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Second Cross Virial Coefficients of Carbon Tetrachloride - Gas Mixtures Determined from Solubility Measurements at High pressures'
S. K. GUPTA AND A. D. KING, JR. Department of Chemistry, University of Georgia. Athens, Georgia 30601
Received August 3 1, 197 1
The solubility of carbon tetrachloride in compressed helium, hydrogen, nitrogen, argon, methane, carbon dioxide, and ethylene has been measured over pressure ranges of 1-60atm at temperatures ranging from - 10 to 75 "C. Second cross virial coefficients representing carbon tetrachloride - gas interactions are evaluated from the data. It is shown that when allowance is made for the effects of quantum deviations and quadrupolar interaction on the critical temperatures and volumes of helium, hydrogen, and carbon dioxide, respectively, ordinary combining rules produce pseudocritical parameters which reduce all of the measured cross virial coefficients to a single function of reduced temperature. When reduced on a Boyle point basis, it is found that the data are best represented by virial coefficients corresponding to a 7-28 Mie type potential or a Kihara core potential having a core radius somewhat smaller than the carbon-chlorine bond length in carbon tetrachloride.
La solubilite du tttrachlorure du carbone dans I'htlium, l'hydrogtne, l'azote, I'argon, le mtthane, le dioxyde de carbone et dans l'tthyltme comprimts a t t t mesurte, dans des domaines de pressions situts entre 1 et 60 atm, a des temperatures entre - 10 a 75 "C. On a evalut les seconds coefficients croises du viriel, qui reprtsentent les interactions entre le tttrachlorure de carbone et le gaz, a partir des donntes. On dtmontre que, lorsque sont permis les effets de deviations quantiques et d'interaction quadrupolaire sur les volumes et temptratures critiques de I'htlium, de 13hydrogi.ne et du dioxyde de carbone, respectivement, les rkgles ordinaires de combi- naison produisent des param6tres pseudo-critiques qui rtduisent tous les coefficients croists du viriel en une fonction simple de temperature rtduite. Quand on les reduit en se basant sur un point de Boyle, on trouve que les donntes sont mieux reprtsenttes par des coefficients du viriel correspondant a un type de potentiel 7-28 de Mie ou a un potentiel de noyau de Kihara ayant comme rayon du noyau une valeur sensiblement plus faible que la longueur de liaison chlore-carbone dans le tetrachlorure de carbone.
Canadian Journal olchemistry, 50. 660 (1972)
Introduction Second cross virial coefficients are a poten-
tially valuable source of information about the nature of intermolecular forces, both physical and chemical, that exist between molecules of different species in the gas phase.' They offer a considerable advantage over pure component virial coefficients as a means for studying inter- molecular forces in that they allow one to investi- gate changes in potential energy brought about by selectively varying one member of a pair of interacting molecules while holding the other constant. This advantage is offset to some extent by the increased experimental difficulties en- countered in making accurate determinations of cross virial coefficients of gaseous mixtures. In " addition, second cross virial coefficients share a weakness common to all virial coefficients in that there is a wide range of temperature, encompas- sing the Boyle point, over which these coeffi- cients are almost totally insensitive to the shape of the potential energy function describing the intermolecular interaction (2). unfortunately,
'An excellent review on this subject can be found in ref. 1.
these temperature ranges often coincide with temperatures readily accessible in the laboratory.
Mixtures involving globular molecules such as the carbon tetrahalides, neopentane, etc., with simple gases are particularly attractive systems for studying intermolecular interactions between dissimilar molecules by virtue of the simple geometries involved. In a recent study of such a system, Douslin and co-workers deter- mined very accurate values for the second cross virial coefficients of the tetrafluoromethane- methane system over temperatures spanning the Boyle point (3). They found that when reduced using pseudocritical constants derived from combining rules first propounded by Guggen- heim and McGlashan (4), the cross virial coefficients did not satisfy the principle of corresponding states but rather deviated in a manner similar to that found for mixtures of neopentane, tetramethylsilane, and sulfur hexa- fluoride with methane (5). When the CF4-CH, data were reduced on a Boyle point basis, how- ever, the reduced cross virial coefficients fol- lowed the same corresponding states curve as
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GUPTA AND KING: SECOND CROSS VlRlAL COEFFICIENTS OF CCI,-GAS MIXTURES 66 1
those of the respective pure components. The Boyle point parameters of the CF4-CH, system differed from the pseudo-Boyle point param- eters generated using simple combining rules in a manner predicted by Hamann, who inter- preted this as resulting from difference in shape of the potential functions describing the inter- action between globular molecules and that for the small gas molecules ( 5 ) .
