10936
J. Phys. Chem. B 2001, 105, 10936-10941
Liquid Mixtures Involving Cyclic Molecules. 2: Xenon + Cyclobutane Luı´s F. G. Martins, Eduardo J. M. Filipe, and Jorge C. G. Calado* Centro de Quı´mica Estrutural, Instituto Superior Te´ cnico,1049-001 Lisboa, Portugal ReceiVed: February 21, 2001; In Final Form: July 24, 2001
The total vapor pressure of liquid mixtures of xenon and cyclobutane has been measured at 182.34 K (the triple point of dinitrogen oxide) and at 195.49 K (the triple point of ammonia), as a function of composition. The mixtures show small positive deviations from Raoult’s law at both temperatures. The liquid densities were also measured at 182.34 K. Both the excess molar Gibbs energy (GmE) and the excess molar volume (VmE) were calculated from the experimental data. For the equimolar mixture GmE ) 9.9 J mol-1 at 182.34 K, GmE ) 24.0 J mol-1 at 195.49 K, and VmE ) -1.077 cm3 mol-1 at 182.34 K. The excess molar enthalpy (HmE) was estimated from the temperature dependence of GmE and found to be -185 J mol-1. The results were interpreted by using the statistical association fluid theory and compared with those for the linear analogue system (xenon + n-butane).
1. Introduction As part of a project to assess the influence of molecular shape on the thermodynamic behavior of liquid mixtures, we have undertaken a detailed investigation of the excess properties of binary mixtures involving small cyclic molecules. Phase equilibria studies and density measurements of the systems (xenon + cyclopropane)1 and (xenon + ethylene oxide)2 as well as those containing their noncyclic analogues (xenon + propane)3 and (xenon + dimethyl ether)4 have already been reported. These systems display a wide variety of behaviors, from a slightly negative molar excess Gibbs energy, GmE, to liquid-liquid immiscibility. The experimental results show that the mixture containing the cyclic component always exhibits larger positive deviations from Raoult’s law (and consequently larger values of GmE) than those occurring with their noncyclic analogues. Systematic studies involving the higher cycloalkanes,5,6 C5-C10, have shown that, as a rule, these molecules behave as quasispherical ones and can act as structure breakers when mixed with linear alkanes. This is reflected, for instance, in positive values for the excess molar volumes. However, mixtures with cyclopentane are an exception to this rule, for they exhibit smaller (negative) excess enthalpies and entropies than those corresponding to the higher cycloalkanes. To explain this, Patterson suggested the occurrence of what he called a “condensation effect”: the cyclopentane molecule would have a tendency to “condense” onto rigid, highly branched or platelike molecules (such as 3,3-diethylpentane and substituted cyclohexanes, respectively), resulting in negative contributions to HmE. This condensation effect results in a restriction of the molecular motion, thermodynamically equivalent to the creation of order in the liquid, and therefore contributing negatively to SmE and positively to CpmE. This behavior was attributed to the platelike molecular structure of cyclopentane, whereas the higher cycloalkanes are more globular. The anisotropic field around the cyclopentane molecule is believed to favor its “condensation”, hindering rotation. In a recent study1 we found that the excess functions for the (xenon + cyclopropane) mixture correlate well with those of mixtures involving cyclopentane. It thus seems that the “condensation” effect can extend to cyclic molecules with a number
