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The excess enthalpies of (carbon dioxide + ethanol) at 308.15, 325.15, 373.15, 413.15, and 473.15 K from 5.00 to 14.91 MPa
O-266 J. Clwnl.
Tiwmodvuzmics
1988, 20, 655-663
The excess enthalpies of (carbon dioxide + ethanol) at 308.15, 325.15, 373.15, 413.15, and 473.15 K from 5.00 to 14.91 MPa D. R. CORDRAY, J. J. CHR1STENSEN.t
R. M. IZATT, and J. L. OSCARSON
Departments of Chemical Enginr,ering Brigham Young University, Provo. Utah 84602, U.S.A. (Received
23 September
1987;
and
in.final,ftirm
Chc~mistr~~,
26 Octohcr
1987)
The excess molar enthalpies H~(xCO, + (1 --.x)C,H,OH) were measured in the vicinity of the critical locus. Large positive and negative HEs were observed depending on the compositions, temperatures, and pressures. Rapid changes with small variations In temperature and composition were observed. An interpolating function used to describe the results is presented. The Soave equation of state was used to correlate His over a temperature range of 308.15 to 473.15 K and a pressure range of 5.00 to 14.91 MPa. The fit ranged from poor to excellent depending upon the pressures and temperatures of the mixtures. The average standard deviation over all pressures, temperatures. and compositions was 242 J mol. ’
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies If: of binary mixtures in the vicinity of their (gas + liquid) critical loci. Results for several examples of (carbon dioxide + a hydrocarbon),“’ (a fluorocarbon + a hydrocarbon),“’ and (carbon dioxide + an alcohol)“) have been reported. In these mixtures, Hz showed increased negative character as the critical point of the component having the lower critical temperature was approached along an isobar. Where the critical point of the second component was approached, large positive lfzs were observed. The present work reports values of Hz{xCOz + ( I -x)C,H,OH} from 308.15 to 473.15 K at 5.00 to 14.91 MPa. In this paper, HE values have been modeled using the Soave equation of state’“’ in an attempt the better to predict mixing behavior in the critical region. 2. Experimental The high-temperature high-pressure flow calorimeters used and the experimental procedure have been described. (4-6) All runs were made in the steady-state (fixedBy acceptance of this article, the publisher acknowledges the right of the U.S. Government nonexclusive royalty-free license in and to any copyright covering this paper. t Died 5 September 1987.
to retain
a
656
D. R. C’ORDRAL’ TABLE
.x
1. Experimental
H,$/{J . mol - ’ ) expt
and calculated Hk/(J.mol-‘)
x
talc
expt
E7’.41>.
excess enthalpies: Y
Hii H:/(J
xC0, mol-
+ ( I - \-)CzH I)
expt
talc
-3210 - 3320 - 3490 - 3650 -3920 -4090
-3120 -3310 -3510 - 3720 - 4070 - 4090
CdC
9
50H \ Hk,‘(J expt
mol..
’ ) CillC
308.15 K, 7.50 MPa 0.1375 0.1769 0.2164 0.2956 0.3352 0.3750
-703 -940 - 1250 - 1650 - 1750 -2010
- 708 -936 -1170 -1630 - 1850 - 2060
0.4148 0.4547 0.4947 0.5347 0.5748 0.5748
-2190 - 2490 - 2670 - 2830 -2980 -2880
-51.6 -73.6 -110 -137 -154 -159 -162 -163 -162
0.2979 0.2979 0.3186 0.3598 0.3598 0.4007 0.4414 0.4817 0.5218
- 153 - 151 - 151 - 139 - 136 -118 -95.8 -68.8 -42.2
-159 -159 -154 -139 -139 -119 -95.3 -68.4 -40.0
-2260 - 2440 -2610 -2780 -2950 - 2950
0.6150 0.6552 0.6955 0.7359 0.8168 0.8574
0.8777 0.8981 0.8981 0.9184 0.9388 0.9796
-4120 - 3890 - 3870 -3560 - 3040 - 1030
0.8514 0.8702 0.8889 0.9076 0.9262 0.9447 0.9632 0.9816
195 204 206 210 210 195 166 108
-4010 - 3820 - 3820 -3510 - 3030 -1350
308.15 K, 12.50 MPa 0.0435 0.0651 0.1081 0.1508 0.1932 0.2143 0.2353 0.2562 0.2771
- 54.2 - 75.6 -117 -143 - 156 -160 - 163 - 159 - 163
0.5616 0.5616 0.6011 0.6403 0.6403 0.6793 0.7564 0.7946 0.8325
- 16.6 - 14.7 13.1 39.2 45.9 79.2 132 166 183
-11.1 -11.1 17.4 45.1 45.1 72.1 I26 154 183
196 207 215 218 212 194 157 95.9
325.15 K, 5.00 MPa 0.0420 0.0828 0.1126 0.1126 0.1299 0.1491
-272 - 650 -882 -817 - 1050 - 1230
-192 - 583 -895 - 895 - 1070 -1240
0.1948 0.2223 0.2375 0.2538 0.2713 0.3106
-1480 - 1690 - 1820 - 1900 -1850 - 1760
-1570 -1700 - 1750 -1780 -1800 -1780
0.0972 0.1363 0.1754 0.2147 0.3330 0.3727 0.4124 0.4323 0.4522
- 543 -SO3 -985 - 1250 - 1900 -2170 - 2360 - 2360 - 2370
- 569 -781 -987 -1220 -2000 -2190 - 2280 - 2290 - 2280
0.4722 0.4722 0.4922 0.4922 0.4922 0.5322 0.5322 0.5724 0.6126
- 2250 - 2230 - 2 150 -2150 -2150 - 1990 - 1940 - 1770 - 1600
-2240 - 2240 -2180 -2180 -2180 -2010 -2010 -1800 -1570
0.0625 0.1040 0.1454 0.1866 0.2276 0.2685 0.2685
-212 -365 -521 -679 - 802 - loo0 -956
-232 - 384 -533 -678 -817 -951 -951
0.3093 0.3499 0.3904 0.3904 0.4307 0.4709 0.5110
