J . Phys. Chem. 1986, 90, 1147-1152
In the present study that body of data has been expanded to include the five diglyme solvates of L i N 0 3 . These spectra represent the first matrix-solvation results for a tridentate ligand. The contrast of the diglyme spectra with those of the T H F and glyme solvates has made it particularly clear that the identification of the solvates having C N values of 1, 2, and 3 is correct in each case. However, based on the diglyme results, a correction has been necessary for the later solvation stages for glyme,.LiN03. Taken together, both the glyme and diglyme matrix-solvation data sets are each best interpreted in terms of five major cation-solvation steps plus one less substantial change that apparently reflects a small but nontrivial effect from solvent contact with the anion. Obviously such contact must occur at some stage in the solvation sequence and evidence is growing that the initial influence occurs as the solvent concentration is increased through the 5 mol % range. On the basis of this new interpretation of the polyether matrix-solvation results, it follows that the dominant room temperature solvate for both glyme and diglyme has a C N value of 4 corresponding to the formula S2.LiN03 (where S is glyme or diglyme). However, cooling of the liquid solutions or formation of the low temperature annealed pure glassy matrix samples results in solvates having identical spectra and which have, therefore, been identified as the C N = 5 ion-paired solvates. The spectroscopic observation of the response of the equilibria between different ion-pair solvates to the reduction of liquid-so-
Vapor-Liquid Equilibrium in the Xenon
1147
lution temperatures has shown that AH, for formation of the final solvent-to-cationcoordinate bond, is small and negative with values ranging from -2.0 kcal/mol for T H F (CN = 4) to approximately -3.0 kcal/mol for glyme. These values may be in error by as much as 50% but the spectroscopic data are of sufficient quality to give promise of the future availability of more accurate values. Meanwhile, there appears to be no comparable published values with which to compare the change in enthalpy values. The AH value of the corresponding gas-phase hydration step for Li+ is nearly an order of magnitude greater (-17 kcal),8 a fact that merely gives emphasis to the obvious need to account for solvent-solvent as well as solvent-ion interaction energies.
Acknowledgment. Support of this research by the National Science Foundation under Grant CHE-8420961 is gratefully acknowledged. Registry No. THF, 109-99-9;LiNOI, 7790-69-4;diglyme, 11 1-96-6: glyme, 110-71-4.
(8) Kebarle, P. Ions and Ion-Solvent Molecule Interactions in the gas phase Mass Spectrometry in Inorganic Chemistry; American Chemical Society: Washington, DC, 1960;.Adv. Chem. Ser. No. 72. (9) The isomeric positions around the C-C bond(s) of glyme and diglyme are properly identified as anti, rather than trans, and gauche, rather than cis (Anderson, M.: Karlstrom, G. J . Phys. Chem. 1985, 89, 4957).
+ Ethene System
M. Nunes da Ponte,' D. Chokappa, J. C. G. Calado,t J. Zollweg, and W. B. Streett* School of Chemical Engineering, Olin Hall, Cornel1 University, Ithaca, New York 14853 (Received: September 30, 1985)
Vapor-liquid equilibrium measurements have been performed on mixtures of xenon and ethene at 17 temperatures, between 203 and 287 K, and pressures up to 5.7 MPa. This system exhibits a positive azeotrope and a critical curve with a minimum in temperature. Nine isotherms lie below this minimum, in the subcritical region, and eight above. Two out of these eight have two branches and two critical points, one on the xenon-rich side and another one on the ethene-rich side. Excess Gibbs energies were calculated by the method of Barker. They are in good agreement with earlier measurements.
+
Introduction A few years ago Calado, Azevedo, and Soares reported measurements of the three major excess functions GE,HE,and for mixtures of ethane or ethene with the rare gases.' They found that, although the ethane and ethene molecules are very similar (they are often well represented by a bicentric model), their behavior when mixed with spherical molecules, xenon in particular, was very different. Whereas the ethene xenon mixtures exhibited the behavior normally associated with simple systems (small positive values for both GE and p), the ethane xenon mixtures were found to form with negative values of all three excess functions. This anomalous behavior is unique among all the mixtures of small, simple molecules studied so far and cannot be explained on the basis of the opposite signs of the quadrupole moments of the ethane and ethene molecules. Since the measurements of Calado et al. were done, at most, at two temperatures (at, or close, to the triple point of the spherical molecule'), in the low-pressure region, it seemed worthwhile to investigate the behavior of those systems over much wider temperature and pressure ranges. In a previous paper we presented
+
+
+On sabbatical leave from Faculdade de CiZncias e Tecnologia, Universidade Nova de Lisboa, 2825 Monte da Caparica, Portugal. *Permanent address: Complexo I, Instituto Superior Tknico, 1096 Lisboa,
Portugal.
