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The excess enthalpies of (carbon dioxide + toluene) at 308.15, 358.15, and 573.15 K from 6.98 to 16.63 MPa
M-1917 .I. Chem. Thermo@namics 1986, 18, 647-656
The excess enthalpies of (carbon dioxide + toluene) at 308.15, 358.15, and 573.15 K from 6.98 to 16.63 M Pa D. R. CORDRAY, J. J. CHRISTENSEN, and R. M. IZATT Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. (Received 19 August 198.5; in revised,form
23 October 1985)
The excess molar enthalpies Hi{ xC0, + (1 - x)C,H,CH,} were measured in the vicinity of the critical locus and in the supercritical region. Large positive and negative Hks were observed depending on the compositions. pressures, and temperatures of the mixtures. A modified Soave equation of state was used to correlate Hz over a temperature range of 308.15 to 573.15 K with an average standard deviation of 384 J mol- I.
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies in the vicinity of the critical points of one or both of the components. Results for several {carbon dioxide + a hydrocarbon}“-“’ and {a fluorohydrocarbon + a hydrocarbon)“‘-“I mixtures have been reported. In these, HE showed increased negative character as the critical temperature of the component having the lower critical temperature was approached along an isobar. In cases where the critical point of the second component was approached, large positive Hzs were observed. Previously Hzs of {?rCO,+(l -x)C,H,CH,J were measured at 308.15, 358.15, 413.15, 470.15, and 573.15 K at 7.60 to 12.67 MPa.‘4q8’ The present work reports values of HE(.wCO, + (1 -X&H&H,] at 308.15, 358.15. and 573.15 K from 6.98 to 16.63 MPa. These HEs should provide an excellent test for equations used to mode1 the behavior of binary mixtures near their critical loci. In this paper a modified form of the Soave equation has been fitted in an initial attempt the better to predict mixing behavior in the critical region. HE of binary mixtures
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (**-*O) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure ISCO syringe pumps supply at a constant By acceptance of this article. the publisher acknowledges non-exclusive royalty-free license in and to any copyright
the right of the U.S. Government covering this paper.
to retain
a
648
D. R. CORDRAY.
TABLE
\-
1. Experimental
J. J. CHRISTENSEN.
and calculated
H;/(J
ffki(J
expt
expt
excess molar
enthalpies
mol-
v
‘)
talc. 308.15
0.0347 0.1010 0.1636 0.1936 0.1936 0.2228 0.3056 0.3822
-90 -475 -961 - 1030 - 1020 - 1250 - 1690 -2180
- 178 - 529 -873 -1040 -1040 ~ 1210 - 1710 -2190
0.4301 0.4756 0.5190 0.5604 0.6000 0.6378 0.6739 0.7254
- 2400 - 2920 -3250 -3350 -3520 -4070 -4150 -4760
0.1714 0.2901 0.3443 0.3954 0.4895
-419 -886 - 1050 - 1250 - 1620
-376 -913 ~ 1050 - 1210 - 1560
0.5329 0.5741 0.686 I 0.8129 0.8412
- 1700 - 1890 -2410 -3130 -3280
0.0404 0.1164 0.1865 0.2515 0.3118 0.3679 0.4203
-59 ~ 274 -499 -649 -851 -1110 -1260
-32 -254 -477 -690 - 889 - 1080 - 1250
0.4694 0.5153 0.5585 0.5991 0.6374 0.6736 0.7079
- 1420 -1580 -1690 -1780 - 1980 -2020 -2070
0.0796 0.1169 0.1873 0.2525 0.3129 0.3691
-172 - 299 -493 - 649 -832 - 1020
- 176 - 280 -479 - 666 -842 - 1010
0.4216 0.4706 0.5166 0.5598 0.6004 0.6386
-1150 -1320 -1440 -1590 -1700 -1810
0.0409 0.1177 0.1885 0.1885 0.2539 0.3145 0.3145 0.3709
-71 -219 -385 -331 - 509 -721 - 695 -832
-64 - 209 - 369 -369 -533 -693 - 693 - 844
0.4234 0.4234 0.4725 0.5184 0.5616 0.6021 0.6403 0.6764
-971 - 1030 -1100 - 1240 -1320 -1420 -1500 -1590
0.0413 0.0413 0.1187 0.1900 0.2558 0.3167 0.3732
-58 -81 - 148 -259 -403 -483 -613
-55 -55 - 165 - 275 - 385 -494 -600
0.4258 0.4750 0.5210 0.5641 0.5641 0.6045 0.6426
-695 -788 -920 -977 -998 -1070 -1110
AND
0.7736 0.8042 0.8336 0.8757 0.8891 0.9024 0.9154 0.9154
-983 -983 -1110 -1230 -1330 -1430 -1520 -1590
0.8945 0.9072 0.9134 0.9318 0.9554
0.7403 0.7710 0.8003 0.8281 0.8545 0.8798 0.9039
ffL,,(J
expt
expt
mol
’i
talc.
