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The excess enthalpies of (carbon dioxide + pyridine) at 470.15 and 573.15 K from 7.50 to 12.50 MPa
M-1781 J. Chem.
Thermodvnamics
1985,
Ii’,
785-795
The excess enthalpies of (carbon dioxide + pyridine) at 470.15 and 573.15 K from 7.50 to 12.50 M Pa a J. J. CHRISTENSEN,
D. M. ZEBOLSKY.b
and R. M. IZATT
Departments of ChemicalEngineeringand Chemistry, and the Thermochemical Institute, Brigham Young University, Provo, Utah 84602, U.S.A (Received8 October 1984; in revisedform 5 February 1985) The excess molar enthalpies HL{xCO, +(l -x)C,H,N} were measured in the vicinity of the critical locus and in the supercritical region. Large positive HEs were observed depending on the compositions, pressures, and temperatures of the mixtures, in contrast to large negative HP’s measured previously at lower temperatures. Two modified Soave equations of state were used to correlate Hi over a temperature range of 308.15 to 573.15 K and a pressure range of 7.50 to 12.50 MPa with average standard deviations of 1.1 kJ.mol-‘.
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies HE of binary mixtures in the vicinity of the critical points of one or both of the components. Results for several (carbon dioxide + a hydrocarbon)“-*’ and (a Freon + a hydrocarbon)“-14’ mixtures have been reported. In these, HE showed increased negative character as the critical temperature of either the carbon dioxide or the Freon was approached from below along an isobar. In most of these,‘1-7*9-12’ the critical point of the second component was far removed from the region of measurement and, thus, did not affect the HE values. With the development in this Laboratory of a high-temperature flow calorimeter, (i5) it became possible to extend the temperature range of the Hi(xCO, +(l -x)C,H,N} measured previously at 308.15, 358.15, and 413.15 K.@’ This paper reports values of Hfi, from {xCO,+(l -x)C,H,N} at 470.15 and 573.15 K from 7.50 to 12.50 MPa. These Hz values should provide an excellent test for equations used to model the behavior of mixtures near the critical points of their components. In this paper, two modified forms of the Soave equation have been fitted to the Hk’s in an attempt to predict mixing behavior better in the critical region. By acceptance of this article, the publisher acknowledges the right of the U.S. Government to retain a non-exclusive royalty-free license in and to any copyright covering this paper. ’ Contribution No. 354 from the Thermochemical Institute. h On leave from Creighton University, Omaha, Nebraska 1983-84.
786
.I. J. CHRISTENSEN
ET .4L.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (15-r7) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure ISCO syringe pumps supply the two fluids to be mixed at a constant rate. The total flow rate was between 0.004167 and 0.008333 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 most of the mole-fraction range (0.2 < x < 0.8). ‘15) Reproducibility of results in the present investigation was f 1 to _+2 per cent. This uncertainty was due mainly 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 pyridine (Aldrich Chemical Co., Spectrophotometric grade, greater 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 pyridine was stored in sealed 1 dm3 bottles over approximately 50 cm3 of Davison molecular sieve (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 cm3. s- ’ 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 at 7.50, 10.50, and 12.50 MPa (0.755, 0.822, and 0.846 g.cmp3, respectively) were calculated by interpolation from the IUPAC Tables.(“) The densities of pyridine at 298.15 K and these pressures (0.985, 0.988, and 0.990 g. cm - 3, respectively) were evaluated using the value at 298.15 K and atmospheric pressure,” 9’ and the isothermal compressibilities at 298.15 K were estimated by interpolation between those obtained at 293.15 and 303.15 K by Freyer et al.‘zo’
3. Results and discussion Excess molar enthalpies were determined for (xC0, +(l - x)CgH5N} over the entire composition range at 470.15 and 573.15 K from 7.50 to 12.50 MPa. The results are given in table 1. The equation: HL/(J.mol-‘)
=
1+ f
D,(f--2x)
n=1
f.C”( 1-2x)“, (1)
was fitted to Hg at each temperature and pressure studied. The coefficients C, and D, are given in table 2 together with standard deviations s. Where the HE values vary linearly with mole fraction in the middle range of composition the equation: HE/(J.mol-‘)
= A,+A,x.
t-3
has been used. The coefficients A, and A,, the standard deviations s, and the molefraction intervals for the linear sections of the isotherms are also given in table 2. Figure 1 gives plots of Hf, against x for the two temperatures studied. The linear
H:{xCO,+(l TABLE x
1. Experimental
H3(J.mol-‘) expt talc.
and calculated x
Hs(J expt
excess molar mol-
‘)
-40 -181 -378 -440 -459 -478 -293 88
-16 -187 -379 -443 -473 -464 -233 73
0.3262 0.3489 0.3713 0.4152 0.4579 0.4995 0.5400 0.5795
380 579 696 895 1260 1460 1760 2010
0.0296 0.0871 0.1425 0.1958 0.2472 0.2967 0.3445 0.3906
-98 -288 -410 -531 -617 -564 -289 55
-105 -287 -429 -527 -578 - 576 -242 23
0.4352 0.4782 0.5199 0.5402 0.5602 0.5602 0.5993 0.6371
304 546 756 830 1020 1010 1250 1430
0.0304 0.0602 0.0893 0.1458 0.2000 0.2522 0.3025
- 104 -157 -224 -389 -479 -562 -630
-88 -171 -247 -379 -482 -554 -588
0.3505 0.3970 0.4418 0.4849 0.5266 0.5668 0.6057
-544 -244 -17 249 412 715 905
0.0274 0.0543 0.1328 0.1582 0.1832 0.2323 0.2562
23 491 1660 2650 3500 4970 5950
92 471 1640 2520 3390 5090 5920
0.2681 0.2799 0.3032 0.3148 0.3262 0.3489 0.3602
6140 6540 7510 7800 8430 9470 9540
0.0296 0.0871 0.1425 0.1958 0.2216 0.2471
156 518 1290 1950 2530 3010
160 590 1200 2010 2490 3010
0.2966 0.3677 0.3906 0.4351 0.4569 0.4782
4070 5720 5950 6670 6730 6790
0.0304 0.0602 0.1178 0.1458 0.1732 0.2000 0.2264 0.2522
74 280 542 766 1050 1290 1730 2020
97 219 555 777 1040 1350 1700 2100
0.3023 0.3266 0.3505 0.3740 0.3970 0.4196 0.4418 0.4849
2970 3470 3870 4260 4630 5000 5190 5370
enthalpies x
talc. 470.15
0.0274 0.0808 0.1328 0.1582 0.1832 0.2079 0.2323 0.2799
787
-x)C,H,N)
371 517 661 944 1220 1490 1750 2000 470.15 280 528 767 884 1000 1000 1220 1440 470.15 -581 -270 -14 231 469 698 919 573.15 6330 6740 7550 7950 8340 9130 9550 573.15 4120 5650 6050 6590 6740 6800 573.15 2970 3410 3850 4260 4620 4920 5150 5430
Hfi, for
{xCO,
+(1 -x)C,H,N} x
HftJ(J.mol-‘)
Hk/(J’mol-‘) expt
talc.