In order to examine the nature of mixed interactions more fully, second cross virial coefficients of a related compound, carbon tetrachloride, with a series of light gases, have been determined from solubility measurements of CCl, in the respective gases. By limiting these measurements to systems involving one large globular molecule with a series of small gas molecules, geometric factors affecting the inter- molecular potential can be expected to be reasonably constant, thus providing a more detailed picture regarding the role the smaller molecule plays in such interactions.
The experiments themselves are based upon the fact that the solubility of a liquid in a com- pressed gas is determined by two factors : varia- tions in the fugacity of the liquid phase caused by hydrostatic pressure and dissolved gas, and deviations from ideal behavior in the fugacity of the liquid component in the gas phase. At the pressures of these experiments, concentrations of dissolved gas in the liquid phase are quite low so that the liquid phase exhibits ideal solution behavior. However, in the gas phase, deviations from ideality caused mainly by pair interactions between molecules of the liquid component and those of the gas are often quite significant. As a consequence, measurements of solubilities of liquids in compressed gases can be used to pro- vide accurate values of second cross virial co- efficients representing such deviations from ideality.
Experimental The experimental technique used here for determining
the solubility of CCI, in compressed gases is a modification of the method used by Prausnitz and Benson (6) and is described in detail in ref. 7. The method entails saturating the gas to be studied with CC1, vapor under pressure and sub- sequently expanding the high pressure vapor-gas mixture into a low pressure system where the CCI, vapor is removed from the gas stream by a series of cold traps maintained at - 80 to -70 "C depending on the gas studied. The volume of the gas accompanying the vapor is measured with a wet
test meter. In these experiments, the amounts of CCI, collected were relatively large, ranging from 0.5 to 8 g depending upon the temperature and duration of each run. The weights ofCCI, collected in each cold trap were routinely examined to monitor the efficiency of the traps. The amount found in the last of the three traps averaged 0.4% and never exceeded 2% of the total weight collected. Before calculating mole fractions, each value for total weight recorded was corrected for losses of CCI, vapor under the assumption that the gas exiting the last trap was in equilibrium with solid CC1,. These corrections seldom exceeded 1% except for the lowest temperature measurements (- I0 "C) with hydrogen and helium where the calculated losses ranged up to 15% of the total CCI, trapped. In the lowest temperature runs with hydrogen, small but measurable amounts of water, as an impurity, were trapped out along with the CCI,. Rather than prepurifying the hydrogen, impurity levels of water in the hydrogen were measured by passing large samples of the gas alone through the trapping section and the low tempera- ture data for CCL with hydrogen were corrected accord- ingly. The maximum correction occurred at - 10 OC where it was estimated that 7% of the total weight collected was due to water vapor impurities in the hydrogen. At temperatures greater than 0 "C, the larger mole fractions of CC1, vapor made such corrections unnecessary. If each of these correc- tions is assumed correct to within 10%. the combined error in measured mole fraction amounts to about 2% for hydrogen at - 10 "C. This has the effect of approximately doubling the error in second cross virial coefficient values over that found at higher temperatures.
Initial data taken at each temperature were examined for variations of measured CCI, concentration with flow rate indicating incomplete saturation. It was found that three equilibrium cells in series were necessary to insure saturation up to 25 "C, while two cells were sufficient for higher tem- peratures. Similarly, no trends with pressure were found in the cross virial coefficients calculated from the mole fraction data taken at different pressures.
The hydrocarbon gases used in these experiments (CP grade) were obtained from Matheson Co. Inc. The other gases, helium, hydrogen, nitrogen, and argon, were obtained from Selox Corp., having quoted purities of 99.995,99.9,99.9, and 99.995%, respectively. Reagent grade carbon tetra- chloride was used in all experiments.
