2405
Anal. Chem. 1904, 56, 2485-2489
Non-Steady-State Gas Chromatography for Activity Coefficient Measurements Anatoly J. Belfer’ and David C. Locke* Department of Chemistry, Queens College, City University of New York, Flushing, New York 11367
I n non-steady-state gas chromatography, a solvent relatively volatlle at the column temperature Is InJectedinto a column packed with solid support. The solvent condenses uniformly on the solld and equlllbrates with the carrler gas. As the solvent slowly evaporates out of the column, solutes are repetltlvely Injected. As the total volume of solvent decreases with tlme, so does the retention time of a solute injected repetltlvely over that tlme. The decrease In retentlon tlme with change In time of lnlectlon at constant column temperature and flow rate Is dlrectly related to the solute-llmlting actlvlty coefflclent In the solvent. Llmlting actlvlty coefflclents of a varlety of solutes In acetonitrile and n-octane solvents agree satlsfactorlly with publlshed data. Wlth the present apparatus, accuracy to about 10% Is expected. I n nonsteady-state GC, nelther the weight of solvent In the column nor the retention tlme of a nonretalned substance need be known, and In addltlon certaln effects cancel that are dlftlcult to correct for In normal GC.
Non-steady-stategas chromatographywas described in 1972 by Belfer (1). The technique is so designated because the solvent phase is not stationary but rather is volatile a t the column temperature. The solvent is itself being eluted from the column during the chromatographic experiment. The solvent phase, however, moves slowly out of the column. Solutes injected into the column move far faster. As carrier gas continues to flow through the column, the total volume of solvent phase decreases with time, so that as repetitive solute injections are made, the retention time decreases in the same fashion. For any given solute injection, however, the solute undergoes normal chromatography. Non-steady-state GC was used to determine activity coefficients of volatile solutes in volatile solvents ( I ) . Little attention seems to have been paid to this development, which it must be said was not readily accessible to those illiterate in Russian. In this paper, we rederive the equations of non-steady-state GC and demonstrate the efficacy of the technique for the determination of activity coefficients of several solutes in octane and in acetonitrile solvents. It might be noted that Olsson et al. (2), who were apparently unaware of Belfer’s work, devised a method to determine the loss of stationary phase in GC from the change in the retention volume and applied this to the estimation of vapor pressures of stationary phases such as n-octadecane and oxydipropionitrile. Activity coefficients of organic compounds in nonelectrolyte solutions are of theoretical as well as practical interest in physical chemistry and chemical engineering. Thermodynamic theories of nonelectrolyte solutions are often expressed in terms of the solute excess partial molar Gibbs free energy, p2e, which is related to the solute activity coefficient, yz, by Permanent address: 66-15 Thornton Place, Rego Park, NY
11374.
RT In y2 = pze
(1)
Activity coefficients, especially the limiting or infinite dilution values, yzm,have various uses in characterizing solution behavior. As end values they are useful in conjunction with various solution models such as the van Laar, Redlich-Kister or Wilson (3),UNIFAC ( 4 ) , ASOG (5), etc. equations for calculating the solubility curves over the entire composition range and for determining the adjustable parameters in these equations. Activity coefficients are the basic data needed in many chemical engineering and solution thermodynamic calculations. Conventional measurement methods such as the McBain balance, vapor-liquid equilibria studies, ebulliometric methods, etc. are generally accurate but tedious and time-consuming and work best at finite solute concentrations,Le., mole fractions in the range of 0.149. New experimental methods are consequently of great interest, especially those that give the limiting values directly. GLC is one such method, which was first used to measure infinite dilution activity Coefficients in 1956 (6). Results of numerous GC studies have been published since (7-9). The GC technique has been highly refined so that precise, accurate, and fully corrected thermodynamic data are obtainable; even partial molar excess heat capacities can be determined (10). However, most GC-derived activity coefficients are primarily of interest in testing theoretical models, because in conventional, steady-state GC, one wants a nonvolatile, stationary solvent phase, which generally restricts one’s choice of solvents to compounds such as nhexadecane and higher homologues, poly(ethy1ene glycols), phthalate esters, etc. A few examples of the use of volatile “stationary” phases in the measurement of activity coefficients have been published (7-9,11,12). In a recent and extensive study, Eckert et al. (I1,12) found good agreement between GC-measured limiting activity Coefficients and literature values for a variety