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Critical properties of CO2, CHF3, SF6, (CO2+ CHF3), and (CHF3+ SF6)
J. Chem. Thermodynamics 1998, 30, 481]496
Critical properties of CO 2 , CHF3 , SF6 , ( CO 2 H CHF3 ) , and ( CHF3 H SF6 ) A. Diefenbacher, M. Crone, and M. Turk ¨ a Institut fur ¨ Technische Thermodynamik und Kaltetechnik, ¨ Uni¨ ersitat 2, ¨ Karlsruhe (TH), Richard-Willstatter-Allee ¨ D-76128 Karlsruhe, F.R.G.
Measurements of the critical properties pc , rc , and Tc for the pure substances CO 2 , CHF3 , SF6 , and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 . were performed by observation of the critical opalescence in a static equilibrium cell. The experimental data were compared to values given in the literature. The experimental results for the binary mixtures are described by the Peng-Robinson equation of state, using only the experimental data for the critical pressure and the critical temperature of the pure components and of one mixture of nearly equal amounts of substance. For the binary systems investigated, this equation of state describes the critical loci, the vapour]liquid equilibrium, and the dependence of the supercritical density on temperature and pressure rather well. Q 1998 Academic Press Limited KEYWORDS: experimental critical data; pure substances; binary mixtures; Peng-Robinson equation of state; supercritical densities
1. Introduction Over the past years there has been a growing interest in the use of binary and multicomponent fluid mixtures in supercritical fluid technologies such as supercritical fluid extraction. The possibility to either introduce polar or non-polar features in order to regulate interactions of the fluid with a specific compound, or to manipulate the critical properties of the mixture is of special interest. So far, however, experimentally determined critical data are not available for all binary mixtures of interest, and the available data for some systems are frequently limited only to a narrow composition range. Progress in supercritical fluid technologies requires the knowledge of the Ž p, r , T . data of pure substances and fluid mixtures under near-critical and supercritical conditions. In the present paper measurements of the critical properties pc , rc , and Tc have been carried out for the pure substances carbon dioxide ŽCO 2 ., trifluoromethane ŽCHF3 , refrigerant R23., sulphur hexafluoride ŽSF6 ., and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. The critical pressures and the critical temperatures of the mixtures are illustrated as a function of composition, and a calculation procedure by means of the Peng-Robinson equation of state is reported using only the experimental a
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0021]9614r98r040481 q 16 $25.00r0rct970320
Q 1998 Academic Press Limited
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FIGURE 1. Scheme of the apparatus: 1, static equilibrium cell; 2, platinum resistance thermometers; 3, magnetic stirrer; 4, controlled heater; 5, cooler; 6, air circulating fan; 7, pressure null indicator; 8, dead-weight gauge; 9, displacer; 10, thermostatted pressure gauges; 11, test fluid; 12, nitrogen supply; 13, vacuum pump; 14, sampling lines.
critical data for the pure components and for one mixture of nearly equal amounts of substance. The capability of this equation of state to represent vapour]liquid equilibrium data and densities in the supercritical region is discussed in comparison with experimental data of other authors.
2. Experimental The apparatus used in the present investigation is shown in figure 1, and was designed for measurements of vapour]liquid equilibria in the temperature range Ž200 to 500. K and for pressures from about 1 kPa to 10 MPa. The static equilibrium cell is installed in a thermostatted chamber, in which with controlled cooling and heating it is possible to maintain a constant temperature in the limits of "10 mK for many hours. The temperature in the equilibrium cell is measured with four platinum resistance thermometers, two located in the vapour phase and two in the liquid phase. The temperature fluctuations as well as the local variations are less than "10 mK. Four piezoresistive pressure gauges with different pressure ranges, mounted in a separate thermostatted box, are used for measuring the pressure. The gauges are separated from the test fluid in the equilibrium cell by a thermostatted high-precision null indicator. By means of a very sensitive displacer, the pressure difference at the null indicator is adjusted to less than "0.01 kPa. The uncertainty of the pressure gauges is "0.05 per cent of their full scale. Above
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
483
atmospheric pressure they were calibrated before each measurement with a highprecision standard dead-weight gauge with a relative uncertainty of "0.01 per cent. The cylindrical test cell of 1406 cm3 inner volume has two windows for the determination of the critical state by observation of the critical opalescence. By decreasing the temperature very slowly from the supercritical state, with carefully adjusted density, the liquid]vapour interface occurring in the middle of the equilibrium cell can be observed, and it is possible to determine the critical temperature within "30 mK to "60 mK and the critical pressure within "6 kPa. From the known cell volume and the mass of the test fluid in the cell it is possible to determine the critical density of the pure components with an experimental uncertainty of less than "2 per cent. Samples for determination of the composition of the test fluid are taken in the supercritical state. The experimental uncertainty of the composition determined by gas-chromatographic analysis is less than "0.3 mole per cent. A more detailed description of the apparatus and the experimental procedure, especially the determination of the critical properties pc , rc , and Tc , can be found elsewhere.Ž1,2. The test fluids were supplied by Messer Griesheim, F.R.G. The mole fraction purities guaranteed by the supplier for CO 2 , CHF3 , and SF6 are 0.999995, 0.99993, and 0.99997, respectively.
3. Results and discussion Measurements of the critical properties pc , rc , and Tc have been carried out for the pure components CO 2 , CHF3 , SF6 , and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. The measured data for the binary mixtures were compared with values calculated by the Peng-Robinson equation of state: Ž3. p s RTr Ž ¨ y b . 4 y a Ž T . r ¨ Ž ¨ q 2 b . y b 2 4 .
Ž 1.
In equation Ž1., where R s 8.31451 J . Ky1 . moly1 , only the parameter a s aŽT . is treated as a function of temperature: 2
a Ž T . s ac . a Ž T . s ac . 1 q m . Ž 1 y 'T * . 4 ,
Ž 2.
where T * is the reduced temperature and m a function of the acentric factor v : m s 0.37464 q 1.54266 . v y 0.26992 . v 2 .
Ž 3.
The parameters ac and b s bc for a pure substance are determined from our measured critical temperature and critical pressure.
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The parameters a and b for a mixture are calculated using the following mixing and combination rules: n
as
n
Ý Ý
x i x j . ai j ,
Ž 4.
x i x j . bi j ,
Ž 5.
1r2
Ž 6.
is1 js1 n
bs
n
Ý Ý is1 js1
with a i j s a ji s Ž a i i a j j .
