2115
Anal. Chem. 1984, 56, 2115-2119 (24) Cottrell, T. L.; Hamilton, R. A.; Taublnger, R. P. Trans. Faraday SOC. 1056, 52, 1310-1312. (25) Gupta. S. K.; Klng, A. D., Jr. Can. J . Chem. 1972, 50, 660-668. (26) Hall, K. R.; Canfield, F. B. Physica (Amsterdam) 1969, 4 7 , 99-108, 2 19-226. (27) Dantzler, E. M.; Knobler, c. M.; Windsor, M. L. J . phys. Chem. 1966, 72, 676-684. (28) Gunn, R. D. Ph.D. Thesis, University of Callfornia at Berkeley, 1956. (29) Hoover, A. E.; Nagata, I.; Leland, T. W., Jr.; Kobayashl, R. J . Chem. Phys. 1966, 48, 2633-2647.
(30) Wormald, C. J.; Lewis, E. J.; Hutchlngs, D. J. J . Chem. Thermodyn. 1979, 1 1 , 1-12.
RECEIVED for review August 25, 1983. Resubmitted and accepted May 17,1984. Support of this work was provided in part by the Department Of Energy and by the National Science Foundation.
Variation of Gas Chromatographic Retentions with Carrier Pressure and Composition R. J. Laub Department of Chemistry, Sun Diego State University, Sun Diego, California 92182
,,
The second-lnteractlon cross virial coefficients B are calculated for the solutes n-hexane, trans-3-hexene, benzene, 3,3dimethylpentane, and cyclohexane wlth hydrogen, heilum, nitrogen, carbon monoxide, carbon dioxide, argon, water, methane, ethane, carbon tetrachiorlde, and fluorotrlchloromethane. The results are then used to evaluate the regresdon of In (solute specific retentlon volume) ( Yoo) wkh carrler pressure and composnlon, and It Is shown theoretically as well as demonstrated experlmentaily that retentlons as well as retention order can accordingly be altered. Plots of solute Yoo or of ( Yo0)-' against mole fracllon of the fiuoroaikane mobile phase In admixture wlth hydrogen are found to be curved, although the curvature Is slight at column pressure drops of 1.1 atm and less. The linear variation of solute capacity factors k' agalnst partial pressure of steam nltrogen as reported by Pretorlus Is thereby explained.
+
An increase in effective column efficiency can be brought about in gas chromatography by increasing the mobile-phase density. This in turn can be effected in several ways, e.g., by increasing the average column pressure with a given carrier or by use of a carrier gas of greater collision cross sectional area. However, dense carriers have heretofore been employed only infrequently since it has thus far been assumed that, in practical terms, the gain in column efficiency is in all instances more than offset by an accompanying lower optimum linear carrier velocity (i.e., longer analysis times). Moreover, there is the common supposition that the choice of mobile phase as well as its composition in admixture with some other gas can only be predicated upon qualitative estimate rather than upon firm calculation. Furthermore, an increase in carrier density (or viscosity) requires higher column inlet pressure. As a result, it is hardly surprising that hydrogen or helium mobile phases are employed almost exclusively inter alia in open-tubular (capillary) column GC. In contrast, and as presented in the previous paper, the selectivity of GC systems can be altered by alteration of the carrier and/or its composition, which effects a change in the solute-carrier virial coefficients. Even so, in order to realize advantage from these nonideal gas-phase effects, methods of at least qualitative prediction of the cross virial term BIMare required and also, techniques of calculating the precise mixture(s) of mobile phases that will yield the desired optimal separation. The latter requirement will evidently be fulfilled 0003-2700/84/0356-2115$01.50/0
by the window diagram strategy first introduced by Laub and Purnell in 1975 (1,2)provided that retentions can be described as some or other function of carrier composition and pressure. We accordingly seek in this work to derive relations with which to do so, thence explore the practicability of mixed carriers in gas chromatography.