-5060 -5300 -5470 -5660 - 5490 -5120 -3930 -4060
-5020 -5260 - 5480 - 5770 ~
0.9154 0.9406 0.9529 0.9650 0.9885
-4270 -3210 -2100 -1620 -625
~~ ~~~
-3460 -3460 -3400 -3440 -3350
-
0.978 I 0.9837 0.9892
-2610 -3200 -1200
~~ ~~ ~~
-2160 -2190 -2090 -1980 -1770 -1460 -1230
-2140 -2140 - 2090 - 1980 - 1800 -1540 - 1210
0.9269 0.9489 0.9700 0.9700 0.9902
-1910 -1880 -1960 -1970 -1980 -1940
- 1890 - 1890 - 1960 -2000 - 2010 - 1980
0.8288 0.8552 0.8803 0.9043 0.9272 0.9492
-1900 -1760 -1540 -1330 -962 -644
-1890 -1750 -1540 -1270 -956 -631
-1680 -1670 -1660 -1690 -1690 -1650 -1610 -1570
- 1640 -1640 - 1680 - 1680 - 1680 - 1650 - 1650 - I590
0.8561 0.8561 0.8811 0.9049 0.9277 0.9495 0.9704 0.9903
-1490 - 1430 -1340 -1140 - 879 - 623 - 324 -71
-1470 - 1470 -1310 -1110 - 876 - 622 - 363 -117
-1170 -1180 - 1230 -1250 -1230 -1230 -1190
--
0.8573 0.8821 0.9284 0.9393 0.9500 0.9707 0.9904
-1120 -1020 - 726 - 622 -544 - 293 -90
-1100 -1000 -732 ~ 647 -554 ~ 350 -123
3450 3470 3480 3470 3300
-892 - 545 -192 - 206 -12
- 847 - 499 -218 -218 -44
K. 13.88 MPa
-1170 -1310 - 1450 -1580 -1700 -1800 358.15
ff;;( J
K. 13.30 MPa
-1410 -1560 -1700 -1830 -1940 -2030 -2100 358.15
lor j \-COL + ( I -- u )C-,,H,C‘H,(
K. 8.01 MPa
~ 1740 -1910 -2440 -3090 -3230 358.15
ff:
K. 6.98 MPa
-2500 -2810 -3110 -3410 -3690 -3980 -4250 -4650 308.15
R. M. IZAT’I
0.6747 0.6747 0.7089 0.7413 0.7719 0.8011
K, 14.91 MPa 0.7104 0.7104 0.7427 0.7427 0.7732 0.8022 0.8022 0.8298
358.15 K, 16.63 MPa -703 0.6786 -802 0.7125 -895 0.7446 -981 0.7750 -981 0.7750 - 1060 0.8038 -1120 0.8312
I 180 1210 1230 1230 I230 1210 1170
H;{xCO,
+(I
TABLF r
Hz/(J
mol-‘)
expt
H:/(J
I
talc.
expt
mol-
649
-.Y)C,H,CH,) I -corrrrnued
‘)
I
talc. ~___
Hk/(J
mol - ‘)
expt
talc.
x
Hz/(J expt
mol-‘) talc.
573.15 I(. 8.01 MPa 0.0366 0.1062 0.1714 0.2326 0.2618 0.3176
438 1700 2850 4010 4700 5920
499 1590 2830 4130 4760 5820
0.3443 0.3702 0.3954 0.4438 0.4670 0.4892
6140 6690 6780 6910 6880 7060
6230 6550 6780 6990 6990 6940
0.5115 0.6133 0.6506 0.686 1 0.7523 0.8129
6890 6050 5530 5040 4210 3220
6850 5990 5550 5100 4170 3250
0.8412 0.8945 0.9437 0.9892
7770 i91O I060 241
2790 I900 1040 270
rate the two fluids to be mixed. The total flow rate was from 0.00278 to 0.01111 cm3.s-l for all temperatures and pressure studied. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over most of the mole-fraction range (0.2 < x < 0.8). (r8) Reproducibility of results in the present investigation was f 1 to +2 per cent mainly due to difficulties in mixing the components in certain mole-fraction regions. The materials employed were carbon dioxide (Whitmore Oxygen Co. 99.98 moles per cent pure) and toluene (Phillips Petroleum Co.. better than 99 moles per cent pure). Before being used, the CO, was filtered through a Matheson gas purifier model 450 which also contains a molecular-sieve desiccant. The toluene was stored in sealed I 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 urn pore diameter) and degassed for 10 min in an ultrasonic bath. Flow rates measured in cm’. s-l were converted to mol. s- ’ and to mole fractions using the densities of the two pure materials estimated as follows. The densities of CO, at 298.15 K and from 6.98 to 16.63 MPa (0.730 to 0.883 g r cm 3respectively) were calculated by interpolation from the IUPAC Tables.“” The densities of toluene at 298.15 K over this pressure range (0.868 to 0.876 g. cm ‘. respectively) were evaluated using the value at 298.15 K and atmospheric pressure,‘“” and the isothermal compressibilities at 298.15 K estimated by interpolation using those obtained at 293.15 and 303.15 K by Freyer er nl.“” 3. Results and discussion Excess molar enthalpies were determined for {.uCO, +(1 -x)C,H,CH,f over the entire composition range at 308.15 K for 6.98 and 8.01 MPa, at 358.15 K for 13.30, 13.88, 14.91, and 16.63 MPa, and at 573.15 K for 8.01 MPa. The results are given in table 1. Values for H,f, at each temperature and pressure studied were curve fitted using the equation: li,$‘(J.mol-‘)
=
1+ f n= 1
L&,(1 -2.x)”
n$O C,(l -2.x)“.
(1)
The coefficients C, and D, are given in table 2 together with standard deviations s.