of carbon atoms smaller than the initial five. To confirm this, we have undertaken the present study with the (xenon + cyclobutane) mixtures. As far as we are aware, no other work has been performed on this system. However, a similar investigation of mixtures of xenon with n-butane, the linear analogue of cyclobutane, has been reported recently.7 In the past few years, we have successfully used the statistical association fluid theory with hard spheres (SAFT-HS) equation of state for chain molecules of hard spheres and its extension to ring molecules to calculate phase diagrams for model mixtures of types (m1-sphere chain + m2-sphere chain) and (m1-sphere chain + m2-sphere ring). The influence of chain/ring length, relative sphere size, relative mean field attraction, and reduced temperature were investigated.8 The available experimental results confirm the trends predicted by the theory for the effect of a cyclic structure on the phase behavior of binary mixtures. The same theoretical approach was used in this work to interpret the experimental results. 2. Experimental Section The techniques used to measure the saturation vapor pressures and orthobaric densities have already been described.9 A triplepoint cryostat was used, the working temperatures being 182.34 K (the triple point of nitrous oxide) and 195.49 K (the triple point of ammonia). The mixtures were prepared by condensing known amounts of each component into a calibrated pyknometer. The vapor pressures were measured by using a quartzspiral gauge (Texas Instruments, model PPG 149) with 500kPa full range and a resolution of 2 Pa, which had been calibrated against a dead-weight gauge. The pyknometer used for the density determinations was calibrated at 182.34 K by filling it with liquid ethane and finding the volume from the data of Haynes and Hiza10 [Vpyk ) (2.1995 ( 0.0002) cm3]. The amount of substance of each component was calculated from pVT measurements. The pressures were measured with a second quartz-spiral manometer (Texas Instruments, model 145) with 130-kPa full range and a resolution of 0.5 Pa, which had been calibrated against mercury manometers. Xenon (from Linde, mole fraction: 0.9999), nitrous oxide, and ammonia (from Air Liquide, mole fraction: 0.999) were
10.1021/jp010676w CCC: $20.00 © 2001 American Chemical Society Published on Web 10/13/2001
Liquid Mixtures Involving Cyclic Molecules further purified by fractionation in a low-temperature column. The final purity of the samples was checked by measuring the constancy of the triple point during melting. The triple-point pressure of xenon was (81.669 ( 0.020) kPa [compared with (81.674 ( 0.011) kPa11]. The measured triple-point pressures of the cryostatic fluids also compare favorably with the literature values: (6.093 ( 0.004) kPa for ammonia [(6.080 ( 0.003) kPa11] and (87.869 ( 0.008) kPa for nitrous oxide [(87.865 ( 0.012) kPa11]. The values of the vapor pressure and molar volume of pure components at the working temperatures provide a further check on the purity of the gases. In xenon the vapor pressure was 248.19 kPa at 182.34 K (compared with 248.24 kPa12) and 436.79 kPa at 195.49 K (compared with 436.82 kPa13), whereas the average value of six determinations obtained for the molar volume at 182.34 K was (46.480 ( 0.009) cm3 mol-1 (compared with 46.485 cm3 mol-1 14). Cyclobutane was synthesized after the procedure of Wiberg et al.15,16 and Connor et al.17 by reacting 1,4-dibromobutane with lithium. Lithium amalgam (502.5 g), previously prepared by mixing 2.5 g of lithium (from Riedel de Ha¨en, 99.5% purity) and 500 g of mercury, was placed in a three-necked flask fitted with an inlet tube, dropping funnel, and an outlet tube leading to reflux condenser and a cold trap. Dried 1,4-dioxane (150 cm3) (from Merck, 99% purity) was added to the flask and a mixture formed by 12 cm3 of 1,4-dibromobutane (from Aldrich, 99% purity) and 30 cm3 of dried 1,4-dioxane placed in the dropping funnel. The flask was then heated to the boiling point of 1,4dioxane, which refluxes in the condenser, whereas the solution of 1,4-dibromobutane in 1,4-dioxane was slowly added during 3 h. The cyclobutane formed is driven to a trap cooled with liquid nitrogen and stored. The reaction and the preparation of reactants were performed in an inert gas atmosphere to prevent contamination. Cyclobutane was purified by fractionation in a low-temperature column. The triple-point pressure of cyclobutane is too low (179.39 Pa) to be measured with sufficient accuracy in our apparatus. The purity was checked by proton nuclear magnetic resonance spectroscopy and by the value of its vapor pressure at 195.49 K, which was found to be 0.725 kPa. This value compares well with a correlation obtained