RESULTS AND DISCUSSION We require means of calculation of the cross virial term B ~ M for the solute (species 1)with the blended mobile phase M (M = carrier A carrier B). The variation of solute retentions with carrier pressure and composition can then be assessed with eq 2,4, and 5 of the previous work. The approach taken is analogous to that used in the preceding paper: first, the composition- and temperature-dependent second-interaction virial coefficients BM are calculated for pairs of carriers at selected intervals of component partial pressure (equal to the mole fraction). Next, solute-carrier pseudo cross volumes V1Mc and temperatures TIMc are determined for each mobile-phase mixture. The cross virial terms BIM are then calculated. Finally, these are used to predict the variation of retentions with carrier composition at selected values of the column inlet/outlet mobile-phase pressure ratio. Properties of the Pure Compounds. The relevant properties (3-5) (323.15 K) of the solutes used in this study are provided in Table I. These were chosen so as to represent a spectrum of commonly encountered chemical types and include aliphatic, olefinic, alicyclic, and aromatic hydrocarbons. Furthermore, three pairs of these present difficult separations with "boiling-point'' stationary phases even with open-tubular columns of high efficiency (5) and so provide a realistic test of the utility of mixed carriers for adjustment of the system selectivity. The mobile phases considered were hydrogen, helium, nitrogen, carbon monoxide, carbon dioxide, argon, water, methane, ethane, carbon tetrachloride, and fluorotrichloromethane, the properties of which are given in Table I of the previous study. The Solute-Carrier Cross Virial Coefficient B lM. Calculation of the Carrier Second-Interaction Virial Coefficient B,. The various relations used to predict the carrier-carrier virial terms BLiand B,, thence B, (M = i + j ) , were detailed and discussed in the preceding paper. Briefly, pure-component virial coefficients were shown to be represented accurately by simple quadratic polynominals (save for water and hydrogen chloride which required quartics), eq 7 of the previous work, the temperature-independent coefficients of which (Table 11) were said to be applicable in most instances
+
0 1984 American Chemical Society
2116
ANALYTICAL CHEMISTRY, VOL. 56,
Table I. Properties of the Pure Solutes
NO. 12, OCTOBER 1984
(323.15
K) trans-
no. TC/K"sb P c/atma,b VC/cm3mol-lnvb 2=c
Id/eVa n
Bll/cm3mol-' clo/atmb vIo/cmSmol-' V t /cm3 8-l
n-hexane
3-hexene
benzene
3,3-dimethylpentane
cyclohexane
1 507.85 29.92 368.041 0.2644 10.18 6 -1515 0.5333 136.36 88.47
2 507.15 30.58 359.346 0.2642 9.11 6 -1471 0.5596 129.67 89.65
3 562.60 48.60 260.334 0.2742 9.24 4.5 -1213 0.3569 92.207 141.7
4 536.15 30.00 419.128 0.2860 10.2 5.5 -1609 0.3042 149.98 146.2
5 554.15 40.57 309.627 0.2764 9.8 4.5 -1382 0.3576 112.12 152.8
"Reference 3. bReference4. cPVC/Rtc.dOv-l stationary phase (5). over the range 200-700 K. The pseudo cross critical volume Vmcand temperature Tmcwere next calculated with sufficient accuracy with the Lorentz (6) and Hudson-McCoubrey (7) relations, eq 8 and 9.b, respectively, of that study, following which the McGlashan-Potter (8) equation (11)was used to provide BAB. B M was then calculated from the relation of Lennard-Jones and Cook (9), eq 6. Calculation of the SolutelMixed-Carrier Pseudo Cross Critical Volume V l w The solute/mixed-carrier pseudo cross critical volumes were calculated in this work with the Lorentz relation
