘5 :; Yb IYX
296 345 397 446
677
31 76 171 379
- 0.5 ~~ 1.9 ~ 2.7 -- 4.2
1153 1317
46 9X 14x 196
‘04 440 685 X97
1.7 3.5 5.3 7.4
242 294 342 446
1053 1266 1401 1861
4b 148 39x
170 640 1597
I .4 4.7 14.1
496 548 597
1780 1880 1936
Y5 193 292 392
393 759 1061 1307
2.7 5.0 1.4 x.9
445 486 495 520
1397 1404 1438 1465
92.1 92.9 93.0 88.4 92.2 T=
308.4 K 44.1 46.6 48.1 47.7 47.8
T=
308.4 K - 1.9 0.3 x.7 13.4
T = 308.4 K 9.6 12.3 15.0 23.5 T = 308.4 K 18.2 19.8 21.2 T = 308.4 K 9.7 10.1 10.5
327
/xCOZ+(I-.x)C,H,)
!O%
Hk J.mol m
V,E
-’ cm”,mol-’
p = 5.5 MPa 447 464 496 517
2629 2660 237X
562
2114
87.3 84.5 83.4 79.0 74.1
662 711 809 898 903
1731 1500 1003 555 515
60.7 53.0 36.0 1X.6 17.X
48.3 45.2 44.6 43.6 39.7
722 772 868 886 917
1503 1156 670 685 424
35.7 30.0 17.7 14.Y 10.6
IX.2 19.5 21.9 25.2
69X 798 897 947
1370 1099 640 3X9
25.x 21.9 15.0 x.9
26.3 30.3 33.5 37.7
691 748 847 898
241x 2354 2039 16X4
3x.7 39.7
22.0 77 7 --.21.3
798 898 945
I665 915 435
lY.4 x.9 2.x
10.6 IO.7 10.7 10.7
643 694 79s 89X
1454 1355 11’1 527
10.5 10.2 X.2 2.x
p = 6.5 MPa 519 568 572 622 673
‘04b 2014 1794 I740 15.59
p = 7.5 MPa 49X 523 547 599
1490 14X6 1647 1617
p = 8.3 MPa 495 546 595 669
2010 2159 22RO 2365
3b.3
30. I
p = 9.0 MPa 647 698 749
1945 1931 IX’0
p = I I .O M Pa 543 570 593 61X
1470 1476 1478 1454
figure 2(a to d) is better than expected. The three curves at 300.1 K shown in figure 2(e, f) correspond to mixing processes where the fluids are under different conditions. Figure 1 shows that at 4.0 MPa both components entered the mixing calorimeter in the gaseous state. and a gaseous mixture was formed. At 7.5 MPa both components entered the calorimeter in the liquid state, and a liquid mixture of density much less than that of the pure components was formed. At 5.5 MPa gaseous carbon dioxide mixed with liquid ethane. For x < 0.15 the mixture was a subcritical liquid and the mixing process was the dissolution of carbon dioxide gas into ethane to form a liquid mixture of higher density than the mole-fractionweighted mean of the pure-component densities. V,” was therefore negative. Above x = 0.15 liquid ethane evaporated into the stream of gaseous carbon dioxide to form
32X
C. J. WORMALD
21 (c)
FIGURE 0, Table
2. Hk 1; -.
,’
,---,,“.5
MPa
AND
J. M. EYEARS
4
and V, measurements for [.uCO,+(l-x)C,H,J drawn with a flexicurve; “. ‘. calculated
from
at 248.1, 272.1. and 300.1 K. the PT equation of state using
k,, = 0.1325.
a supercritical mixture of gas-like density, and V,” was large and positive. The PT equation reproduces the behaviour remarkably well. Mole-fraction scans in the supercritical region at 308.4 K, made at seven pressures from 4.0 to 11.0 MPa, are shown in figure 3. The curves are most skewed at 5.5 and 8.3 MPa. Those pressures are nearest to the point of intersection of the isothermal locus with the extrapolated vapour-pressure curves, where H,!$ and V,Es calculated from the PT equation are greatest and most skewed. The curves skew towards a high mole fraction of the component with the nearest intersection. At 4.0 and 11.0 MPa the pure fluids and the mixtures are of gas-like and liquid-like
Hi
AND
V, OF
;uC02+(l-.x)(‘,H,~
329
‘t (a)
FIGURE 3. Hk and Vk ~--, drawn with a tlexicurve;
measurements for - - -, calculated
{xCO,+( 1 -- u)C,H,I from the PT equation
at 308.4 K. 0. Table of state using k, z 7 0.1325.