from the determinations of Heisig,18 Benson,19 and Rathjens and Gwinn20 (0.714 kPa). As usual, the nonideality of the vapor phase was taken into account in the calculations of the phase compositions. Because the pressures never rise above 450 kPa, second virial coefficients should be enough. At room temperature, these were taken from Dymond and Smith21 both for xenon and cyclobutane. At low temperatures, second virial coefficients were estimated from the correlation of Leland and Chappelaar22 for cyclobutane, and taken from Brewer23 for xenon. The values obtained for cyclobutane were B ) -4651 cm3 mol-1 at 182.34 K, B ) -3221 cm3 mol-1 at 195.49 K, and B ) -680 cm3 mol-1 at 298.15 K. For xenon, these values have already been given elsewhere.12 The cross virial coefficients were estimated with the correlation of Van Ness and Abbott, as discussed by Prausnitz et al.24 (B12 ) -821 cm3 mol-1 at 182.34 K, B12 ) -705 cm3 mol-1 at 195.49 K, and B12 ) -291 cm3 mol-1 at 298.15 K). 3. Results The total vapor pressures, p, for (xenon + cyclobutane) mixtures at 182.34 and 195.49 K are recorded in Table 1 and plotted in Figure 2 as a function of the liquid mole fraction of xenon, x. At 182.34 K the vapor pressure of pure cyclobutane
J. Phys. Chem. B, Vol. 105, No. 44, 2001 10937 TABLE 1: Total Vapor Pressure p and Excess Molar Gibbs Energy (GmE) of Xenon + Cyclobutane at 182.34 and 195.49 Ka p (kPa)
δp (kPa)
GmE (J mol-1)
x
y
0 0.28747 0.47001 0.58991 0.74733 0.87728 0.92933 0.96764 1
0 0.99807 0.99910 0.99944 0.99971 0.99987 0.99993 0.99997 1
182.34 K 0.177 69.25 +0.039 115.09 0.16 145.85 +0.18 184.89 0.039 216.96 +0.0032 229.69 0.27 239.43 0.25 248.19
0 2.91 7.71 14.85 17.63 14.43 8.42 3.52 0
0 0.12816 0.22674 0.35831 0.47248 0.59424 0.71277 0.86780 1
0 0.98769 0.99369 0.99659 0.99782 0.99862 0.99914 0.99964 1
195.49 K 0.725 53.46 95.38 152.65 202.76 257.70 309.95 377.26 247.79
0 5.93 11.79 17.88 20.86 28.76 32.45 26.25 0
0.30 +0.20 +0.32 0.43 +0.0083 +0.084 +0.25 0
a
x and y are the liquid and the vapor phase mole fractions of xenon, respectively; δp are the pressure residuals
Figure 1. Vapor-liquid equilibrium for xenon + cyclobutane mixtures at: b, 182.34 K; 0, 195.49 K.
Figure 2. Excess molar Gibbs energy for xenon + cyclobutane mixtures: b, at 182.34 K; 0, at 195.49 K.
could not be determined experimentally because at this temperature cyclobutane has a tendency to condense in the pyknometer inlet tube. Furthermore, this temperature already lies 0.23 K below the triple-point temperature of cyclobutane. For the calculations we used the vapor pressure of the
10938 J. Phys. Chem. B, Vol. 105, No. 44, 2001
Martins et al.
TABLE 2: Molar Volumes (Vm) and Excess Molar Volumes (VmE) of Xenon + Cyclobutane Liquid Mixtures at 182.34 K and at Saturation Vapor Pressure x
Vm (cm3 mol-1)
VmE (cm3 mol-1)
δV (cm3 mol-1)
0 0.14604 0.40662 0.42203 0.58814 0.65859 0.70423 0.82659 1
(69.620) 66.331 59.308 58.970 54.915 53.373 52.324 49.959 46.480
0 0.0899 -0.903 -0.884 -1.095 -1.008 -1.001 -0.534 0
+0.0055 -0.045 +0.021 +0.029 +0.038 -0.056 +0.0026
a
V are the volume residuals, the difference between experimental and calculated (from eq 3) excess molar volumes.
owing to the low pressures involved, these corrections were, at most, 0.0003 cm3 mol-1, well within experimental error. The molar volume of pure cyclobutane, Vm (C4H8), could not be determined experimentally with our technique because the substance condenses in the pyknometer inlet tube, forming droplets and bubbles. It was estimated from the extrapolation of the measured values for the mixtures by:
Vm(C4H8) ) lim xf0
Vm - xVm(Xe) (1 - x)
(2)
where Vm is the molar volume of the mixture at composition x and Vm(Xe) is the molar volume of pure xenon. A value of (69.62 ( 0.13) cm3 mol-1 was obtained. A similar procedure applied to xenon leads to a value of (46.33 ( 0.43) cm3 mol-1, which compares well with the experimental value of (46.480 ( 0.009) cm3 mol-1. The excess molar volume results were fitted to a RedlichKister equation,
VmE (cm3 mol-1) ) x(1 - x)[D + E(1 - 2x) + F(1 - 2x)2] (3)
Figure 3. Excess molar volumes for xenon + cyclobutane mixtures at 182.34 K.