650
D. R. CORDRAY.
J. J. CHRISTENSEN.
AND
R. M. IZATI
Figure 1 gives plots of Hi against x for the temperatures and pressures studied. The large changes in HE with temperature have been observed in other mixtures where measurements were taken near the critical points of one or both of the components. (l-l’) Ng and Robinson have determined the critical locus of this mixture which is shown in figure 2. (24’ Also shown in figure 2 are points indicating the conditions for which Hg was measured in this study and in two previous studies.‘4*8) The critical points of the pure components are also indicated. The observed large changes in HE with temperature and pressure can be examined with respect to changes in the various fluid properties of the components near their critical points. The change in the excess enthalpy with temperature at constant pressure may be expressed as
(aHE/aT), = AC,<, = C,,,{xCO,
+(l -.u)C,H,CH,J- xC,.,W,) - Cl- W,,,(C,H,CH,L
(2)
where C,., is the molar heat capacity at constant pressure. The change in HE with pressure at constant temperature is given by
@HE/@), = V,"- TA(crV,),
(3)
where V,” and a are the excess molar volume and the isobaric expansivity, respectively, at temperature T. Large changes in C,,,, V,, and a can be expected in the vicinity of the critical locus. These changes could explain the considerable variations observed in HE with both pressure and temperature. Unfortunately, there are not enough values to apply equations (2) and (3) to (xC0, + (1 -x)C,H,CH,}. Changes in the HE have also been qualitatively explained in terms of the states and densities of both pure components and the resulting mixtures.(2-4~25*261 The changes result from a phase change below the critical ~ocus@,~~.~~’ and from a low-densityto-high-density fluid transition above the critical locus.“” Negative Hfs are caused
TABLE
PIMPa
2. Coefficients
co.~
and standard deviations {xCO, +(1 -x)C,H,CH,j
Cl
c2
0 11556
0 0
s for least-squares representation by equation (1)
D,
D*
of
4
D4
Hi
for
s
308.15 K 6.98 8.01
-11912 -6408.1
1.1665 -0.5526
0.1796 -2.1085
0 -0.6145
0 0
91 64
-0.8347 -0.8639 0.3111 0.4443
-0.9959 -0.9650 0.3683 0
0 0 0.5320 0
37 28 25 21
0
80
358.15 K 13.30 13.88 14.91 16.63
- 6058.4 -5602.0 -4725.5 -3411.4
589.02 981.99 0 0
6107.4 4825.1 0 0
0.9869 0.8956 1.0755 1.1861 573.15
8.01
27611
- 30479
19808
K
- 1.4105
1.7047
0
H:(xCO,+(I
FIGURE T=308.15K: 14.91 MPa:
-x)C,H,CH,)
I. Plot of Hk against x for (xC0, +(l -x)C,H,CH,} 0, 6.98Pa; 0, 8.01Pa; (b), at T=358.15K: 0. x . 16.63 MPa; and (c)+ at T = 573.15 K: 0. 8.01 MPa.
651
as a function 13.30MPa:
of pressure (a), at 0, 13.88MPa: A.
by gas or low-density liquid forming a liquid or high-density mixture while positive Hks are caused by a liquid or high-density fluid forming a gas or low-density mixture. We have modeled the Hzs for several previous examples of (carbon dioxide + a hydrocarbon}@-“) and of {a fluorocarbon + a hydrocarbon}‘16. ’ 7, using various equations of state. A combination of the hard-sphere repulsion term derived by Andrews and Ellerby’27) with the attraction term proposed by Soave’28’ has given the best correlation of past results. Here we have compared the observed variation of Hz with the Andrews-Soave (ASV) equation of state; HEs from both this study and from previous studiesC4**’ were used in the correlations. The ASV equation may be written as p = po-a[l+m{l--(T/T,)“*~]*/(V,(l/,+b)~.
(4ab
652
D. R. CORDRAY.
3(M)
J. J. CHRISTENSEN.
400
350
450 T/K
AND R. M. IZATT
S(N)
550
600
FIGURE 2. Plot of p against 7’ for (xCO,+( 1 -x)C,H,CH,} showing critical points and critical locus. The conditions at which the measurements were made are indicated: 0, this study: 0. previous studies.“‘,” The critical locus is from reference 24.
or as p = Po-4{MI/,+b))~
(4b)
where m = (0.48508+ 1.551710-0.15613~2) and III is Pitzer’s acentric factor.‘29’ The coefficients in the equation for m were taken from the correlation of Graboski and Daubert.‘30’ The values of w from Reid, Prausnitz. and Sherwood’31’ were used. The hard-sphere repulsion term p. is RT[28q2/bq -(4/b)ln(
1 -r]) - (14.38/b)ln q -(47.31/b)ln{(l-0.7210~)/(1-
1.350~)}],
where g = b/41/, and q = (1 -2.071q+0.9736q2). The derivation of residual enthalpies Hk(l/,, T) from an equation been outlined by Lewis, Mosedale, and Wormald’26’ and yields Hk(J$,/,, T) = (cc+m(~/~)‘i2cc1i2}(a/~)ln{I/,/(I/,+b)}+pl/,-RT.
(5)
of state has (6)
The predicted excess molar enthalpy is given by Hz = H:{xCO,
+ (1 -x)C,H,CH
3) -xH:(co,)-(
1 -x)H;(c,H,cH,).
(7)
The constants a and b in equation (6) for the pure components were obtained from the critical conditions (+/aV,), = 0 and (a2p/aV,“), = 0:‘27*32,33’ a = 0.461891R2T,2/pF,
(8)
b = O.l05007RTJp,.
(9)
The mixtures were treated as single fluids having the constants: h = CiXibi.