which in essence assumes spherical geometry for colliding species. There is the tacit assumption made in utilizing this formulation also that VIMCremains invariant with the carrier composition. This of course cannot be so; however, the results, albeit approximate in this regard, hardly affect the cross virial term as shown below and so are used throughout in what follows. Calculation of the Solute-Carrier Pseudo Cross Critical Temperature TIM.The pseudo cross critical temperatures of the solute-carrier mixtures were calculated from the Hudson-McCoubrey combining relation (7), since as shown in the previous work it provides at least as reasonable a fit to experimental data as any other
where the effective ionization potentials of the carrier mixtures IMd were taken as the geometric means of those for the pure carriers: IMd = (IAdIBd)1/2. We note that, as with the pseudo cross critical volumes, TIMCis thereby said to be independent of the carrier composition. The Second-InteractionCross Virial Coefficient B1M. The pseudo cross critical volumes and temperatures were next used with the empirical relation of McGlashan and Potter (8) to calculate B1M
where the effective carbon numbers of the ternary mixtures nlMwere taken as the geometric means of the carbon numbers
~~
~~~
Table 11. Comparison of Calculated (Equations 1-3) with Experimental B 1for~ Benzene Solute with Indicated Mobile Phases at 323.15 K carrier
hydrogen
helium
BlW/cm3mol-' calcd exptl 4.64
41.57
nitrogen
-94.46
argon
-99.99
carbon monoxide
-106.2
carbon dioxide
-286.1
methane
-169.7
-5 f 8 -6.0 f 9.0 4f3 -7.5 i 4 49 f 8 57 f 8 67 f 4 -87 f 8 -91.0 f 6.0 -104.5 i 6.0 -98.5 f 7.5 -97.0 i 3.0 -85 f 3 -79 f 8 -85 f 8 -95 f 3 -113 i 8 -122 f 8 -114 f 4 -257.5 i 6.0 -259.0 i 6.0 -256.0 f 6.0 -155 f 15 -171 f 3
ref 10 11 12 13
10 10 12 10 11 11 11 11 12 10 10 12 10 10 13 11 11 11 10 12
of the solutes and carriers, ni being unity for most common inorganic mobile phases, 4 for COz, 2 for HzO, and equal to the carbon number of straight-chain alkanes. The value of 4.5 was employed for the cyclic hydrocarbons cyclohexane and benzene, while branching carbons were given values of 0.25. For example, that for 3,3-dimethylpentane was taken as 5 + 2(0.25) = 5.5. A representative portion of the results is provided in Table 11,where a comparison of predicted (eq 1-3) with experimental BIMis given for benzene solute with several neat carriers at 323.15 K. The agreement is quite remarkable considering that only purely molecular properties were employed in the calculations and in view of the fact that, as pointed out in the preceding paper, eq 3 is an empirical fit designed initially only for the n-alkanes methane through n-octane. Nevertheless, the expression generally predicts at least the correct sign of BIMand, in most cases, a fair approximation to the order of magnitude as well. Moreover, our results substantiate the finding of Everett, Gainey, and Young (IO) that the Hudson-McCoubrey combining rule, eq 2, is superior to the simple geometric mean method of calculation of pseudo cross critical temperatures.