TABLE 3: Excess Molar Gibbs Energy (G1/2E) for Equimolar Mixtures of Xenon + Cyclobutane and Values of the Coefficients for Equation 1 at 182.34 and 195.49 K A
B
C
G1/2E (J mol-1)
182.34 K 0.026 ( 0.011 -0.056 ( 0.014 0.034 ( 0.016 9.9 ( 4.2 195.49 K -0.059 ( 0.0040 -0.066 ( 0.0055 0.053 ( 0.0082 24.0 ( 1.6
supercooled liquid, obtained from the correlation by Daubert et al.25 A value of 0.177 kPa was obtained. The xenon mole fractions in the vapor phase, y, were evaluated with use of Barker’s method26 which minimizes the pressure residuals δp ) p - pcalc. The GmE values were then calculated at zero pressure and fitted to a Redlich-Kister type equation,
GmE/RT ) x(1 - x)[A + B(1 - 2x) + C(1 - 2x)2] (1) The fitting parameters A, ,B and C together with their standard deviations and the values of excess molar Gibbs energy for the equimolar mixture, GmE (x ) 0.5), at both temperatures are recorded in Table 3. The GmE curves are shown in Figure 2. As can be seen, the vapor-liquid equilibrium data shows an almost ideal behavior at both temperatures, with very small positive deviations to Raoult’s law. This is reflected in the very small positive values of GmE, although the GmE(x) curve is fairly asymmetrical. From the temperature dependence of GmE, an average value of the excess molar enthalpy, HmE, could be estimated with the Gibbs-Helmholtz equation. For the equimolar mixture a value of -185 J mol-1 was obtained. The excess molar entropy is thus also negative, SmE ) -1.1 J mol-1. The orthobaric molar volumes, Vm, and excess molar volumes, VmE, of the same mixture at 182.34 K are given in Table 2. The VmE values were not corrected to zero pressure because,
where, as before, x is the liquid mole fraction of xenon. The calculated values of the coefficients are: D ) (-4.31 ( 0.25) cm3 mol-1, E ) (2.93 ( 0.61) cm3 mol-1 and F ) (5.81 ( 0.92) cm3 mol-1. The molar volume residuals, δV ) VmE VmE(calc), are also given in Table 2. The experimental and fitted VmE results are presented in Figure 3. The (xenon + cyclobutane) mixtures show large negative excess volumes and a S-shaped VmE(x) curve, with the minimum displaced toward the more volatile component. For the equimolar mixture, VmE(x ) 0.5) ) (-1.077 ( 0.063) cm3 mol-1. 4. Discussion The excess properties of the equimolar mixtures of (xenon + cyclobutane) are compared with those of the (xenon + n-butane)7 mixtures in Table 4. For the sake of generalization, the corresponding values for the (xenon + propane)3 and the (xenon + cyclopropane)1 were also included. Whereas the (xenon + n-butane) system follows the usual behavior of the xenon + n-alkane mixtures (small negative GmE and VmE, and positive HmE), the case of cyclobutane, as well as that of cyclopropane, is entirely different. Although there is an increase in GmE relative to that for the xenon + n-butane mixture, HmE and SmE are now both negative. This suggests a stronger interaction between xenon and the cyclic molecule, as well as an ordering of the liquid mixture at the molecular level. Also, VmE is now much more negative. However, the excess molar volume is very sensitive to high-density packing, which makes the assessment of the relative importance of different contributions extremely difficult. Apparently, both the (xenon + cyclobutane) and (xenon + cyclopropane) mixtures follow the trend found by Patterson et al. for mixtures involving cyclopentane. Patterson’s “condensation effect” can thus be extended to smaller cyclic molecules. Unlike the higher cycloalkanes, these molecules are oblate (platelike), anisotropic rotors, a shape that seems to favor the interaction with the xenon atom (and other large molecules). Such an interaction acts as a restricting factor in what rotation is concerned, bringing order to the mixture. This shape effect should be more pronounced as the number of carbon atoms decreases, because in cyclobutane and cyclopropane the CH2 groups lie in a much more rigid eclipsed conformation,
Liquid Mixtures Involving Cyclic Molecules
J. Phys. Chem. B, Vol. 105, No. 44, 2001 10939 5. Theory
Figure 4. Vapor-liquid equilibrium at 182.34 K for: (a) xenon + n-butane mixtures; data points are experimental results and the solid line is the SAFT-HS prediction for chain molecules; (b) data points are experimental results for xenon + cyclobutane mixtures; the solid line is the SAFT-HS prediction for xenon + n-butane using the ring term (eq 9) for cyclic molecules.