0022-3654/86/2090-1147$01.50/0
results on the vapor-liquid equilibrium for the xenon ethane mixtures up to the critical curve.* Here we report similar measurements for the xenon ethene mixtures. A comparison between the two systems can now be made on a much firmer basis. We performed vapor-liquid equilibrium measurements at 17 temperatures, ranging from 203 to 287 K, close to the critical point temperature of xenoil (289.74 K). The system exhibits a positive azeotrope at compositions ranging from xXe 0.8 mole fraction in xenon at 161 K (Calado and Soares3) to xXe 0.5 at 283 K, where it merges into the mixture critical line. This line has a minimum in temperature, below the critical temperatures of both pure components. Nine isotherms lie below this minimum, in the subcritical region, and eight above. Of these eight, two correspond to temperatures between the critical curve minimum and the critical temperature of ethene and exhibit two critical points each, one on the ethene-rich side and another one on the xenon-rich side. Excess Gibbs energies GEwere calculated as a function of composition for the eight lower isotherms, at zero reference pressure, by using Barker's method! Comparison with the results of Calado
+
--
(1) Calado, J. C. G.; Comes de Azevedo, E. J . S.; Soares, V. A. M. Chem. Eng. Commun. 1980, 5 , 149. (2) Nunes da Ponte, M.; Chokappa, D.; Calado, J . C. G.; Clancy, P.; Streett, W. B. J . Phys. Chem. 1985, 89, 2746. (3) Calado, J. C. G.; Soares, V. A. M. J . Chem. Thermodyn. 1977, 9, 91 1.
0 1986 American Chemical Society
, Nunes da Ponte et al.
1148 The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
5.8
P MPa
5.6
5.4
3t
1 5.2
I 5.0
0
0
.,
0.5
+
0.5
0
161K
1
Xe
Figure 1. P, x , y isotherms for xenon ethene mixtures at the indicated temperatures: 0 , liquid: vapor; 0,critical point; ---,azeotropic line. To avoid overcrowding, the isotherm at 282.00 K was omitted and no indication of temperature was given between 281 and 287 K. The isotherm at 161 K is from ref 3.
and Soares3 shows very good agreement between the two sets of data.
Experimental Results The experimental setup was described in detail in our previous paper on Xe C2H6 mixtures.2 Two apparatus were used, apparatus I consisting essentially of a stainless steel cell and cryostat, for temperatures below 265 K, and apparatus 11, consisting of a transparent thick-walled glass cell immersed in a thermostatized aqueous bath, for temperatures above 265 K. Magnetic circulation pumps were used to circulate the vapor phase and speed up the attainment of equilibrium. Pressure was measured with a direct reading Ruska quartz spiral gage, of f 0 . 6 kPa precision. Temperature was measured with calibrated platinum resistance thermometers, to zkO.01 K accuracy, on the IPTS-68. Samples withdrawn from the vapor and liquid phases through capillary lines were passed through a thermal conductivity detector. The accuracy of the composition measurement is estimated to be f 0 . 0 0 3 mole fraction, but the sensitivity of the detector is much higher, of t h e order of mole fraction. The uncertainties in composition measurement are mainly determined by the sampling process. Union Carbide research grade xenon, of stated minimum purity 99.99 mol %, and Air Products CP grade ethene, further distilled to a purity of at least 99.99 mol % in a low-temperature distillation ~ o l u m n were , ~ used in this work. The experimental p , T, x , y results are recorded in Table I for the eight lower temperature isotherms and in Table I1 for the other nine. As usual, x stands for the liquid mole fraction and y for the corresponding vapor composition. Figure 1 displays the whole
+
(4) Barker, J. A. A m f . J . Chem. 1953, 6, 207. (5) Davies, R. H.; Duncan, A. G.; Saville, G.; Staveley, L. A. K. Trans. Faraday SOC.1967, 63, 855.