ANALYTICAL CHEMISTRY, VOL. 56, NO. 12, OCTOBER 1984
2117
Table 111. Specific Retention Volumes for Solutes of Table I with Indicated Carriers at 5 and 10 atm Column Pressure Drop (323.15 K) Vgo/cm3g-'
pressure carrier
hydrogen carbon dioxide fluorotrichloromethane carbon tetrachloride
drop
n-hexane
3-hexene
benzene
3,3-dimethylpentane
cyclohexane
5
87.16
140.0 138.7
143.8 141.6
10
85.88 80.40 73.14
88.41 87.21
150.7
10 5
81.74 74.60
131.9 119.1
5
67.76
69.26
5
52.05 64.25
53.65 65.77
10
46.83
48.42
129.5 118.5 111.5 88.02 106.6 80.52
trans-
10
Absolute Retentions with Pure Carriers. The solute specific retention volumes of Table I were utilized at this point with eq 4 to assess the variation of retentions with pressure for individual carriers In Vgo = In Vgo(0) /3poJ34 (4)
148.7 138.9 126.4
108.9 81.43
117.9 91.16 112.1
102.7
82.57
72.35
5.1,
I
+
where In Vgo(0)is a retention volume a t hypothetical zero column pressure drop and where /3 and J34are defined by
J34=
-[ 3
( P ~ / P , ) ~ -1
4
(P~/P,)~1
]
4.1;
Vlo is the solute bulk molar volume, while pi and p o are the column inlet and outlet pressures. The specific retention volume data Vgofor all solutes with hydrogen, carbon dioxide, fluorotrichloromethane, and carbon tetrachloride at 5 and 10 atm are presented as examples of the results in Table 111. The very large shifts in absolute retentions on passing to haloalkane mobile phases seem at first glance to belie the common notion that analysis times are fastest with hydrogen or helium carriers. In fact, at a given linear carrier velocity, the retentions are very nearly halved on passing from the light to the dense mobile phases. The effect is a consequence of the variation of the solute activity coefficient at infinite dilution in a stationary phase of molar volume Vs (14)
(7) where ylmand ypm,the fugacity- and pressure-based activity coefficients, are related to KRo and KR, respectively, via
KR, the experimentally observed partition coefficient, is therefore dependent upon both the fugacity of the pure solute as well as solute-carrier virial interactions in addition to the column pressure. For most organic solutes, B 1 is~sufficiently positive with helium carrier a t temperatures commonly employed in gas chromatography so as to produce (2BlM - Vlo) positive, which in turn results in plots of In KRagainst p0J34sloped positively. With hydrogen carrier, B 1 M approximately cancels with Vlo and so retentions are frequently found to be independent of pressure with this mobile phase. BIMis negative for all other gases aa are, accordingly, the slopes of plots of log (retention) against column pressure. Further, and as first pointed out
3.8;
H,
I
H,
'
L
1
'
I
*
'
'
I
H,O CH, C,H, CCI, He
N,
CO, Ar
N,
CO, Ar H,O CH, C,H, CCI, He
1
Figure 1. Plots of In V g o (323.15 K) against indicated carrier gas at (a) 5 atm and at (b) 10 atm column pressure drop. Solute numbers correspond to those In Table I. Llnes drawn between points are wlthout regard for intermediate carrier composltlons.
by Cruickshank, Windsor, and Young (15),elution times will vary as a function of pressure even at temperatures for which B1* is zero since the ratio VloIRTmust always be finite. The slopes of the retention plots will be negative in these instances also. Retention Order with Pure Carriers. We illustrate in Figure 1the variation of In Vgofor the solutes of Table I from one pure carrier to the next calculated (a) with 5 and (b) with 10 atm at the column inlet (with 1 atm assumed at the outlet; the two pressures representing those typically encountered both in open-tubular and packed-column gas chromatography), where straight lines have been drawn between each datum point without regard for intermediate compositions. We see immediately that in addition to considerable changes in absolute retentions, the order of elution is altered as well on passing from one carrier to another. For example, reversals are found for solutes 3 and 4 (benzene and 3,3-dimethylpentane) from ethane to carbon tetrachloride to helium in (a), while inversions occur in (b) for the same solutes from methane to ethane and from carbon tetrachloride to helium. There
2118
ANALYTICAL CHEMISTRY, VOL. 56, NO. 12, OCTOBER
I 5.0
1984
I
H2
4.8
5 3 4
4.6 0 0 ,
5'
4
3
13 12
3
t
4.0 3.8;
3 18
I 0.2 0.4 0.6 0.8 1.0 'Freon
Figure 2. Plots of V g oagainst mole fraction of Freon 11 in admixture with hydrogen carrier at 323.15 K. Primed numbers indicate 10 atm, those without primes referring to 5 atm column pressure drop. is also near-coelution of these compounds with ethane at 5 atm and with carbon dioxide, methane, and ethane carriers a t 10 atm. Solutes 1 and 2 (n-hexane and trans-3-hexene) nearly coelute with ethane and helium a t 5 atm and with methane and helium carriers a t 10 atm. Retention Order with Blended Carriers. Specific retention volumes of the solutes of Table I were next calculated with the 55 pairs of the 11 mobile phases at mole fraction intervals of the latter of 0.1. The largest alterations of retentions and retention orders were found for gas blends containing a haloalkane, as might be deduced also from tabulations (16) of the second-interaction virial coefficients of these species. Of this class of compounds, fluorotrichloromethane (Freon 11)appears overall to be the most promising for use as a mobile-phase additive, since it is readily available and has a boiling point of 24 "C. The latter property offers the distinct practical advantage of permitting control of the partial pressure of the gas simply by passing the diluent carrier (e.g., hydrogen, helium, etc.) through a container of liquid Freon 11 that is thermostated so as to provide the desired vapor pressure. This in turn can be calculated quite accurately from the Antoine equation
B
22
22
24
26
25
27
29
Time. mrn.