0.8464 0.8626 0.8786 0.8944 0.9254 0.9557 0.9854
3390 3150 2740 2430 1680 1080 367
3340 3060 2760 2440 1760 1050 343
1650 1860 2060 2250 2440 2530 2620 2710
0.8720 0.9018 0.9308 0.959 1 0.9865
2260 1820 1340 817 227
2230 1830 1350 823 ‘17
1150 1340 1520 1750 1940 2100 2280
1130 1340 1540 1740 1920 2110 2250
0.8600 0.8750 0.9042 0.9325 0.9601 0.9869
2150 1970 1630 1160 714 222
2140 1990 1620 1180 712 235
9520 9430 9300 9100 8940 7890 6760
9480 9430 9290 9120 8920 7910 6780
0.7628 0.8301 0.8626 0.9254 0.9854
4630 3310 2800 1530 266
4560 3400 2780 1510 275
6700 6560 6180 5610 5210 4820
6740 6490 6130 5700 5240 4770
0.7772 0.8413 09018 0.9308 0.9865
3790 2850 1850 1296 302
3810 2840 1830 1320 265
5440 5510 5450 5440 5470 5270 5210 4960
5490 5500 5500 5470 5400 5310 5200
0.6796 0.7148 0.7489 0.7819 0.8139 0.8750 0.9325 0.9869
4640 4360 4010 3590 3080 2270 1200 220
4650 4320 3970 3580 3160 2230 1220 227
expt
talc.
2210 2510 2650 2960 3200 3410 3520 3510
2250 2490 2730 2960 3180 3400 3510 3590
1700 1800 2080 2280 2370 2610 2610 2670
K, 7.50 MPa 0.6180 0.6555 0.6922 0.7279 0.7628 0.7968 0.8136 0.8301 K, 10.50 MPa 0.6738 0.7093 0.7438 0.7773 0.8098 0.8257 0.8413 0.8568 K. 1250 MPa 0.6433 0.6796 0.7148 0.7489 0.7819 0.8139 0.8449 K, 7.50 MPa 0.3824 0.3934 0.4152 0.4367 0.4579 0.5400 0.6180 K. 10.50 MPa 0.5199 0.5602 0.5993 0.6371 0.6737 0.7093 K. 12.50 MPa 0.5059 0.5266 0.5266 0.5460 0.5668 0.5864 0.6057 0.6433
788
J. J. CHRISTENSEN
TABLE 2. Coefficients {SO, +(l -x)C,HsN}
ET AL.
and standard deviations s for least-squares representation by equations (1) and (2). and liquid and vapor equilibrium-phase Y, and x8 Equation
C,
PIMPa
C*
c3
1694.7 0 0
18723 0 0
(1)
Cd
c,
470.15 7.50 10.50 12.50
10352 831.67 -708.02
- 29922 - 14220 - 11877
7.50 10.50 12.50
33744 27204 21913
-29481 0 0
-36662 0 0
0 0
A0
A,
7.50 10.50 12.50
- 1728.8 - 2224.5 -2531.8
6433.8 5754.9 5697.7
7.50 10.50 12.50
- 2963.2
470.15
D,
4
D,
D,
s
K 00 0 0
1.4661 1.8058
0 1.1956 1.4311
0 0 0
0 0 0
50 34 23
-1.6156 -0.1204 0.1886
0 1.4889 1.5756
0 2.2622 3.0670
0 1.0284 1.9682
53 59 44
K
19079 0 0
Equation PIMPa
._______
0 0 0 573.15
-27806
of H: for compositions,
43565 0 0 (2)
s
interval x, $ x < I*
37 39 25
0.20 < x < 0.82 0.28 6 x < 0.83 0.35 < x < 0.85
161
0.13 < x < 0.36 none none
K
573.15 K 34663
sections correspond to changes in the amounts of gaseous and liquid mixtures (both of fixed composition) as the two-phase regions at constant T and p are traversed. The CO2 vapor and liquid equilibrium-phase compositions (xB and x, respectively) can be determined from figure 1 as the x coordinates of the intersections of the extrapolated straight lines and the curves describing the excess enthalpy outside the two-phase region. These values of xs and x, are given in table 2. Shown in figure 2 are points indicating the conditions under which the Hk values were measured in this study and in a previous study. N) A critical locus is reported in figure 2 based on enthalpy tie lines determined from the results reported here and from a previous study on this mixture.@’ The two-phase regions of this mixture show clearly which experimental (T, p) values are within the two-phase region and which are supercritical. The observed large changes in Hi with temperature and pressure can be examined with respect to changes in the various fluid properties of CO, near its critical point. The change in the excess enthalpy with temperature at constant pressure may be expressed as (aHf&T),
= AC,,
= C,,&CO,+U
+-+2-W) -xC;,,(CO,)-(1
-W,*.,W-W),
(3)
H:{xCO,+(l-x)C,H,N}
789
790
J. J. CHRISTENSEN
300
350
400
450
ET AL.