(10)
a = cj =yi xixjaij,
(II)
~~(lxco,+(l-.y)C,H,CH,)
653
and where A = CO, and B = C,H,CH,. An arithmetic mean of the w values of the pure components was used for the o values of the mixtures {equation (10) with w replacing b}. Similarly, a geometric mean of the T, values of the pure components was used for the pseudo-critical temperature of each mixture with TAB= (T,,T,,)‘~’ (equation (11) with T, replacing a). By varying the interaction parameter k,, a best fit (lowest standard deviation) of current and previous results at all temperatures and pressures was obtained. resulting in a standard deviation of 772 J. mall’ and a k,, of 0.901. When results from individual temperatures and pressures were COrreldted independently, the optimum values of k,, were found to vary strongly with temperature and weakly with pressure. A plot of the averaged optimum k,, values for all pressures at each temperature is shown in figure 3. The straight line: k,, = 0.4612+0.00125T!K.
(13)
fits these points. Incorporating this temperature variation into the ASV equation resulted in a standard deviation of 384 J. mall ‘. Table 3 lists the standard deviations for each temperature and pressure studied using both a constant value of k,, of 0.901 and that value found by using equation (13). A large improvement in the standard deviation is seen for most mixtures when equation (13) is used. Figure 4 shows the correlation of the ASV equation with experimental results at two conditions using both a constant and a temperature-dependent (equation 13) value for k,,. In figure 4(a), little improvement is seen by using k,, determined from equation ( 13). whereas in figure 4(b) a large improvement is obtained. In an attempt further to improve the correlation of the ASV equation with the results. the averaged k,, values were fitted with a cubic equation in temperature. Using this
FIGURE 3. Plot of k,, against T for {xCO,+(l-x)C,H,CH,} studies; 0. average k,, giving best correlation L AB = (0.4612+0.00125T/K).
at
each
for this study temperature;
and two previous -. based on
654 TABLE
T/K
D. R. CORDRAY, 3. Comparison
s/(J,mol-‘) k,,
6.98 7.60 8.01 10.64 12.67 7.60 10.64 12.67 13.30 13.88 14.91 16.63
358.15
AND
R. M. 1ZATT
of fit of Hk by ASV equation using a constant value with temperature for {uCO, + (1 -.x)C,H,CH,i
PIMPa
308.15
J. J. CHRISTENSEN,
T.!K
of k,,
1263 688 526 528 375 206 172 298 474 476 395 306
k,,
937 127 411 253 377 256 214 307 425 427 361 301
413.15
470.15
573.15
variation
of/i,”
s/(J.mol-‘)
pIMPa
k,, = 0.4612 +O.O0125T/K
= 0.901
and a linear
7.60 10.64 12.67 7.60 10.64 12.67 7.60 8.01 10.64 12.67
k,, = 0.4612 +O.O0125T/K
= 0.901 427 408 505 829 837 887 696 1391 1398 1175
358 340 351 596 479 409 120 341 219 202
equation resulted in a standard deviation of 392 J. mol- ‘. There are not enough results, however, to justify the use of anything but a linear variation of k,, with temperature. Weak variation of k,, with temperature has also been reported by others(34’ using solubilities obtained in supercritical carbon dioxide and supercritical ethylene. The results, however, covered only a small range of temperature. Usually
0
0.2
0.4
0.6
0.x
I
0
0.2
0.4
x FIGURE 4. Plot of Hi against x for {xCO,+(l -x)C,H,CH,} 6.98 MPa; (b) at T = 573.15 K and p = 8.01 MPa. 0, Experimental; k,, = 0.901: - - -. from ASV equation with k,, = (0.4612 +0,00125T/K).
p=
(1.6
0.8
I
x (a), -,
at T = 308.15 K and from ASV equation with
H:{xCO,+(l
-x)C,H,CH,j
655
k,, is assumed to be independent of temperature, pressure, and composition. It is apparent that further understanding is needed of the interaction parameter and of its physical significance. This work was funded by U.S. Department Sciences, Contract No. DE-AC02-82ER13024 Research Fund administered by the American aid given to us in collecting the data by P. W. T. A. C. Walker.
of Energy, Office of and by the Donors of Chemical Society. We Faux. P. R. Harding,
Basic Energy the Petroleum appreciate the C. Orme, and
REFERENCES I. Pando. C.: Renuncio. J. A. R.: MeFall. T. A.: Izatt. R. M.: Christensen. J. J. J. Chm~. Thermodynamics 1983, 15, 173. 2. Pando. C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen. J. J. J. Chem. Thermo&wamics 1983, 15. 259. 3. Pando, C.; Renuncio. J. A. R.; Izatt. R. M.; Christensen. J. J. J. Chem. Thermo
656
D. R. CORDRAY.
J. J. CHRISTENSEN.
AND
R M. lZhT-I
19. Pxtzer, K. S. Phase Eyuilihriu und Fluid Proprrws 01 ( ‘htwrmrl Intlu.rtr~~. A (..5 .S~wrp~~ut~~ .S~YM 1977. p. I. 30. Graboski. M. S.; Dauber?. T. E. Ind. Eng. Chem. Process Des. Del,. 1978, 17. 443. 3 I. Reid. R. C.; Prausnitr, J. M.; Sherwood. T. K T/w Proper/kr ,I/’ Gu.ws md Liquidr. 3rd Ed McGraw-Hill: New York. 1977. 32. Carnahan. N. F.; Starling, K. E. .41C/& Journal 1972, IX. 1184. 33. Henderson, D. Equa/ions of Stule in Engineering and Research. Chao, K. C.; Robinson, Jr.. R. L. editors. ACS: Washington, DC. 1979, p. 1. 34. Kurnik. R. T.; Holla, S. J.; Reid, R. C. J. Chem. Eng. Dafu 1981, 26. 47.