-
- 1080 - 1200 -1320 -1320 - 1420 -1530 - 1620
0.0645 0.1072 0.1495 0.1917 0.2335 0.2751
-103 - 167 -218 -274 -319 - 369
-106 -168 - 224 -273 -317 -355
0.3164 0.3575 0.3983 0.4389 0.4792 0.5193
0.3328 0.3328 0.4121 0.4439 0.5184 0.5624
- 1680 - 1680 - 1480 - 1390 -1150 - 1020
-1740 -1740 -1500 -1380 -1120 -989
0.6683 0.7330 0.7690 0.8079 0.8957 0.9455
- 694 -515 -423 - 274 - 17.9 139
-712 -533 -418 - 282 20.7 108
-1560 - 1380 - 1200 - 1170 - 1030 -791 - 774 -617 -400
-1570 -1350 -1160 -1160 -984 -821 -821 -644 -430
0.8972 0.9177 0.9382 0.9485 0.9588 0.9691 0.9794 0.9897
-201 - 58.0 -28.1 36.1 109 133 221 176
- 182 - 58.9 46.8 87.0 114 124 112 72.9
- 1720 - 1820 - 1810 - 1890 - 1960 -2030 - 2030
- 1720 -1800 -1800 - I880 - 1960 - 2010 - 2050
0.7875 0.8264 0.8652 0.9039 0.9232 0.9424 0.9617
-2010 - 1950 - 1880 - 1670 - 1430 - 1150 -709
- 2050 - 1990 - 1850 -1590 -1400 -If50 -844
-492 -489 -481 -480 -469 -451
-493 -495 -491 -482 -467 -444
0.7929 0.8311 0.8690 0.8690 0.9067 0.9442
-419 -368 -321 -312 -236 - 166
-412 -370 -316 -316 - 247 -163
325.15 K. 7.50 MPa
325.15 1070 1210 1350 1300 1410 I520 1590
0.6126 0.6530 0.6934 0.6934 0.7339 0.7746 0.7746 0.8153 0.8562
K, 10.00 MPa 0.5509 0.5907 0.5907 0.6303 0.6698 0.7091 0.7484
325.15 K, 12.50 MPa -386 -406 -433 - 466 -481 -493
-388 -416 -440 -460 -475 -486
0.5591 0.5987 0.6380 0.6771 0.7159 0.7546
657
H~jxCO,+(l-x)C,H,OHI TABLE Hz/(J
molt
‘)
x
HE/(J
expt
talc
0.0397 0.0596 0.0993 0.1391 0.1789 0.2187 0.2386 0.2586 0.2984 0.2984
-- 178 220 ~~ 367 -534 -655 -795 - 826 - 768 636 - 589
-98.3 - 193 - 403 - 586 ~ 706 -751 - 746 -725 -638 -638
0.3383 -490 0.3782 - 321 0.4182 - 162 0.4581 - 13.2 0.4581 39.4 0.4981 144 0.498 1 201 0.538 1 321 0.5782 403 0.5782 427
0.0639 0.1063 0.1483 0.1902 0.2318 0.2732 0.2938 0.3144 0.3349
- 186 --368 -436 -519 -654 - 71 I - 770 -831 -837
-154 - 303 -447 -579 -687 -759 - 776 - 779 - 768
0.3553 0.3961 0.4366 0.4768 0.5169 0.5169 0.5568 0.5964
- 780 -662 - 476 -310 -215 - 125 - 14.2 106
0.0449 0.0672 0.1114 0.1552 0.1985 0.1985 0.2414 0.2414 0.2839 0.3259
- 101 - 171 -248 -346 -454 -420 -474 -473 - 542 - 577
-130 -176 -253 - 327 -406 -406 - 486 -486 -560 - 620
0.3676 0.4088 0.4496 0.4496 0.4496 0.4901 0.5301 0.5698 0.6091
-615 -647 -673 -667 -657 -631 -454 -309 -170
0.0468 0.0699 0.1157 0.1608 0.2054 0.2493 0.2926 0.3354 0.3775
~ 70.2 - IO5 -157 -205 - 238 - 277 - 302 -312 - 334
-61.5 -96.2 - I61 -213 -250 -277 - 296 -313 - 328
0.3775 0.4191 0.4602 0.4805 0.5007 0.5208 0.5407 0.5605 0.5605
- 333 -361 -349 - 359 -365 - 328 -325 -313 -312
0.2196 0.2596 0.2995 0.3395 0.4195 0.4594 0.4994
174 502 763 I080 1610 1910 2190
- __
expt
mol-
I--continued
‘)
I
talc 373.15
Hz,‘(J
‘mole’)
x
expt _._..... .-
H&/(J
mol
’)
expt
talc
K, 7.50 MPa
-506 -345 -170 5.94 5.94 173 173 324 461 461
0.5982 0.6182 0.6583 0.6984 0.6984 0.7385 0.7385 0.7787 0.7988
553 568 749 817 868 1030 1040 1180 1280
524 586 709 844 844 loo0 loo0 1190 1300
0.8189 0.8591 0.8792 0.8792 0.8993 0.8993 0.9194 0.9396 0.9597
1440 1520 1610 1670 1630 1690 1760 1560 1090
1400 1600 I660 1660 1680 I680 1630 1480 1200
169 281 403 545 550 711 825 959
148 289 418 545 545 682 838 1010
0.8680 0.8870 0.9059 0.9059 0.9248 0.9437 0.9625 0.9813
1130 1190 1280 1300 1280 1050 813 359
1160 1210 127-O 1’20 II90 I080 869 522
- I I .2 127 331 478 633 687 762 837 860
-39.1 135 316 495 665 742 811 867 867
0.8739 0.8739 0.8739 0.8922 0.9103 0.9103 0.9284 0.9465 0.9644
936 961 977 977 916 936 838 731 544
908 908 908 92s 914 914 863 762 597
-268 - 298 -256 -152 - 70.5 -65.5 77.4 229 365
-319 -299 -241 -157 -45.8 -45.8 87.2 234 382
0.8429 0.8607 0.8785 0.8785 0.8962 0.9138 0.9312 0.9486 0.9658
500 584 601 623 668 612 543 442 325
Cl0 559 594 594 609 600 563 490
2800 3100 3320 3610 4140 4250 4190
2710 3030 3380 3740 4200 4200 4190
0.8097 0.8197 0.8597 0.8998 0.9399 0.9599
4310 4160 3570 2680 1640 1090
4150 4100 3650 2800 1630 1010
373.15 K. IO.00 MPa - 743 -652 -518 -355 -180 -180 -9.00 148 373.15 -656 -661 -632 -632 - 632 - 569 - 473 - 349 -203
0.5964 0.6358 0.6750 0.7140 0.7140 0.7528 0.7914 0.8298 K. 12.50 MPa 0.6480 0.6865 0.7247 0.7625 0.8000 0.8186 0.8371 0.8555 0.8555
373.15 K, 14.91 MPa -328 -341 -350 -351 - 349 - 343 -334 -319 -319 413.15 0.0599 0.0998 0.1397 0.1397 0.1797 0.1797 0.1096
- 20.0 -29.2 m~27.2 - 26.2 - 4.93 ..- 3.73 III
-21.2 -48.7 -42.2 - 42.2 35.3 35.3 106
199 443 741 1060 1670 1940 2180
0.5605 0.5802 0.6192 0.6576 0.6956 0.6956 0.7331 0.7702 0.8067
?Vl
K. 7.50 MPa 0.5795 0.6195 0.6595 0.6995 0.7796 0.7896 0.7996
658
D. R. CORDRAY TABLE
x
H$‘(J.mol-‘) expt
x
HQ(J.mol-‘)
talc
E7‘.-1L.