T/K
500
600
620
FIGURE 2. Plot of p against T for {xCO, +(I -x)C,H,N} showing critical points and critical locus. The conditions at which the measurements were made are indicated: 0, this study; 0, previous study.@’
where C,,, is the molar heat capacity at constant pressure. The change in HE with pressure at constant temperature is given by
(aHvap), = v,"- qav,E/aq,,
(4)
where Vi is the excess molar volume at temperature T. Large changes in the values of c,, m and V, can be expected in the vicinity of the critical locus. These changes could account for the considerable variations observed in the values of Hk with both pressure and temperature. Unfortunately, there are not enough values to apply equations (3) and (4) to (xCO,+(l -x)C,H,N). In this paper we have compared the observed variation of Hk with two modified Soave equations of state. HKs both from this study and from a previous study at lower temperatures’6’ were used in the correlations. We have modeled Hz for {propane + dichlorodifluoromethane (Freon-12)} by using the Carnahan-Starling-Redlich-Kwong (CSRK) and the CarnahanStarling-~ Soave (CSSV) equations. (14) The CSSV equation was found to fit better than the CSRK equation. Recently,“” we have found that replacement of the Carnahan Starling hard-sphere pressure with the hard-sphere pressure of Andrews”” gives equal or better correlation of Hk. In this paper, we have compared the observed variation of H,!f, with both the Andrews-Soave (ASV) and the CSSV equations. The Soave equation may be written either as p = p,--a[l+m{l
-(T/T,)"'}]"*,
or as P = PO-W
(54 W
where p. is the hard-sphere repulsion term, m = (0.48508+ 1.55171w-0.15613w2), and w is Pitzer’s acentric factor. (23) The coefficients in the equation for m were taken
H:{xCO,+(l
791
-x)C,H,N}
from the correlation of Graboski and Daubert.(24) The values of o from Reid et a1.(25)were used. The hard-sphere repulsion term is for the CSSV equation: po = (RT/K,,/,)(1 +v+~~~-v~)/U
-d3,
(64
and for the ASV equation: p. = RT[28~2/bq-(4/b)ln(l-~)-(14.38/b)ln
q
-(47.31/b)ln{(l-0.7210$/(1-
1.350~)}],
where q = b/4I$, and q = (l -2.071q +0.9736q2). The derivation of residual molar enthalpies Hk(vm/,, T) from an equation has been outlined by Lewis et ~1.‘~~) and yields HL(i&/,, T) = {a+m(T/T,)“2a1’2
}(a/b)ln{I/,(V,+b)}+pvm--RR
(6b)
of state (7)
The predicted excess molar enthalpy is given by H: = H;{xCO,
+(l -x)C,H,N}
-xH:(CO,)-(1
-x)H:(C,H,N).
(8)
The constants a and b in equation (7) for the pure components were obtained from the critical conditions (ap/aV,), = 0 and (a2p/aI$ = 0:(27-29) a = 0.461891R2T,2a.,/p,
(9)
and b = O.l05007RT,/p,.
(10)
The mixtures were treated as single fluids having the constants: b = xi xibi,
(11)
a = cj xi xixjati,
(12)
and uAB
=
kAB(aAAaBB)“2.
(13)
where A = CO, and B = C,H,N. An arithmetic mean of the o values of the pure components was used for o of the mixtures {equation (11) 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 {equation (12) with T, replacing u}. Results of the fit of the calculated Hi values with the experimental values for the two equations of state are displayed in table 3. Representative fits of the ASV equations to experimental results at 358.15 and 510.15 K are shown in figures 3(a) and 3(b) respectively. In general, both equations predict the correct shape of the curves of iYE against x but fail to predict the correct magnitudes and especially the maximum values of Ni. The interaction parameter k,, was varied until the best overall fit (lowest standard deviation) at all temperatures, pressures, and mole fractions in this paper and the preceding one@) was achieved for each equation. Raising the value of k,, causes the calculated Hz values to be more negative while lowering the value of k,, has the opposite effect. The values of kAB, 0.957 for the CSSV equation and 0.953 for the ASV equation, reported in table 3, achieve the best fits. Other Values of kAB are 0.938 for (ethane + chlorodifluoromethane),“3*2” 0.924 4h
792
J. J. CHRISTENSEN TABLE
m
3. Comparison
PIMPa
of fit by CSSV Standard
ET AL
and ASV equations
deviations
s
of Hk for (.uCOz
TIK
p/MPa
cssv ASV k,, = 0.957 k,, = 0.953 308.15
358.15
413.15
a Two-phase
7.50 10.50 12.50 7.50 10.50 12.50
865 618 485 122 157 187
873 616 484 127 164 196
7.50 10.50
375 425
376 429
12.50
431
437
region
corresponding
to enthalpy
+(I -z)C,H,N/ Standard
’
deviations
s
cssv ASV k*R = 0.957 k,, = 0.953 470. I5
7.50 10.50 12.50 7.50 10.50 12.50
573.15
Overall
tie lines omitted
280 points
from
1084 927 767 1859 1895 1921
1093 937 777 1891 1932 1960
1059
1077
fit.
for (carbon dioxide + hexane),(30) and 0.979 for (propane + dichlorodifluoromethane). (14) The value of k,, is expected to decrease as differences in molecular size and electronic structure between components increase.(31) Calculated maxima and minima in Hfi, are greater than experimental values as shown in figure 3. This behavior is not seen in other cases.(‘4p21) The inability to fit the experimental Hfi, may be due either to physical effects, to chemical interactions, or to some combination of these. Physical effects could arise from a phase change below the critical loc~s.~*~~~~~~~or from a change from a low-density to a highdensity fluid above the critical locus. (14) Negative HFs are caused by a gas or lowdensity fluid forming a liquid or high- density mixture while positive Hzs are caused by a liquid or high-density fluid forming a gas or low-density mixture. It is also possible that chemical interactions are present due to the acid-base nature of the (carbon dioxide + pyridine) components. This interaction would be expected to make Hi more negative than is predicted by the CSSV and ASB equations. Chemical interactions, probably of the hydrogen-bonding type, have been observed by us(l 2, for (chlorodifluoromethane + N,N-dimethylacetamide); the negative minimum of HL was increased by approximately 3 kJ . mol- ‘. There is little difference between the values of Hk calculated from the CSSV and the ASV equations. The CSSV equation does slightly better at all temperatures and pressures in this study. The overall deviations in this study are greater than for other mixtures for which HFs have been fitted with various equations of state as shown in table 4. Apparently, it is either harder to fit Hzs over several pressures, some of which are above and some of which are below the critical locus, than at only one supercritical pressure, or there is a specific chemical interaction which is not accounted for by the CSSV and ASV equations. Conceptually, the ASV model is preferred to the CSSV model. The Andrews hardsphere pressure is derived from readily understood considerations.‘22’ The Carnahan-Starling pressure is a sum of l/3 “virial” and 2/3 “compressibility” pressures calculated from the hard-sphere solution to the Percus-Yevick integral
FIGURE
3.
t
plot
-7 z E 3 ‘= *E
-
-I
-.