. Ž1 y k i j . ,
bi j s bji s Ž bii q bj j . r2 . Ž 1 y l i j . ,
Ž 7.
for i / j. The binary interaction parameters k i j and l i j are fitted exclusively to our experimental critical data for one single mixture of nearly equal amounts of substance. For the calculation a procedure proposed by Heidemann and Khalil,Ž4. based on the consideration of thermodynamic stability of the critical point of mixtures, is applied. More details about its application are given elsewhere.Ž2. To show the capability of the apparatus, additional vapour pressure measurements for pure CO 2 in the temperature range from T s 283 K up to the critical temperature were performed. The relative deviations of our measured vapour pressures from the correlation given by Span and Wagner Ž5. within the complete range of our investigation were smaller than 0.07 per cent, which is less than the total experimental uncertainty of our data. The experimental results for the critical properties of the pure components are listed in tables 1 to 3. The experimental uncertainties of the individual quantities pc , rc , and Tc were discussed in previous publications.Ž1,2. In general, the experimental error is less than "6 kPa for pc , "2 per cent for rc , and less than "0.06 K for Tc . As it can be seen from table 1, our experimental results for the critical temperature and the critical pressure of pure CO 2 show a very good agreement with values published by other authors, especially with the accurate data TABLE 1. Critical temperature Tc , critical pressure pc , and critical density rc of CO 2 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 Tc rK
pcrMPa
rcrŽkg . my3 .
304.122 304.212 " 0.02 304.0992 304.1992 304.1192 304.1282 " 0.015 304.158 " 0.06
7.375 7.376 7.3719 7.37479 7.3753 7.3773 " 0.003 7.3785 " 0.006
467 468 467.67 466.5 467.83 467.6 " 0.6 463.4 " 8
Reference Moldover et al.Ž7. ReileŽ8. Albright et al.Ž9. Ely et al.Ž10. Chen et al.Ž11. Duschek et al.Ž6. This work
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
485
TABLE 2. Critical temperature Tc , critical pressure pc , and critical density rc of CHF3 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 TcrK
pc rMPa
rcrŽkg . my3 .
299.07 299.164 " 0.02 299.00 " 0.01 299.29 " 0.02 298.97 299.005 " 0.06 298.992 " 0.06
4.836 4.877 4.8162 " 0.0018 4.828 4.820 4.7988 " 0.006 4.7961 " 0.006
525 527 529 " 5 526 525.5 517.5 " 8 519.5 " 8
Reference Hou and MartinŽ12. ReileŽ8. Hori et al.Ž13. Ohgaki et al.Ž14. McLinden et al.Ž15. This work This work
reported by Duschek et al.Ž6. However, a significant deviation in the critical density is observed, owing to the high experimental uncertainty of our apparatus for density measurements in comparison, for instance, with the apparatus used by Duschek et al.Ž6. For CHF3 and SF6 only few sets of reliable data for the critical properties are known in the literature. Comparison of our measured critical properties with values published by other authors is shown in tables 2 and 3. It is significant that the critical pressure of CHF3 measured in this work is lower than the values of the literature. This lower value was confirmed in a second series of very carefully performed measurements, in which the critical opalescence in the region close to the critical point was observed at six different densities between Ž5.11 " 8. kg . my3 and Ž528.5 " 8. kg . my3 . These measurements resulted in the second set of values for the critical properties listed in the last row of table 2. However, data for the critical temperature of CHF3 reported by Hori et al.Ž13. and McLinden et al.Ž15. agree with our results within the uncertainty of our measurements, whereas their data of the critical density are higher than our results by 1.83 per cent and 1.15 per cent, respectively. The markedly higher values for the critical pressure might be attributed to the extrapolation of the vapour pressure correlation used by many other authors such as Hori et al.Ž13. to determine the critical pressure, which might lead to higher errors than assumed because of the very steep temperature gradient of the vapour pressure curve in the vicinity of the critical point. The comparison of our results for
TABLE 3. Critical temperature Tc , critical pressure pc , and critical density rc of SF6 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 TcrK
pc rMPa
rc rŽkg . my3 .
Reference
318.675 " 0.003 318.691 " 0.0001 318.688 " 0.02 318.708 " 0.02 .018 318.718q0 y0 .005 318.742 " 0.06
3.7608 " 0.003 ] 3.7590 " 0.0017 3.745 3.7546q0.014 y0.004 3.7555 " 0.006
730 730.47 " 1.6 740 " 2 741 742.1 " 1.5 729.7 " 14
MacCormack and Schneider Ž16. Ley-Koo and GreenŽ17. Watanabe et al.Ž18. ReileŽ8. Pieperbeck Ž19. This work
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TABLE 4. Experimental results for the critical temperature Tc , critical pressure pc , and critical density rc of xCO 2 q Ž1 y x .CHF3 4 ŽITS-90. x ŽCO 2 .
Tc rK
pc rMPa
rcrŽkg . my3 .
0.0000 0.3374 0.5188 0.6674 1.0000
298.992 " 0.06 299.901 " 0.06 300.531 " 0.06 301.215 " 0.06 304.158 " 0.06
4.7961 " 0.006 5.5987 " 0.006 6.0541 " 0.006 6.4383 " 0.006 7.3785 " 0.006
519.5 " 8 506.7 " 8 498.9 " 8 488.0 " 8 463.4 " 8
the critical properties pc , rc , and Tc of SF6 with values published by different other authors shows good agreement. As shown in table 3, the very accurate data of the critical temperature and the critical pressure published by Pieperbeck Ž19. agree with our results within 0.024 K and 0.9 kPa. These deviations are markedly smaller than the experimental uncertainty of our measurements. His higher value for the critical density agrees with our result within the uncertainty of our measurements. Our experimental results for the two binary mixtures examined are listed in tables 4 and 5, where x denotes the mole fraction. The composition dependence of the critical pressure and the critical temperature for ŽCO 2 q CHF3 . are plotted in figures 2 and 3. The experimental values of Suehiro et al.Ž20. and the values calculated by the Peng-Robinson equation of state are also depicted for comparison. In table 6 the parameters for the pure substances CO 2 , CHF3 , SF6 and the interaction parameters of the binary systems investigated are given for the PengRobinson equation of state. For ŽCO 2 q CHF3 . the critical pressure can be described quite well by the mole fraction-weighted means of the pure components values, whereas the values
TABLE 5. Experimental results for the critical temperature Tc , critical pressure pc , and critical density rc of xCHF3 q Ž1 y x .SF6 4 ŽITS-90. x ŽCHF3 .
Tc rK
pc rMPa
rcrŽkg . my3 .