Results and Discussion Under conditions where the concentration of
gas dissolved in liquid carbon tetrachloride, XI, is low, the vapor concentration of CCI,, ex- pressed as mole fraction Y,, in equilibrium with the liquid phase is related to the total pressure P, by (677)
Here V:(L) and P; are the molar volume and saturated vapor pressure of liquid CCl, at temperature T while 4; and 4, represent the fugacity coefficients of pure CCl, vapor and
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662 CANADIAN JOURNAL OF CHEMISTRY. VOL. 50. 1972
CCI, vapor in the dense gas, respectively. If contributions from third and higher virial co- efficients are neglected, the fugacity coefficient of CCl, in a gaseous mixture can be expressed as
where Y , represents the mole fraction of diluent gas in the gas phase, V is the molar volume of the gas mixture, and the symbols B(T) denote second virial coefficients representing deviations from ideality caused by pair interactions between species designated by the subscripts. Z is the compressibility factor for the gaseous mixture.
It is seen from eq. 1 that any given experi- mental measurement of the mole fraction of carbon tetrachloride vapor in some diluent gas at a known temperature and pressure and a knowledge of the liquid phase composition under these conditions are sufficient to evaluate the ratio of fugacity coefficients (6:/42. The second cross virial coefficient for this particular CC1,-gas system can then be determined from this ratio through an iterative procedure using eq. 2 and a trial value of B,,(T) in the appro- priate virial expansions for V and Z to make initial estimates of these quantities. In the com- putations used here, gas fugacities along with
75 %
50-C
25 'C
O'C
-0.7-c
FIG. 2. Mole fraction of CCI, in methane as a function of pressure.
Henry's law constants obtained from data found in refs. 8 and 9 were used to calculate the mole fractions of dissolved gas, X I of eq. 1, as a function of pressure for the various gases used. In the case of helium for which no such data are available, it was assumed that the solubility of He in CC1, is the same as that in the physically similar liquid benzene (9). Because of the ex- ceedingly low solubility of helium in these solvents, this approximation does not introduce any significant error in values of B12(T) derived from the experimental data. Values of pure com- ponent second virial coefficients used in eq. 2 are found in refs. 10-17.
The experimentally determined mole fractions of carbon tetrachloride vapor with the various gases studied are not tabulated here for the sake of brevity., However, the data for two CC1,-gas systems are shown graphically in Figs. 1 and 2. These systems were chosen because they illus- trate the two limiting types of behavior exhibited by gaseous mixtures at high pressures. In Fig. 1, measured mole fractions of CCl, in He are com- pared with the hypothetical concentration of
P i o l m l 'Tabular data are available from the Depository of FIG. 1. Mole fraction of CCI, in helium as a function of Unpublished Data, National Science Library, National
pressure. Research Council of Canada, Ottawa, Canada KIA 0S2.
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GUPTA AND KING: SECOND CROSS VlRlAL COEFFICIENTS OF CCI,-GAS MIXTURES 663
TABLE 1. Second cross virial coefficients for CC14 with various gases
Gas Temperature ("C) BIZ(T)*
*Error expressed as average deviation from mean.
CCI, that would exist if intermolecular forces were absent (calculated from eq. 1 letting @/4, = 1). It is seen that helium suppresses the vapor concentration, indicating that repulsive interactions exert a dominant role at these tem- peratures. In the case of CCl, with methane, Fig. 2, the opposite is true. Here attractive forces prevail, resulting in a significant enhancement of CCl, vapor concentration.
Second cross virial coefficients for the various carbon tetrachloride - gas mixtures have been calculated from the experimental mole fraction data and average values of these B , , ( T ) are listed in column 3 of Table 1. With the exception of the - 10 "C data discussed previously, the error limits quoted represent the average devia- tion from the mean. The cross coefficients are shown graphically in Fig. 3 along with values obtained previously by Prausnitz and Benson (6)
for CCI, with Hz, N,, and CO, at the higher temperatures. With the exception of nitrogen, the agreement between the data is seen to be reasonably good.