1
XXe
Figure 2. P,x, y isotherms for xenon + ethene mixtures, in the critical region: 0 , experimental VLE points; m, critical points; - * - , azeotropic line: a , 287.18 K; b, 286.19 K; c, 285.19 K; d, 284.20 K; e, 283.17 K: f, 282.61 K; g, 282.25 K; h, 282.08 K; i, 282.00 K; j, 281.12 K. The isotherms g and h have two branches, one on the xenon-rich side and the other one on the ethene-rich side.
set of (p,x, y ) isotherms, with the exception of the points at 282.00 K, to avoid overcrowding of the drawing, but including the results of Calado and so are^,^ at the triple point temperature of xeiion (161.39 K). Figure 2 shows in greater detail the isotherms near the critical region. Table I also records values of the difference between the experimental compositions of the gas phase and compositions calculated by Barker’s thermodynamic consistency m e t h ~ din , ~the form used by Calado et aL6 For this purpose, second v i a l coefficients of xenon and ethene and the third virial coefficients of ethene were taken from the review by Dymond and Smith.’ The third virial coefficients of xenon were calculated according to Caligaris and Henderson.* Volumetric properties of liquid xenon were taken from Streett, Sagan, and S t a ~ e l e ywhile , ~ those of ethene were taken from the compilation of McCarty and Jacobsen. l o The Redlich-Kister expansion for the excess Gibbs energy GE was used in the form
GE = R T x ~ x ~+[ A B ( x ~- ~
2
+) C(X,
- ~ 2 ) * ]
(1)
where x, and x2 are the liquid-phase compositions, in mole fraction, of xenon and ethene, respectively. Calculations were referred to zero pressure, and A , B, and C are constants obtained by a least-squares fitting to the vapor pressures. In Table 111 these constants are given for each isotherm, together with the rootmean-square deviation between calculated and experimental ( 6 ) Calado, J . C. G.;Chang, E.; Streett, W. 9. Physicu A 1983, 1 1 7 , 127. (7) Dtmond, J.; Smith, E. 9. “The Virial Coefficients of Pure Gases and
Mixtures , Clarendon Press: Oxford, 1980. (8) Caligaris, R. E.; Henderson, D. Mol. Phys. 1975, 30, 1853. (9) Streett, W. 9.;Sagan, L. S.; Staveley, L. A. K. J . Chem. Thermodyn. 1973, 5, 633.
(IO) McCarty, R. D.; Jacobsen, R. T. NBS Technical Nore 1045, National Bureau of Standards, Boulder, CO, 1981.
Vapor-Liquid Equilibrium in Xenon
+ Ethene
The Journal of Physical Chemistry, Vol. 90, No. 6, 1986 1149 2
t
I
I
I
I
I
I
I
/I
-I 5'8
I
/.I
I
5.6
-1
c /
5.4
It
5.2
5.0 282
I
-l
-2
1 284
I
.,
I 286
T/ K
I
I
I
288
I
P'"
i I
290
+
Figure 3. P , T projection of the critical locus for xenon ethene mixtures: m, pure components: experimental critical points of the mixtures.
gas-phase compositions, and GE(x=0.5), the value of the excess Gibbs energy for the equimolar liquid mixture. Table I1 includes the (p, T, x) vapor-liquid critical values obtained in this work, using the same procedure of visual detection of the critical point as for xenon + ethane mixtures.2 In Figure 3, we plot the temperature-pressure projection of the mixture critical locus. As stated above, this curve has a minimum in temperature. The isotherm at 282.00 K is continuous and does not intercept the critical curve, but the isotherm at 282.08 K does and has two critical points (see Figure 2). The minimum must therefore lie between these two temperatures. We estimate its coordinates to be 282.04 K, 5.14 MPa, and 0.18 mole fraction in Xe. The isotherm at 282.25 K is still below the critical temperature of ethene (282.34 K) and also exhibits two critical points: one on the ethene-rich side and the other one on the xenon-rich side. The azeotropic line is shown in Figures 1 and 2. For each of the lower eight isotherms the azeotropic composition was calculated from eq 1, with the parameters of Table 111, by solving for x = y . The results are given in Table IV. The azeotrope locus is a linear function of pressure above 244 K but curves to the xenon-rich side at lower temperatures, as seen in Figure 1. Graphical extrapolation gives the interception with the critical line at 283.2 K, 5.35 MPa, and 0.497 mole fraction in Xe.