-
against
equation
of fjk
,V
with
for i.&O,+(l kAB = 0.953: (a).
at
-x)C,H,N) T =
10.50 MPa
as
K.
of experimental
a function
308.15
values
pressure.
0.
previous
study:“’
Cl, A. Experimental from
vahx
--.
r-
(b). at T = 470.15
.
K.
the Andw-Sowe
E
794
J. J. CHRISTENSEN
ET AL.
TABLE 4. A comparison of overall deviations s for systems studied using various equations of state 5
System {xC,H,+(l -x)CCl,F,}, {xC,H,+(l -x)CHClF,}, {xCO,+(l -x)n-C,H,,},’ {xCO,+(l-x)C,H,N}, ’ References 14 and 21.
209 319 577 1077
353.15 to 383.15 K, 4.45 MPa 293.15 to 383.15 K, 5.15 MPa 308.15 to 373.15 K, 7.50 to 12.50 MPa 308.15 to 573.15 K, 7.50 to 12.50 MPa b References 13 and 21.
’ References 30.
d This study.
equation. (22v28)Andrews has suggested that various attractive terms be added to the hard-sphere pressure based on the assumption made about the form of the intermolecular potential. (34) The effect of replacing the Soave term with such additional terms seems also worthwhile to explore. This work was funded by U.S. Department of Energy Contract No. DE-AC0282ER13024 and by the Donors of the Petroleum Research Fund administered by the American Chemical Society. We appreciate the aid given to us in collecting the data by D. Cordray, P. Faux, P. R. Harding, C. Orme, and T. A. C. Walker. Thanks are due to Dr R. L. Snow, Chemistry Department, Brigham Young University, for discussions concerning the ASV equation of state. REFERENCES 1. Pando, C.; Renuncio, J. A. R.; McFall. T. A.; Izatt. R. M.; Christensen, J. J. J. C/wm. Thermodynamics 1983, 15, 173. 2. Pando, C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen, J. J. J. Chem. Thermodynamics 1983, 15, 259. 3. Pando, C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen, J. J. J. Chem. Thermodynamics 1983, 15, 231. 4. Pando, C.; Renuncio, J. A. R.; Schofield, R. S.; Izatt, R. M.: Christensen, J. J. J. Chem. Thermodynamics 1983, 15. 747. 5. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding. P. R.; Izatt, R. M. J. Chem. Thermodynamics 1983, 15, 1I5 1. 6. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt. R. M. J. Chem. Thermodynamics l!W, 16, 249. 7. Christensen, J. J.; Walker, T. A. C.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt, R. M. J. Chem. Thermodynamics 1984, 16. 445. 8. Christensen, J. J.; Zebolsky, D. M.; Izatt, R. M. J. Chem. Thermodynamics 1985, 17, 1, 9. Christensen, J. J.; Post, M. E.; McFall, T. A.; Izatt, R. M. Thermochim. Acta 1981, 50, 73. 10. Schofield, R. S.; Post, M. E.; McFall, T. A.; Izatt, R. M.; Christensen. J. J. J. C&m. Thermodynamics 1983, 15, 217. 11. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt, R. M. Thermochim. Acia 1983, 67, 315. 12. Izatt, R. M.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Christensen, S. P.; Christensen, J. J. Thermochim. Acta 1983, 68, 223. 13. Christensen, J. J.; Zebolsky, D. M.; Schofield, R. S.; Cordray, D. R.; Izatt, R. M. J. Chem. Thermodynamics 1984, 16. 905. 14. Christensen. J. J.: Cordray. D. R.: Zebolsky. D. M.; lzatt, R. M. J. Chem. Thermor{tnumic~.s 1985, 17, 335. 15. Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1984, 73. 117.
H:{xCO,+(l-x)C,H,N}
795
16. Christensen, J. J.; Izatt. R. M.; Eatough, D. J.; Hansen, L. D. J. Chem. Thermodynumics 1978, IO. 25. 17. McFall, T. A.; Post, M. E.; Collins, S. G.; Christensen, J. J.: Izatt, R. M. J. Chem. Thermodynamics 1981, 13, 41. 18. Carbon Dioxide. IUPAC Thermodynamic Tables of the Fluid State. Pergamon Press: Oxford. 1976. 19. Handbook of Chemistry and Physics. 61st edition. The Chemical Rubber Company: Boca Raton. Florida. l!BO-1981. 20. Freyer, E. B.; Hubbard, .I. C.; Andrews, D. H. J. Am. Chem. Sot. 1929, 51. 759. 2 I. Zebolsky. D. Unpublished calculations. 22. Andrews, F. C. J. Chem. Phys. 1975, 62. 272; Andrew% F. C.: Ellerby. H. M. J. Chem. Phys. 1981, 75. 3542. 23. Pitzer, K. S. Phase Equilibria and Fluid Properties in Chemical Industry. Am. Chem. Sot. Symposium Series: Washington, D.C. 1977, p. 1. 24. Graboski, M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 443. 25. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties qf Gases and Liquids. 3rd edition. McGraw-Hill: New York. 1977. 26. Lewis, K. L.; Mosedale, S. E.; Wormald, C. J. J. Chem. Thermodvnamics 1977, 9, 121. 27. Soave, G. Chem. Eng. Sci. 1972,27, 1197. 28. Carnahan, N. F.; Starling, K. E. AIChE Journal 1972. 18, 1184; Carnahan. N. F.; Starling. K. E. J. Chem.
Phys.
1%9,
51, 635.
29. Henderson, D. Equations of State in Engineering and Research. Am. Chem. Sot. Symposium Series: Washington, D.C. 1979, p. 1. 30. Christensen, J. J.; Zebolsky. D. M.: Izatt. R. M. unpublished calculations. 31. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions. Van Nostrand Reinhold: New York. 1970, p. 56. 32. Levelt Sengers, J. M. H.; Morrison, G.; Chang, R. F. Fluid Phase Equilibria 1983, 14, 19. 33. Kay, W. B. Act. Chem. Res. 1968, I, 344. 34. Andrews. F. C. J. Chem. Phys. 1976,&t, 1948.