The excess enthalpies of (carbon dioxide + toluene) at 308.15, 358.15, and 573.15 K from 6.98 to 16.63 M Pa D. R. CORDRAY, J. J. CHRISTENSEN, and R. M. IZATT Departments of Chemical Engineering and Chemistry, Brigham Young University, Provo, Utah 84602, U.S.A. (Received 19 August 198.5; in revised,form
23 October 1985)
The excess molar enthalpies Hi{ xC0, + (1 - x)C,H,CH,} were measured in the vicinity of the critical locus and in the supercritical region. Large positive and negative Hks were observed depending on the compositions. pressures, and temperatures of the mixtures. A modified Soave equation of state was used to correlate Hz over a temperature range of 308.15 to 573.15 K with an average standard deviation of 384 J mol- I.
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies in the vicinity of the critical points of one or both of the components. Results for several {carbon dioxide + a hydrocarbon}“-“’ and {a fluorohydrocarbon + a hydrocarbon)“‘-“I mixtures have been reported. In these, HE showed increased negative character as the critical temperature of the component having the lower critical temperature was approached along an isobar. In cases where the critical point of the second component was approached, large positive Hzs were observed. Previously Hzs of {?rCO,+(l -x)C,H,CH,J were measured at 308.15, 358.15, 413.15, 470.15, and 573.15 K at 7.60 to 12.67 MPa.‘4q8’ The present work reports values of HE(.wCO, + (1 -X&H&H,] at 308.15, 358.15. and 573.15 K from 6.98 to 16.63 MPa. These HEs should provide an excellent test for equations used to mode1 the behavior of binary mixtures near their critical loci. In this paper a modified form of the Soave equation has been fitted in an initial attempt the better to predict mixing behavior in the critical region. HE of binary mixtures
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (**-*O) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure ISCO syringe pumps supply at a constant By acceptance of this article. the publisher acknowledges non-exclusive royalty-free license in and to any copyright
the right of the U.S. Government covering this paper.
to retain
a
648
D. R. CORDRAY.
TABLE
\-
1. Experimental
J. J. CHRISTENSEN.
and calculated
H;/(J
ffki(J
expt
expt
excess molar
enthalpies
mol-
v
‘)
talc. 308.15
0.0347 0.1010 0.1636 0.1936 0.1936 0.2228 0.3056 0.3822
-90 -475 -961 - 1030 - 1020 - 1250 - 1690 -2180
- 178 - 529 -873 -1040 -1040 ~ 1210 - 1710 -2190
0.4301 0.4756 0.5190 0.5604 0.6000 0.6378 0.6739 0.7254
- 2400 - 2920 -3250 -3350 -3520 -4070 -4150 -4760
0.1714 0.2901 0.3443 0.3954 0.4895
-419 -886 - 1050 - 1250 - 1620
-376 -913 ~ 1050 - 1210 - 1560
0.5329 0.5741 0.686 I 0.8129 0.8412
- 1700 - 1890 -2410 -3130 -3280
0.0404 0.1164 0.1865 0.2515 0.3118 0.3679 0.4203
-59 ~ 274 -499 -649 -851 -1110 -1260
-32 -254 -477 -690 - 889 - 1080 - 1250
0.4694 0.5153 0.5585 0.5991 0.6374 0.6736 0.7079
- 1420 -1580 -1690 -1780 - 1980 -2020 -2070
0.0796 0.1169 0.1873 0.2525 0.3129 0.3691
-172 - 299 -493 - 649 -832 - 1020
- 176 - 280 -479 - 666 -842 - 1010
0.4216 0.4706 0.5166 0.5598 0.6004 0.6386
-1150 -1320 -1440 -1590 -1700 -1810
0.0409 0.1177 0.1885 0.1885 0.2539 0.3145 0.3145 0.3709
-71 -219 -385 -331 - 509 -721 - 695 -832
-64 - 209 - 369 -369 -533 -693 - 693 - 844
0.4234 0.4234 0.4725 0.5184 0.5616 0.6021 0.6403 0.6764
-971 - 1030 -1100 - 1240 -1320 -1420 -1500 -1590
0.0413 0.0413 0.1187 0.1900 0.2558 0.3167 0.3732
-58 -81 - 148 -259 -403 -483 -613
-55 -55 - 165 - 275 - 385 -494 -600
0.4258 0.4750 0.5210 0.5641 0.5641 0.6045 0.6426
-695 -788 -920 -977 -998 -1070 -1110
AND
0.7736 0.8042 0.8336 0.8757 0.8891 0.9024 0.9154 0.9154
-983 -983 -1110 -1230 -1330 -1430 -1520 -1590
0.8945 0.9072 0.9134 0.9318 0.9554
0.7403 0.7710 0.8003 0.8281 0.8545 0.8798 0.9039
ffL,,(J
expt
expt
mol
’i
talc.