Discussion and Comparison with Other Results The vapor pressures of pure xenon and pure ethene obtained in this work, and reported in Tables I and 11, are compared in Figure 4 with the results of Theeuwes and Bearman" for xenon and with values calculated following McCarty and Jacobsenlo for ethene. The agreement is excellent for both substances. The thermodynamic consistency of our subcritical VLE results was checked by analysis of the differences between experimental vapor-phase composition and those calculated by Barker's method. The root-mean-square deviations given in Table I11 for all isotherms are lower than 0.01 mole fraction. However, at the lower temperatures, where measurements were performed in the lowtemperature apparatus, the calculated vapor compositions are systematically further apart from the liquid compositions than the experimental values, that is, the calculated isotherms are ( 1 1 ) Theeuwes, F.; Bearman, R. J . J . Chem. Thermodyn. 1970, 2, 507.
0.1
I
1
I 4
5
I 6
lo3 K/T
Figure 5. Equimolar excess Gibbs energies divided by temperature as a function of inverse temperature: a, this work; B, Calado and so are^.^ The solid line represents a least-squares fitting (excluding points at 203.03 and 250.16 K). The dashed line corresponds to the critical temperature of ethene.
slightly but discernibly wider than the experimental ones. On the contrary, there is no systematic trend of this kind for the isotherms above 265 K obtained in the "high-temperature" apparatus. Since the magnetic circulation pump is located much further from the equilibrium cell in apparatus I than in apparatus 11, the longer vapor circulation loop in apparatus I may slow down the attainment of equilibrium. Lower temperatures and pressures also contribute to greater difficulty for the phases to reach equilibrium. However, this kind of discrepancy has also been found in other vapor-liquid equilibrium studies conducted in both apparatuses, at lower or higher temperatures.61'2 It could, to a certain extent, reflect the inability of the virial equation of state, truncated after the third term (as used in our Barker's method calculations), to accurately describe the imperfection of the vapor phase. The calculations are particularly sensitive in a case like the present one, when the compositions of the liquid and vapor phases in equilibrium are very similar. Consistency between VLE results at different temperatures is best assessed through comparison of excess Gibbs energies. In Figure 5 we plot the equimolar GE (calculated from Barker's method, as described above), divided by temperature, as a function of inverse temperature. The slope of the G E / Tvs. 1/ T curve gives the excess enthalpy H E at each temperature. The overall picture is one of very good agreement between the two sets of results (the present one and that of ref 3) and of good internal consistency of our results, although GE(x=0.5)values corresponding to the temperatures of 203.03 and 250.16 K seem to be slightly too high. (12) Pozo, M. E.;Zollweg, J. A,; Calado, J . C. G.; Streett, W. B., to be submitted for publication.
Nunes da Ponte et al.
1150 The Journal of Physical Chemistry, Vol. 90, No. 6, 1986