I:
densities, respectively, and the Hi(x) curves are relatively small and symmetric. At 6.5 and 7.5 MPa the V$ at low mole fractions of CO, are negative though the corresponding Hzs remain positive. At both pressures the densities of the pure fluids are quite different: carbon dioxide is of gas-like density (0.185 and 0.285 g. cm ‘) and ethane is of liquid-like density (0.314 and 0.333 g’ cmm3). At low mole fractions of CO, the mixing process is the dissolution of gas-like carbon dioxide in liquid-like cthane to form a mixture of liquid-like density. V,” is therefore negative.
4. Comparison with other work Measurements of HE(x) at 217.0 and 230.0 K reported by Wallis et ~1.‘“’ were made at the bubble pressure of the mixture. To compare these measurements with ours we calculated { aHE(x) T,x and {aH~(x)/i?V),, X from the PT equation and adjusted their measurements to 248.1 K and 3.0 MPa. The adjustments were not large; about 2 per cent. Comparison with our measurements at 248.1 K and 3.0 MPa is made in figure 4(a); the agreement is very good. The unbroken line shown in figure 4(a) is a
c‘. J. WORMALD
AND
.I. M. EYEARS I
I
(h) I +’
+‘+
,--. ++ ++
-5’ +/
\ \
,i’P-+, to.3
+,’
l
y+;
,
‘a;,
+/
‘\ \
+‘, _
‘\ \
+,’
’ o\
/
’ +\
\ +\
l
,
\
+/+ :
/ +
/ /*//
,‘O
’ A\ A
+/
\ ‘O\
0
‘\ /
0’0
d 0
0.2
0.4
0.6
0.8
1 (I
0.2
0.4
0.6
0.8
1
FIGURE 4. Comparison of Hk and V,” measurements for [xCO,+( 1 -.x)C,H,) with other work. p, Parabolas fitted to the measurements: - - -, calculated from the PT equation of state using klZ = 0.1325; (a), Hi measurements at 3.0 MPa: 0, table 1. measurements at 248.1 K; A. reference 2 (adjusted from 230.0 K to 248.1 K); V, reference 2 (adjusted from 217.0 K to 248.1 K). (b), Hi measurements at 7.5 MPa: 0. table 1. measurements at 308.4 K; +, reference 1 (measurements at 308.15 K and 7.58 MPd near lower curve); +, reference 1 (measurements at 293. I.5 K and 7.58 MPa near upper curve). (c). V, measurements at 3.0 MPa; 0, table I. measurements at 248.1 K; 0, reference 14 (measurements at 255.35 K): 0, reference 14 (measurements at 241.45 K).
parabola; the measurements are only slightly skewed towards the ethane-rich side. Comparison of our measurements at 308.4 K and 7.5 MPa with Pando et ul.‘s”’ measurements at 308.15 K and 7.58 MPa is made in figure 4(b). The broken line was calculated from the PT equation using k,, = 0.1325 as before. For x > 0.5 the two sets of measurements are in excellent agreement; for .Y< 0.5 the agreement is less good. Over the whole composition range Pando et al.‘s measurements lie on the curve generated by the PT equation. Comparison of their measurements at 293.15 K with the PT equation shows that the calculated maximum is too great and is skewed too far toward the ethane-rich end. A similar comparison (not shown) of their measurements at 323.15 K shows that the PT equation gives a maximum which is too small and is again skewed too far to the ethane-rich end. The agreement between their measurements at 308.15 K and the PT equation must therefore be seen as coincidental. Their measurements in the region x < 0.5 might be more accurate than ours but the good agreement with the PT equation is not evidence for that. Densities of (xC0, +(l -x)C,H,j and of the pure components at 241.45 and 255.35 K and at the bubble pressure have been measured by Gugnoni et ~1.“~’
If;
AND
V, OF
;.xCO,+(l
-.x.)C2Hhj
331
IJsing the PT equation values of (aV,/ap),. for the mixture were calculated and used to obtain V,” at 3.0 MPa. As the adjustments were no more than 2 per cent uncertainties arising from inadequacies of the PT equation were negligible. r/:s calculated from their densities are compared with our t$ at 248.1 K and 3.0 MPa in figure 4(c). The unbroken curves are parabolas. Our I/,“s lie between their I/zs at 241.45 and 255.35 K. Within the large experimental uncertainties ( +0.25 cm3. mol-‘) the two sets are in good accord. In conclusion we note that the PT equation fits both Hz and V,” measurements surprisingly well. This is because the T,s for the pure components are close together and T, for the mixture is only 14 K less. Under these circumstances the equation fails to fit pure-component and mixture properties by similar amounts, and the error in the excess functions is smaller than it might otherwise be. We are grateful to the British their interest in the work.