When compared with the data of Table 2, it is. seen that with the exception of CO,, the cross virial coefficients become more negative as the critical temperature and molecular polarizability of the gas increase as might be expected for mixed systems in which dispersion forces repre- sent the dominant mode of attraction. The fact that CO, seems to have an unusually high critical temperature in comparison with the other gases, particularly ethylene, in Table 2, has been noted previously (18). This stems from the fact that carbon dioxide differs from the other gases ofTable 2 in that its molecules, while not highly polarizable, possess a large quad- rupole moment, so that angle dependent quad- rupolar interactions play a significant role in determining its critical properties. As a result, experimental critical constants of CO, do not accurately reflect the extent to which carbon dioxide interacts with other molecules of systems in which dispersion forces predominate. It is possible, however, to make estimates of the critical temperature and volume that carbon
FIG. 3. Second cross virial coefficients of CCL with He, Hz, N,, Ar, CH,, CO,, and C,H,. Dashed lines correspond to curve described by reduced cross virial coefficients in Fig. 4. Broken circles denote values from ref. 6 .
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664 CANADIAN JOURNAL OF CHEMISTRY. VOL. 50, 1972
TABLE 2. Critical constants and molecular parameters
Average Quadrupole PcVc polarizability Moment
Substance Tc (OK)* V c (cc/rnol) RF (a x 1025cm3)t (0 x loz6 e.s.u. cm2)f
'Critical constant data are taken from ref. 33. tData taken from ref. 34. !Recommended values from ref. 35. Ethylene is assumed to be axially symmetric. $Critical constants in parentheses for He, H,, are "classical" values derived from reduced critical constants found in ref. 23. IlCritical constants in parentheses for CO, reflecting dispersion contributions only from ref. 36.
dioxide would exhibit if quadrupolar interac- tions were absent using equations developed by Rowlinson and Cook (19, 20):
These equations relate the hypothetical critical temperature T,', and volume V;, that CO, would possess if dispersion forces alone were operative, to the corresponding experimentally determined properties T,' and V:. The parameter 6', which serves as a measure of the importance of quadrupole-quadrupole forces relative to dispersion forces at the critical point has been assigned a value of 0.13 on the basis of inde- pendent thermodynamic data(l8,20). This value has been shown to be consistent with the directly measured value of the molecular quadrupole moment of carbon dioxide (21). Values for the hypothetical critical constants TG and V,', estimated from eas. 3 and 4 with 6' = 0.13, are listed in parentheses after the experimental values for carbon dioxide. It is seen that they are intermediate with the values for methane and those of ethylene, as are the cross virial coefficients for this system.
A similar situation exists in the case of hydro- gen and helium in that quantum effects signif- icantly influence the physical properties of these substances at their critical points. For this reason, the experimental critical constants of these substances are inappropriate for cor- relating intermolecular interactions at higher temperatures where classical statistics prevail.
"Classical" values for the critical constants of these compounds which do not reflect quantum effects can be readily derived by requiring that "classical" and experimental values for each critical constant be proportionate to the corre- sponding reduced quantities listed by de Boer (22). This procedure has an advantage over that used by Prausnitz et al. (23) for the purposes here in that no assumption is made regarding the critical compressibility factor in arriving at a classical estimate for the critical volume, al- though the values derived by each method are substantially the same. Classical values for critical temperatures and volumes of hydrogen and helium obtained in this manner are listed in parentheses in Table 2.
Figure 4 shows the graph that results when the data of Table 1 are plotted in reduced form using pseudocritical temperatures Tf,, and volumes VE,, constructed according to the simple com- bining rules:
and
[6 I Vf, = + [(V;)ll3 + (V;)ll3 l 3 using quadrupole and quantum corrected critical constants for CO,, He, and H,. It is seen that the reduced cross virial coefficients correlate well in describing a single function of reduced tempera- ture. The fact that the CO, data fall on this curve when the quadrupole corrected critical constants are used indicates that angle dependent inter- actions between CO, and CCI, make no
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GUPTA AND KING: SECOND CROSS VIRIAL COEFFICIENTS OF CCI,-GAS MIXTURES 665
reduced cross virial coefficients resulted from using the Hudson and McCoubrey combining
- rule (25)
TC - ( T C T C ) ~ / ~ 2(1112)112 26 v; v; 1 2 - 1 2
I l + 12 [(v;)ll3 + (V;)I13l6
d- C C k G A S
ARGON
- - - - - .. C C h
FIG. 4 . Reduced virial coefficients as a function of reduced temperature. Broken circles denote CCL-CO, data reduced with uncorrected critical constants for CO,.
significant contribution to the intermolecular potential energy. This is to be expected consider- ing the weakness and short range nature of quadrupole - induced dipole and quadrupole- octupole forces. The broken lines shown in Fig. 4 represent the curves described by reduced pure component virial coefficients of CCI, and argon (taken as typical of the gases). Values recommended by Dymond and Smith (24) were used to generate these curves. It is apparent, as found by Hamann, Douslin, and co-workers (5, 3), that the virial coefficients for the mixed systems do not satisfy the principle of corre- sponding states but rather are displaced towards lower reduced temperatures from the pure component data.