0.0000 0.3416 0.5089 0.6673 0.8015 1.0000 0.235 0.353 0.504 0.702 0.752 0.852
318.742 " 0.06 304.942 " 0.06 299.830 " 0.06 296.971 " 0.06 296.419 " 0.06 298.992 " 0.06 309.08 " 0.12 304.36 " 0.12 299.87 " 0.12 296.53 " 0.12 296.29 " 0.12 296.57 " 0.12
3.7555 " 0.006 4.2648 " 0.006 4.3625 " 0.006 4.4483 " 0.006 4.5580 " 0.006 4.7961 " 0.006 4.163 " 0.01 4.274 " 0.01 4.365 " 0.01 4.473 " 0.01 4.515 " 0.01 4.614 " 0.01
729.7 " 14 688.0 " 14 653.3 " 14 616.3 " 14 577.9 " 14 519.5 " 8 ) ) ) ) ) )
* Measurements performed in an old apparatus similar to that described in this paper. The experimental errors for these data are "0.12 K for the critical temperature, and "0.01 MPa for the critical pressure. The temperatures of these measurements have been converted from IPTS-68 to ITS-90. No densities were determined in these experiments.
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
487
FIGURE 2. a, Composition dependence of the critical pressure pc for xCO 2 q Ž1 y x .CHF3 4: B, This work; ^, Suehiro et al.;Ž20. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
measured for the critical temperature are slightly smaller than the mole fractionweighted means of the pure components critical temperatures. As shown in the lower diagrams in figures 2 and 3, the relative deviations of the critical pressure and the critical temperature from the values calculated by the Peng-Robinson equation of state are less than 0.1 per cent and 0.05 per cent, respectively, whereas the data published by Suehiro and coworkersŽ20. show deviations from the values calculated by the Peng-Robinson equation of state by up to 0.35 per cent for the critical pressure, and by up to 0.15 per cent for the critical temperature.
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FIGURE 3. a, Composition dependence of the critical temperature Tc for xCO 2 q Ž1 y x .CHF3 4: ^, Suehiro et al.;Ž20. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
B, This work;
However, ŽCHF3 q SF6 . exhibits a much more non-ideal behaviour than ŽCO 2 q CHF3 .. The critical pressure and the critical temperature are plotted against the CHF3 mole fraction in figures 4 and 5, respectively. Again, the values calculated by
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
489
TABLE 6. Parameters ac and bc of the Peng-Robinson equation of state, and the binary interaction parameters k i j and l i j of the mixtures used for calculations. M is the molar mass and v is the acentric factor Substance
ac . 10y9 . kPa cm6 . moly2
bc
M
cm3 . moly1
g . moly1
CO 2 CHF3 SF6
0.396273 0.588828 0.855018
26.664 40.303 54.899
44.0098 70.0140 146.0450
ŽCO 2 q CHF3 . ŽCHF3 q SF6 .
ki j
li j
0.05025 0.17793
0.05830 0.06374
v 0.224Ž26. 0.263Ž26. 0.286Ž21.
the Peng-Robinson equation of state and the experimental values of ReileŽ8. are depicted for comparison. The critical pressure of this system shows significantly stronger deviations from the mole fraction-weighted means and the critical temperature has even a minimum in its composition dependence at a mole fraction of about x ŽCHF3 . s 0.75. Considering that the interaction parameters are fitted only to the critical data of a single mixture of nearly equal amounts of substance, it is remarkable that the Peng-Robinson equation of state is capable of describing the location of this minimum quite well. As expected, the deviations between the experimental values for the critical pressure as well as for the critical temperature and those calculated with the Peng-Robinson equation of state are larger than for ŽCO 2 q CHF3 .. However, the difference is always less than 1 per cent for the critical pressure and 0.4 per cent for the critical temperature. The former results for the critical pressure and the critical temperature, performed in our laboratory, are in good agreement with our new results. On the other hand, the measurements by ReileŽ8. for the critical pressure and critical temperature show deviations rising up to 1.5 per cent and 0.6 per cent, respectively. As shown below the Peng-Robinson equation of state with its parameters determined as described above is not only suitable for the calculation of the critical locus but also for the prediction of the vapour]liquid equilibrium and the supercritical density of fluid mixtures. Experimental values for the bubble point pressures of ŽCO 2 q CHF3 . have been published by Roth et al.Ž22. at four temperatures between T s 254.00 K and T s 293.15 K for different compositions. Figure 6 demonstrates the capability of the Peng-Robinson equation of state with the parameters listed in table 6 to represent the vapour]liquid equilibrium data of ŽCO 2 q CHF3 .. In the two diagrams the relative deviations of the experimental results for the vapour-phase composition measured by Roth et al.Ž22. from values calculated by the PengRobinson equation of state were plotted against pressure for two different
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A. Diefenbacher, M. Crone, and M. Turk ¨
FIGURE 4. a, Composition dependence of the critical pressure pc for xCHF3 q Ž1 y x .SF6 4: B, This work; I, this work Žsee table 5.; ^, Reile,Ž8. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
temperatures. Considering the experimental error in the determination of the vapour-phase composition given by the authors, the calculation shows a very good
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
491
FIGURE 5. a, Composition dependence of the critical temperature Tc for xCHF3 q Ž1 y x .SF6 4: B, , predicted by the Peng-Robinson equation of This work; I, this work Žsee table 5.; ^, Reile,Ž8. state.Ž3. b, Relative deviations of the measured values from the calculated values.
agreement for the temperature 293.15 K, which is close to the critical temperature, as well as for T s 254.00 K, which is far below the critical temperature. The
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FIGURE 6. Relative deviations of the vapour]liquid equilibrium experimental data by Roth et al.Ž22. Ž^. for vapour-phase compositions in xCO 2 q Ž1 y x .CHF3 4 from the values predicted by the Peng-Robinson equation of state.Ž3. The dashed lines represent the experimental error given by Roth et al.Ž22.