Petroleum
Company
for financial support and for
REFERENCES I. Pando. C.: Renuncio. J. A. R.: Izatt. R. M.: Christensen. J. J. J. C/rem. Thermo&nanric~.x 1983, IS. 231. ’ Wallis, K. P.; Clancy, P.: Zollweg, J. A.; Streett, W. B. J. Chem. Thermodvnumics 1984, 16, XI I. ? Lesnevskaya, L. S.: Nikiforova. M. B.; Domracheva, T. 1. Zh. Fiz. Khim. i975, 49, 1921. 4. IUPAC Thermodynamic Tables qf’the Fluid Slure. Carbon Dioxide. Pergamon Press: Oxford. 1976. 5. Douslin, D. R.; Harrison, R. H. J. Chem. Thermodynamics 1973, 5. 491. h. Kuenen. J. B. Z. Phys. Chem. 1897, 24. 661. 7. Khazanova, N. E.: Lesnevskaya, L. S.: Zakharova, A. V. Khim. Prom. 1966, 44. 364 s. Ohgaki, K.; Katayama. T. Fluid Phase Equilibria 1977, I, 27. 9. Fredenslund. A.; Mollerup, J. J. Chem. Sot. Faraday Trans. 1974, 70. 1653. It). Wormald, C. J.; Eyears, J. M. J. Chem. Thermo+uzmics 1987, 19, 845. I I. Thermophysical properties of ethane,fiom 90 10 600 K ar pressures up to 700 bar. National Bureau of Standards: Washington. 1976. 12. Patel. N. C.: Teja. A. S. Chem. Eng. Sci. 1982, 37, 463. 13. Yerlett. T. K.: Wormald, C. J. J. Chem. Thermodwzamics 1986, 18. 37 I IJ. Gugnoni. R. J.; Eldridge. R. W.: Okay. V. C.: Lee. T. J. .4IChE J. 1974, 20, 357.
AND
J. M. EYEARS
School uf’ Chemistry, Universit~~ qf’ Bristol. Bristol BS8 ITS. U.K. i Received 9 March
1987; in ,fincd,form 10 Ju(I, 1987)
Measurements of the excess molar enthalpy Hk and excess molar volume 12 for ivCOz +( I -Y)C,H,) are described. The measurements cover the range 248.1 to 308.4 K at pressures from 4.0 to It .O MPa. The uncertainty of the His is + 2 per cent, and of the V:s is +_4 per cent. The Patel-Teja equation of state reproduces all the main features of H:(x) and Vi(x). and tits the measurements better than expected. Agreement with results from other laboratories is within the combined experimental uncertainties.