-5060 -5300 -5470 -5660 - 5490 -5120 -3930 -4060
-5020 -5260 - 5480 - 5770 ~
0.9154 0.9406 0.9529 0.9650 0.9885
-4270 -3210 -2100 -1620 -625
~~ ~~~
-3460 -3460 -3400 -3440 -3350
-
0.978 I 0.9837 0.9892
-2610 -3200 -1200
~~ ~~ ~~
-2160 -2190 -2090 -1980 -1770 -1460 -1230
-2140 -2140 - 2090 - 1980 - 1800 -1540 - 1210
0.9269 0.9489 0.9700 0.9700 0.9902
-1910 -1880 -1960 -1970 -1980 -1940
- 1890 - 1890 - 1960 -2000 - 2010 - 1980
0.8288 0.8552 0.8803 0.9043 0.9272 0.9492
-1900 -1760 -1540 -1330 -962 -644
-1890 -1750 -1540 -1270 -956 -631
-1680 -1670 -1660 -1690 -1690 -1650 -1610 -1570
- 1640 -1640 - 1680 - 1680 - 1680 - 1650 - 1650 - I590
0.8561 0.8561 0.8811 0.9049 0.9277 0.9495 0.9704 0.9903
-1490 - 1430 -1340 -1140 - 879 - 623 - 324 -71
-1470 - 1470 -1310 -1110 - 876 - 622 - 363 -117
-1170 -1180 - 1230 -1250 -1230 -1230 -1190
--
0.8573 0.8821 0.9284 0.9393 0.9500 0.9707 0.9904
-1120 -1020 - 726 - 622 -544 - 293 -90
-1100 -1000 -732 ~ 647 -554 ~ 350 -123
3450 3470 3480 3470 3300
-892 - 545 -192 - 206 -12
- 847 - 499 -218 -218 -44
K. 13.88 MPa
-1170 -1310 - 1450 -1580 -1700 -1800 358.15
ff;;( J
K. 13.30 MPa
-1410 -1560 -1700 -1830 -1940 -2030 -2100 358.15
lor j \-COL + ( I -- u )C-,,H,C‘H,(
K. 8.01 MPa
~ 1740 -1910 -2440 -3090 -3230 358.15
ff:
K. 6.98 MPa
-2500 -2810 -3110 -3410 -3690 -3980 -4250 -4650 308.15
R. M. IZAT’I
0.6747 0.6747 0.7089 0.7413 0.7719 0.8011
K, 14.91 MPa 0.7104 0.7104 0.7427 0.7427 0.7732 0.8022 0.8022 0.8298
358.15 K, 16.63 MPa -703 0.6786 -802 0.7125 -895 0.7446 -981 0.7750 -981 0.7750 - 1060 0.8038 -1120 0.8312
I 180 1210 1230 1230 I230 1210 1170
H;{xCO,
+(I
TABLF r
Hz/(J
mol-‘)
expt
H:/(J
I
talc.
expt
mol-
649
-.Y)C,H,CH,) I -corrrrnued
‘)
I
talc. ~___
Hk/(J
mol - ‘)
expt
talc.
x
Hz/(J expt
mol-‘) talc.
573.15 I(. 8.01 MPa 0.0366 0.1062 0.1714 0.2326 0.2618 0.3176
438 1700 2850 4010 4700 5920
499 1590 2830 4130 4760 5820
0.3443 0.3702 0.3954 0.4438 0.4670 0.4892
6140 6690 6780 6910 6880 7060
6230 6550 6780 6990 6990 6940
0.5115 0.6133 0.6506 0.686 1 0.7523 0.8129
6890 6050 5530 5040 4210 3220
6850 5990 5550 5100 4170 3250
0.8412 0.8945 0.9437 0.9892
7770 i91O I060 241
2790 I900 1040 270
rate the two fluids to be mixed. The total flow rate was from 0.00278 to 0.01111 cm3.s-l for all temperatures and pressure studied. Previous results obtained with the calorimeter were reproducible to 0.8 per cent or better over most of the mole-fraction range (0.2 < x < 0.8). (r8) Reproducibility of results in the present investigation was f 1 to +2 per cent mainly due to difficulties in mixing the components in certain mole-fraction regions. The materials employed were carbon dioxide (Whitmore Oxygen Co. 99.98 moles per cent pure) and toluene (Phillips Petroleum Co.. better than 99 moles per cent pure). Before being used, the CO, was filtered through a Matheson gas purifier model 450 which also contains a molecular-sieve desiccant. The toluene was stored in sealed I 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 urn pore diameter) and degassed for 10 min in an ultrasonic bath. Flow rates measured in cm’. s-l were converted to mol. s- ’ and to mole fractions using the densities of the two pure materials estimated as follows. The densities of CO, at 298.15 K and from 6.98 to 16.63 MPa (0.730 to 0.883 g r cm 3respectively) were calculated by interpolation from the IUPAC Tables.“” The densities of toluene at 298.15 K over this pressure range (0.868 to 0.876 g. cm ‘. respectively) were evaluated using the value at 298.15 K and atmospheric pressure,‘“” and the isothermal compressibilities at 298.15 K estimated by interpolation using those obtained at 293.15 and 303.15 K by Freyer er nl.“” 3. Results and discussion Excess molar enthalpies were determined for {.uCO, +(1 -x)C,H,CH,f over the entire composition range at 308.15 K for 6.98 and 8.01 MPa, at 358.15 K for 13.30, 13.88, 14.91, and 16.63 MPa, and at 573.15 K for 8.01 MPa. The results are given in table 1. Values for H,f, at each temperature and pressure studied were curve fitted using the equation: li,$‘(J.mol-‘)
=
1+ f n= 1
L&,(1 -2.x)”
n$O C,(l -2.x)“.
(1)
The coefficients C, and D, are given in table 2 together with standard deviations s.