corresponding mean relative deviations between the calculated and the measured values of the bubble point pressures are 0.35 per cent and 0.45 per cent, respectively. Similarly results are obtained for the other temperatures investigated by the above named authors. For many applications such as supercritical extraction the ability to calculate the densities in the supercritical region is of special interest. Therefore, it is necessary to compare the density calculated by the Peng-Robinson equation of state with accurate Ž p, r , T . measurements. From previous investigations of the gas density, reliable sets of data for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 ., including the pure substances, are available for two supercritical temperatures.Ž23 ] 25. The relative deviations between the measured and the calculated densities for the fluid mixtures are of the same order of magnitude as the pure substances. In figures 7 and 8 the density for the mixtures of nearly equal amounts of substance are plotted against the pressure for two different temperatures above the critical temperature for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. In all the cases shown in figures 7 and 8, with the exception of ŽCO 2 q CHF3 . at T s 333.15 K, it was possible to calculate the density of the mixtures at supercritical conditions with a maximum relative deviation less than 7 per cent. In figure 9 the plot for ŽCHF3 q SF6 . at T s 373.15 K is extended to three different compositions. Again, the maximum relative deviations between measured and calculated densities are less than 7 per cent. In the pressure range of interest for supercritical fluid extraction, which is about three- to four-fold
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
493
FIGURE 7. a, Density r against pressure p for xCO 2 q Ž1 y x .CHF3 4: I, HoinkisŽ23. T s 333.15 K, x ŽCO 2 . s 0.500; B, HoinkisŽ23. T s 373.15 K, x ŽCO 2 . s 0.487; , predicted by the Peng-Robinson equation of state.Ž3. Figures 7Žb. and 7Žc. show the relative deviations of the measured values from the calculated values.
the critical pressure of the solvent, the relative deviations between the measured and the calculated densities are even smaller than 5 per cent. These deviations are not larger than the deviations obtained, when the parameters a and b of the Peng-Robinson equation of state were fitted directly to the experimental Ž p, r , T . data.Ž23 ] 25.
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FIGURE 8. a, Density r against pressure p for xCHF3 q Ž1 y x .SF6 4. I, Freyhof Ž24. T s 333.15 K, Ž25. x ŽCHF3 . s 0.474; B, Buhner T s 373.15 K, x ŽCHF3 . s 0.536; , predicted by the Peng¨ Robinson equation of state.Ž3. Figures 8Žb. and 8Žc. show the relative deviations of the measured values from the calculated values.
In conclusion, it can be said that the simple Peng-Robinson equation of state, which is based only on the experimental data of the critical pressure and the critical temperature for the pure substances and one mixture of nearly equal amounts of substance, gives a good description of the vapour]liquid equilibrium and the supercritical density of fluid mixtures over a wide range of pressure and temperature.
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
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FIGURE 9. a, Density r against pressure p for xCHF3 q Ž1 y x .SF6 4. Experimental values by Ž25. Buhner at T s 373.15 K: I, x ŽCHF3 . s 0.226, B, x ŽCHF3 . s 0.536; `, x ŽCHF3 . s 0.780; , ¨ predicted by the Peng-Robinson equation of state.Ž3. Figures 9Žb. and 9Žc. show the relative deviations of the measured values from the calculated values.
The financial support by previous grants of the Deutsche Forschungsgemeinschaft for the construction and maintenance of the experimental set-up used in the present investigation is gratefully acknowledged.
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REFERENCES 1. Turk, ¨ M.; Zhai, J.; Nagel, M.; Bier, K. Messungen des Dampfdruckes und der kritischen Zustandsgroßen ¨ ¨ on neuen Kaltemitteln, VDI-Fortschritt-Berichte, Reihe 19, Nr. 79. Dusseldorf: VDI-Verlag. 1994. ¨ ¨ 2. Nagel, M.; Bier, K. Das DampfrFlussigkeits-Gleichgewicht neuer binarer and ternarer ¨ ¨ ¨ Kaltemittelgemische. VDI-Fortschritt-Berichte, Reihe 19, Nr. 93. Dusseldorf: VDI-Verlag. 1996. ¨ ¨ 3. Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59]64. 4. Heidemann, R. A.; Khalil, A. M. AIChE. J. 1980, 26, 769]779. 5. Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509]1596. 6. Duschek, W.; Kleinrahm, R.; Wagner, W. J. Chem. Thermodynamics 1990, 22, 841]864. 7. Moldover, M. R.; Sengers, J. V.; Gammon, R. W.; Hocken, R. J. Re¨ . Mod. Phys. 1979, 51, 79]99. 8. Reile, E. Dissertation, TU Munchen. 1981. ¨ 9. Albright, P. C.; Edwards, T. J.; Chen, Z. Y.; Sengers, J. V. J. Chem. Phys. 1987, 87, 1717]1725. 10. Ely, J. F.; Magee, J. W.; Haynes, W. M. Research Report RR-110. National Bureau of Standards: Boulder. 1987. 11. Chen, Z. Y.; Albright, P. C.; Sengers, J. V. Phys. Re¨ . A 1990, 41, 3161]3177. 12. Hou, Y. C.; Martin, J. J. AIChE J. 1959, 5, 125]129. 13. Hori, K.; Okazaki, S.; Uematsu, M.; Watanabe, K. Proceedings of the 8th Symposium on Thermophys. Properties, Gaithersburg. 1981. 14. Ohgaki, K.; Umezono, S.; Katayama, T. J. Supercritical Fluids 1990, 3, 78]84. 15. McLinden, M. O.; Huber, M. L.; Outcalt, S. L. ASME Winter Annual Meeting, New Orleans. 1993. 16. MacCormack, K. E.; Schneider, W. G. Can. J. Chem. 1951, 29, 699]714. 17. Ley-Koo, M.; Green, M. S. Phys. Re¨ . A 1977, 16, 2483]2487. 18. Watanabe, K.; Watanabe, H.; Oguchi, K. Proceedings of the 7th Symposium on Thermophys. Properties, New York. 1977. 19. Pieperbeck, B. Dissertation, Ruhr-Universitat ¨ Bochum. 1990; and Wagner, W.; Kurzeja, N.; Pieperbeck, B. Fluid Phase Equilibria 1992, 79, 151]174. 20. Suehiro, Y.; Nakajiama, K.; Yamada, K.; Uematsu, M. J. Chem. Thermodynamics 1996, 28, 1153]1164. 21. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Properties of Gases and Liquids. McGraw-Hill: New York. 1987. 22. Roth, H.; Peters-Gerth, P.; Lucas, K. Fluid Phase Equilibria 1992, 73, 147]166. 23. Hoinkis, J. Dissertation, Universitat ¨ Karlsruhe ŽTH.. 1989. 24. Freyhof, R. Dissertation, Universitat ¨ Karlsruhe ŽTH.. 1986. 25. Buhner, K. Dissertation, Universitat ¨ ¨ Karlsruhe ŽTH.. 1982. 26. Platzer, B.; Maurer, G. Fluid Phase Equilibria 1989, 51, 223]236.