l-continued
x talc
Hj./(J
mol
‘)
expt
CdC
expt
1940 2150 2620 2880 3170 3280
1890 2130 2650 2920 3250 3300
0.8113 0.8305 0.8685 0.9063 0.9440 0.9627
3440 3320 2870 2180 1360 941
3300 3250 2920 2280 1360 857
1770 2060 2460 2650 2760 2860 2760
1760 2020 2530 2700 2750 2760 2740
0.835 1 0.8538 0.8723 0.8908 0.9092 0.9457 0.9639
2670 2550 2350 2100 1830 1170 791
2670 2550 2370 2140 1860 1150 756
1980 2160 2180 2200 2220 2240 2280
2000 2160 2160 2220 2260 2260 2270
0.8026 0.8210 0.8394 0.8757 0.9117 0.9473 0.9649
2270 2250 2140 1920 1520 997 680
2260 2220 2140 1900 1520 1010 699
9630 9590 9360 9050 8920 8310
9620 9620 9350 9140 8890 8280
0.6995 0.7396 0.7796 0.8597 0.9198
6800 6100 5190 3430 2030
6820 6030 5220 3470 2000
7350 7310 7400 7410 7100 6680 6200
7370 7380 7340 7340 7110 6710 6200
0.7538 0.7923 0.8305 0.8686 0.9064 0.9440 0.9627
5020 4290 3620 2880 2080 1290 861
4980 4310 3620 2880 2100 1270 847
5830 5620 5680 5560 5520 5390 4860 4830
5760 5770 5730 5660 5550 5250 4840 4840
0.7409 0.7599 0.7977 0.8351 0.8723 0.8908 0.9457
4740 4340 3730 3220 2570 2290 1190
4610 4350 3800 3210 2590 2260 1230
413.15 K, 10.00 MPa 0.0429 0.1067 0.1490 0.1909 0.2327 0.2742
-2.97 -2.14 18.8 45.0 88.0 145
-8.59 5.33 17.0 34.8 84.4 190
0.3154 0.3565 0.3972 0.4378 0.478 1 0.5181
384 655 812 1130 1350 1660
0.0443 0.1100 0.1100 0.1533 0.1962 0.2388 0.2809
15.0 43.0 44.0 74.1 109 163 227
2.82 47.1 47.1 79.9 110 150 215
0.3227 0.3642 0.3848 0.4053 0.4460 0.4864 0.5265
322 417 496 621 861 1050 1190
0.0456 0.1130 0.201 I 0.2444 0.2872 0.2872 0.3296 0.3714
36.2 94.7 195 252 315 321 388 476
19.4 91.3 203 257 314 314 381 466
0.4128 0.4537 0.4942 0.5342 0.5738 0.6130 0.6517 0.6517
555 720 868 1090 1370 1540 1800 1810
362 592 857 1130 1400 1650 413.15 315 450 530 617 809 1020 1250 413.15 576 717 890 1090 1320 1560 1790 1790 473.15
0.0599 0.0798 0.1597 0.1797 0.2196 0.2596
556 839 2670 3430 4530 5670
539 873 2730 3300 4520 5780
0.2995 0.3795 0.3995 0.4195 0.4794 0.4794
6990 8910 9150 9400 9680
0.0643 0.0643 0.1068 0.1490 0.1701 0.1910 0.2119 0.2328
431 440 798 1180 1420 1710 2070 2490
435 435 793 1190 1430 1720 2060 2440
0.3155 0.3566 0.4176 0.4379 0.458 1 0.4782 0.4982
4210 5240 6530 6710 7050 7110 7280
0.0663 0.1100 0.1533 0.1962 0.2387 0.2809 0.3227 0.3642
321 685 961 1280 1980 2470 3260 3740
277 588 958 1400 1940 2540 3190 3830
0.4053 0.4460 0.4864 0.5265 0.5265 0.5464 0.5464 0.5662
4480 4990 5580 5610 5650 5660 5770 5710
6980 8840 9150 9390 9670 9670 473.15 4290 5240 6440 6740 6990 7180 7300 473.15 4440 4960 5370 5640 5640 5720 5720 5760
0.5579 0.5976 0.6761 0.7150 0.7730 0.7922 K, 12.50 MPa 0.6056 0.6447 0.7218 0.7599 0.7788 0.7977 0.8164 K. 14.91 MPa 0.6901 0.7280 0.7280 0.7468 0.7655 0.7655 0.7841 K, 7.50 MPa 0.4994 0.4994 0.5394 0.5594 0.5795 0.6195 K, 10.00 MPa 0.5182 0.5382 0.5581 0.5581 0.5977 0.6370 0.6762 K, 12.50 MPa 0.5662 0.5860 0.6056 0.6252 0.6447 0.6834 0.7218 0.7218
H:{xC02+(l
-x)C,H,OH)
659
TABLE I-continued Ht/(J
mol-
‘)
expt
talc
208 397 685 993 1300 1650 2040
200 364 694 998 1310 1650 2050
x
Hf,/(J.mol-‘) expt
x talc 473.15
0.0456 0.0682 0.1130 0.1573 0.7011 0.2444 0.2872
0.2872 0.3296 0.3714 0.4128 0.4537 0.4942 0.4942
2070 2500 3000 3460 3900 4290 4330
2050 2510 2990 3470 3920 4290 4290
K. 14.91 MPa 0.5342 0.5738 0.6130 0.6517 0.6901 0.7280 0.7655
H2(J.molm’)
X
expt
talc
4550 4800 4770 4750 4560 4230 3890
4580 4760 4810 4740 4550 4260 3870
Hz/(J
molt. ’ )
expt
0.8026 0.8394 0.8757 0.9117 0.9473 0.9649
3370 2930 2310 1700 1040 689
GilC
3410 2880 2310 1700 1050 716
composition) mode. Two high-pressure ISCO syringe pumps supplied at a constant rate the two fluids to be mixed. The total flow rate was from 0.0028 to 0.0278 cm3. s- 1 for all temperatures and pressures studied. Previous results. obtained with the calorimeter were reproducible to 0.8 per cent or better over the range 0.2 < x < 0.8. (1.3) Reproducibility of results in the present investigation was :t 3 per cent. This uncertainty was due mainly to difficulties in mixing the components in certain mole fraction regions. The materials employed were CO2 (Whitmore Oxygen Co., 99.98 moles per cent pure) and punctilious ethanol (Midwest Grain Products, Inc., Atkinson, Kansas, 200 proof). Prior to use, the CO, was filtered through a Matheson gas purifier model 450 which also contained a molecular-sieve desiccant. The ethanol was stored in sealed 1 dm3 bottles over approximately 50 cm3 of Davison molecular sieves (0.3 nm effective pore diameter) and, just prior to use, was filtered through a Whatman filter (0.45 pm pore diameter) and degassed for IO min in an ultrasonic bath. Flow rates measured in cm3. s-l were converted to mol. s-l and to mole fractions using the densities of the two pure materials estimated as follows. The densities of CO* at 298.15 K from 5.00 to 14.91 MPa were calculated by interpolation of the values from the IUPAC tables. (” The densities of the ethanol at 298.15 K and these pressures were calculated by averaging the density at 298.15 K and 101.325 kPa reported by Ortega@’ with that reported by Diaz Peiia and Tardajos”’ and correcting for the pressure using the values for isothermal compressibility from Diaz Pefia and Tardajos.“’ 3. Results and discussion Table 1 gives values for Hi{xCO, + (I -x)C,H,OH} over the entire composition range at 308.15, 325.15, 373.15, 413.15, and 473.15 K at pressures ranging from 5.00 to 14.91 MPa. The experimental values for each temperature and pressure were curve fitted using the equation: HfiJ(J .mol-‘) 4-x)
= [
exp(-~x)“~~E.(l--?xr+(*-exp(-nx)J
5 F,(1-2~)” n=O
1
(1)
660 TABLE
TIK PIMPa
2.
I>. R. CORDRAY Coefficients
308.15 7.50
and
standard deviations s [or (xCO,+(l -x)CZH,OH)