650
D. R. CORDRAY.
J. J. CHRISTENSEN.
AND
R. M. IZATI
Figure 1 gives plots of Hi against x for the temperatures and pressures studied. The large changes in HE with temperature have been observed in other mixtures where measurements were taken near the critical points of one or both of the components. (l-l’) Ng and Robinson have determined the critical locus of this mixture which is shown in figure 2. (24’ Also shown in figure 2 are points indicating the conditions for which Hg was measured in this study and in two previous studies.‘4*8) The critical points of the pure components are also indicated. The observed large changes in HE with temperature and pressure can be examined with respect to changes in the various fluid properties of the components near their critical points. The change in the excess enthalpy with temperature at constant pressure may be expressed as
(aHE/aT), = AC,<, = C,,,{xCO,
+(l -.u)C,H,CH,J- xC,.,W,) - Cl- W,,,(C,H,CH,L
(2)
where C,., is the molar heat capacity at constant pressure. The change in HE with pressure at constant temperature is given by
@HE/@), = V,"- TA(crV,),
(3)
where V,” and a are the excess molar volume and the isobaric expansivity, respectively, at temperature T. Large changes in C,,,, V,, and a can be expected in the vicinity of the critical locus. These changes could explain the considerable variations observed in HE with both pressure and temperature. Unfortunately, there are not enough values to apply equations (2) and (3) to (xC0, + (1 -x)C,H,CH,}. Changes in the HE have also been qualitatively explained in terms of the states and densities of both pure components and the resulting mixtures.(2-4~25*261 The changes result from a phase change below the critical ~ocus@,~~.~~’ and from a low-densityto-high-density fluid transition above the critical locus.“” Negative Hfs are caused
TABLE
PIMPa
2. Coefficients
co.~
and standard deviations {xCO, +(1 -x)C,H,CH,j
Cl
c2
0 11556
0 0
s for least-squares representation by equation (1)
D,
D*
of
4
D4
Hi
for
s
308.15 K 6.98 8.01
-11912 -6408.1
1.1665 -0.5526
0.1796 -2.1085
0 -0.6145
0 0
91 64
-0.8347 -0.8639 0.3111 0.4443
-0.9959 -0.9650 0.3683 0
0 0 0.5320 0
37 28 25 21
0
80
358.15 K 13.30 13.88 14.91 16.63
- 6058.4 -5602.0 -4725.5 -3411.4
589.02 981.99 0 0
6107.4 4825.1 0 0
0.9869 0.8956 1.0755 1.1861 573.15
8.01
27611
- 30479
19808
K
- 1.4105
1.7047
0
H:(xCO,+(I
FIGURE T=308.15K: 14.91 MPa:
-x)C,H,CH,)
I. Plot of Hk against x for (xC0, +(l -x)C,H,CH,} 0, 6.98Pa; 0, 8.01Pa; (b), at T=358.15K: 0. x . 16.63 MPa; and (c)+ at T = 573.15 K: 0. 8.01 MPa.
651
as a function 13.30MPa:
of pressure (a), at 0, 13.88MPa: A.
by gas or low-density liquid forming a liquid or high-density mixture while positive Hks are caused by a liquid or high-density fluid forming a gas or low-density mixture. We have modeled the Hzs for several previous examples of (carbon dioxide + a hydrocarbon}@-“) and of {a fluorocarbon + a hydrocarbon}‘16. ’ 7, using various equations of state. A combination of the hard-sphere repulsion term derived by Andrews and Ellerby’27) with the attraction term proposed by Soave’28’ has given the best correlation of past results. Here we have compared the observed variation of Hz with the Andrews-Soave (ASV) equation of state; HEs from both this study and from previous studiesC4**’ were used in the correlations. The ASV equation may be written as p = po-a[l+m{l--(T/T,)“*~]*/(V,(l/,+b)~.
(4ab
652
D. R. CORDRAY.
3(M)
J. J. CHRISTENSEN.
400
350
450 T/K
AND R. M. IZATT
S(N)
550
600
FIGURE 2. Plot of p against 7’ for (xCO,+( 1 -x)C,H,CH,} showing critical points and critical locus. The conditions at which the measurements were made are indicated: 0, this study: 0. previous studies.“‘,” The critical locus is from reference 24.
or as p = Po-4{MI/,+b))~
(4b)
where m = (0.48508+ 1.551710-0.15613~2) and III is Pitzer’s acentric factor.‘29’ The coefficients in the equation for m were taken from the correlation of Graboski and Daubert.‘30’ The values of w from Reid, Prausnitz. and Sherwood’31’ were used. The hard-sphere repulsion term p. is RT[28q2/bq -(4/b)ln(
1 -r]) - (14.38/b)ln q -(47.31/b)ln{(l-0.7210~)/(1-
1.350~)}],
where g = b/41/, and q = (1 -2.071q+0.9736q2). The derivation of residual enthalpies Hk(l/,, T) from an equation been outlined by Lewis, Mosedale, and Wormald’26’ and yields Hk(J$,/,, T) = (cc+m(~/~)‘i2cc1i2}(a/~)ln{I/,/(I/,+b)}+pl/,-RT.
(5)
of state has (6)
The predicted excess molar enthalpy is given by Hz = H:{xCO,
+ (1 -x)C,H,CH
3) -xH:(co,)-(
1 -x)H;(c,H,cH,).
(7)
The constants a and b in equation (6) for the pure components were obtained from the critical conditions (+/aV,), = 0 and (a2p/aV,“), = 0:‘27*32,33’ a = 0.461891R2T,2/pF,
(8)
b = O.l05007RTJp,.
(9)
The mixtures were treated as single fluids having the constants: h = CiXibi.