(Recei¨ ed 8 July 1997; in final form 29 October 1997)
WA97r051
Critical properties of CO 2 , CHF3 , SF6 , ( CO 2 H CHF3 ) , and ( CHF3 H SF6 ) A. Diefenbacher, M. Crone, and M. Turk ¨ a Institut fur ¨ Technische Thermodynamik und Kaltetechnik, ¨ Uni¨ ersitat 2, ¨ Karlsruhe (TH), Richard-Willstatter-Allee ¨ D-76128 Karlsruhe, F.R.G.
Measurements of the critical properties pc , rc , and Tc for the pure substances CO 2 , CHF3 , SF6 , and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 . were performed by observation of the critical opalescence in a static equilibrium cell. The experimental data were compared to values given in the literature. The experimental results for the binary mixtures are described by the Peng-Robinson equation of state, using only the experimental data for the critical pressure and the critical temperature of the pure components and of one mixture of nearly equal amounts of substance. For the binary systems investigated, this equation of state describes the critical loci, the vapour]liquid equilibrium, and the dependence of the supercritical density on temperature and pressure rather well. Q 1998 Academic Press Limited KEYWORDS: experimental critical data; pure substances; binary mixtures; Peng-Robinson equation of state; supercritical densities
1. Introduction Over the past years there has been a growing interest in the use of binary and multicomponent fluid mixtures in supercritical fluid technologies such as supercritical fluid extraction. The possibility to either introduce polar or non-polar features in order to regulate interactions of the fluid with a specific compound, or to manipulate the critical properties of the mixture is of special interest. So far, however, experimentally determined critical data are not available for all binary mixtures of interest, and the available data for some systems are frequently limited only to a narrow composition range. Progress in supercritical fluid technologies requires the knowledge of the Ž p, r , T . data of pure substances and fluid mixtures under near-critical and supercritical conditions. In the present paper measurements of the critical properties pc , rc , and Tc have been carried out for the pure substances carbon dioxide ŽCO 2 ., trifluoromethane ŽCHF3 , refrigerant R23., sulphur hexafluoride ŽSF6 ., and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. The critical pressures and the critical temperatures of the mixtures are illustrated as a function of composition, and a calculation procedure by means of the Peng-Robinson equation of state is reported using only the experimental a
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FIGURE 1. Scheme of the apparatus: 1, static equilibrium cell; 2, platinum resistance thermometers; 3, magnetic stirrer; 4, controlled heater; 5, cooler; 6, air circulating fan; 7, pressure null indicator; 8, dead-weight gauge; 9, displacer; 10, thermostatted pressure gauges; 11, test fluid; 12, nitrogen supply; 13, vacuum pump; 14, sampling lines.
critical data for the pure components and for one mixture of nearly equal amounts of substance. The capability of this equation of state to represent vapour]liquid equilibrium data and densities in the supercritical region is discussed in comparison with experimental data of other authors.
2. Experimental The apparatus used in the present investigation is shown in figure 1, and was designed for measurements of vapour]liquid equilibria in the temperature range Ž200 to 500. K and for pressures from about 1 kPa to 10 MPa. The static equilibrium cell is installed in a thermostatted chamber, in which with controlled cooling and heating it is possible to maintain a constant temperature in the limits of "10 mK for many hours. The temperature in the equilibrium cell is measured with four platinum resistance thermometers, two located in the vapour phase and two in the liquid phase. The temperature fluctuations as well as the local variations are less than "10 mK. Four piezoresistive pressure gauges with different pressure ranges, mounted in a separate thermostatted box, are used for measuring the pressure. The gauges are separated from the test fluid in the equilibrium cell by a thermostatted high-precision null indicator. By means of a very sensitive displacer, the pressure difference at the null indicator is adjusted to less than "0.01 kPa. The uncertainty of the pressure gauges is "0.05 per cent of their full scale. Above
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
483
atmospheric pressure they were calibrated before each measurement with a highprecision standard dead-weight gauge with a relative uncertainty of "0.01 per cent. The cylindrical test cell of 1406 cm3 inner volume has two windows for the determination of the critical state by observation of the critical opalescence. By decreasing the temperature very slowly from the supercritical state, with carefully adjusted density, the liquid]vapour interface occurring in the middle of the equilibrium cell can be observed, and it is possible to determine the critical temperature within "30 mK to "60 mK and the critical pressure within "6 kPa. From the known cell volume and the mass of the test fluid in the cell it is possible to determine the critical density of the pure components with an experimental uncertainty of less than "2 per cent. Samples for determination of the composition of the test fluid are taken in the supercritical state. The experimental uncertainty of the composition determined by gas-chromatographic analysis is less than "0.3 mole per cent. A more detailed description of the apparatus and the experimental procedure, especially the determination of the critical properties pc , rc , and Tc , can be found elsewhere.Ž1,2. The test fluids were supplied by Messer Griesheim, F.R.G. The mole fraction purities guaranteed by the supplier for CO 2 , CHF3 , and SF6 are 0.999995, 0.99993, and 0.99997, respectively.
3. Results and discussion Measurements of the critical properties pc , rc , and Tc have been carried out for the pure components CO 2 , CHF3 , SF6 , and for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. The measured data for the binary mixtures were compared with values calculated by the Peng-Robinson equation of state: Ž3. p s RTr Ž ¨ y b . 4 y a Ž T . r ¨ Ž ¨ q 2 b . y b 2 4 .
Ž 1.
In equation Ž1., where R s 8.31451 J . Ky1 . moly1 , only the parameter a s aŽT . is treated as a function of temperature: 2
a Ž T . s ac . a Ž T . s ac . 1 q m . Ž 1 y 'T * . 4 ,
Ž 2.
where T * is the reduced temperature and m a function of the acentric factor v : m s 0.37464 q 1.54266 . v y 0.26992 . v 2 .
Ž 3.
The parameters ac and b s bc for a pure substance are determined from our measured critical temperature and critical pressure.
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The parameters a and b for a mixture are calculated using the following mixing and combination rules: n
as
n
Ý Ý
x i x j . ai j ,
Ž 4.
x i x j . bi j ,
Ž 5.
1r2
Ž 6.
is1 js1 n
bs
n
Ý Ý is1 js1
with a i j s a ji s Ž a i i a j j .