Thermodvnamics
1985,
Ii’,
785-795
The excess enthalpies of (carbon dioxide + pyridine) at 470.15 and 573.15 K from 7.50 to 12.50 M Pa a J. J. CHRISTENSEN,
D. M. ZEBOLSKY.b
and R. M. IZATT
Departments of ChemicalEngineeringand Chemistry, and the Thermochemical Institute, Brigham Young University, Provo, Utah 84602, U.S.A (Received8 October 1984; in revisedform 5 February 1985) The excess molar enthalpies HL{xCO, +(l -x)C,H,N} were measured in the vicinity of the critical locus and in the supercritical region. Large positive HEs were observed depending on the compositions, pressures, and temperatures of the mixtures, in contrast to large negative HP’s measured previously at lower temperatures. Two modified Soave equations of state were used to correlate Hi over a temperature range of 308.15 to 573.15 K and a pressure range of 7.50 to 12.50 MPa with average standard deviations of 1.1 kJ.mol-‘.
1. Introduction A program is under way in this laboratory to measure the excess molar enthalpies HE of binary mixtures in the vicinity of the critical points of one or both of the components. Results for several (carbon dioxide + a hydrocarbon)“-*’ and (a Freon + a hydrocarbon)“-14’ mixtures have been reported. In these, HE showed increased negative character as the critical temperature of either the carbon dioxide or the Freon was approached from below along an isobar. In most of these,‘1-7*9-12’ the critical point of the second component was far removed from the region of measurement and, thus, did not affect the HE values. With the development in this Laboratory of a high-temperature flow calorimeter, (i5) it became possible to extend the temperature range of the Hi(xCO, +(l -x)C,H,N} measured previously at 308.15, 358.15, and 413.15 K.@’ This paper reports values of Hfi, from {xCO,+(l -x)C,H,N} at 470.15 and 573.15 K from 7.50 to 12.50 MPa. These Hz values should provide an excellent test for equations used to model the behavior of mixtures near the critical points of their components. In this paper, two modified forms of the Soave equation have been fitted to the Hk’s in an attempt to predict mixing behavior better in the critical region. By acceptance of this article, the publisher acknowledges the right of the U.S. Government to retain a non-exclusive royalty-free license in and to any copyright covering this paper. ’ Contribution No. 354 from the Thermochemical Institute. h On leave from Creighton University, Omaha, Nebraska 1983-84.
786
.I. J. CHRISTENSEN
ET .4L.
2. Experimental The high-pressure flow calorimeter used for the measurements and the experimental procedure have been described. (15-r7) All runs were made in the steady-state (fixedcomposition) mode. Two high-pressure ISCO syringe pumps supply the two fluids to be mixed at a constant rate. The total flow rate was between 0.004167 and 0.008333 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 most of the mole-fraction range (0.2 < x < 0.8). ‘15) Reproducibility of results in the present investigation was f 1 to _+2 per cent. This uncertainty was due mainly 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 pyridine (Aldrich Chemical Co., Spectrophotometric grade, greater 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 pyridine was stored in sealed 1 dm3 bottles over approximately 50 cm3 of Davison molecular sieve (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 cm3. s- ’ 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 at 7.50, 10.50, and 12.50 MPa (0.755, 0.822, and 0.846 g.cmp3, respectively) were calculated by interpolation from the IUPAC Tables.(“) The densities of pyridine at 298.15 K and these pressures (0.985, 0.988, and 0.990 g. cm - 3, respectively) were evaluated using the value at 298.15 K and atmospheric pressure,” 9’ and the isothermal compressibilities at 298.15 K were estimated by interpolation between those obtained at 293.15 and 303.15 K by Freyer et al.‘zo’
3. Results and discussion Excess molar enthalpies were determined for (xC0, +(l - x)CgH5N} over the entire composition range at 470.15 and 573.15 K from 7.50 to 12.50 MPa. The results are given in table 1. The equation: HL/(J.mol-‘)
=
1+ f
D,(f--2x)
n=1
f.C”( 1-2x)“, (1)
was fitted to Hg at each temperature and pressure studied. The coefficients C, and D, are given in table 2 together with standard deviations s. Where the HE values vary linearly with mole fraction in the middle range of composition the equation: HE/(J.mol-‘)
= A,+A,x.
t-3
has been used. The coefficients A, and A,, the standard deviations s, and the molefraction intervals for the linear sections of the isotherms are also given in table 2. Figure 1 gives plots of Hf, against x for the two temperatures studied. The linear
H:{xCO,+(l TABLE x
1. Experimental
H3(J.mol-‘) expt talc.
and calculated x
Hs(J expt
excess molar mol-
‘)
-40 -181 -378 -440 -459 -478 -293 88
-16 -187 -379 -443 -473 -464 -233 73
0.3262 0.3489 0.3713 0.4152 0.4579 0.4995 0.5400 0.5795
380 579 696 895 1260 1460 1760 2010
0.0296 0.0871 0.1425 0.1958 0.2472 0.2967 0.3445 0.3906
-98 -288 -410 -531 -617 -564 -289 55
-105 -287 -429 -527 -578 - 576 -242 23
0.4352 0.4782 0.5199 0.5402 0.5602 0.5602 0.5993 0.6371
304 546 756 830 1020 1010 1250 1430
0.0304 0.0602 0.0893 0.1458 0.2000 0.2522 0.3025
- 104 -157 -224 -389 -479 -562 -630
-88 -171 -247 -379 -482 -554 -588
0.3505 0.3970 0.4418 0.4849 0.5266 0.5668 0.6057
-544 -244 -17 249 412 715 905
0.0274 0.0543 0.1328 0.1582 0.1832 0.2323 0.2562
23 491 1660 2650 3500 4970 5950
92 471 1640 2520 3390 5090 5920
0.2681 0.2799 0.3032 0.3148 0.3262 0.3489 0.3602
6140 6540 7510 7800 8430 9470 9540
0.0296 0.0871 0.1425 0.1958 0.2216 0.2471
156 518 1290 1950 2530 3010
160 590 1200 2010 2490 3010
0.2966 0.3677 0.3906 0.4351 0.4569 0.4782
4070 5720 5950 6670 6730 6790
0.0304 0.0602 0.1178 0.1458 0.1732 0.2000 0.2264 0.2522
74 280 542 766 1050 1290 1730 2020
97 219 555 777 1040 1350 1700 2100
0.3023 0.3266 0.3505 0.3740 0.3970 0.4196 0.4418 0.4849
2970 3470 3870 4260 4630 5000 5190 5370
enthalpies x
talc. 470.15
0.0274 0.0808 0.1328 0.1582 0.1832 0.2079 0.2323 0.2799
787
-x)C,H,N)
371 517 661 944 1220 1490 1750 2000 470.15 280 528 767 884 1000 1000 1220 1440 470.15 -581 -270 -14 231 469 698 919 573.15 6330 6740 7550 7950 8340 9130 9550 573.15 4120 5650 6050 6590 6740 6800 573.15 2970 3410 3850 4260 4620 4920 5150 5430
Hfi, for
{xCO,
+(1 -x)C,H,N} x
HftJ(J.mol-‘)
Hk/(J’mol-‘) expt
talc.