(10)
a = cj =yi xixjaij,
(II)
~~(lxco,+(l-.y)C,H,CH,)
653
and where A = CO, and B = C,H,CH,. An arithmetic mean of the w values of the pure components was used for the o values of the mixtures {equation (10) with w replacing b}. Similarly, a geometric mean of the T, values of the pure components was used for the pseudo-critical temperature of each mixture with TAB= (T,,T,,)‘~’ (equation (11) with T, replacing a). By varying the interaction parameter k,, a best fit (lowest standard deviation) of current and previous results at all temperatures and pressures was obtained. resulting in a standard deviation of 772 J. mall’ and a k,, of 0.901. When results from individual temperatures and pressures were COrreldted independently, the optimum values of k,, were found to vary strongly with temperature and weakly with pressure. A plot of the averaged optimum k,, values for all pressures at each temperature is shown in figure 3. The straight line: k,, = 0.4612+0.00125T!K.
(13)
fits these points. Incorporating this temperature variation into the ASV equation resulted in a standard deviation of 384 J. mall ‘. Table 3 lists the standard deviations for each temperature and pressure studied using both a constant value of k,, of 0.901 and that value found by using equation (13). A large improvement in the standard deviation is seen for most mixtures when equation (13) is used. Figure 4 shows the correlation of the ASV equation with experimental results at two conditions using both a constant and a temperature-dependent (equation 13) value for k,,. In figure 4(a), little improvement is seen by using k,, determined from equation ( 13). whereas in figure 4(b) a large improvement is obtained. In an attempt further to improve the correlation of the ASV equation with the results. the averaged k,, values were fitted with a cubic equation in temperature. Using this
FIGURE 3. Plot of k,, against T for {xCO,+(l-x)C,H,CH,} studies; 0. average k,, giving best correlation L AB = (0.4612+0.00125T/K).
at
each
for this study temperature;
and two previous -. based on
654 TABLE
T/K
D. R. CORDRAY, 3. Comparison
s/(J,mol-‘) k,,
6.98 7.60 8.01 10.64 12.67 7.60 10.64 12.67 13.30 13.88 14.91 16.63
358.15
AND
R. M. 1ZATT
of fit of Hk by ASV equation using a constant value with temperature for {uCO, + (1 -.x)C,H,CH,i
PIMPa
308.15
J. J. CHRISTENSEN,
T.!K
of k,,
1263 688 526 528 375 206 172 298 474 476 395 306
k,,
937 127 411 253 377 256 214 307 425 427 361 301
413.15
470.15
573.15
variation
of/i,”
s/(J.mol-‘)
pIMPa
k,, = 0.4612 +O.O0125T/K
= 0.901
and a linear
7.60 10.64 12.67 7.60 10.64 12.67 7.60 8.01 10.64 12.67
k,, = 0.4612 +O.O0125T/K
= 0.901 427 408 505 829 837 887 696 1391 1398 1175
358 340 351 596 479 409 120 341 219 202
equation resulted in a standard deviation of 392 J. mol- ‘. There are not enough results, however, to justify the use of anything but a linear variation of k,, with temperature. Weak variation of k,, with temperature has also been reported by others(34’ using solubilities obtained in supercritical carbon dioxide and supercritical ethylene. The results, however, covered only a small range of temperature. Usually
0
0.2
0.4
0.6
0.x
I
0
0.2
0.4
x FIGURE 4. Plot of Hi against x for {xCO,+(l -x)C,H,CH,} 6.98 MPa; (b) at T = 573.15 K and p = 8.01 MPa. 0, Experimental; k,, = 0.901: - - -. from ASV equation with k,, = (0.4612 +0,00125T/K).
p=
(1.6
0.8
I
x (a), -,
at T = 308.15 K and from ASV equation with
H:{xCO,+(l
-x)C,H,CH,j
655
k,, is assumed to be independent of temperature, pressure, and composition. It is apparent that further understanding is needed of the interaction parameter and of its physical significance. This work was funded by U.S. Department Sciences, Contract No. DE-AC02-82ER13024 Research Fund administered by the American aid given to us in collecting the data by P. W. T. A. C. Walker.
of Energy, Office of and by the Donors of Chemical Society. We Faux. P. R. Harding,
Basic Energy the Petroleum appreciate the C. Orme, and
REFERENCES I. Pando. C.: Renuncio. J. A. R.: MeFall. T. A.: Izatt. R. M.: Christensen. J. J. J. Chm~. Thermodynamics 1983, 15, 173. 2. Pando. C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen. J. J. J. Chem. Thermo&wamics 1983, 15. 259. 3. Pando, C.; Renuncio. J. A. R.; Izatt. R. M.; Christensen. J. J. J. Chem. Thermo
656
D. R. CORDRAY.
J. J. CHRISTENSEN.
AND
R M. lZhT-I
19. Pxtzer, K. S. Phase Eyuilihriu und Fluid Proprrws 01 ( ‘htwrmrl Intlu.rtr~~. A (..5 .S~wrp~~ut~~ .S~YM 1977. p. I. 30. Graboski. M. S.; Dauber?. T. E. Ind. Eng. Chem. Process Des. Del,. 1978, 17. 443. 3 I. Reid. R. C.; Prausnitr, J. M.; Sherwood. T. K T/w Proper/kr ,I/’ Gu.ws md Liquidr. 3rd Ed McGraw-Hill: New York. 1977. 32. Carnahan. N. F.; Starling, K. E. .41C/& Journal 1972, IX. 1184. 33. Henderson, D. Equa/ions of Stule in Engineering and Research. Chao, K. C.; Robinson, Jr.. R. L. editors. ACS: Washington, DC. 1979, p. 1. 34. Kurnik. R. T.; Holla, S. J.; Reid, R. C. J. Chem. Eng. Dafu 1981, 26. 47.