TABLE I: Experimental p , T , x, y Vapor-Liquid Equilibrium Results at Temperatures below the Minimum in the Critical Curve PlMPa XXe Yx e Y - YCalJ PlMPa Xxe Yxe Y - Ycalcd’ T = 262.18 K T = 203.03 K 0.0482 0.0525 -0.001 4 3.2026 0.0000 0.0000 0.5 154 0.1822 0.1932 -0.001 7 3.2799 -0.0127 0.2527 0.2906 0.5709 0.3534 0.3618 -0.0018 3.3454 -0.0061 0.4301 0.4632 0.5916 0.3725 0.3807 -0.001 3 3.3509 -0.0064 0.5 134 0.5355 0.5992 0.3830 0.3914 -0.0007 3.3529 -0.0085 0.5727 0.5841 0.6033 0.4661 0.47 10 -0.0002 3.3640 -0.00047 0.6412 0.6460 0.6054 0.5007 0.5043 0.0003 3.3681 -0.0019 0.6934 0.6934 0.6054 0.5384 0.5409 0.001 2 0.0103 3.3702 0.7987 0.7983 0.6047 0.5918 0.5916 0.0013 0.0000 3.3702 0.9034 0.8892 0.5964 0.6045 0.6037 0.0014 3.3702 1 .oooo 1.oooo 0.5834 0.7726 0.7645 0.0004 3.3419 T = 224.03 K 0.8408 0.8397 0.0079 3.3219 0.0000 0.0000 1.0942 0.9343 0.9336 0.0052 3.2826 0.0065 0.3277 0.3638 1.1914 1 .oooo 1 .oooo 3.2419 -0.0048 0.5802 0.5838 1.2190 T = 269.54 K -0.0030 0.6400 0.6395 1.2231 0.1166 0.1229 0.0016 0.00 14 3.8438 0.7171 0.7 142 1.223 1 0.1545 0.1631 0.002 1 0.0038 3.8680 0.7694 0.7654 1.2204 0.2214 0.23 18 0.0014 3.9028 0.0080 0.8242 0.8221 1.2135 -0.0008 0.2770 0.2862 3.9269 T = 238.00 K 0.3483 0.3580 0.0001 3.9524 1.6754 0.0000 0.0000 0.3702 0.3776 -0.001 8 3.9593 -0.0182 0.2058 0.21 19 1.7582 0.4653 0.4698 -0.0010 3.9780 -0.01 77 0.4143 0.4175 1.8113 0.4993 0.5015 -0.001 5 3.9814 -0.0064 0.5006 0.508 1 1.8340 0.5482 0.5485 -0.0006 3.9831 -0.0043 0.5675 0.5707 1.8375 0.651 1 0.6495 0.0033 3.9762 -0.0005 0.6255 0.6268 1.8409 0.6763 0.6721 0.0019 3.9731 0.0031 0.7050 0.7029 1.8388 0.7343 0.7290 0.0028 3.9593 0.0078 0.7515 0.7509 1.8299 0.8081 0.7936 -0.0055 3.9362 0.0041 0.8 158 0.8088 1.8216 0.9070 0.9022 0.0016 3.8852 0.0091 0.9014 0.9003 1.8113 1.oooo 1 .oooo 3.8249 T = 250.16 K T = 274.67 K 0.0000 0.0000 2.3401 0.0000 0.0000 4.2417 -0.0085 0.0883 0.09 I9 2.3884 0.1612 0.1679 0.0007 4.3568 -0.0079 0.4478 0.4543 2.5380 0,2771 0.2822 -0.0016 4.4134 -0.0071 0.5085 0.5097 2.5476 0.4426 0.4467 0.0005 4.4513 -0.0046 0.5413 0.5415 2.5556 0.4702 0.4720 -0.00 I O 4.4602 -0.0005 0.5834 0.5833 2.5566 0.5305 0.5300 -0.001 2 4.4623 0.006 1 0.6416 0.6423 2.5552 0.6608 0.6577 0.001 1 4.4485 0.004 1 0.7424 0.7341 2.5331 0.6985 0.6856 -0.0075 4.4402 0.001 1 0.901 1 0.8916 2.4828 0.7845 0.7752 -0.001 8 4.4078 1 .oooo 1 .oooo 2.4352 -0.001 8 0.8461 0.8366 4.3789 T = 281.12 K 0.0437 0.0457 0.1855 0.1887 0.2846 0.2867 0.4318 0.4324 0.5683 0.5602 0.6309 0.6266 0.7168 0.7039 0.7961 0.7894
4.9553 5.0539 5.1021 5.1366 5.1366 5.1249 5.0994 5.0615 ayca,cd is the
-0.0006 -0.0021 -0.0023 -0.0009 -0.0064 -0.00 1 2 -0.008 1 -0.00 10
gas-phase mole fraction, calculated by Barker’s method.
The linearity of the plot in Figure 5 indicates that HE changes very little with temperature. A least-squares straight line through all points, except those corresponding to 203.03 and 250.16 K, gives @(x=0.5) = 280 J mol-I. This leads to positive values for the equimolar excess entropy SE(x=0.5),in contrast with what Calado et al. have found for xenon-ethane mixtures, where SE(x=0.5) is negative at the triple point temperature of xenon (161.39 K). This is just another of the surprising differences in thermodynamic behavior of the xenon ethene and xenon + ethane systems. It could be said that, while xenon + ethane mixtures behave in an “abnormal” way, different from any other simple mixture studied to date, the xenon ethene system is more and SEat low temperatures. ”normal”, showing positive GE, HE, Figure 5 shows a curious feature: the GE/Tvs. l/Tplot remains linear up to very close to the critical temperature of ethene. The characteristic shape of this type of plot for simple liquid m i x t ~ r e s ’ ~
+ +
(13) Calado, J . C. G.; Guedes, H. J.
R.; Nunes da Ponte, M.; Streett, W.