1. Introduction Excess molar enthalpies Hi of several mixtures of (carbon dioxide + a hydrocarbon) made using a flow-mixing calorimeter have been reported by Pando YI ~1.“’ Measurements of Hk{xCO,+( 1-x)C,H,) were made at 7.58 MPa and at the temperatures 293.15, 308.15, and 323.15 K. ‘l’ For the same mixture Wallis ef ~1.‘~’used a batch calorimeter to make liquid-phase measurements at 217.0 and 230.0 K and at the saturation pressureof the mixture. Lesnevskaya et a1.‘3’reported enthalpies of mixing of (carbon dioxide + ethane)(g) from 298 to 319 K at pressures up to 1.5 MPa. Using a computer-controlled flow-mixing calorimeter connected in serieswith a vibrating-tube densimeter we have made extensive measurementsof Hli, and V,” for :.xCO, +( 1-x)C,H,) in both subcritical and supercritical regions at temperatures between 248.1 and 308.4 K, at pressures up to 11.OMPa. A phase diagram showing the regions studied is shown in figure 1. For CO,, T, is 304.2I K and p is 7.38 MPa;(4) for C,H,, T, is 305.33 K and pc is 4.87 MPa.‘5) The critical locus ‘of the mixture has been studied by several workers.‘h-8’ T,(x = 0.5) is (1420.5) K below the mean of the pure-component T,s. (Liquid + vapour) equilibrium measurements show‘9’ that the mixture has a positive azeotrope with a maximum at x = 0.62 and 223 K, and at x = 0.75 and 283 K. The locus of the aLeotrope is shown by the broken line in figure I. Temperature and pressure * To whom
correspondence
0021-9614/88,'030323+09
should
%02.00/O
be addressed (’ 108X Academic
Press Limited
324
C. J. WORMALD I
0
AND
I
J. M. EYEARS I
0
1
1
I
0
IO0 0
X-
+
6-
’ in the critical region. --~-. The upper FIGURE 1. The phase diagram for /xCO,+(l -.x)C,H,, curve is the vapour pressure of carbon dioxide and the lower curve is the vapour pressure of ethane. The curves terminate at the critical points of the pure fluids where they are joined by the (p, 7) projection of the critical locus; - - -, locus of the azeotrope, reference 9. P,(x), T,(x) measurements: 0, references 6; A. references 7 and 8; 0. conditions at which Hi and V, measurements listed in table I were made: +, conditions at which Hi measurements of reference I were made.
conditions at which our H:(x) and V,“(x) measurementswere made are indicated by circles. So that we could compare our results with those of Pando et al.“’ (marked by crossesin figure 1) we made measurementsat 308.4 K at 7.5 MPa, just above p, for COz. To explore the behaviour of the excessfunctions in the supercritical region close to the critical temperatures of the pure components we made measurementsat 300.1. 306.4, and 308.4 K at pressuresfrom 4.0 to 11.OMPa.
2. Experimental The apparatus was the same as that used for (xCO,+(l -x)C,H,CH,j.“O’ The flow-mixing calorimeter was fitted with both a heater and a Peltier-cooling device. Mixture leaving the calorimeter passedthrough a heat-exchange coil before entering the vibrating-tube densimeter. The carbon dioxide was 99.99 moles per cent CO,. The ethane used was (0.9940C,H, + O.O035C,H, + O.O025C,H,). The materials were used without further purification. The pure components were stored as liquids in cylindrical vesselsmaintained at (253.2f0.1) K. The liquids were displaced from the vessels by mercury pumped from similar cylinders, and this in turn was displaced by water from metering pumps. The molar flow rate and the composition of the mixture were calculated from the flow rate of water entering the metering pumps, the density of the liquefied gasesat 253.2 K, and the pressure chosen for the experiment. Densities of carbon dioxide were taken from reference 4 and densities of ethane from reference 11. All measurements were made by scanning the mole fraction x at a chosen temperature and pressure under computer control. Scans were begun by passing pure carbon dioxide through the apparatus, and were completed
HE AND
V; OF
(.X0,+(1
-.v)C,H,;
325
by passing pure ethane. Runs on the pure components were used to calibrate the densimeter and to check the calibration of the Peltier device. The fluid bath containing the calorimeter and the densimeter was controlled to + 10 mK. Fluid leaving the densimeter was pumped into a receiver back-pressured with nitrogen controlled to k2 kPa. Small fluctuations in temperature, pressure, and flow rate caused corresponding fluctuations in the output from the calorimeter and densimeter. These were reduced by using the computer to sample the output at 10 s intervals and to average the signal. The uncertainty on the HLs is +2 per cent. As V,Es were obtained from measurements of the density of the pure components and the mixture, the uncertainty is correspondingly greater, and is estimated to be Ifr4 per cent. Occasionally, excessive noise in the signal resulted in the standard deviation of the calculated Hzs and Vzs being unacceptably large; such runs were rejected by the computer.