0.8464 0.8626 0.8786 0.8944 0.9254 0.9557 0.9854
3390 3150 2740 2430 1680 1080 367
3340 3060 2760 2440 1760 1050 343
1650 1860 2060 2250 2440 2530 2620 2710
0.8720 0.9018 0.9308 0.959 1 0.9865
2260 1820 1340 817 227
2230 1830 1350 823 ‘17
1150 1340 1520 1750 1940 2100 2280
1130 1340 1540 1740 1920 2110 2250
0.8600 0.8750 0.9042 0.9325 0.9601 0.9869
2150 1970 1630 1160 714 222
2140 1990 1620 1180 712 235
9520 9430 9300 9100 8940 7890 6760
9480 9430 9290 9120 8920 7910 6780
0.7628 0.8301 0.8626 0.9254 0.9854
4630 3310 2800 1530 266
4560 3400 2780 1510 275
6700 6560 6180 5610 5210 4820
6740 6490 6130 5700 5240 4770
0.7772 0.8413 09018 0.9308 0.9865
3790 2850 1850 1296 302
3810 2840 1830 1320 265
5440 5510 5450 5440 5470 5270 5210 4960
5490 5500 5500 5470 5400 5310 5200
0.6796 0.7148 0.7489 0.7819 0.8139 0.8750 0.9325 0.9869
4640 4360 4010 3590 3080 2270 1200 220
4650 4320 3970 3580 3160 2230 1220 227
expt
talc.
2210 2510 2650 2960 3200 3410 3520 3510
2250 2490 2730 2960 3180 3400 3510 3590
1700 1800 2080 2280 2370 2610 2610 2670
K, 7.50 MPa 0.6180 0.6555 0.6922 0.7279 0.7628 0.7968 0.8136 0.8301 K, 10.50 MPa 0.6738 0.7093 0.7438 0.7773 0.8098 0.8257 0.8413 0.8568 K. 1250 MPa 0.6433 0.6796 0.7148 0.7489 0.7819 0.8139 0.8449 K, 7.50 MPa 0.3824 0.3934 0.4152 0.4367 0.4579 0.5400 0.6180 K. 10.50 MPa 0.5199 0.5602 0.5993 0.6371 0.6737 0.7093 K. 12.50 MPa 0.5059 0.5266 0.5266 0.5460 0.5668 0.5864 0.6057 0.6433
788
J. J. CHRISTENSEN
TABLE 2. Coefficients {SO, +(l -x)C,HsN}
ET AL.
and standard deviations s for least-squares representation by equations (1) and (2). and liquid and vapor equilibrium-phase Y, and x8 Equation
C,
PIMPa
C*
c3
1694.7 0 0
18723 0 0
(1)
Cd
c,
470.15 7.50 10.50 12.50
10352 831.67 -708.02
- 29922 - 14220 - 11877
7.50 10.50 12.50
33744 27204 21913
-29481 0 0
-36662 0 0
0 0
A0
A,
7.50 10.50 12.50
- 1728.8 - 2224.5 -2531.8
6433.8 5754.9 5697.7
7.50 10.50 12.50
- 2963.2
470.15
D,
4
D,
D,
s
K 00 0 0
1.4661 1.8058
0 1.1956 1.4311
0 0 0
0 0 0
50 34 23
-1.6156 -0.1204 0.1886
0 1.4889 1.5756
0 2.2622 3.0670
0 1.0284 1.9682
53 59 44
K
19079 0 0
Equation PIMPa
._______
0 0 0 573.15
-27806
of H: for compositions,
43565 0 0 (2)
s
interval x, $ x < I*
37 39 25
0.20 < x < 0.82 0.28 6 x < 0.83 0.35 < x < 0.85
161
0.13 < x < 0.36 none none
K
573.15 K 34663
sections correspond to changes in the amounts of gaseous and liquid mixtures (both of fixed composition) as the two-phase regions at constant T and p are traversed. The CO2 vapor and liquid equilibrium-phase compositions (xB and x, respectively) can be determined from figure 1 as the x coordinates of the intersections of the extrapolated straight lines and the curves describing the excess enthalpy outside the two-phase region. These values of xs and x, are given in table 2. Shown in figure 2 are points indicating the conditions under which the Hk values were measured in this study and in a previous study. N) A critical locus is reported in figure 2 based on enthalpy tie lines determined from the results reported here and from a previous study on this mixture.@’ The two-phase regions of this mixture show clearly which experimental (T, p) values are within the two-phase region and which are supercritical. The observed large changes in Hi with temperature and pressure can be examined with respect to changes in the various fluid properties of CO, near its critical point. The change in the excess enthalpy with temperature at constant pressure may be expressed as (aHf&T),
= AC,,
= C,,&CO,+U
+-+2-W) -xC;,,(CO,)-(1
-W,*.,W-W),
(3)
H:{xCO,+(l-x)C,H,N}
789
790
J. J. CHRISTENSEN
300
350
400
450
ET AL.