Combining rules other than eqs. 5 and 6 were tested with these data under the assumption that a constant proportionality exists between the critical constants T c and V c and the respective molecular parameters E and r*3 for all the pure substances involved; E and r* being the energy and distance parameters characterizing the interaction potentials of these pure substances. No improvement in the correlation among
where I i is the ionization potential ofcomponent i, and a decidedly poorer correlation resulted when the Fender and Halsey rule (26)
2Tf T," T" -- 1 2 - T ; + T,"
was used. Likewise, the use of a geometric mean combining rule for VE2 (27) did not affect the scatter of data. The fact that neither the Hudson and McCoubrey combining rule nor the geo- metric mean combining rule for V,", affect the correlation among the reduced cross virial coefficients of the various CC1,-gas pairs is not surprising considering the ratio of VE2 calcu- lated from a geometric mean to V;, of eq. 6 varies by only 15 % in going from helium to ethylene.
Since the reduced virial coefficient data of Fig. 4 extend through the Boyle point, one can recast these data on a Boyle point reduction basis. In Fig. 5, the second cross virial coefficients
FIG. 5. Experimental data and virial coefficients cal- culated from various potentials reduced on a Boyle point basis. Dashed lines represent error bounds for the experi- mental data estimated from the standard error in the ratios relating Boyle point parameters to pseudocritical constants.
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666 CANADIAN JOURNAL OF CHEMISTRY. VOL. 50, 1972
reduced with the Boyle volume, B,,(T)/VL, are shown plotted as a function of reciprocal reduced temperature. The transformation from Fig. 4 to Fig. 5 requires knowledge of the ratios VL/V,', and T,B,/T;,, where the Boyle temperature, T;, is defined to be the temperature at which B12(7J = O for a mixed system and the Boyle volume, VL, is defined as
These ratios were obtained through a least squares fit of a second degree polynomial to B12(T)/VF2 data expressed as a function of T,',/T, yielding values of
T ~ / T F ~ = 1.78 f 0.06 and
The family of curves in Fig. 5 represents the temperature dependence of reduced virial co- efficients generated by various spherically sym- metric potential functions. These curves clearly illustrate the point made by Klein(2) that second virial coefficients offer little discrimination be- tween potential functions at temperatures greater than
The combining rules, eqs. 5 and 6, used to reduce the cross virial coefficients in Figs. 4 and 5 are, of course, empirical in nature. However, the fact that the reduced cross virial coefficients correlate well with the calculated curves over the entire range in the insensitive region (T* > 2) of Fig. 5, gives one some confidence that they, in particular the combining rule for temperature, are appropriate for generating pseudoconstants representative of the energy and distance param- eters of the interaction potential for dissimilar pairs. Outside the region of insensitivity (at temperatures lower than T* = 2), the reduced cross virial coefficients describe a curve which approximates that generated by a 7-28 potential more closely than that of the more traditional 6-12 potential. Cross virial coefficients reduced using the Hudson-McCoubrey combining rule and those reduced using eq. 5 are indistinguish-
able within experimental error when recast on a Boyle point basis.
According to Pitzer's interpretation of the principle of corresponding states (28) in order for virial coefficients of a given class of compounds to correlate as a function of temperature: (a) the interactions between molecules must be de- scribed by a two-parameter potential function of the form
with r* and E being distance and energy param- eters characterizing the minimum of the poten- tial well and, (b) the function, f(r*/r), must be the same for all members of a particular class. Since the data of Fig. 5 correlate well outside as well as inside the region of insensitivity, it can be inferred that carbon tetrachloride - gas interactions are adequately described by a single potential function of the form above and that a constant proportionality exists between the pseudocritical constants TF,, Vf2 of eqs. 5 and 6 and the corresponding molecular parameters E, r*3, independent of the nature of the gas.