3. Results and discussion Results of Hi and V,” measurements are listed in table I and plotted in figures 3 and 3. Unbroken lines were drawn with a flexicurve. For guidance as to what H:s and 1/,Es might be expected, and to assist comparison with other work, we used the Patel-Teja”” (PT) equation of state. It was shown previously”3’ that the PT equation is a better fit to saturated liquid and vapour densities than other recent cubic equations of state. The fit, however, is far from perfect; one would not expect the equation simultaneously to fit both Hz and V,” measurements, nor would one expect it to fit either Hz or V,” over anything but a small range of temperature or pressure. The method for the calculation of the enthalpy was given previously.“3’ To obtain the parameters u, b. and c for the mixture the l-fluid combining rules were used. a=x2u,a,+x(l-.u)(l-k,z)(a,a,+u,a~)”’+(l-~~)2~,aZ~
(1)
where a = {l +F(ro))(l
- T,““)‘.
(3)
an d F(o) = 0.480 + 1.574~ - 0.176~‘. where Q is the acentric factor. Parameter
(3)
h was obtained from
b = xb, +(I -x)h,.
(4)
and a similar expression was used to obtain c. After experimenting with different values of the adjustable parameter k,, we decided not to make it temperature dependent and chose k,, = 0.1325 which gives a reasonable fit over the whole temperature range. This is close to the value k,, = 0.128 used by Pate1 and Teja”” to fit the bubble-pressure curve. The broken lines shown in figures 2, 3. and 4 were calculated using k,, = 0.1325. The fit to the results in the subcritical region at 248.1 and 272.1 K shown in
C. J. WORMALD
326 TABLE
105
H’ m J.mol-’
153 410
671 1301
93 152 202
274 599 795
41 125 172 213 256
1. Excess molar Vm’
cm3.molm’
1.5
enthalpies
He l0J.x m J.mol-’
459 509
1465 1509
I.1 1.6
305 357 407
1113 1215 1292
137 429 792 1055 1264
3.8 3.7 4.9
299 340 425 465 508
I328 1519 1641 1655 1670
loo 152 202 254
260 547 762 901
2.1 2.9 3.7 4.0
353 403 455 506
1196 1277 1353 1381
98 197 247
218 399 474
14.2 26.3 29.3
298 400 499
511 545 522
46 95 122 134 153
8 82 128 318 449
- 7.0 - 12.6 - 16.0 - 15.0 ~ 14.3
169 199 248 299 371
754 1142 2459 2982 2912
96 148 198 290
475 752 974 1403
4.3 6.4 8.4 12.3
351 398 500 548
1602 1782 2130 2299
96 194 243 294
188 302 415 542
334 398 450 504
683 898 1078 1301
106 210
236 356
313 512
436 433
AND
Hk and excess molar
ft 103.x ~ J.moi-’
T = 248.1 K
p = 3.0 MPa
3.0 3.1
2.1 2.3 2.5 T = 272.1 K 5.2 5.6
6.6 T=27?.1K 4.6 4.3 4.4 4.8 T=3OO.lK 31.6 33.9 34.1 T = 300.1 K -9.5 12.0 42.5 68.7 73.0 T=3OO.lK 15.8 17.6 23.5 26.2 T = 306.4 K -1.2 1.3 8.1 12.3 T=
14.0 24.5
volumes
VP m cm3,molm’
T = 248.1 K
-2.0 -3.3 -3.6 -3.5
J. M. EYEARS
308.4 K 29.7 30.3
609 709
VL of [rCOL c’ E m cm3,molF’
+ (I -~ .y)CLHb
IO”!. ~J.;;;-
I
I
cm-
1 .!;,,,~~I
2.8 2.5
807 904
1048 519
2.0 0.5
2.6 2.6 2.3
706 806 903
1203 923 480
7.1 1.6 0.x
1702 1626 1595 1475 1416
6.5 6.3 5.9 5.4
796 838 870 918 959
1075 906 725 432 194
4.0 3.3 7.3 1.9 1.2
1319 1345 1285 II74
4.5 4.2 4.2 3.7
803 851 900 950
913 665 408 206
2.7 1.5 1.4 0.5
510 473 435
32.6 31.1 ‘7.8
698 749 850
398 343 219
24.8 20.3 12.2