11
log,, p o = A - t+C
20
(9)
where t is in degrees Centigrade and where A , E , and C are empirical constants, those for Freon 11 being (17): A = 6.89034, E = 1043.700, C = 236.596. Thus, the vapor pressure varies from 70 torr at -30 "C to 760 torr at 24 "C, a temperature range that is easily within the capability of commonly available and inexpensive thermostats. In addition, pneumatic lines from the saturation bottle to the gas chromatograph need be kept only above the latter temperature to prevent condensation, which amounts to little more than ambient temperature. This method of generation of carrier blends also avoids the need for (comparatively expensive) gas-blending manifolds. However, the detection system will have to be of a differential type, since the compound gives a finite response even with an FID. Figure 2 provides an example of the results for the five solutes of Table I with hydrogen + Freon 11,where the primed numbers indicate a column inlet pressure of 10 atm, while those without primes refer to 5 atm. The data for all solutes clearly describe curves, those for 1 and 2 being virtually concentric. Also, as in Figure 1,the absolute retentions decrease sharply on passing from pure hydrogen to pure haloalkane. Moreover, the retention order of solutes 3 and 4
Figure 3. Portions of chromatogramsof gasoline sample with indicated carriers: capillary column containing poly(dimethylsiloxane)stationary phase (79). inverts, the points of cross-over occurring at x = 0.5 at 10 atm and at x = 0.6 at 5 atm. Further, while the relative retentions (values of a ) of solutes 1and 2 do not pass through unity at either pressure, they are nonetheless enhanced considerably with pure Freon since the absolute retentions are diminished. The values are in fact 1.014 with hydrogen at 5 atm and 1.031 with Freon at 10 atm which require, respectively, 188850 and 39 820 theoretical plates for k' exceeding 10. Thus, a reduction in overall column length, hence analysis time also, of a factor of very nearly 5 can be realized with the latter mobile phase. Indeed, this required plate count is entirely within the realm of packed-column gas chromatography (18),and the attendant advantages of such column systems for the analysis a t hand thereby accrue as well. There is of course the additional likelihood that secondinteraction cross virial coefficients will be considerably larger for all carriers with solutes other than the simple hydrocarbons considered here (e.g., esters, alcohols, and so forth), in which case alteration of the carrier pressure and makeup will accordingly prove to be even more powerful for the quantitative adjustment of separations. Alternatively, with columns of high efficiency, only comparatively small changes in relative retentions may be required in order to bringabout the desired level of resolution. Carriers exhibiting slight virial interactions may then prove to be entirely adequate. Experimental verification of this situation is provided in Figure 3, where portions of the chromatograms of a gasoline sample are shown with pure hydrogen carrier, a 50:50 blend of hydrogen + nitrogen, and pure nitrogen a t a common inlet pressure (19). The elution orders of several of the peaks (all of which are of unknown identity) clearly shift rather substantially on proceeding through this series of mobile phases. For example, solutes 1and 2 are fully resolved with hydrogen but are nearly completely overlapped with Hz + N,. Resolution is almost restored for this pair with pure Nzbut with no. 1 preceded by no. 2. Reversals in retention order can also be seen for the solute pairs 4 with 5 and 15 with 16. In addition, a new peak, that labeled a, is uncovered only with mobile phases of Hz + N, and pure N,and would have been missed entirely had Hz been the only carrier used. In contrast, resolution of the two left-most peaks is very good with Hz mobile phase but is decreased with H, + N,and is destroyed completely with pure Nz.Thus, even comparatively trivial virial interactions can be utilized t o adjust the system selectivity. [It might be argued in this instance that the reversals observed in the elution orders could be due to the slower linear carrier velocity on passing from left to right in Figure 3, that is, that the later-eluting solutes spent more time on the column