In previous studies concerning the properties of gaseous systems containing globular mole- cules, Hamann and co-workers (5,29) proposed a specific potential function which is applicable, in principle, to these CC1,-gas systems. Accord- ing to this model, it is assumed that the overall interaction of two quasi-spherical molecules, or one such molecule and a small gas molecule, can be approximated by summing individual atom-atom interaction energies (assumed to be 6-12) and averaging the resulting potential over all orientations of the respective molecules. If it is assumed that the carbon tetrachloride and gas molecules differ in size to the extent that the polyatomic gases can be treated as being effectively monatomic in n a t ~ r e , ~ then according to the Hamann model, the potential function for the CC1,-gas pairs becomes
'This assumption is supported by the nearly identical values of the critical compressibility factors of the non- quadrupolar heavier gases; C,H,, CH,, N,, and Ar listed in Table 2.
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GUPTA A N D KING: SECOND CROSS VIRIAL COEFFICIENTS OF CC1,-GAS MIXTURES 667
where calculated with
and
Here p is the carbon-chlorine bond distance in CCl, (taken to be 1.77 A), r* and E are the force constants describing the interaction of gas molecules with the peripheral chlorine atoms of CCl,, with E' being the force constant charac- terizing interactions involving the central carbon atom and the gases.
Equation 8 satisfies the conditions outlined by Pitzer provided, (a ) C , and C , are independent of the nature of the gas and (b) E and r*3 are proportional to TE, and V,",, respectively. The London formulation of dispersion forces sug- gests that it is reasonable to expect C , to be constant; furthermore for values of C , ranging between 0 and 2, the overall potential function is almost totally insensitive to the value assigned to C,. Thus, according to this model, CCl, molecules behave as if they consist only of chlorine atoms distributed symmetrically about the center of mass so that only parameters characterizing the chlorine atoms and their distribution in space are significant in deter- mining the shape of the overall potential. The ratio, C,, is just such a parameter and, as ex- pected, the shape of the potential well of eq. 8 is considerably more sensitive to changes in this parameter. It is difficult to see how C , can re- main constant independent of the gas involved since estimates of r* based on collision radii listed in ref. 30 suggest that C , might be expected to vary some 30% in going from helium to ethylene. Nevertheless it will be assumed on the basis of the correlations in Figs. 4 and 5 that r* takes on a constant value, taken to be 3.3 A, the arithmetic mean of the van der Waals radius of the chlorine atom listed by Hildebrand (31) and that for argon found in ref. 30. It is seen in Fig. 6 that the potential function of eq. 8,
and C , equal to unity, indeed more nearly approximates the 7-28 potential than the broader well of the 6-12 potential. It is also seen in Fig. 6 that a Kihara core potential of the form
191 4 ( r ) = E [ ( L ) ' 2 - 2 ( z ) 6 ] r - a r - a
where a denotes the core radius of CCl,, also approximates the 7-28 and Hamann potentials when the ratio alr* = 0.413. A comparison of this ratio to the ratio plr* = 0.54 of eq. 8 take^ as typical for these CC1,-gas systems indicates that a core radius 25% shorter than the C-Cl bond length is appropriate for describing these mixed interactions. This "shrinkage" reflects the effect of multiple attractions by peripheral chlorine atoms which are absorbed by the core radius when the Kihara core model is used to represent carbon tetrachloride-gas interactions. This decrease in core radius is virtually identical to that predicted (28) and later found (32) by Pitzer and Danon for interactions between globular molecules themselves. This suggests
FIG. 6. Potential functions generating reduced second virial coefficients denoted by solid lines in Fig. 5.
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668 CANADIAN JOURNAL OF CHEMISTRY. VOL. 50, 1972
that while less shrinkage occurs in globular molecule - gas interactions than when two glob- ular molecules interact, it is accommodated by one rather than two cores, with the result that the core radii characterizing the globular mole- cule in these two types of systems are the same. Thus, through such cancellation effects, core radii take on the role of a true molecular param- eter for the types of systems considered here.
This work was supported by the National Science Foundation
1. E. A. MASON and T. H. SPURLING. The virial equation of state. The international encyclopedia of physical chemistry and chemical physics. Topic 10, Vol. 2. Pergamon Press, New York. 1969.