308. I5 12.50 . ..~_._.
i
- 2293.9 - 3.0508
- 1575.2 -5.3614
EY E2 4 FO F, F2 F3 F4 F5 s
- 1661.4 - 1722.9 1256.4 0 0 0 0 0 0 96
169.58 107.80 -0.0158 - 1674.7 0 0 0 0 0 5.4
T/K PiMPa ; EY ~52
6 4 4 FO F, F2 F3 F4 F5 Fb s
TIK PIMPa a
El3 F, -v F, E;,
F3 F4 F5 s
373.15 IO.00 6.0000 0 0 0 0 0 0 - 1070.3 -9387.3 - 1851.7 8679.1 13742 -22031 0 55 473.15 7.50 5.7076 0 40824 15407 - 27704 - 42446 17273 35462 58
E7' :tf
373.15 12.50 - 1.0954 - 1267.1 - 3228.0 2975.7 1744.1 278.92 - 4246.4 0 0 0 0 0 0 0 37 473.15 10.00 5.8228 0 30934 -4586.0 - 40697 - 22024 41146 35769 43
325.15 5.00 ~~~ ~~ -01.9318 0 0 0 - 7647.9 - 15480 - 25465 - 23432 0 0 55 373.15 14.91 0.4531 - 1015.2 0 0 0 0 0 -2891.7 -3317.7 11588 -29412 0 0 0 23 473.15 12.50 5.9999 0 23072 -11821 - 19898 7910.6 18744 0 83
.._~~~
least-squares by equation 325.15 7.50 05.4453 0 0 0
-9215.5 - 9842.2 9301.4 27470 - 13206 - 39728 53 413.15 7.50 0.7871 0 0 0 0 0 0 26900 - 15705 21515 - 117930 - 33443 118440 0 70
representation
of
H:/(J
'mol
')
lor
(I) 325.15 IO.00
- 2.7585 - 1608.6 - 1006. I - 1095.2 0 0 0 0 0 0 0 38 413.15 10.00 3.8690 0 0 0 0 0 0 7203.4 - 12228 -318.03 -24233 48401 25726 -49414 62
325.15 12.50
-
-0.9403 - 1203.7 ~ 224.48 -341.40 0 0 0 0 0 0 0 6.6 413.15 12.50 5.0262 0 0 0 0 0 0 4774.1 - 11229 9813.2 - 11456 15931 12614 -22c00 39
373.15 7.50 0.0257 0 0 0 0 56469 - 566750 -887110 -1194700 96027 - 679550 52 413.15 14.91 0.0803 0 0 0 0 0 0 93276 - 152910 195680 82356 -82116 0 0 20
473.15 14.91 h.cooo 0 18276 - 14036 -9826.8 15663 14669 0 23
The exponential acts as a factor to switch between the left and right summations in the term in square brackets in equation (1). The adjustable parameters of equation (1) were found using a non-linear curve-fitting program which employs the Marquardt algorithm.(“) The coefficients En and F, are given in table 2 along with the standard deviations. In the current study, most of the results were found to be
H$CO,+(l
-x)C,H,OH]
661
FIGURE I. Plot of H:(x) for {xCO, + (1 -x)C,H,OHJ at (a), 308.15 K: 0, 7.50 MPa; [I, 12.50 MPa; (b), 325.15 K: 0, 5.00 MPa; 0. 7.50 MPa: A. 10.00 MPa: 0. 12.50 MPa; (c), 373.15 K: 0, 7.50 MPa; 0, 10.00 MPa: A. 12.50 MPa; 0, 14.39 MPa; (d). 413.15 K: 0. 7.50 MPa; 0, 10.00 MPa: A, 12.50 MPa: 0. 14.39 MPa: and (e), 473.15 K: 0, 7.50 MPa; C 1. 10.00 MPa; A, 12.50 MPa: 0. 14.39 MPa: -. calculated using equation (1).
best fitted by using only the right or left summation alone. The curve-fitted values are given in table 1. Equation (1) is a good interpolating function for the results for all compositions, including linear sections of the isotherms. However, differentiation of equation (1) for the determination of other thermodynamic properties is not recommended.
662
D. R. CORDRAY
TABLE
3. Liquid
T/K
PIMPa
xl
xg
T/K
7.50 5.00 7.50 7.50
0.92 0.25 0.46 0.29
1.00 0.95 0.98 0.92
373.15 373.15 373.15 413.15
308.15 325.15 325.15 373.15
(x,) and vapor
(x,)
ET AL.
mole fractions for (xC0, Hk values p/MPa 10.00 12.50 14.91 7.50
+( I -x)C,H,OHJ
X,
xg
T/K
0.36 0.50 0.69 0.19
0.92 0.89 0.87 0.81
413.15 413.15 473.15
as determined
from
p/MPa
x,
.xg
10.00 12.50 7.50
0.30 0.39 0.12
0.81 0.80 0.40
Figure 1 shows plots of HE(x) for the five temperatures studied along with the fit by equation (1). The linear sections of the plots (in the middle of the mole-fraction range) correspond to regions where a gaseous phase and a liquid phase, both of fixed composition, are in equilibrium. The CO, liquid-phase and gas-phase compositions (x, and xg, respectively) can be estimated from figure 1 as the x coordinates at the two ends of the linear region where the results begin to deviate from linearity. (11) The values of x, and xg are given in table 3. The estimated uncertainty in the compositions reported is fO.O1. We have modeled the observed HE{xCO,+(l-x)C,H,OH) with the Soave equation of state. U) The process of fitting the Soave equation to the experimental results consisted of varying an adjustable interaction parameter k,, until the best fit (lowest standard deviation) was found. The Soave equation provided an excellent fit at higher temperatures and pressures. The fit was poor at 308 K at the higher pressure, failing even to predict the correct sign for the Hz. For temperatures where the two-phase region was crossed, the equation described the shape of the Hz(x) curves but predicted greater magnitudes for HE than were observed in the region of higher x. This behavior can be seen in figure 2. The usual assumption that k,, is independent of temperature has been found to be false over large ranges of temperature.“~‘*’ For (xC0, + (1 -x)C,H,OH), a slight temperature dependence of k,, was observed, with values ranging from 0.872 to 0.923 depending upon the temperature. The equation: k,, = 1.78519-4.71528
x 10-3(T/K)+6.15524x
FIGURE 2. Plot of H:(x) for (xC0, 0, experimental results; ~, calculated using
+ (l-x)C,HsOH) ASV equation with
10-6(T/K)Z,
k,,
at 373.15 K and found from equation
(2)
12.50MPd; (2).
H:{xCO,+(l-x)C,H,OH;
663
gives the best fit of the k,, values over the range of the experimental measurements. 1Jsing k,, values calculated from equation (2) resulted in a fit with a standard deviation of 242 J mol- ‘. This work was funded by U.S. Department of Energy, Office of Basic Energy Sciences, Grant No. DE-FG02-85ER13443, by the Donors of the Petroleum Research Fund administered by the American Chemical Society, and by Air Products and Chemicals Co. We appreciate the aid given to us in collecting and processing the data by P. R. Harding, C. Orme, P. W. Faux, L. D. Gunderson. and T. A. C. Walker. REFERENCES I. Christensen, J. J.; Faux, P. W.; Cordray, D.; Izatt. R. M. J. Chem. Thermodynamics 1986, 18, 1053. 2. Christensen, J. J.; Cordray, D. R.; Oscarson. J. L.; Izatt, R. M. J. Chem. Thermodynamics 1988, 20. in the press. 3. Soave. Ci. Chem. Eng. Sci. 1972, 21, 1197. 3. Christensen, J. J.; Izatt, R. M. Thermochim. Acfa 1984, 73, 117. 5. Christensen, J. J.: Izatt. R. M.; Eatough. D. J.; Hansen. L. D. J. Chem. Thermodynamics 1978, IO. 25.
6. McFall, T. A.; Post, M. E.; Collins, S. G.; Christensen. J. J.: Izatt, R. M. J. Chem. Thermodynumkv 1981, 13, 41. 7. Carbon Dioxide. IUPAC Thermodynamic Tables 01 the Fluid Stare. Pergamon Press: Oxford. 1976. 8. Ortega, J. J. Chem. Eng. Data 1982, 27, 312. 9. Diaz Petia, M.; Tardajos, G. J. Chem. Thermodynamics 1979, I I. 441. 10. Marquardt. D. W. J. Sot. Indust. Appl. Math. 1%3, 1I. 431. 1 I. Cordray. D. R.; Christensen, J. J.; Izatt. R. M. Sep. Sci. Technol. 1987, 22. 1169. I?. Kurnik. R. T.; Holla. S. J.: Reid, R. C. J. Chcm. Eng. Dam 1981. 26. 47.