T/K
500
600
620
FIGURE 2. Plot of p against T for {xCO, +(I -x)C,H,N} showing critical points and critical locus. The conditions at which the measurements were made are indicated: 0, this study; 0, previous study.@’
where C,,, is the molar heat capacity at constant pressure. The change in HE with pressure at constant temperature is given by
(aHvap), = v,"- qav,E/aq,,
(4)
where Vi is the excess molar volume at temperature T. Large changes in the values of c,, m and V, can be expected in the vicinity of the critical locus. These changes could account for the considerable variations observed in the values of Hk with both pressure and temperature. Unfortunately, there are not enough values to apply equations (3) and (4) to (xCO,+(l -x)C,H,N). In this paper we have compared the observed variation of Hk with two modified Soave equations of state. HKs both from this study and from a previous study at lower temperatures’6’ were used in the correlations. We have modeled Hz for {propane + dichlorodifluoromethane (Freon-12)} by using the Carnahan-Starling-Redlich-Kwong (CSRK) and the CarnahanStarling-~ Soave (CSSV) equations. (14) The CSSV equation was found to fit better than the CSRK equation. Recently,“” we have found that replacement of the Carnahan Starling hard-sphere pressure with the hard-sphere pressure of Andrews”” gives equal or better correlation of Hk. In this paper, we have compared the observed variation of H,!f, with both the Andrews-Soave (ASV) and the CSSV equations. The Soave equation may be written either as p = p,--a[l+m{l
-(T/T,)"'}]"*,
or as P = PO-W
(54 W
where p. is the hard-sphere repulsion term, m = (0.48508+ 1.55171w-0.15613w2), and w is Pitzer’s acentric factor. (23) The coefficients in the equation for m were taken
H:{xCO,+(l
791
-x)C,H,N}
from the correlation of Graboski and Daubert.(24) The values of o from Reid et a1.(25)were used. The hard-sphere repulsion term is for the CSSV equation: po = (RT/K,,/,)(1 +v+~~~-v~)/U
-d3,
(64
and for the ASV equation: p. = RT[28~2/bq-(4/b)ln(l-~)-(14.38/b)ln
q
-(47.31/b)ln{(l-0.7210$/(1-
1.350~)}],
where q = b/4I$, and q = (l -2.071q +0.9736q2). The derivation of residual molar enthalpies Hk(vm/,, T) from an equation has been outlined by Lewis et ~1.‘~~) and yields HL(i&/,, T) = {a+m(T/T,)“2a1’2
}(a/b)ln{I/,(V,+b)}+pvm--RR
(6b)
of state (7)
The predicted excess molar enthalpy is given by H: = H;{xCO,
+(l -x)C,H,N}
-xH:(CO,)-(1
-x)H:(C,H,N).
(8)
The constants a and b in equation (7) for the pure components were obtained from the critical conditions (ap/aV,), = 0 and (a2p/aI$ = 0:(27-29) a = 0.461891R2T,2a.,/p,
(9)
and b = O.l05007RT,/p,.
(10)
The mixtures were treated as single fluids having the constants: b = xi xibi,
(11)
a = cj xi xixjati,
(12)
and uAB
=
kAB(aAAaBB)“2.
(13)
where A = CO, and B = C,H,N. An arithmetic mean of the o values of the pure components was used for o of the mixtures {equation (11) 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 {equation (12) with T, replacing u}. Results of the fit of the calculated Hi values with the experimental values for the two equations of state are displayed in table 3. Representative fits of the ASV equations to experimental results at 358.15 and 510.15 K are shown in figures 3(a) and 3(b) respectively. In general, both equations predict the correct shape of the curves of iYE against x but fail to predict the correct magnitudes and especially the maximum values of Ni. The interaction parameter k,, was varied until the best overall fit (lowest standard deviation) at all temperatures, pressures, and mole fractions in this paper and the preceding one@) was achieved for each equation. Raising the value of k,, causes the calculated Hz values to be more negative while lowering the value of k,, has the opposite effect. The values of kAB, 0.957 for the CSSV equation and 0.953 for the ASV equation, reported in table 3, achieve the best fits. Other Values of kAB are 0.938 for (ethane + chlorodifluoromethane),“3*2” 0.924 4h
792
J. J. CHRISTENSEN TABLE
m
3. Comparison
PIMPa
of fit by CSSV Standard
ET AL
and ASV equations
deviations
s
of Hk for (.uCOz
TIK
p/MPa
cssv ASV k,, = 0.957 k,, = 0.953 308.15
358.15
413.15
a Two-phase
7.50 10.50 12.50 7.50 10.50 12.50
865 618 485 122 157 187
873 616 484 127 164 196
7.50 10.50
375 425
376 429
12.50
431
437
region
corresponding
to enthalpy
+(I -z)C,H,N/ Standard
’
deviations
s
cssv ASV k*R = 0.957 k,, = 0.953 470. I5
7.50 10.50 12.50 7.50 10.50 12.50
573.15
Overall
tie lines omitted
280 points
from
1084 927 767 1859 1895 1921
1093 937 777 1891 1932 1960
1059
1077
fit.
for (carbon dioxide + hexane),(30) and 0.979 for (propane + dichlorodifluoromethane). (14) The value of k,, is expected to decrease as differences in molecular size and electronic structure between components increase.(31) Calculated maxima and minima in Hfi, are greater than experimental values as shown in figure 3. This behavior is not seen in other cases.(‘4p21) The inability to fit the experimental Hfi, may be due either to physical effects, to chemical interactions, or to some combination of these. Physical effects could arise from a phase change below the critical loc~s.~*~~~~~~~or from a change from a low-density to a highdensity fluid above the critical locus. (14) Negative HFs are caused by a gas or lowdensity fluid forming a liquid or high- density mixture while positive Hzs are caused by a liquid or high-density fluid forming a gas or low-density mixture. It is also possible that chemical interactions are present due to the acid-base nature of the (carbon dioxide + pyridine) components. This interaction would be expected to make Hi more negative than is predicted by the CSSV and ASB equations. Chemical interactions, probably of the hydrogen-bonding type, have been observed by us(l 2, for (chlorodifluoromethane + N,N-dimethylacetamide); the negative minimum of HL was increased by approximately 3 kJ . mol- ‘. There is little difference between the values of Hk calculated from the CSSV and the ASV equations. The CSSV equation does slightly better at all temperatures and pressures in this study. The overall deviations in this study are greater than for other mixtures for which HFs have been fitted with various equations of state as shown in table 4. Apparently, it is either harder to fit Hzs over several pressures, some of which are above and some of which are below the critical locus, than at only one supercritical pressure, or there is a specific chemical interaction which is not accounted for by the CSSV and ASV equations. Conceptually, the ASV model is preferred to the CSSV model. The Andrews hardsphere pressure is derived from readily understood considerations.‘22’ The Carnahan-Starling pressure is a sum of l/3 “virial” and 2/3 “compressibility” pressures calculated from the hard-sphere solution to the Percus-Yevick integral
FIGURE
3.
t
plot
-7 z E 3 ‘= *E
-
-I
-.
-
against
equation
of fjk
,V
with
for i.&O,+(l kAB = 0.953: (a).
at
-x)C,H,N) T =
10.50 MPa
as
K.
of experimental
a function
308.15
values
pressure.