2861 2769 248 I 2350 2147
72.6 74.8 63.9 60.8 55.5
699 747 799 848 899
I893 1615 1330 999 681
48.8 41.8 33.8 25.0 15.4
2361 2420 2429 2319
28.7 30.4 30.8 29.0
798 850 546
2040 1501 1101
‘4.5 17.1 11.4
19.1 22.7 26.0 27.1
798 850 901 952
1271 1051 809 460
25.8 ‘2.5 18.0 10.1
26.3 23.5
809 903
1514 1365
p = 10.9 MPa 505 557 655
1363 1370 1370
p = 4.5 MPa 525 597 633 673 7138 ~=11.0MPa 556 605 655 706 p=4.0MPa 548 600 650
/I = 5.5 MPa 398 413 559 598 648 p=7.5MPa 600 651 698 749
p = 7.5 MPa 555 607 660 747
1438 I523 1519 1415
p = 4.0 MPa 616 711
402 340
249 133
18.4 9.4
Hk
AND
V,” OF TABLE
]OJr
-2
If’
J mol-’
V’ 103x
cm”.&-’
Hk J molt
m
VL ’ cm3. mol
l--continurd
I
T = 308.4 K Y7 I 20 14X 171 I ox
IX11 2200 2552 2738 2964
45.8 5x.2 73.1 79.8 X7.6
208 297 321 372 374
291 I 3028 303 1 2897
YX 14x 230 243 294
317 659 I680 1998
4.2 -3.2 19.4 20.0 31.6
374 424 473 519 519
2156 2160 2201 2008 2016
‘5 :; Yb IYX
296 345 397 446
677
31 76 171 379
- 0.5 ~~ 1.9 ~ 2.7 -- 4.2
1153 1317
46 9X 14x 196
‘04 440 685 X97
1.7 3.5 5.3 7.4
242 294 342 446
1053 1266 1401 1861
4b 148 39x
170 640 1597
I .4 4.7 14.1
496 548 597
1780 1880 1936
Y5 193 292 392
393 759 1061 1307
2.7 5.0 1.4 x.9
445 486 495 520
1397 1404 1438 1465
92.1 92.9 93.0 88.4 92.2 T=
308.4 K 44.1 46.6 48.1 47.7 47.8
T=
308.4 K - 1.9 0.3 x.7 13.4
T = 308.4 K 9.6 12.3 15.0 23.5 T = 308.4 K 18.2 19.8 21.2 T = 308.4 K 9.7 10.1 10.5
327
/xCOZ+(I-.x)C,H,)
!O%
Hk J.mol m
V,E
-’ cm”,mol-’
p = 5.5 MPa 447 464 496 517
2629 2660 237X
562
2114
87.3 84.5 83.4 79.0 74.1
662 711 809 898 903
1731 1500 1003 555 515
60.7 53.0 36.0 1X.6 17.X
48.3 45.2 44.6 43.6 39.7
722 772 868 886 917
1503 1156 670 685 424
35.7 30.0 17.7 14.Y 10.6
IX.2 19.5 21.9 25.2
69X 798 897 947
1370 1099 640 3X9
25.x 21.9 15.0 x.9
26.3 30.3 33.5 37.7
691 748 847 898
241x 2354 2039 16X4
3x.7 39.7
22.0 77 7 --.21.3
798 898 945
I665 915 435
lY.4 x.9 2.x
10.6 IO.7 10.7 10.7
643 694 79s 89X
1454 1355 11’1 527
10.5 10.2 X.2 2.x
p = 6.5 MPa 519 568 572 622 673
‘04b 2014 1794 I740 15.59
p = 7.5 MPa 49X 523 547 599
1490 14X6 1647 1617
p = 8.3 MPa 495 546 595 669
2010 2159 22RO 2365
3b.3
30. I
p = 9.0 MPa 647 698 749
1945 1931 IX’0
p = I I .O M Pa 543 570 593 61X
1470 1476 1478 1454
figure 2(a to d) is better than expected. The three curves at 300.1 K shown in figure 2(e, f) correspond to mixing processes where the fluids are under different conditions. Figure 1 shows that at 4.0 MPa both components entered the mixing calorimeter in the gaseous state. and a gaseous mixture was formed. At 7.5 MPa both components entered the calorimeter in the liquid state, and a liquid mixture of density much less than that of the pure components was formed. At 5.5 MPa gaseous carbon dioxide mixed with liquid ethane. For x < 0.15 the mixture was a subcritical liquid and the mixing process was the dissolution of carbon dioxide gas into ethane to form a liquid mixture of higher density than the mole-fractionweighted mean of the pure-component densities. V,” was therefore negative. Above x = 0.15 liquid ethane evaporated into the stream of gaseous carbon dioxide to form
32X
C. J. WORMALD
21 (c)