B. Fluid Phase Equilib. 1984, 16, 185.
is one where the curves goes through a minimum and then G E / T increases as the critical temperature of the more volatile component is approached. This, of course, corresponds to the equimolar excess enthalpy going through zero and becoming negative when temperature increases. Xenon ethene mixtures seem to deviate from this, p ( x = 0 . 5 ) being relatively unaffected by temperature, even at temperatures within 2 K of the critical temperature of ethene (282.34 K ) . Although this conclusion should be taken as tentative, because the precision of the calculation of GE from VLE data is lower at higher temperatures (as explained for xenon + ethane by Nunes da Ponte et aL2), it suggests that a complete calorimetric study of xenon + ethene mixtures should prove very interesting. The above-mentioned effect of temperature on the excess enthalpy of simple liquid mixtures is possibly a consequence of a situation whereby one of the components is approaching the critical point, and therefore becoming an expanded liquid, while the other, far from its critical state, is still a dense liquid. Xenon and ethene have very similar vapor pressure curves and critical temperatures
+
Vapor-Liquid Equilibrium in Xenon
+ Ethene
The Journal of Physical Chemistry, Vol. 90, No. 6 , 1986 1151
TABLE 11: Experimental p , T , x, y Vapor-Liquid Equilibrium Results in the Critical Region
PlMPa
xxe
5.0022 5.1111 5.1132 5.1256 5.1366 5.1470 5.1608 5.1835 5.1959
Yxe
T = 282.00 K 0.0000
0.0000
0.1319 0.1356 0.1556 0.1746 0.1935 0.227 1 0.2762 0.3078
0.1330 0.1381 0.1571 0.1762 0.1946 0.2293 0.2783 0.3008
Ethene-Rich Branch 0.0000
0.0000
0.0388 0.1036
0.0451 0.1048 (critical)
0.110
Xenon-Rich Branch 1.oooo
4.9946 5.0622 5.1297 5.1904 5.2311 5.2373 5.2366 5.2297 5.2235 5.2104 5.2055 5.1925 5.1794 5.177
0.9324 0.8370 0.7181 0.5959 0.5169 0.4633 0.4207 0.3766 0.3253 0.3118 0.2753 0.2544 0.248
1.oooo 0.9250 0.8321 0.7096 0.5880 0.5166 0.4633 0.4220 0.3805 0.3276 0.3141 0.278 1 0.2563 (critical)
T = 282.25 K
Ethene-Rich Branch 5.0298 5.0415 5.0635 5.066 5.2001 5.2407 5.2511 5.2545 5.2545 5.2497 5.2442 5.2366 5.226
0.0000
0.0000
0.0175 0.0408 0.044
0.0175 0.0408 (critical)
Xenon-Rich Branch 0.7423 0.6295 0.5788 0.5299 0.4940 0.4116 0.3817 0.3483 0.319
0.7364 0.6271 0.5767 0.5299 0.4940 0.41 18 0.3832 0.3495 (critical)
TABLE 111: Parameters of Eq 1, Root-Mean-Square Deviations between Experimental and Calculated Gas Compositions, and Equimolar Excess Gibbs Energies for Xenon Ethene Liquid Mixtures, Calculated from Barker’s Method A B C G€,,*/J m o P TI K UY
+
203.03 224.03 238.00 250.16 262.18 269.54 274.67 281.12
0.2994 0.2021 0.1715 0.1714 0.1.169 0.1026 0.0875 0.0770
0.0252 0.0058 0.0317 0.0250 0.0041
0.0121 0.0002 0.0025
0.034 0.01 1
-0.009 -0.038 0.007 -0.003
0.005 0.012
0.0074 0.0051 0.0099 0.0057 0.0028 0.0021 0.0031 0.0039
126.3 94.1 84.8 89.1 63.7 57.5 50.0 45.0
that are only 7 K apart. As temperature increases the effect of the closing in on the critical temperature of ethene is possibly cancelled out by xenon also getting close to its critical temperature, resulting in no net effect on HE. As for the higher temperature isotherms, the detailed study of the critical region of xenon ethene mixtures was made possible by the high sensitivity of the pressure and composition measuring systems and by the use of a transparent cell. The mixture critical points obtained in this work fall on a smooth curve, as shown in
+
xx.