Tiwmodvuzmics
1988, 20, 655-663
The excess enthalpies of (carbon dioxide + ethanol) at 308.15, 325.15, 373.15, 413.15, and 473.15 K from 5.00 to 14.91 MPa D. R. CORDRAY, J. J. CHR1STENSEN.t
R. M. IZATT, and J. L. OSCARSON
Departments of Chemical Enginr,ering Brigham Young University, Provo. Utah 84602, U.S.A. (Received
23 September
1987;
and
in.final,ftirm
Chc~mistr~~,
26 Octohcr
1987)
The excess molar enthalpies H~(xCO, + (1 --.x)C,H,OH) were measured in the vicinity of the critical locus. Large positive and negative HEs were observed depending on the compositions, temperatures, and pressures. Rapid changes with small variations In temperature and composition were observed. An interpolating function used to describe the results is presented. The Soave equation of state was used to correlate His over a temperature range of 308.15 to 473.15 K and a pressure range of 5.00 to 14.91 MPa. The fit ranged from poor to excellent depending upon the pressures and temperatures of the mixtures. The average standard deviation over all pressures, temperatures. and compositions was 242 J mol. ’
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies If: of binary mixtures in the vicinity of their (gas + liquid) critical loci. Results for several examples of (carbon dioxide + a hydrocarbon),“’ (a fluorocarbon + a hydrocarbon),“’ and (carbon dioxide + an alcohol)“) have been reported. In these mixtures, Hz showed increased negative character as the critical point of the component having the lower critical temperature was approached along an isobar. Where the critical point of the second component was approached, large positive lfzs were observed. The present work reports values of Hz{xCOz + ( I -x)C,H,OH} from 308.15 to 473.15 K at 5.00 to 14.91 MPa. In this paper, HE values have been modeled using the Soave equation of state’“’ in an attempt the better to predict mixing behavior in the critical region. 2. Experimental The high-temperature high-pressure flow calorimeters used and the experimental procedure have been described. (4-6) All runs were made in the steady-state (fixedBy acceptance of this article, the publisher acknowledges the right of the U.S. Government nonexclusive royalty-free license in and to any copyright covering this paper. t Died 5 September 1987.
to retain
a
656
D. R. C’ORDRAL’ TABLE
.x
1. Experimental
H,$/{J . mol - ’ ) expt
and calculated Hk/(J.mol-‘)
x
talc
expt
E7’.41>.
excess enthalpies: Y
Hii H:/(J
xC0, mol-
+ ( I - \-)CzH I)
expt
talc
-3210 - 3320 - 3490 - 3650 -3920 -4090
-3120 -3310 -3510 - 3720 - 4070 - 4090
CdC
9
50H \ Hk,‘(J expt
mol..
’ ) CillC
308.15 K, 7.50 MPa 0.1375 0.1769 0.2164 0.2956 0.3352 0.3750
-703 -940 - 1250 - 1650 - 1750 -2010
- 708 -936 -1170 -1630 - 1850 - 2060
0.4148 0.4547 0.4947 0.5347 0.5748 0.5748
-2190 - 2490 - 2670 - 2830 -2980 -2880
-51.6 -73.6 -110 -137 -154 -159 -162 -163 -162
0.2979 0.2979 0.3186 0.3598 0.3598 0.4007 0.4414 0.4817 0.5218
- 153 - 151 - 151 - 139 - 136 -118 -95.8 -68.8 -42.2
-159 -159 -154 -139 -139 -119 -95.3 -68.4 -40.0
-2260 - 2440 -2610 -2780 -2950 - 2950
0.6150 0.6552 0.6955 0.7359 0.8168 0.8574
0.8777 0.8981 0.8981 0.9184 0.9388 0.9796
-4120 - 3890 - 3870 -3560 - 3040 - 1030
0.8514 0.8702 0.8889 0.9076 0.9262 0.9447 0.9632 0.9816
195 204 206 210 210 195 166 108
-4010 - 3820 - 3820 -3510 - 3030 -1350
308.15 K, 12.50 MPa 0.0435 0.0651 0.1081 0.1508 0.1932 0.2143 0.2353 0.2562 0.2771
- 54.2 - 75.6 -117 -143 - 156 -160 - 163 - 159 - 163
0.5616 0.5616 0.6011 0.6403 0.6403 0.6793 0.7564 0.7946 0.8325
- 16.6 - 14.7 13.1 39.2 45.9 79.2 132 166 183
-11.1 -11.1 17.4 45.1 45.1 72.1 I26 154 183
196 207 215 218 212 194 157 95.9
325.15 K, 5.00 MPa 0.0420 0.0828 0.1126 0.1126 0.1299 0.1491
-272 - 650 -882 -817 - 1050 - 1230
-192 - 583 -895 - 895 - 1070 -1240
0.1948 0.2223 0.2375 0.2538 0.2713 0.3106
-1480 - 1690 - 1820 - 1900 -1850 - 1760
-1570 -1700 - 1750 -1780 -1800 -1780
0.0972 0.1363 0.1754 0.2147 0.3330 0.3727 0.4124 0.4323 0.4522
- 543 -SO3 -985 - 1250 - 1900 -2170 - 2360 - 2360 - 2370
- 569 -781 -987 -1220 -2000 -2190 - 2280 - 2290 - 2280
0.4722 0.4722 0.4922 0.4922 0.4922 0.5322 0.5322 0.5724 0.6126
- 2250 - 2230 - 2 150 -2150 -2150 - 1990 - 1940 - 1770 - 1600
-2240 - 2240 -2180 -2180 -2180 -2010 -2010 -1800 -1570
0.0625 0.1040 0.1454 0.1866 0.2276 0.2685 0.2685
-212 -365 -521 -679 - 802 - loo0 -956
-232 - 384 -533 -678 -817 -951 -951
0.3093 0.3499 0.3904 0.3904 0.4307 0.4709 0.5110
-
- 1080 - 1200 -1320 -1320 - 1420 -1530 - 1620
0.0645 0.1072 0.1495 0.1917 0.2335 0.2751