TABLE 4: Excess Molar Functions for the Equimolar Mixtures of (Xenon + Propane), (Xenon + n-Butane), (Xenon + Cyclopropane), and (Xenon + Cyclobutane) at 182.34 K E
E
system
G1/2 (J mol-1)
H1/2 (J mol-1)
V1/2E (cm3 mol-1)
xenon + propane xenon + n-butane xenon + cyclopropane xenon + cyclobutane
-32.8 -47.6 124.1 9.9
142 17 -168 -185
-0.308* -0.806 -0.758 -1.077
*At 161.40 K.
whereas cyclopentane still shows considerable conformational changes. Mixtures of xenon and cyclopentane are currently being studied. Finally, it should be noted that a change in molecular shape always implies other structural modifications. The observed thermodynamic behavior cannot be exclusively ascribed to cyclization alone, because there is simultaneous modification of other chemical features, namely: (i) the cyclic molecule has two fewer hydrogen atoms; (ii) in small cyclic molecules, the distortion of the bond angles causes a large strain that pushes the electronic density out of the ring, a distortion which, no doubt, will interfere with the hydrogen atoms. The interaction energy between groups is thus likely to be different from the corresponding one in noncyclic molecules. Any attempt to separate the various contributions and quantitatively assess the effect of each individual factor is, however, difficult to conceive.
A wide variety of binary systems, involving either linear, branched or cyclic alkanes with xenon, have been investigated in our laboratory. In what concerns the interpretation of the results, it is advisable to apply the same theoretical approach to the various systems. Comparisons can then be made directly between mixtures, and the effects of chain length, cyclization, etc easily assessed. Given the nature of the systems involved the obvious candidate is the SAFT-HS, based on a string model of hard spheres, and which has already been extended to ring molecules.27 Our aim is to assess, in a quantitative way, the effect of substituting, in a binary mixture, a cyclic molecule for the corresponding linear one. We have thus modeled the phase diagram for the (xenon + n-butane) mixture by using the SAFTHS theory for linear molecules and then repeated that same calculation with the expressions for cyclic molecules, while keeping the pure component parameters of n-butane. With this approach the theoretical results should be a direct consequence of changes in molecular shape. At this point it is convenient to summarize the main features of the theory. (For further details the reader should refer to the original papers of the theory.28,29) In the SAFT-HS approach, molecules are described with a simple united-atom model: m hard-sphere segments of equal diameter σ are bonded tangentially to form either a chain or a ring. An attractive interaction is then added to the system, usually a van der Waals meanfield term with an integrated interaction energy of a associated with each segment. The Helmholtz free energy A of an n-component mixture of associating chain or ring-like molecules can be separated into several contributions, as follows
Aideal Ahs Achain/ring Aassoc Amf A ) + + + + NkT NkT NkT NkT NkT NkT
(4)
where N, T, and k are the total number of molecules, temperature, and Boltzmann constant, respectively. The ideal contribution to the free energy is given by30
Aideal NkT
n
xilnFiΛi3) - 1 ∑ i)1
)(
(5)
The sum is over all species i of the mixture, xi ) Ni/N is the mole fraction, Fi ) Ni/V the number density, Ni the number of molecules of species i, Λi the corresponding thermal de Broglie wavelength, and V the volume of the system. For the reference hard-sphere contribution, an expression attributable to Boublı´k31 (equivalent to that of Mansoori et al.32) for a multicomponent mixture of hard spheres has been used, i.e.,
[( )
]
3 3ζ1ζ2 ζ23 Ahs 6 ζ2 - ζ0 ln(1 - ζ3) + + ) NkT πF ζ 2 (1 - ζ3) ζ3(1 - ζ3)2 3 (6)
where F ) N/V is the total number density of the mixture and the reduced densities ζl are defined as
ζl )
πF n [ ximi(σi)l] 6 i)1
∑
(7)
ζ3 ) η is the overall packing fraction of the mixture, and mi is the number and σi the diameter of spherical segments of chain
10940 J. Phys. Chem. B, Vol. 105, No. 44, 2001
Martins et al.