FIGURE 0, Table
2. Hk 1; -.
,’
,---,,“.5
MPa
AND
J. M. EYEARS
4
and V, measurements for [.uCO,+(l-x)C,H,J drawn with a flexicurve; “. ‘. calculated
from
at 248.1, 272.1. and 300.1 K. the PT equation of state using
k,, = 0.1325.
a supercritical mixture of gas-like density, and V,” was large and positive. The PT equation reproduces the behaviour remarkably well. Mole-fraction scans in the supercritical region at 308.4 K, made at seven pressures from 4.0 to 11.0 MPa, are shown in figure 3. The curves are most skewed at 5.5 and 8.3 MPa. Those pressures are nearest to the point of intersection of the isothermal locus with the extrapolated vapour-pressure curves, where H,!$ and V,Es calculated from the PT equation are greatest and most skewed. The curves skew towards a high mole fraction of the component with the nearest intersection. At 4.0 and 11.0 MPa the pure fluids and the mixtures are of gas-like and liquid-like
Hi
AND
V, OF
;uC02+(l-.x)(‘,H,~
329
‘t (a)
FIGURE 3. Hk and Vk ~--, drawn with a tlexicurve;
measurements for - - -, calculated
{xCO,+( 1 -- u)C,H,I from the PT equation
at 308.4 K. 0. Table of state using k, z 7 0.1325.
I:
densities, respectively, and the Hi(x) curves are relatively small and symmetric. At 6.5 and 7.5 MPa the V$ at low mole fractions of CO, are negative though the corresponding Hzs remain positive. At both pressures the densities of the pure fluids are quite different: carbon dioxide is of gas-like density (0.185 and 0.285 g. cm ‘) and ethane is of liquid-like density (0.314 and 0.333 g’ cmm3). At low mole fractions of CO, the mixing process is the dissolution of gas-like carbon dioxide in liquid-like cthane to form a mixture of liquid-like density. V,” is therefore negative.
4. Comparison with other work Measurements of HE(x) at 217.0 and 230.0 K reported by Wallis et ~1.‘“’ were made at the bubble pressure of the mixture. To compare these measurements with ours we calculated { aHE(x) T,x and {aH~(x)/i?V),, X from the PT equation and adjusted their measurements to 248.1 K and 3.0 MPa. The adjustments were not large; about 2 per cent. Comparison with our measurements at 248.1 K and 3.0 MPa is made in figure 4(a); the agreement is very good. The unbroken line shown in figure 4(a) is a
c‘. J. WORMALD
AND
.I. M. EYEARS I
I
(h) I +’
+‘+
,--. ++ ++
-5’ +/
\ \
,i’P-+, to.3
+,’
l
y+;
,
‘a;,
+/
‘\ \
+‘, _
‘\ \
+,’
’ o\
/
’ +\
\ +\
l
,
\
+/+ :
/ +
/ /*//
,‘O
’ A\ A
+/
\ ‘O\
0
‘\ /
0’0
d 0
0.2
0.4
0.6
0.8
1 (I
0.2
0.4
0.6
0.8
1
FIGURE 4. Comparison of Hk and V,” measurements for [xCO,+( 1 -.x)C,H,) with other work. p, Parabolas fitted to the measurements: - - -, calculated from the PT equation of state using klZ = 0.1325; (a), Hi measurements at 3.0 MPa: 0, table 1. measurements at 248.1 K; A. reference 2 (adjusted from 230.0 K to 248.1 K); V, reference 2 (adjusted from 217.0 K to 248.1 K). (b), Hi measurements at 7.5 MPa: 0. table 1. measurements at 308.4 K; +, reference 1 (measurements at 308.15 K and 7.58 MPd near lower curve); +, reference 1 (measurements at 293. I.5 K and 7.58 MPa near upper curve). (c). V, measurements at 3.0 MPa; 0, table I. measurements at 248.1 K; 0, reference 14 (measurements at 255.35 K): 0, reference 14 (measurements at 241.45 K).