. Ž1 y k i j . ,
bi j s bji s Ž bii q bj j . r2 . Ž 1 y l i j . ,
Ž 7.
for i / j. The binary interaction parameters k i j and l i j are fitted exclusively to our experimental critical data for one single mixture of nearly equal amounts of substance. For the calculation a procedure proposed by Heidemann and Khalil,Ž4. based on the consideration of thermodynamic stability of the critical point of mixtures, is applied. More details about its application are given elsewhere.Ž2. To show the capability of the apparatus, additional vapour pressure measurements for pure CO 2 in the temperature range from T s 283 K up to the critical temperature were performed. The relative deviations of our measured vapour pressures from the correlation given by Span and Wagner Ž5. within the complete range of our investigation were smaller than 0.07 per cent, which is less than the total experimental uncertainty of our data. The experimental results for the critical properties of the pure components are listed in tables 1 to 3. The experimental uncertainties of the individual quantities pc , rc , and Tc were discussed in previous publications.Ž1,2. In general, the experimental error is less than "6 kPa for pc , "2 per cent for rc , and less than "0.06 K for Tc . As it can be seen from table 1, our experimental results for the critical temperature and the critical pressure of pure CO 2 show a very good agreement with values published by other authors, especially with the accurate data TABLE 1. Critical temperature Tc , critical pressure pc , and critical density rc of CO 2 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 Tc rK
pcrMPa
rcrŽkg . my3 .
304.122 304.212 " 0.02 304.0992 304.1992 304.1192 304.1282 " 0.015 304.158 " 0.06
7.375 7.376 7.3719 7.37479 7.3753 7.3773 " 0.003 7.3785 " 0.006
467 468 467.67 466.5 467.83 467.6 " 0.6 463.4 " 8
Reference Moldover et al.Ž7. ReileŽ8. Albright et al.Ž9. Ely et al.Ž10. Chen et al.Ž11. Duschek et al.Ž6. This work
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
485
TABLE 2. Critical temperature Tc , critical pressure pc , and critical density rc of CHF3 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 TcrK
pc rMPa
rcrŽkg . my3 .
299.07 299.164 " 0.02 299.00 " 0.01 299.29 " 0.02 298.97 299.005 " 0.06 298.992 " 0.06
4.836 4.877 4.8162 " 0.0018 4.828 4.820 4.7988 " 0.006 4.7961 " 0.006
525 527 529 " 5 526 525.5 517.5 " 8 519.5 " 8
Reference Hou and MartinŽ12. ReileŽ8. Hori et al.Ž13. Ohgaki et al.Ž14. McLinden et al.Ž15. This work This work
reported by Duschek et al.Ž6. However, a significant deviation in the critical density is observed, owing to the high experimental uncertainty of our apparatus for density measurements in comparison, for instance, with the apparatus used by Duschek et al.Ž6. For CHF3 and SF6 only few sets of reliable data for the critical properties are known in the literature. Comparison of our measured critical properties with values published by other authors is shown in tables 2 and 3. It is significant that the critical pressure of CHF3 measured in this work is lower than the values of the literature. This lower value was confirmed in a second series of very carefully performed measurements, in which the critical opalescence in the region close to the critical point was observed at six different densities between Ž5.11 " 8. kg . my3 and Ž528.5 " 8. kg . my3 . These measurements resulted in the second set of values for the critical properties listed in the last row of table 2. However, data for the critical temperature of CHF3 reported by Hori et al.Ž13. and McLinden et al.Ž15. agree with our results within the uncertainty of our measurements, whereas their data of the critical density are higher than our results by 1.83 per cent and 1.15 per cent, respectively. The markedly higher values for the critical pressure might be attributed to the extrapolation of the vapour pressure correlation used by many other authors such as Hori et al.Ž13. to determine the critical pressure, which might lead to higher errors than assumed because of the very steep temperature gradient of the vapour pressure curve in the vicinity of the critical point. The comparison of our results for
TABLE 3. Critical temperature Tc , critical pressure pc , and critical density rc of SF6 ŽITS-90.. Early data, which were taken on IPTS-68, have been converted to ITS-90 TcrK
pc rMPa
rc rŽkg . my3 .
Reference
318.675 " 0.003 318.691 " 0.0001 318.688 " 0.02 318.708 " 0.02 .018 318.718q0 y0 .005 318.742 " 0.06
3.7608 " 0.003 ] 3.7590 " 0.0017 3.745 3.7546q0.014 y0.004 3.7555 " 0.006
730 730.47 " 1.6 740 " 2 741 742.1 " 1.5 729.7 " 14
MacCormack and Schneider Ž16. Ley-Koo and GreenŽ17. Watanabe et al.Ž18. ReileŽ8. Pieperbeck Ž19. This work
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TABLE 4. Experimental results for the critical temperature Tc , critical pressure pc , and critical density rc of xCO 2 q Ž1 y x .CHF3 4 ŽITS-90. x ŽCO 2 .
Tc rK
pc rMPa
rcrŽkg . my3 .
0.0000 0.3374 0.5188 0.6674 1.0000
298.992 " 0.06 299.901 " 0.06 300.531 " 0.06 301.215 " 0.06 304.158 " 0.06
4.7961 " 0.006 5.5987 " 0.006 6.0541 " 0.006 6.4383 " 0.006 7.3785 " 0.006
519.5 " 8 506.7 " 8 498.9 " 8 488.0 " 8 463.4 " 8
the critical properties pc , rc , and Tc of SF6 with values published by different other authors shows good agreement. As shown in table 3, the very accurate data of the critical temperature and the critical pressure published by Pieperbeck Ž19. agree with our results within 0.024 K and 0.9 kPa. These deviations are markedly smaller than the experimental uncertainty of our measurements. His higher value for the critical density agrees with our result within the uncertainty of our measurements. Our experimental results for the two binary mixtures examined are listed in tables 4 and 5, where x denotes the mole fraction. The composition dependence of the critical pressure and the critical temperature for ŽCO 2 q CHF3 . are plotted in figures 2 and 3. The experimental values of Suehiro et al.Ž20. and the values calculated by the Peng-Robinson equation of state are also depicted for comparison. In table 6 the parameters for the pure substances CO 2 , CHF3 , SF6 and the interaction parameters of the binary systems investigated are given for the PengRobinson equation of state. For ŽCO 2 q CHF3 . the critical pressure can be described quite well by the mole fraction-weighted means of the pure components values, whereas the values
TABLE 5. Experimental results for the critical temperature Tc , critical pressure pc , and critical density rc of xCHF3 q Ž1 y x .SF6 4 ŽITS-90. x ŽCHF3 .
Tc rK
pc rMPa
rcrŽkg . my3 .