-103 - 167 -218 -274 -319 - 369
-106 -168 - 224 -273 -317 -355
0.3164 0.3575 0.3983 0.4389 0.4792 0.5193
0.3328 0.3328 0.4121 0.4439 0.5184 0.5624
- 1680 - 1680 - 1480 - 1390 -1150 - 1020
-1740 -1740 -1500 -1380 -1120 -989
0.6683 0.7330 0.7690 0.8079 0.8957 0.9455
- 694 -515 -423 - 274 - 17.9 139
-712 -533 -418 - 282 20.7 108
-1560 - 1380 - 1200 - 1170 - 1030 -791 - 774 -617 -400
-1570 -1350 -1160 -1160 -984 -821 -821 -644 -430
0.8972 0.9177 0.9382 0.9485 0.9588 0.9691 0.9794 0.9897
-201 - 58.0 -28.1 36.1 109 133 221 176
- 182 - 58.9 46.8 87.0 114 124 112 72.9
- 1720 - 1820 - 1810 - 1890 - 1960 -2030 - 2030
- 1720 -1800 -1800 - I880 - 1960 - 2010 - 2050
0.7875 0.8264 0.8652 0.9039 0.9232 0.9424 0.9617
-2010 - 1950 - 1880 - 1670 - 1430 - 1150 -709
- 2050 - 1990 - 1850 -1590 -1400 -If50 -844
-492 -489 -481 -480 -469 -451
-493 -495 -491 -482 -467 -444
0.7929 0.8311 0.8690 0.8690 0.9067 0.9442
-419 -368 -321 -312 -236 - 166
-412 -370 -316 -316 - 247 -163
325.15 K. 7.50 MPa
325.15 1070 1210 1350 1300 1410 I520 1590
0.6126 0.6530 0.6934 0.6934 0.7339 0.7746 0.7746 0.8153 0.8562
K, 10.00 MPa 0.5509 0.5907 0.5907 0.6303 0.6698 0.7091 0.7484
325.15 K, 12.50 MPa -386 -406 -433 - 466 -481 -493
-388 -416 -440 -460 -475 -486
0.5591 0.5987 0.6380 0.6771 0.7159 0.7546
657
H~jxCO,+(l-x)C,H,OHI TABLE Hz/(J
molt
‘)
x
HE/(J
expt
talc
0.0397 0.0596 0.0993 0.1391 0.1789 0.2187 0.2386 0.2586 0.2984 0.2984
-- 178 220 ~~ 367 -534 -655 -795 - 826 - 768 636 - 589
-98.3 - 193 - 403 - 586 ~ 706 -751 - 746 -725 -638 -638
0.3383 -490 0.3782 - 321 0.4182 - 162 0.4581 - 13.2 0.4581 39.4 0.4981 144 0.498 1 201 0.538 1 321 0.5782 403 0.5782 427
0.0639 0.1063 0.1483 0.1902 0.2318 0.2732 0.2938 0.3144 0.3349
- 186 --368 -436 -519 -654 - 71 I - 770 -831 -837
-154 - 303 -447 -579 -687 -759 - 776 - 779 - 768
0.3553 0.3961 0.4366 0.4768 0.5169 0.5169 0.5568 0.5964
- 780 -662 - 476 -310 -215 - 125 - 14.2 106
0.0449 0.0672 0.1114 0.1552 0.1985 0.1985 0.2414 0.2414 0.2839 0.3259
- 101 - 171 -248 -346 -454 -420 -474 -473 - 542 - 577
-130 -176 -253 - 327 -406 -406 - 486 -486 -560 - 620
0.3676 0.4088 0.4496 0.4496 0.4496 0.4901 0.5301 0.5698 0.6091
-615 -647 -673 -667 -657 -631 -454 -309 -170
0.0468 0.0699 0.1157 0.1608 0.2054 0.2493 0.2926 0.3354 0.3775
~ 70.2 - IO5 -157 -205 - 238 - 277 - 302 -312 - 334
-61.5 -96.2 - I61 -213 -250 -277 - 296 -313 - 328
0.3775 0.4191 0.4602 0.4805 0.5007 0.5208 0.5407 0.5605 0.5605
- 333 -361 -349 - 359 -365 - 328 -325 -313 -312
0.2196 0.2596 0.2995 0.3395 0.4195 0.4594 0.4994
174 502 763 I080 1610 1910 2190
- __
expt
mol-
I--continued
‘)
I
talc 373.15
Hz,‘(J
‘mole’)
x
expt _._..... .-
H&/(J
mol
’)
expt
talc
K, 7.50 MPa
-506 -345 -170 5.94 5.94 173 173 324 461 461
0.5982 0.6182 0.6583 0.6984 0.6984 0.7385 0.7385 0.7787 0.7988
553 568 749 817 868 1030 1040 1180 1280
524 586 709 844 844 loo0 loo0 1190 1300
0.8189 0.8591 0.8792 0.8792 0.8993 0.8993 0.9194 0.9396 0.9597
1440 1520 1610 1670 1630 1690 1760 1560 1090
1400 1600 I660 1660 1680 I680 1630 1480 1200
169 281 403 545 550 711 825 959
148 289 418 545 545 682 838 1010
0.8680 0.8870 0.9059 0.9059 0.9248 0.9437 0.9625 0.9813
1130 1190 1280 1300 1280 1050 813 359
1160 1210 127-O 1’20 II90 I080 869 522
- I I .2 127 331 478 633 687 762 837 860
-39.1 135 316 495 665 742 811 867 867
0.8739 0.8739 0.8739 0.8922 0.9103 0.9103 0.9284 0.9465 0.9644
936 961 977 977 916 936 838 731 544
908 908 908 92s 914 914 863 762 597
-268 - 298 -256 -152 - 70.5 -65.5 77.4 229 365
-319 -299 -241 -157 -45.8 -45.8 87.2 234 382
0.8429 0.8607 0.8785 0.8785 0.8962 0.9138 0.9312 0.9486 0.9658
500 584 601 623 668 612 543 442 325
Cl0 559 594 594 609 600 563 490
2800 3100 3320 3610 4140 4250 4190
2710 3030 3380 3740 4200 4200 4190
0.8097 0.8197 0.8597 0.8998 0.9399 0.9599
4310 4160 3570 2680 1640 1090
4150 4100 3650 2800 1630 1010
373.15 K. IO.00 MPa - 743 -652 -518 -355 -180 -180 -9.00 148 373.15 -656 -661 -632 -632 - 632 - 569 - 473 - 349 -203
0.5964 0.6358 0.6750 0.7140 0.7140 0.7528 0.7914 0.8298 K. 12.50 MPa 0.6480 0.6865 0.7247 0.7625 0.8000 0.8186 0.8371 0.8555 0.8555
373.15 K, 14.91 MPa -328 -341 -350 -351 - 349 - 343 -334 -319 -319 413.15 0.0599 0.0998 0.1397 0.1397 0.1797 0.1797 0.1096
- 20.0 -29.2 m~27.2 - 26.2 - 4.93 ..- 3.73 III
-21.2 -48.7 -42.2 - 42.2 35.3 35.3 106
199 443 741 1060 1670 1940 2180
0.5605 0.5802 0.6192 0.6576 0.6956 0.6956 0.7331 0.7702 0.8067
?Vl
K. 7.50 MPa 0.5795 0.6195 0.6595 0.6995 0.7796 0.7896 0.7996
658
D. R. CORDRAY TABLE
x
H$‘(J.mol-‘) expt
x
HQ(J.mol-‘)
talc
E7‘.-1L.