YW,
T = 282.61 K
T = 282.08 K
5.0104 5.0470 5.0966 5.101
PlMPa 5.0477 5.1221 5.2269 5.2697 5.2959 5.2973 5.2973 5.2945 5.2938 5.293
1 .oooo
1 .oooo
0.9302 0.7778 0.6820 0.5422 0.5081 0.4564 0.4258 0.4244 0.418
0.9269 0.7738 0.6794 0.5422 0.508 1 0.4569 0.4265 0.4244 (critical)
5.1952 5.2566 5.3152 5.3469 5.3552 5.3600 5.3593 5.3614 5.361
T = 283.17 K 0.9061 0.8206 0.7077 0.621 1 0.5739 0.5370 0.5302 0.5 I70 0.504
0.9022 0.8 124 0.7046 0.6205 0.5746 0.5370 0.5305 0.5 170 (critical)
T = 284.20 K
5.3207 5.3883 5.4234 5.4496 5.4648 5.470
0.8963 0.8036 0.7421 0.6904 0.6430 0.625
0.8925 0.8004 0.7394 0.6882 0.6430 (critical)
T = 285.19 K
5.4165 5.4517 5.5020 5.5386 5.544
0.9051 0.8603 0.7816 0.7175 0.705
0.8987 0.8524 0.7789 0.7161 (critical)
T = 286.19 K
5.4317 5.5000 5.5558 5.5986 5.61I7 5.617
.oooo
1
1 .oooo
0.9319 0.8663 0.8086 0.7892 0.776
0.9299 0.8636 0.8059 0.7848 (critical)
T = 287.18 K
5.5420 5.5607 5.6199 5.6682 5.6772 5.685
1.oooo
1.oooo 0.9847 0.9241 0.8681 0.8578 (critical)
0.9852 0.9261 0.8699 0.8592 0.845
TABLE IV: Azeotrope Compositions, Calculated from Eq 1 with the Parameters of Table 111, by Solving for x = y
TIK
XXe
203.03 224.03 238.00 250.16
0.7069 0.6665 0.6451 0.5868
T/K 262.18 269.54 274.67 281.12
XXe
0.5630 0.5631 0.5485 0.4960
Figures 2 and 3, and temperature-composition cross plots show good internal consistency of the data. There are no other published results to compare our data with, and the lack of experimental volumetric data on xenon ethene made it unadvisable to try to perform any thermodynamic consistency tests at these temperatures. However, other systems have been studied where a positive azeotrope merges with the mixture critical curve, resulting in a minimum in temperature in this curve. Examples of such behavior are the CO, C2H4and CO, + CzH6 systems (see Fredenslund et al.I4 for a list of publications on these systems).
+
+
(14) Fredenslund, A.; Mollerup, J. J. Chem. SOC., Faraday Trans. 1 1974, 70, 1653.
J. Phys. Chem. 1986, 90, 1152-1 155
1152
The current set of results should provide a demanding test of modern statistical theories of liquid mixtures. Perturbation theory was successfully used by Clancy, Gubbins, and Gray15 to predict the excess Gibbs energies and the excess volumes of xenon ethene at the triple point temperature of xenon. This theory has also proved successful for ethane ethene rnixturesl6 but failed for xenon ethane.2 This seems to indicate that, in order to simultaneously account for the properties of the xenon + ethene and the xenon + ethane systems, a perturbation theory will have to use a nonspherical reference system. A promising scheme is
Acknowledgment. This work was supported by Grant No. CPE-8 104708 from the National Science Foundation. M.N.P. thanks the Council for International Exchange of Scholars and JNICT-INVOTAN (Portugal) for grants. Registry No. Xe, 7440-63-3; ethene, 74-85-1.
(15) Clancy, P.; Gubbins, K. E.; Gray, C. J. Discuss. Faraday SOC.1978, 66, 116. (16) Calado, J. C. G.; Azevedo, E. J. S. G.; Clancy, P.; Gubbins, K. E. J . Chem. Soc., Faraday Trans. 1 1983, 79, 2657.
( 1 7) Azevedo, E. J. S.G.; Lobo, L. Q.; Staveley, L. A. K.; Clancy. P. Fluid Phase Equilib. 1982, 9, 267. ( 1 8 ) Fischer, J.; Lago, S.; Lustig, S . ; Bohn, M. to be submitted for publication.