2. M. KLEIN. J. Res. Natl. Bur. Stand. A, 70,259 (1966). 3. D. R. DOUSLIN, R. H. HARRISON, and R. T. MOORE.
J. Phys. Chem. 71, 3477 (1967). 4. E. A. GUGGENHEIM and M. L. MCGLASHAN. Proc.
Roy. Soc. London, A, 206,448 (1951). 5. S. D. HAMANN, J. A. LAMBERT, and R. B. THOMAS.
Aust. J. Chem. 8, 149 (1955). 6. J . M . P R A u s N ~ T z ~ ~ ~ P . R . B E N s o N . A.I.Ch.E.J.5,161,
(1959). 7. C. R. COAN and A. D. KING, JR. J. Chromatogr. 44,
429 (1969). 8. G. JUST. Z. Phys Chem. 37,342 (1901). 9. J. HORIUTI. Sci. Pap. Inst. Phys. Chem. Res. Tokyo,
17(341), 125 (1931). 10. J. D. LAMBERT, G. A. H. ROBERTS, J. S. ROWLINSON, and
V. J. WILKMSON. Proc. Roy. SOC. A, 1%, 113 (1949). 11. W. G. SCHNEIDER and J. A. H. DUFFIE. J. Chem. Phys.
17,751 (1949). 12. A. M I C H E L S ~ ~ ~ M. GOUDEKET. Physica, 8,347 (1941). 13. A. MICHELS, H. WOUTERS, and J. DE BOER. Physics, 1,
587 (1934).
15. A. MICHELS and M. GELDERMANS. Physica, 9, 967 (1942).
16. A. MICHELS, HUB. WIJKER, and HK. WIJKER. Physica, 15.627 (1949). . . .
17. A. MICHELS and C. MICHELS. Proc. Roy. Soc. A, 153, 201 (1935).
18. A. D. KING, JR. J. Chem. Phys. 49,4083 (1968). 19. D. COOK and J. S. ROWLINSON. Proc. Roy. Soc.
London, A, 219,405 (1951). 20. J. S. ROWLINSON. Trans. Faraday Soc. 50,647 (1954). 21. A. D. KING, JR. J. Chem. Phys. 51, 1262 (1969). 22. J. DE BOER. Physica, 14, 139 (1948). 23. R. D. GUNN, P. L. CHUEH, and J. M. PRAUSNITZ.
A.1.Ch.E.J. 12, 937 (1966). 24. J. H. DYMOND and E. B. SMITH. The virial coefficients
of gases. Clarendon Press, Oxford. 1969. 25. G. H. HUDSON and J. C. MCCOUBREY. Trans. Faraday
SOC. 56, 761 (1960). 26. B. E. F. FENDERand G. D. HALSEY, JR. J. Chem. Phys.
36, 1881 (1962). 27. R. J. GOOD and C. J . HOPE. J. Chem. Phys. 53, 540
(1970). 28. K. S. PITZER. J. Am. Chem. Soc. 77,3427 (1955). 29. S. D. HAMANN and J. A. LAMBERT. Aust. J. Chem. 7,
1 (1954). 30. J. 0. HIRSCHFELDER, C. F. CURTISS, and R. B. BIRD.
Molecular theory of gases and liquids. John Wiley and Sons, Inc., New York. 1934. Append. I-A.
31. J. H. HILDEBRAND. J. Chem. Phys. 15,727 (1947). 32. F. DANON and K. S. PITZER. J. Chem. Phys. 36, 425
(1962). 33. K. A. KOBE and R. E. LYNN. Chem. Rev. 52, 117
(1953). 34. H. A. LANDOLT and R. B~RNSTEIN. Zahlenwerte und
Functionen. 6th ed. Springer, Berlin. 1951. Vol. 1, Pt. 1, p. 401 ; Pt. 2, p. 509.
35. D. E. STOGRYN and A. P. STOGRYN. Mol. Phys. 24, 1002 (1956).
36. H. BRADLEY, JR. and A. D. KING, JR. J. Chem. Phys. 52 (6), 2851 (1970).
14. D. R. DOUSLIN, R. H. HARRISON, R. T. MOORE, and J. P. MCCULLOUGH. J. Chem. Eng. Data, 9,358 (1964).
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