ANALYTICAL CHEMISTRY, VOL. 56, NO. 12, OCTOBER 1984 2.2
1.a
2 X
'E 0
1.4
1
>O
\
1 .o
0.6
I
0.2
0.4
0.6
0.8
XFreori 1 1
Figure 4. Plots of V g o(right-hand ordinate) and (Vgo)-' (323.15 K) against mole fraction of Freon 11 in admixture with hydrogen carrier for n-hexane solute at indicated column pressure drops.
and, hence, interacted somehow more extensively with the stationary phase. However, we would then have to assume that the enthalpies of sorption for these (presumed) hydrocarbons differ rather substantially from one solute to the next. Laub and Purnell(20) (among others) have argued that this might in fact be the case when multiple retention mechanisms contribute to elution times. But, as was established a t the outset of gas-liquid chromatography (21),even in such instances as those, classes of compounds (e.g., aliphatic hydrocarbons, aromatic hydrocarbons, etc.) still exhibit nearparallel van't Hoff plots. As a result, in order to support the argument that the elution reversals were merely a consequence of linear carrier velocity, we would have to assume that upwards of half of the compounds shown in Figure 3 are not closely related chemically. This seems unreasonable in view of the nature of the sample, that is, refined petroleum hydrocarbons.] A further point to be made with regard to the effects of the virial interactions on elution order is the possibility of substantial influence of one solute eluting in the near vicinity of another. This situation arises commonly in the instance of compounds eluting, for example, on the tailing edge of solvent peaks, where it is generally assumed that any shifts in retentions are due to solvent solubility in (hence alteration of the selectivity of) the stationary phase. However, depending upon the solutes and solvent it is clear that, in fact, certainly retentions and perhaps even retention orders can be affected substantially depending upon the solvent partial pressure in the carrier gas along the length of column over which the compounds coelute. Graphical Presentation of Retentions as a Function of Carrier Pressure and Composition. Finally, we illustrate in Figure 4 the variation of the specific retention volumes (right-hand ordinate) and the inverse of Vgo(left-hand or-
2119
dinate) of n-hexane as a function of the mole fraction of Freon 11 in admixture with hydrogen at inlet/outlet pressure ratios of 1.1, 5 , and 10. As in Figure 2, the data are described everywhere by curves. However, those presented as inverse retentions are rather considerably less so. Furthermore, the curves for p , / p , = 1.1are very nearly linear, and indeed become so a t column pressure drops close to zero. Thus, at moderate column inlet pressure, both retentions and inverse retentions may well regress linearly against mole fractional composition of the mobile phase. This accounts for the successful prediction of optimal carrier compositions with window diagrams by Pretorius (22), who found in contrast to eq 4 that the solute capacity factors of three sterols varied linearly with the partial pressure of steam in admixture with nitrogen. (k' increased for one of the solutes in that work, which indicates substantial interaction also of the mobile phase with the presumed adsorbent stationary phase; this effect, too, can of course be used to enhance separations, a quantitative treatment of which we intend taking up in a later report.) Registry No. Hz, 1333-74-0;He, 7440-59-7;NP,7727-37-9;CO, 630-08-0; CO,, 124-38-9; Ar, 7440-37-1; H20, 7732-18-5; CH,, 74-82-8; C2Hs, 74-84-0; CCl,, 56-23-5; fluorotrichloromethane, 75-69-4; n-hexane, 110-54-3;truns-3-hexene, 13269-52-8;benzene, 71-43-2; 3,3-dimethylpentane, 562-49-2; cyclohexane, 110-82-7.