0.0000 0.3416 0.5089 0.6673 0.8015 1.0000 0.235 0.353 0.504 0.702 0.752 0.852
318.742 " 0.06 304.942 " 0.06 299.830 " 0.06 296.971 " 0.06 296.419 " 0.06 298.992 " 0.06 309.08 " 0.12 304.36 " 0.12 299.87 " 0.12 296.53 " 0.12 296.29 " 0.12 296.57 " 0.12
3.7555 " 0.006 4.2648 " 0.006 4.3625 " 0.006 4.4483 " 0.006 4.5580 " 0.006 4.7961 " 0.006 4.163 " 0.01 4.274 " 0.01 4.365 " 0.01 4.473 " 0.01 4.515 " 0.01 4.614 " 0.01
729.7 " 14 688.0 " 14 653.3 " 14 616.3 " 14 577.9 " 14 519.5 " 8 ) ) ) ) ) )
* Measurements performed in an old apparatus similar to that described in this paper. The experimental errors for these data are "0.12 K for the critical temperature, and "0.01 MPa for the critical pressure. The temperatures of these measurements have been converted from IPTS-68 to ITS-90. No densities were determined in these experiments.
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
487
FIGURE 2. a, Composition dependence of the critical pressure pc for xCO 2 q Ž1 y x .CHF3 4: B, This work; ^, Suehiro et al.;Ž20. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
measured for the critical temperature are slightly smaller than the mole fractionweighted means of the pure components critical temperatures. As shown in the lower diagrams in figures 2 and 3, the relative deviations of the critical pressure and the critical temperature from the values calculated by the Peng-Robinson equation of state are less than 0.1 per cent and 0.05 per cent, respectively, whereas the data published by Suehiro and coworkersŽ20. show deviations from the values calculated by the Peng-Robinson equation of state by up to 0.35 per cent for the critical pressure, and by up to 0.15 per cent for the critical temperature.
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FIGURE 3. a, Composition dependence of the critical temperature Tc for xCO 2 q Ž1 y x .CHF3 4: ^, Suehiro et al.;Ž20. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
B, This work;
However, ŽCHF3 q SF6 . exhibits a much more non-ideal behaviour than ŽCO 2 q CHF3 .. The critical pressure and the critical temperature are plotted against the CHF3 mole fraction in figures 4 and 5, respectively. Again, the values calculated by
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
489
TABLE 6. Parameters ac and bc of the Peng-Robinson equation of state, and the binary interaction parameters k i j and l i j of the mixtures used for calculations. M is the molar mass and v is the acentric factor Substance
ac . 10y9 . kPa cm6 . moly2
bc
M
cm3 . moly1
g . moly1
CO 2 CHF3 SF6
0.396273 0.588828 0.855018
26.664 40.303 54.899
44.0098 70.0140 146.0450
ŽCO 2 q CHF3 . ŽCHF3 q SF6 .
ki j
li j
0.05025 0.17793
0.05830 0.06374
v 0.224Ž26. 0.263Ž26. 0.286Ž21.
the Peng-Robinson equation of state and the experimental values of ReileŽ8. are depicted for comparison. The critical pressure of this system shows significantly stronger deviations from the mole fraction-weighted means and the critical temperature has even a minimum in its composition dependence at a mole fraction of about x ŽCHF3 . s 0.75. Considering that the interaction parameters are fitted only to the critical data of a single mixture of nearly equal amounts of substance, it is remarkable that the Peng-Robinson equation of state is capable of describing the location of this minimum quite well. As expected, the deviations between the experimental values for the critical pressure as well as for the critical temperature and those calculated with the Peng-Robinson equation of state are larger than for ŽCO 2 q CHF3 .. However, the difference is always less than 1 per cent for the critical pressure and 0.4 per cent for the critical temperature. The former results for the critical pressure and the critical temperature, performed in our laboratory, are in good agreement with our new results. On the other hand, the measurements by ReileŽ8. for the critical pressure and critical temperature show deviations rising up to 1.5 per cent and 0.6 per cent, respectively. As shown below the Peng-Robinson equation of state with its parameters determined as described above is not only suitable for the calculation of the critical locus but also for the prediction of the vapour]liquid equilibrium and the supercritical density of fluid mixtures. Experimental values for the bubble point pressures of ŽCO 2 q CHF3 . have been published by Roth et al.Ž22. at four temperatures between T s 254.00 K and T s 293.15 K for different compositions. Figure 6 demonstrates the capability of the Peng-Robinson equation of state with the parameters listed in table 6 to represent the vapour]liquid equilibrium data of ŽCO 2 q CHF3 .. In the two diagrams the relative deviations of the experimental results for the vapour-phase composition measured by Roth et al.Ž22. from values calculated by the PengRobinson equation of state were plotted against pressure for two different
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FIGURE 4. a, Composition dependence of the critical pressure pc for xCHF3 q Ž1 y x .SF6 4: B, This work; I, this work Žsee table 5.; ^, Reile,Ž8. , predicted by the Peng-Robinson equation of state.Ž3. b, Relative deviations of the measured values from the calculated values.
temperatures. Considering the experimental error in the determination of the vapour-phase composition given by the authors, the calculation shows a very good
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
491
FIGURE 5. a, Composition dependence of the critical temperature Tc for xCHF3 q Ž1 y x .SF6 4: B, , predicted by the Peng-Robinson equation of This work; I, this work Žsee table 5.; ^, Reile,Ž8. state.Ž3. b, Relative deviations of the measured values from the calculated values.
agreement for the temperature 293.15 K, which is close to the critical temperature, as well as for T s 254.00 K, which is far below the critical temperature. The
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FIGURE 6. Relative deviations of the vapour]liquid equilibrium experimental data by Roth et al.Ž22. Ž^. for vapour-phase compositions in xCO 2 q Ž1 y x .CHF3 4 from the values predicted by the Peng-Robinson equation of state.Ž3. The dashed lines represent the experimental error given by Roth et al.Ž22.