parabola; the measurements are only slightly skewed towards the ethane-rich side. Comparison of our measurements at 308.4 K and 7.5 MPa with Pando et ul.‘s”’ measurements at 308.15 K and 7.58 MPa is made in figure 4(b). The broken line was calculated from the PT equation using k,, = 0.1325 as before. For x > 0.5 the two sets of measurements are in excellent agreement; for .Y< 0.5 the agreement is less good. Over the whole composition range Pando et al.‘s measurements lie on the curve generated by the PT equation. Comparison of their measurements at 293.15 K with the PT equation shows that the calculated maximum is too great and is skewed too far toward the ethane-rich end. A similar comparison (not shown) of their measurements at 323.15 K shows that the PT equation gives a maximum which is too small and is again skewed too far to the ethane-rich end. The agreement between their measurements at 308.15 K and the PT equation must therefore be seen as coincidental. Their measurements in the region x < 0.5 might be more accurate than ours but the good agreement with the PT equation is not evidence for that. Densities of (xC0, +(l -x)C,H,j and of the pure components at 241.45 and 255.35 K and at the bubble pressure have been measured by Gugnoni et ~1.“~’
If;
AND
V, OF
;.xCO,+(l
-.x.)C2Hhj
331
IJsing the PT equation values of (aV,/ap),. for the mixture were calculated and used to obtain V,” at 3.0 MPa. As the adjustments were no more than 2 per cent uncertainties arising from inadequacies of the PT equation were negligible. r/:s calculated from their densities are compared with our t$ at 248.1 K and 3.0 MPa in figure 4(c). The unbroken curves are parabolas. Our I/,“s lie between their I/zs at 241.45 and 255.35 K. Within the large experimental uncertainties ( +0.25 cm3. mol-‘) the two sets are in good accord. In conclusion we note that the PT equation fits both Hz and V,” measurements surprisingly well. This is because the T,s for the pure components are close together and T, for the mixture is only 14 K less. Under these circumstances the equation fails to fit pure-component and mixture properties by similar amounts, and the error in the excess functions is smaller than it might otherwise be. We are grateful to the British their interest in the work.
Petroleum
Company
for financial support and for
REFERENCES I. Pando. C.: Renuncio. J. A. R.: Izatt. R. M.: Christensen. J. J. J. C/rem. Thermo&nanric~.x 1983, IS. 231. ’ Wallis, K. P.; Clancy, P.: Zollweg, J. A.; Streett, W. B. J. Chem. Thermodvnumics 1984, 16, XI I. ? Lesnevskaya, L. S.: Nikiforova. M. B.; Domracheva, T. 1. Zh. Fiz. Khim. i975, 49, 1921. 4. IUPAC Thermodynamic Tables qf’the Fluid Slure. Carbon Dioxide. Pergamon Press: Oxford. 1976. 5. Douslin, D. R.; Harrison, R. H. J. Chem. Thermodynamics 1973, 5. 491. h. Kuenen. J. B. Z. Phys. Chem. 1897, 24. 661. 7. Khazanova, N. E.: Lesnevskaya, L. S.: Zakharova, A. V. Khim. Prom. 1966, 44. 364 s. Ohgaki, K.; Katayama. T. Fluid Phase Equilibria 1977, I, 27. 9. Fredenslund. A.; Mollerup, J. J. Chem. Sot. Faraday Trans. 1974, 70. 1653. It). Wormald, C. J.; Eyears, J. M. J. Chem. Thermo+uzmics 1987, 19, 845. I I. Thermophysical properties of ethane,fiom 90 10 600 K ar pressures up to 700 bar. National Bureau of Standards: Washington. 1976. 12. Patel. N. C.: Teja. A. S. Chem. Eng. Sci. 1982, 37, 463. 13. Yerlett. T. K.: Wormald, C. J. J. Chem. Thermodwzamics 1986, 18. 37 I IJ. Gugnoni. R. J.; Eldridge. R. W.: Okay. V. C.: Lee. T. J. .4IChE J. 1974, 20, 357.