l-continued
x talc
Hj./(J
mol
‘)
expt
CdC
expt
1940 2150 2620 2880 3170 3280
1890 2130 2650 2920 3250 3300
0.8113 0.8305 0.8685 0.9063 0.9440 0.9627
3440 3320 2870 2180 1360 941
3300 3250 2920 2280 1360 857
1770 2060 2460 2650 2760 2860 2760
1760 2020 2530 2700 2750 2760 2740
0.835 1 0.8538 0.8723 0.8908 0.9092 0.9457 0.9639
2670 2550 2350 2100 1830 1170 791
2670 2550 2370 2140 1860 1150 756
1980 2160 2180 2200 2220 2240 2280
2000 2160 2160 2220 2260 2260 2270
0.8026 0.8210 0.8394 0.8757 0.9117 0.9473 0.9649
2270 2250 2140 1920 1520 997 680
2260 2220 2140 1900 1520 1010 699
9630 9590 9360 9050 8920 8310
9620 9620 9350 9140 8890 8280
0.6995 0.7396 0.7796 0.8597 0.9198
6800 6100 5190 3430 2030
6820 6030 5220 3470 2000
7350 7310 7400 7410 7100 6680 6200
7370 7380 7340 7340 7110 6710 6200
0.7538 0.7923 0.8305 0.8686 0.9064 0.9440 0.9627
5020 4290 3620 2880 2080 1290 861
4980 4310 3620 2880 2100 1270 847
5830 5620 5680 5560 5520 5390 4860 4830
5760 5770 5730 5660 5550 5250 4840 4840
0.7409 0.7599 0.7977 0.8351 0.8723 0.8908 0.9457
4740 4340 3730 3220 2570 2290 1190
4610 4350 3800 3210 2590 2260 1230
413.15 K, 10.00 MPa 0.0429 0.1067 0.1490 0.1909 0.2327 0.2742
-2.97 -2.14 18.8 45.0 88.0 145
-8.59 5.33 17.0 34.8 84.4 190
0.3154 0.3565 0.3972 0.4378 0.478 1 0.5181
384 655 812 1130 1350 1660
0.0443 0.1100 0.1100 0.1533 0.1962 0.2388 0.2809
15.0 43.0 44.0 74.1 109 163 227
2.82 47.1 47.1 79.9 110 150 215
0.3227 0.3642 0.3848 0.4053 0.4460 0.4864 0.5265
322 417 496 621 861 1050 1190
0.0456 0.1130 0.201 I 0.2444 0.2872 0.2872 0.3296 0.3714
36.2 94.7 195 252 315 321 388 476
19.4 91.3 203 257 314 314 381 466
0.4128 0.4537 0.4942 0.5342 0.5738 0.6130 0.6517 0.6517
555 720 868 1090 1370 1540 1800 1810
362 592 857 1130 1400 1650 413.15 315 450 530 617 809 1020 1250 413.15 576 717 890 1090 1320 1560 1790 1790 473.15
0.0599 0.0798 0.1597 0.1797 0.2196 0.2596
556 839 2670 3430 4530 5670
539 873 2730 3300 4520 5780
0.2995 0.3795 0.3995 0.4195 0.4794 0.4794
6990 8910 9150 9400 9680
0.0643 0.0643 0.1068 0.1490 0.1701 0.1910 0.2119 0.2328
431 440 798 1180 1420 1710 2070 2490
435 435 793 1190 1430 1720 2060 2440
0.3155 0.3566 0.4176 0.4379 0.458 1 0.4782 0.4982
4210 5240 6530 6710 7050 7110 7280
0.0663 0.1100 0.1533 0.1962 0.2387 0.2809 0.3227 0.3642
321 685 961 1280 1980 2470 3260 3740
277 588 958 1400 1940 2540 3190 3830
0.4053 0.4460 0.4864 0.5265 0.5265 0.5464 0.5464 0.5662
4480 4990 5580 5610 5650 5660 5770 5710
6980 8840 9150 9390 9670 9670 473.15 4290 5240 6440 6740 6990 7180 7300 473.15 4440 4960 5370 5640 5640 5720 5720 5760
0.5579 0.5976 0.6761 0.7150 0.7730 0.7922 K, 12.50 MPa 0.6056 0.6447 0.7218 0.7599 0.7788 0.7977 0.8164 K. 14.91 MPa 0.6901 0.7280 0.7280 0.7468 0.7655 0.7655 0.7841 K, 7.50 MPa 0.4994 0.4994 0.5394 0.5594 0.5795 0.6195 K, 10.00 MPa 0.5182 0.5382 0.5581 0.5581 0.5977 0.6370 0.6762 K, 12.50 MPa 0.5662 0.5860 0.6056 0.6252 0.6447 0.6834 0.7218 0.7218
H:{xC02+(l
-x)C,H,OH)
659
TABLE I-continued Ht/(J
mol-
‘)
expt
talc
208 397 685 993 1300 1650 2040
200 364 694 998 1310 1650 2050
x
Hf,/(J.mol-‘) expt
x talc 473.15
0.0456 0.0682 0.1130 0.1573 0.7011 0.2444 0.2872
0.2872 0.3296 0.3714 0.4128 0.4537 0.4942 0.4942
2070 2500 3000 3460 3900 4290 4330
2050 2510 2990 3470 3920 4290 4290
K. 14.91 MPa 0.5342 0.5738 0.6130 0.6517 0.6901 0.7280 0.7655
H2(J.molm’)
X
expt
talc
4550 4800 4770 4750 4560 4230 3890
4580 4760 4810 4740 4550 4260 3870
Hz/(J
molt. ’ )
expt
0.8026 0.8394 0.8757 0.9117 0.9473 0.9649
3370 2930 2310 1700 1040 689
GilC
3410 2880 2310 1700 1050 716
composition) mode. Two high-pressure ISCO syringe pumps supplied at a constant rate the two fluids to be mixed. The total flow rate was from 0.0028 to 0.0278 cm3. s- 1 for all temperatures and pressures studied. Previous results. obtained with the calorimeter were reproducible to 0.8 per cent or better over the range 0.2 < x < 0.8. (1.3) Reproducibility of results in the present investigation was :t 3 per cent. This uncertainty was due mainly to difficulties in mixing the components in certain mole fraction regions. The materials employed were CO2 (Whitmore Oxygen Co., 99.98 moles per cent pure) and punctilious ethanol (Midwest Grain Products, Inc., Atkinson, Kansas, 200 proof). Prior to use, the CO, was filtered through a Matheson gas purifier model 450 which also contained a molecular-sieve desiccant. The ethanol was stored in sealed 1 dm3 bottles over approximately 50 cm3 of Davison molecular sieves (0.3 nm effective pore diameter) and, just prior to use, was filtered through a Whatman filter (0.45 pm pore diameter) and degassed for IO min in an ultrasonic bath. Flow rates measured in cm3. s-l were converted to mol. s-l and to mole fractions using the densities of the two pure materials estimated as follows. The densities of CO* at 298.15 K from 5.00 to 14.91 MPa were calculated by interpolation of the values from the IUPAC tables. (” The densities of the ethanol at 298.15 K and these pressures were calculated by averaging the density at 298.15 K and 101.325 kPa reported by Ortega@’ with that reported by Diaz Peiia and Tardajos”’ and correcting for the pressure using the values for isothermal compressibility from Diaz Pefia and Tardajos.“’ 3. Results and discussion Table 1 gives values for Hi{xCO, + (I -x)C,H,OH} over the entire composition range at 308.15, 325.15, 373.15, 413.15, and 473.15 K at pressures ranging from 5.00 to 14.91 MPa. The experimental values for each temperature and pressure were curve fitted using the equation: HfiJ(J .mol-‘) 4-x)
= [
exp(-~x)“~~E.(l--?xr+(*-exp(-nx)J
5 F,(1-2~)” n=O
1
(1)
660 TABLE
TIK PIMPa
2.
I>. R. CORDRAY Coefficients
308.15 7.50
and
standard deviations s [or (xCO,+(l -x)CZH,OH)