0.
previous
study:“’
Cl, A. Experimental from
vahx
--.
r-
(b). at T = 470.15
.
K.
the Andw-Sowe
E
794
J. J. CHRISTENSEN
ET AL.
TABLE 4. A comparison of overall deviations s for systems studied using various equations of state 5
System {xC,H,+(l -x)CCl,F,}, {xC,H,+(l -x)CHClF,}, {xCO,+(l -x)n-C,H,,},’ {xCO,+(l-x)C,H,N}, ’ References 14 and 21.
209 319 577 1077
353.15 to 383.15 K, 4.45 MPa 293.15 to 383.15 K, 5.15 MPa 308.15 to 373.15 K, 7.50 to 12.50 MPa 308.15 to 573.15 K, 7.50 to 12.50 MPa b References 13 and 21.
’ References 30.
d This study.
equation. (22v28)Andrews has suggested that various attractive terms be added to the hard-sphere pressure based on the assumption made about the form of the intermolecular potential. (34) The effect of replacing the Soave term with such additional terms seems also worthwhile to explore. This work was funded by U.S. Department of Energy Contract No. DE-AC0282ER13024 and by the Donors of the Petroleum Research Fund administered by the American Chemical Society. We appreciate the aid given to us in collecting the data by D. Cordray, P. Faux, P. R. Harding, C. Orme, and T. A. C. Walker. Thanks are due to Dr R. L. Snow, Chemistry Department, Brigham Young University, for discussions concerning the ASV equation of state. REFERENCES 1. Pando, C.; Renuncio, J. A. R.; McFall. T. A.; Izatt. R. M.; Christensen, J. J. J. C/wm. Thermodynamics 1983, 15, 173. 2. Pando, C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen, J. J. J. Chem. Thermodynamics 1983, 15, 259. 3. Pando, C.; Renuncio, J. A. R.; Izatt, R. M.; Christensen, J. J. J. Chem. Thermodynamics 1983, 15, 231. 4. Pando, C.; Renuncio, J. A. R.; Schofield, R. S.; Izatt, R. M.: Christensen, J. J. J. Chem. Thermodynamics 1983, 15. 747. 5. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding. P. R.; Izatt, R. M. J. Chem. Thermodynamics 1983, 15, 1I5 1. 6. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt. R. M. J. Chem. Thermodynamics l!W, 16, 249. 7. Christensen, J. J.; Walker, T. A. C.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt, R. M. J. Chem. Thermodynamics 1984, 16. 445. 8. Christensen, J. J.; Zebolsky, D. M.; Izatt, R. M. J. Chem. Thermodynamics 1985, 17, 1, 9. Christensen, J. J.; Post, M. E.; McFall, T. A.; Izatt, R. M. Thermochim. Acta 1981, 50, 73. 10. Schofield, R. S.; Post, M. E.; McFall, T. A.; Izatt, R. M.; Christensen. J. J. J. C&m. Thermodynamics 1983, 15, 217. 11. Christensen, J. J.; Christensen, S. P.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Izatt, R. M. Thermochim. Acia 1983, 67, 315. 12. Izatt, R. M.; Schofield, R. S.; Faux, P. W.; Harding, P. R.; Christensen, S. P.; Christensen, J. J. Thermochim. Acta 1983, 68, 223. 13. Christensen, J. J.; Zebolsky, D. M.; Schofield, R. S.; Cordray, D. R.; Izatt, R. M. J. Chem. Thermodynamics 1984, 16. 905. 14. Christensen. J. J.: Cordray. D. R.: Zebolsky. D. M.; lzatt, R. M. J. Chem. Thermor{tnumic~.s 1985, 17, 335. 15. Christensen, J. J.; Izatt, R. M. Thermochim. Acta 1984, 73. 117.
H:{xCO,+(l-x)C,H,N}
795
16. Christensen, J. J.; Izatt. R. M.; Eatough, D. J.; Hansen, L. D. J. Chem. Thermodynumics 1978, IO. 25. 17. McFall, T. A.; Post, M. E.; Collins, S. G.; Christensen, J. J.: Izatt, R. M. J. Chem. Thermodynamics 1981, 13, 41. 18. Carbon Dioxide. IUPAC Thermodynamic Tables of the Fluid State. Pergamon Press: Oxford. 1976. 19. Handbook of Chemistry and Physics. 61st edition. The Chemical Rubber Company: Boca Raton. Florida. l!BO-1981. 20. Freyer, E. B.; Hubbard, .I. C.; Andrews, D. H. J. Am. Chem. Sot. 1929, 51. 759. 2 I. Zebolsky. D. Unpublished calculations. 22. Andrews, F. C. J. Chem. Phys. 1975, 62. 272; Andrew% F. C.: Ellerby. H. M. J. Chem. Phys. 1981, 75. 3542. 23. Pitzer, K. S. Phase Equilibria and Fluid Properties in Chemical Industry. Am. Chem. Sot. Symposium Series: Washington, D.C. 1977, p. 1. 24. Graboski, M. S.; Daubert, T. E. Ind. Eng. Chem. Process Des. Dev. 1978, 17, 443. 25. Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. The Properties qf Gases and Liquids. 3rd edition. McGraw-Hill: New York. 1977. 26. Lewis, K. L.; Mosedale, S. E.; Wormald, C. J. J. Chem. Thermodvnamics 1977, 9, 121. 27. Soave, G. Chem. Eng. Sci. 1972,27, 1197. 28. Carnahan, N. F.; Starling, K. E. AIChE Journal 1972. 18, 1184; Carnahan. N. F.; Starling. K. E. J. Chem.
Phys.
1%9,
51, 635.
29. Henderson, D. Equations of State in Engineering and Research. Am. Chem. Sot. Symposium Series: Washington, D.C. 1979, p. 1. 30. Christensen, J. J.; Zebolsky. D. M.: Izatt. R. M. unpublished calculations. 31. Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. Regular and Related Solutions. Van Nostrand Reinhold: New York. 1970, p. 56. 32. Levelt Sengers, J. M. H.; Morrison, G.; Chang, R. F. Fluid Phase Equilibria 1983, 14, 19. 33. Kay, W. B. Act. Chem. Res. 1968, I, 344. 34. Andrews. F. C. J. Chem. Phys. 1976,&t, 1948.