corresponding mean relative deviations between the calculated and the measured values of the bubble point pressures are 0.35 per cent and 0.45 per cent, respectively. Similarly results are obtained for the other temperatures investigated by the above named authors. For many applications such as supercritical extraction the ability to calculate the densities in the supercritical region is of special interest. Therefore, it is necessary to compare the density calculated by the Peng-Robinson equation of state with accurate Ž p, r , T . measurements. From previous investigations of the gas density, reliable sets of data for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 ., including the pure substances, are available for two supercritical temperatures.Ž23 ] 25. The relative deviations between the measured and the calculated densities for the fluid mixtures are of the same order of magnitude as the pure substances. In figures 7 and 8 the density for the mixtures of nearly equal amounts of substance are plotted against the pressure for two different temperatures above the critical temperature for ŽCO 2 q CHF3 . and ŽCHF3 q SF6 .. In all the cases shown in figures 7 and 8, with the exception of ŽCO 2 q CHF3 . at T s 333.15 K, it was possible to calculate the density of the mixtures at supercritical conditions with a maximum relative deviation less than 7 per cent. In figure 9 the plot for ŽCHF3 q SF6 . at T s 373.15 K is extended to three different compositions. Again, the maximum relative deviations between measured and calculated densities are less than 7 per cent. In the pressure range of interest for supercritical fluid extraction, which is about three- to four-fold
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
493
FIGURE 7. a, Density r against pressure p for xCO 2 q Ž1 y x .CHF3 4: I, HoinkisŽ23. T s 333.15 K, x ŽCO 2 . s 0.500; B, HoinkisŽ23. T s 373.15 K, x ŽCO 2 . s 0.487; , predicted by the Peng-Robinson equation of state.Ž3. Figures 7Žb. and 7Žc. show the relative deviations of the measured values from the calculated values.
the critical pressure of the solvent, the relative deviations between the measured and the calculated densities are even smaller than 5 per cent. These deviations are not larger than the deviations obtained, when the parameters a and b of the Peng-Robinson equation of state were fitted directly to the experimental Ž p, r , T . data.Ž23 ] 25.
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FIGURE 8. a, Density r against pressure p for xCHF3 q Ž1 y x .SF6 4. I, Freyhof Ž24. T s 333.15 K, Ž25. x ŽCHF3 . s 0.474; B, Buhner T s 373.15 K, x ŽCHF3 . s 0.536; , predicted by the Peng¨ Robinson equation of state.Ž3. Figures 8Žb. and 8Žc. show the relative deviations of the measured values from the calculated values.
In conclusion, it can be said that the simple Peng-Robinson equation of state, which is based only on the experimental data of the critical pressure and the critical temperature for the pure substances and one mixture of nearly equal amounts of substance, gives a good description of the vapour]liquid equilibrium and the supercritical density of fluid mixtures over a wide range of pressure and temperature.
Critical properties of xCO 2 q Ž1 y x .CHF3 4 and xCHF3 q Ž1 y x .SF6 4
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FIGURE 9. a, Density r against pressure p for xCHF3 q Ž1 y x .SF6 4. Experimental values by Ž25. Buhner at T s 373.15 K: I, x ŽCHF3 . s 0.226, B, x ŽCHF3 . s 0.536; `, x ŽCHF3 . s 0.780; , ¨ predicted by the Peng-Robinson equation of state.Ž3. Figures 9Žb. and 9Žc. show the relative deviations of the measured values from the calculated values.
The financial support by previous grants of the Deutsche Forschungsgemeinschaft for the construction and maintenance of the experimental set-up used in the present investigation is gratefully acknowledged.
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REFERENCES 1. Turk, ¨ M.; Zhai, J.; Nagel, M.; Bier, K. Messungen des Dampfdruckes und der kritischen Zustandsgroßen ¨ ¨ on neuen Kaltemitteln, VDI-Fortschritt-Berichte, Reihe 19, Nr. 79. Dusseldorf: VDI-Verlag. 1994. ¨ ¨ 2. Nagel, M.; Bier, K. Das DampfrFlussigkeits-Gleichgewicht neuer binarer and ternarer ¨ ¨ ¨ Kaltemittelgemische. VDI-Fortschritt-Berichte, Reihe 19, Nr. 93. Dusseldorf: VDI-Verlag. 1996. ¨ ¨ 3. Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Fundam. 1976, 15, 59]64. 4. Heidemann, R. A.; Khalil, A. M. AIChE. J. 1980, 26, 769]779. 5. Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509]1596. 6. Duschek, W.; Kleinrahm, R.; Wagner, W. J. Chem. Thermodynamics 1990, 22, 841]864. 7. Moldover, M. R.; Sengers, J. V.; Gammon, R. W.; Hocken, R. J. Re¨ . Mod. Phys. 1979, 51, 79]99. 8. Reile, E. Dissertation, TU Munchen. 1981. ¨ 9. Albright, P. C.; Edwards, T. J.; Chen, Z. Y.; Sengers, J. V. J. Chem. Phys. 1987, 87, 1717]1725. 10. Ely, J. F.; Magee, J. W.; Haynes, W. M. Research Report RR-110. National Bureau of Standards: Boulder. 1987. 11. Chen, Z. Y.; Albright, P. C.; Sengers, J. V. Phys. Re¨ . A 1990, 41, 3161]3177. 12. Hou, Y. C.; Martin, J. J. AIChE J. 1959, 5, 125]129. 13. Hori, K.; Okazaki, S.; Uematsu, M.; Watanabe, K. Proceedings of the 8th Symposium on Thermophys. Properties, Gaithersburg. 1981. 14. Ohgaki, K.; Umezono, S.; Katayama, T. J. Supercritical Fluids 1990, 3, 78]84. 15. McLinden, M. O.; Huber, M. L.; Outcalt, S. L. ASME Winter Annual Meeting, New Orleans. 1993. 16. MacCormack, K. E.; Schneider, W. G. Can. J. Chem. 1951, 29, 699]714. 17. Ley-Koo, M.; Green, M. S. Phys. Re¨ . A 1977, 16, 2483]2487. 18. Watanabe, K.; Watanabe, H.; Oguchi, K. Proceedings of the 7th Symposium on Thermophys. Properties, New York. 1977. 19. Pieperbeck, B. Dissertation, Ruhr-Universitat ¨ Bochum. 1990; and Wagner, W.; Kurzeja, N.; Pieperbeck, B. Fluid Phase Equilibria 1992, 79, 151]174. 20. Suehiro, Y.; Nakajiama, K.; Yamada, K.; Uematsu, M. J. Chem. Thermodynamics 1996, 28, 1153]1164. 21. Reid, R. C.; Prausnitz, J. M.; Poling, B. E. Properties of Gases and Liquids. McGraw-Hill: New York. 1987. 22. Roth, H.; Peters-Gerth, P.; Lucas, K. Fluid Phase Equilibria 1992, 73, 147]166. 23. Hoinkis, J. Dissertation, Universitat ¨ Karlsruhe ŽTH.. 1989. 24. Freyhof, R. Dissertation, Universitat ¨ Karlsruhe ŽTH.. 1986. 25. Buhner, K. Dissertation, Universitat ¨ ¨ Karlsruhe ŽTH.. 1982. 26. Platzer, B.; Maurer, G. Fluid Phase Equilibria 1989, 51, 223]236.
(Recei¨ ed 8 July 1997; in final form 29 October 1997)
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