308. I5 12.50 . ..~_._.
i
- 2293.9 - 3.0508
- 1575.2 -5.3614
EY E2 4 FO F, F2 F3 F4 F5 s
- 1661.4 - 1722.9 1256.4 0 0 0 0 0 0 96
169.58 107.80 -0.0158 - 1674.7 0 0 0 0 0 5.4
T/K PiMPa ; EY ~52
6 4 4 FO F, F2 F3 F4 F5 Fb s
TIK PIMPa a
El3 F, -v F, E;,
F3 F4 F5 s
373.15 IO.00 6.0000 0 0 0 0 0 0 - 1070.3 -9387.3 - 1851.7 8679.1 13742 -22031 0 55 473.15 7.50 5.7076 0 40824 15407 - 27704 - 42446 17273 35462 58
E7' :tf
373.15 12.50 - 1.0954 - 1267.1 - 3228.0 2975.7 1744.1 278.92 - 4246.4 0 0 0 0 0 0 0 37 473.15 10.00 5.8228 0 30934 -4586.0 - 40697 - 22024 41146 35769 43
325.15 5.00 ~~~ ~~ -01.9318 0 0 0 - 7647.9 - 15480 - 25465 - 23432 0 0 55 373.15 14.91 0.4531 - 1015.2 0 0 0 0 0 -2891.7 -3317.7 11588 -29412 0 0 0 23 473.15 12.50 5.9999 0 23072 -11821 - 19898 7910.6 18744 0 83
.._~~~
least-squares by equation 325.15 7.50 05.4453 0 0 0
-9215.5 - 9842.2 9301.4 27470 - 13206 - 39728 53 413.15 7.50 0.7871 0 0 0 0 0 0 26900 - 15705 21515 - 117930 - 33443 118440 0 70
representation
of
H:/(J
'mol
')
lor
(I) 325.15 IO.00
- 2.7585 - 1608.6 - 1006. I - 1095.2 0 0 0 0 0 0 0 38 413.15 10.00 3.8690 0 0 0 0 0 0 7203.4 - 12228 -318.03 -24233 48401 25726 -49414 62
325.15 12.50
-
-0.9403 - 1203.7 ~ 224.48 -341.40 0 0 0 0 0 0 0 6.6 413.15 12.50 5.0262 0 0 0 0 0 0 4774.1 - 11229 9813.2 - 11456 15931 12614 -22c00 39
373.15 7.50 0.0257 0 0 0 0 56469 - 566750 -887110 -1194700 96027 - 679550 52 413.15 14.91 0.0803 0 0 0 0 0 0 93276 - 152910 195680 82356 -82116 0 0 20
473.15 14.91 h.cooo 0 18276 - 14036 -9826.8 15663 14669 0 23
The exponential acts as a factor to switch between the left and right summations in the term in square brackets in equation (1). The adjustable parameters of equation (1) were found using a non-linear curve-fitting program which employs the Marquardt algorithm.(“) The coefficients En and F, are given in table 2 along with the standard deviations. In the current study, most of the results were found to be
H$CO,+(l
-x)C,H,OH]
661
FIGURE I. Plot of H:(x) for {xCO, + (1 -x)C,H,OHJ at (a), 308.15 K: 0, 7.50 MPa; [I, 12.50 MPa; (b), 325.15 K: 0, 5.00 MPa; 0. 7.50 MPa: A. 10.00 MPa: 0. 12.50 MPa; (c), 373.15 K: 0, 7.50 MPa; 0, 10.00 MPa: A. 12.50 MPa; 0, 14.39 MPa; (d). 413.15 K: 0. 7.50 MPa; 0, 10.00 MPa: A, 12.50 MPa: 0. 14.39 MPa: and (e), 473.15 K: 0, 7.50 MPa; C 1. 10.00 MPa; A, 12.50 MPa: 0. 14.39 MPa: -. calculated using equation (1).
best fitted by using only the right or left summation alone. The curve-fitted values are given in table 1. Equation (1) is a good interpolating function for the results for all compositions, including linear sections of the isotherms. However, differentiation of equation (1) for the determination of other thermodynamic properties is not recommended.
662
D. R. CORDRAY
TABLE
3. Liquid
T/K
PIMPa
xl
xg
T/K
7.50 5.00 7.50 7.50
0.92 0.25 0.46 0.29
1.00 0.95 0.98 0.92
373.15 373.15 373.15 413.15
308.15 325.15 325.15 373.15
(x,) and vapor
(x,)
ET AL.
mole fractions for (xC0, Hk values p/MPa 10.00 12.50 14.91 7.50
+( I -x)C,H,OHJ
X,
xg
T/K
0.36 0.50 0.69 0.19
0.92 0.89 0.87 0.81
413.15 413.15 473.15
as determined
from
p/MPa
x,
.xg
10.00 12.50 7.50
0.30 0.39 0.12
0.81 0.80 0.40
Figure 1 shows plots of HE(x) for the five temperatures studied along with the fit by equation (1). The linear sections of the plots (in the middle of the mole-fraction range) correspond to regions where a gaseous phase and a liquid phase, both of fixed composition, are in equilibrium. The CO, liquid-phase and gas-phase compositions (x, and xg, respectively) can be estimated from figure 1 as the x coordinates at the two ends of the linear region where the results begin to deviate from linearity. (11) The values of x, and xg are given in table 3. The estimated uncertainty in the compositions reported is fO.O1. We have modeled the observed HE{xCO,+(l-x)C,H,OH) with the Soave equation of state. U) The process of fitting the Soave equation to the experimental results consisted of varying an adjustable interaction parameter k,, until the best fit (lowest standard deviation) was found. The Soave equation provided an excellent fit at higher temperatures and pressures. The fit was poor at 308 K at the higher pressure, failing even to predict the correct sign for the Hz. For temperatures where the two-phase region was crossed, the equation described the shape of the Hz(x) curves but predicted greater magnitudes for HE than were observed in the region of higher x. This behavior can be seen in figure 2. The usual assumption that k,, is independent of temperature has been found to be false over large ranges of temperature.“~‘*’ For (xC0, + (1 -x)C,H,OH), a slight temperature dependence of k,, was observed, with values ranging from 0.872 to 0.923 depending upon the temperature. The equation: k,, = 1.78519-4.71528
x 10-3(T/K)+6.15524x
FIGURE 2. Plot of H:(x) for (xC0, 0, experimental results; ~, calculated using
+ (l-x)C,HsOH) ASV equation with
10-6(T/K)Z,
k,,
at 373.15 K and found from equation
(2)
12.50MPd; (2).
H:{xCO,+(l-x)C,H,OH;
663
gives the best fit of the k,, values over the range of the experimental measurements. 1Jsing k,, values calculated from equation (2) resulted in a fit with a standard deviation of 242 J mol- ‘. This work was funded by U.S. Department of Energy, Office of Basic Energy Sciences, Grant No. DE-FG02-85ER13443, by the Donors of the Petroleum Research Fund administered by the American Chemical Society, and by Air Products and Chemicals Co. We appreciate the aid given to us in collecting and processing the data by P. R. Harding, C. Orme, P. W. Faux, L. D. Gunderson. and T. A. C. Walker. REFERENCES I. Christensen, J. J.; Faux, P. W.; Cordray, D.; Izatt. R. M. J. Chem. Thermodynamics 1986, 18, 1053. 2. Christensen, J. J.; Cordray, D. R.; Oscarson. J. L.; Izatt, R. M. J. Chem. Thermodynamics 1988, 20. in the press. 3. Soave. Ci. Chem. Eng. Sci. 1972, 21, 1197. 3. Christensen, J. J.; Izatt, R. M. Thermochim. Acfa 1984, 73, 117. 5. Christensen, J. J.: Izatt. R. M.; Eatough. D. J.; Hansen. L. D. J. Chem. Thermodynamics 1978, IO. 25.
6. McFall, T. A.; Post, M. E.; Collins, S. G.; Christensen. J. J.: Izatt, R. M. J. Chem. Thermodynumkv 1981, 13, 41. 7. Carbon Dioxide. IUPAC Thermodynamic Tables 01 the Fluid Stare. Pergamon Press: Oxford. 1976. 8. Ortega, J. J. Chem. Eng. Data 1982, 27, 312. 9. Diaz Petia, M.; Tardajos, G. J. Chem. Thermodynamics 1979, I I. 441. 10. Marquardt. D. W. J. Sot. Indust. Appl. Math. 1%3, 1I. 431. 1 I. Cordray. D. R.; Christensen, J. J.; Izatt. R. M. Sep. Sci. Technol. 1987, 22. 1169. I?. Kurnik. R. T.; Holla. S. J.: Reid, R. C. J. Chcm. Eng. Dam 1981. 26. 47.