LITERATURE CITED (1) Laub, R. J.; Purnell, J. H. J . Chromatog. 1975, 112, 71-79. (2) Laub, R. J. I n "Physical Methods in Modern Chemical Analysls", Kuwana, T., Ed., Academic Press: New York, 1983; Vol. 3, Chapter 4. (3) Weast, R. C., Ed. "Handbook of Chemistry and Physics", 50th ed.; Chemlcal Rubber Co.: Cleveland, OH, 1970. (4) Dreisbach, R. R. "Physical Properties of Chemical Compounds"; American Chemical Society: Washington, DC. Vols. I (1955), I 1 (19591, and I11 (1961). (5) Chien, C.-F.; Kopecni, M. M.; Laub, R. J. HRC CC, J . High Resolut. Chromatogr. Chromatogr. Commun. 1981,4 , 539-543. (6) Guggenheim, E. A.; McGlashan, M. L. f r o c . R . SOC. (London) Ser. A 1951,206,448-463. (7) Hudson, G. H.; McCoubrey, J. C. Trans. Faraday SOC. 1980, 56. 761-766. (8) McGlashan, M. L.; Potter, D. J. E. R o c . R . SOC. London, Ser. A 1982,267, 478-500. (9) LennardJones, J. E.; Cook, W. R. Proc. R . SOC. London, Ser. A 1927, 115,334-348. (10) Everett, D. H.; Gainey, E. W.; Young, C. L. Trans. Faraday SOC. 1988, 6 4 , 2667-2674. (11) Cruickshank, A. J. B.; Gainey, E. W.; Hicks, C. P.; Letcher, T. M.; Moody, R. W.; Young, C. L. Trans. Faraday SOC. 1989, 6 5 , 1014-1031. (12) Coan, C. R.; Klng A. D., Jr. J . Chromatogr. 1989,4 4 , 429-436. (13) Connolly, J. F. Data cited in Everett, D. H.; Gainey, B. W.; Young, C.L. Trans. Faraday Soc. 1968, 6 4 , 2667-2674. (14) Everett, D. H. Trans. Faraday Soc. 1985,61, 1637-1645. (15) Cruickshank, A. J. E.; Windsor, M. L.; Young, C. L. Proc. R . SOC. London, Ser. A 1968,295, 259-270. (16) Dymond, J. H.; Smlth, E. E. "The Virial Coefficients of Pure Gases and Mixtures"; Clarendon Press: Oxford, England, 1980. (17) Benning, A. F.; McHarness, R. C. Ind. Eng. Chem. 1940, 3 2 , 497-499. (18) Laub, R. J.; Purneli, J. H. HRC CC, J . High Resolut. Chromatogr. Chromatogr. Commun. lW0, 3 , 195. (19) Smith, C. A. Ph.D. Thesis, The Ohio State University, Columbus, OH, 1982. (20) Laub, R. J.; Purnell, J. H. J . Chromatogr. 1978, 161,49-57. (21) Littlewood, A. E.; Phillips, C. S. G.; Price, D. T. J . Chem. SOC. 1955, 1480- 1489. (22) Pretorius, V. HRC CC, J . Hlgh Resolut. Chromatogr. Chromatogr. Commun. 1978, 1 , 199-200.
RECEIVED for review August 25, 1983. Resubmitted and accepted May 17, 1984. Support of this work was provided in part by the Department of Energy and by the National Science Foundation.