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the perturbated hard-sphere treatment of Azevedo et a].” A more elaborate procedure that gave good results for xenon ethane at the lower temperatures is the Boltzmann averaging perturbation theory of Fisher et al.’*
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CHEMICAL KINETICS Thermodynamic and Kinetic Properties of the Cyclohexadienyl Radical W. Tsang Chemical Kinetics Division, National Bureau of Standards, Gaithersburg, Maryland 20899 (Received: January 28, 1985; In Final Form: October 7, 1985)
The experimental data on cyclohexadienyl (1,3-cyclohexadien-5-y1)radical decomposition have been examined. In combination with an estimated entropy for cyclohexadienyl of 375 f 7 J/(K mol) at 550 K, and the measured rates of hydrogen addition to benzene and the reverse we find the heat of formation of cyclohexadienyl to be 209 f 5 kJ/mol (300 K j . This leads to exp(-13100 & 700/7‘)/s in the vicinity of 550 K. The HC-H bond energy k(cyclohexadieny1- benzene + H) = 1013,3”0,6 in cyclohexadiene is 318 kJ, leading to a resonance energy of 96 kJ. The second-orderdisappearance rate of cyclohexadienyl radical at 425 K has been found to be 7 X lo-” cm3/(molecule s). This is in excellent agreement with direct measurements at room temperature.
Introduction Recently, Nicovich and Ravishankaral published the results of a study on the reactions of hydrogen atoms with benzene. From the temperature region where hydrogen atom decay was nonexponential they found the rate expression for cyclohexadienyl (1,3-cyclohexadien-5-y1 and related forms) decomposition to be
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k(cyclohexadieny1
benzene + H ) = 1.3 X 10l6 exp(-16700 f 3900/T)/s
In combination with the rate expression for the reverse reaction cyclohexadienyl) = k(benzene H 6.7 X lo-’’ exp(-2170/p cm3/(molecule s)
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they obtained equilibrium constants whose temperature dependence was such that a heat of formation for cyclohexadienylradical of 191.2 f 11.7 kJ/mol (298 K) was derived. This is in satisfactory agreement with the recommendation of McMillen and Golden2 for a heat of formation for cyclohexadienyl of 196.6 f 2 1 kJ/mol. Earlier, Benson and co-workers3recommended values ( 1 ) Nicovich, J. M.; Ravishankara, A. R. J . Phys. Chem. 1984, 88, 2534.
(2) McMillen, D. F.; Golden, D. M. In “Annual Reviews of Physical Chemistry”; Rabinovitch, B. S.. Ed.; Annual Reviews: Palo Alto, CA, 1982; 493. (3) (a) Benson, S. W. “Thermochemical Kinetics”, 2nd Ed.; Wiley: New York, 1976. (b) Shaw, R.; Cruickshank, F. R.; Benson, S. W. J . Phys. Chem. 1961, 71. 4538.
in the 184-209 kJ/mol range. The experimental results of James and Suart4 yield
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k(cyclohexadieny1 benzene H) /k’’2(2cyclohexadienyl combination and disproportionation products) = exp(-15710 f 2370/T) (molecules/(cm3 S))I/~ Combining this with the results of Sauer and Ward5 leads to a decomposition rate of 10*6.0 exp(-15710/T)/s. On this basis they recommend a heat of formation of cyclohexadienylof 184 kJ/mol. These are very difficult experiments. Although the similarities in rate expressions may lead to the conclusion that the results support each other, examination of Figure 1 shows that there are gross disagreements in extrapolated absolute rates if we take the rate expressions at face value. However, the experimental rate expressions are highly uncertain. Note that the 32-kJ uncertainty in the activation energy from the results of Nicovich and Ravishankaral implies an uncertainty in the A factor of a factor of 1000. Of interest is the extraordinarily high A factor for unimolecular decomposition. This would suggest “loose” complexes and are much different from the “normal” complexes for alkyl radical decomposition.6 In this note we present an alternative treatment of the data. We begin by showing the consequences (4) James, D. G. L.; Suart, R. D. Trans. Faraday Soc. 1968, 64, 2752.
(5) Sauer, M. C.; Ward, B. J . Phys. Chem. 1967, 71, 3971. (6) O’Neal, H. E.; Benson, S.W. In “Free Radicals”; Kochi, J. K., Ed.; Wiley: New York, 1973; Vol. 2, p 272.
This article not subject to U S . Copyright. Published 1986 by the American Chemical Society