or ring i. The monomer hard-sphere contribution is not the only hard-core repulsive contribution to the free energy, because we must also take into account the effect of forming the hard-sphere chains33
Achain
nchain
)-
NkT
xi(mi - 1)ln ghs(σi) ∑ i)1
(8)
or rings27
Aring
nring
)-
NkT
xj(mj)lnghs(σj) ∑ j)1
(9)
The basic difference between these two equations is that for a chain molecule (m - 1) contacts are counted, whereas in a ring the number of contacts equals the number of spheres, m. The contact value of the pair radial distribution function for the spherical segments of species i and j in the reference hardsphere mixture is usually calculated from the appropriate Boublı´k31 expression,
ghs(σij) )
ζ2 σiσj 1 + +3 σi + σj (1 - ζ )2 (1 - ζ3) 3
( )
σiσj 2 ζ22 (10) 2 σi + σj (1 - ζ )3 3 In the present case the contribution due to association is zero,
Aassoc )0 NkT
(11)
Finally, the contribution due to the dispersive attractive interactions can be approximated by the mean-field level term of the van der Waals one-fluid theory of mixing,
Amf NkT
)-
F
n
n
∑∑aijxixjmimj
kT i)1 j)1
(12)
This mean-field contribution is written in terms of segmentsegment (and not molecule-molecule) interactions, i.e., aij represent the integrated strength of the mean-field attraction per segment. All the other thermodynamic properties can be obtained from the Helmholtz free energy by using the standard relationships. In the present model, the number of carbon atoms C in an alkyl chain is related to the number of spherical segments, m, by the following empirical equation34
m ) 1 + (C - 1)/3
(13)
A value of m ) 1.33 thus corresponds to ethane, m ) 1.67 to propane, m ) 2 to n-butane, etc. This relation is consistent with the fact that, in a n-alkane, the carbon-carbon bond length is about 1/3 of the diameter of the cross-section of the alkane molecule. Likewise, a ring of less than three spheres can be viewed as a ring of overlapping spheres. In a previous paper3 it was shown that the xenon atom can be described by a single sphere, m)1, with almost the same diameter, σ, and attractive parameter, a, as those of the alkanes. The unlike interaction parameters, σ12 and a12, were calculated with use of the Lorentz-Berthelot rules,
a12 ) (a11‚a22)1/2, σ12 ) (σ11 + σ22)/2
(14)
Given the similarity of the pure substance parameters for both components, there was no need to allow for deviations from these rules. For the (xenon + n-butane) mixture, the values of the molecular parameters were the following: m1 ) 1, a11 ) 3198 K, and σ11 ) 0.392 nm for xenon; and m2 ) 2.00, a22 ) 3048 K, and σ22 ) 0.385 nm for n-butane.8 Equation 8 was used to estimate the chain contribution to the Helmholtz energy. The results are compared with the experimental results in Figure 4a. The theory is able to predict the negative deviation to Raoult’s law in excellent agreement with the experimental data. The calculation was then repeated using the ring contribution term (eq 9) instead of (eq 8), but using the same pure component parameters. The resulting phase diagram will be that of a mixture of xenon not with cyclobutane, because this substance would have different effective σ2 and a2 parameters, but with a hypothetical cyclic butane molecule. As seen in Figure 4b, the theory now predicts an almost ideal behavior that compares excellently with the (xenon + cyclobutane) experimental data, also plotted. We believe that this result indicates that the change in molecular shape dominates, in this case, over all other contributions. In other words, the effect of substituting, in a binary mixture, a linear molecule for an equivalent cyclic one can be assessed comparing directly the phase diagrams of both systems. References and Notes (1) Calado, J. C. G.; Filipe, E. J. M.; Lopes, J. N. C.; Lu´cio, J. M. R.; Martins, J. F.; Martins, L. F. G. J. Phys. Chem. B 1997, 101, 7135. (2) Calado, J. C. G.; Deiters, U.; Filipe, E. J. M. J. Chem. Thermodyn. 1996, 28, 201. (3) Filipe, E. J. M.; Gomes de Azevedo, E. J. S.; Martins, L. F. G.; Soares, V. A. M.; Calado, J. C. G.; McCabe, C.; Jackson, G. J. Phys. Chem. B 2000, 104, 1315. (4) Calado, J. C. G.; Rebelo, L. P. N.; Streett, W. B.; Zollweg, J. A. J. Chem. Thermodyn. 1986, 18, 931. (5) St. Romain, P.; Van, H. T.; Patterson, D. J. Chem. Soc., Faraday Trans. 1 1979, 75, 1700. (6) St. Romain, P.; Van, H. T.; Patterson, D. J. Chem. Soc., Faraday Trans. 1 1979, 75, 1708. (7) Filipe, E. J. M.; Martins, L. F. G.; Calado, J. C. G.; McCabe, C.; Jackson, G. J. Phys. Chem. B 2000, 104, 1322. (8) Filipe, E. J. M.; Pereira, L. A. M.; Dias, L. M. B.; Calado, J. C. G.; Sear, R.; Jackson, G. J. Phys. Chem. B 1997, 101, 11243. (9) Calado, J. C. G.; Gomes de Azevedo, E. J. S.; Soares, V. A. M. Chem. Eng. Commun. 1980, 5, 149. (10) Haynes, W. M.; Hiza, M. J. J. Chem. Thermodyn. 1977, 9, 179. (11) Staveley, L. A. K.; Lobo L. Q.; Calado, J. C. G. Cryogenics 1981, 21, 131. (12) Calado, J. C. G.; Azevedo, E. J. S. G.; Soares, V. A. M.; Lucas, K.; Shukla, K. Fluid Phase Equilibria 1984, 16, 171. (13) Calado, J. C. G.; Kozdon, A. F.; Morris, P. J.; Nunes da Ponte, M.; Staveley, L. A. K.; Woolf, L. A. J. Chem. Soc., Faraday Trans. 1 1975, 71, 1372. (14) Calado, J. C. G.; Rebelo, L. P. N.; Streett, W. B.; Zollweg, J. A. J. Chem. Thermodyn. 1986, 18, 931. (15) Wiberg, K. B.; Connor, D. S.; Lampman, G. M. Tetrahedron Lett. 1964, 531. (16) Wiberg, K. B.; Connor, D. S. J. Am. Chem. Soc. 1966, 88, 4437. (17) Connor, D. S.; Wilson, E. R. Tetrahedron Lett. 1967, 4925. (18) Heisig, G. B. J. Am. Chem. Soc. 1941, 63, 1698. (19) Benson, S. W. Ind. Eng. Chem., Anal. Ed. 1942, 14 (2), 189. (20) Rathjens, G. W.; Gwinn, W. D. J. Am. Chem. Soc. 1953, 75, 5629. (21) Dymond, J. B.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures; Clarendon Press: Oxford, 1980. (22) Leland, T. W.; Chappelaar, P. S. Ind. Eng. Chem. 1968, 60, 15. (23) Brewer, J. Report No. MRL-2915-C, AFOSR-67-2795, 1968. (24) Prausnitz, J. M.; Lichtenthaler, R. N.; Gomes de Azevedo, E. J. Molecular Thermodynamocs of Fluid-Phase Equilibria; Prentice-Hall: Englewood Cliffs, NJ, 1986. (25) Daubert, T. E.; Danner, R. P.; Sibul, H. M.; Stebbins, C. C. Physical and Thermodynamic Properties of Pure Chemicals; Department of Chemical Engineering, The Pennsylvania State University, Taylor and Francis: Leavittown, PA, 1987; cyclobutane sheet. (26) Barker, J. A. Aust. J. Chem. 1953, 6, 207. (27) Sear, R. P.; Jackson, G. Mol. Phys. 1994, 81, 801.
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