of solutes in industrially important solvents such as acetonitrile, benzene, heptane, and water. Much of the problem of interpretation of GC data obtained in the conventional way with a volatile solvent derives from the uncertainty in the weight of the solvent in the column. Eckert et al. (11, 12) approached this problem by presaturating the carrier gas with solvent and by using a literature value for the activity coefficient of a reference compound in conjunction with its experimental retention volume, to calculate the moles of solvent present. They also pointed out the problem of reduced sensitivity of the thermal conductivity detector (TCD) when using a mobile phase with heat-transfer properties comparable to those of the solute. Overall, for activity coefficients less than about 100, accuracy to 15% or better was expected (11). For many practical applications, this is acceptable, although improvements would naturally be desirable. THEORETICAL SECTION
In non-steady-state GC, a slug of a liquid solvent having appreciable vapor pressure at the column temperature is evaporated in the injection port and condenses in the column packed only with a solid support. As the liquid equilibrates 0 1984 American Chemical Society
2488
ANALYTICAL CHEMISTRY, VOL. 58, NO. 13, NOVEMBER 1984
n II 2
II
2
"
5
a !;;
A
0
Flgure 2. Schematic representation of non-steady-state gas chromatograms. (A) Injection port, (B) column in early and late stages of lifetime,(C) detector and recorder. (1) Solute Injected at an early time in column life; recorder base line adjusted downscale from Figures 1-3. (2) Solute injected at later stage of column life. Difference in retentlon times is exaggerated. teractions in various ways (7-9), perhaps most simply by use of an equation preferred by chemical engineers (11)
C
RTnJzZ,
D
Flgure 1. Schematic representation of non-steady-state gas chromatography. (A) Injection port, (B) column packed with solid support, (C) thermal conductivity detector, (D) recorder. Hatched lines represent IiquM solvent and dots the solvent vapor. (1) Liquid solvent Is injected, evaporates, and condenses on solid support as carrler gas moves vapors through column, recorder reads carrier gas base ilne. (2) Solvent fills column, begins to elute into hot TCD; recorder shows solvent breakthrough front. (3 and 4) Carrier gas continues to elute solvent, and solvent tall moves slowly through column; recorder shows Mgh base line because of solvent vapors. (5) Solvent completely eluted from column; recorder shows return of base line down solvent tall to carrler gas reading as solvent vapor tail moves through detector. with the support, the latter becomes uniformly coated with a fairly heavy load of liquid solvent. Because of its volatility, solvent will equilibrate with the carrier gas and will bleed out of the column at a slow, uniform, continuous rate, as depicted in Figure 1. This will give rise to a steady base line, which can be adjusted to a low-scale value. Solutes are injected, in the usual fashion, repetitively over a period of time in which there is substantial loss by volatilization of the solvent in the column. The retention times of a solute injected over this period of time will decrease at the same rate as the rate of solvent evaporation, because the total weight of solvent in the column decreases, as depicted in Figure 2. Let us first reiterate the definition of the net retention volume and its relationship to the thermodynamic property of interest, the limiting activity coefficient, for steady-state GC. The net retention volume, VN, Le., the solute retention volume less that of a nonretained substance ("air"), corrected for the column pressure drop, is determined from the experimental net retention time, tN = t, - to,and the carrier gas flow rate, F, by VN (t, - tJFJ2' = F'tN (2) where J23is the Martin and James gas compressibility factor and F'is the corrected flow rate. It is readily shown (7-9) that VN is related to the solute distribution coefficient K and to the solute activity coefficient according to RTwl RTnl VN = KVl -= (3) P2OMlY2
P2OY2
where Vl is the volume of the liquid phase in the column, w1 is its weight and Ml its molecular weight, pZ0is the solute vapor pressure at T, the column temperature, and nl is the number of moles of solvent in the column. If the solutions are sufficiently dilute, i.e., in the Henry's law region, then y2 is the limiting value, y2-. These equations assume the vapor phase is ideal. It is possible to correct for vapor-phase in-
exp(-u2-P/Rt)
=
(4) f$PZo V N where fi is the vapor-phase fugacity coefficient of solute at P, the total system pressure, f; is the fugacity coefficient of the solute vapor under its saturation vapor pressure, 2, is the mixture compressibility, and uZm is the solute-limiting partial molar volume. Now the change in net retention volume and net retention time with loss of the stationary phase in non-steady-state GC can be expressed as 72-
dVN = Frat, KdVi (5) It is not necessary to use or even to know the absolute rate of loss of the solvent phase, since at constant flow rate and temperature the change is linear with time; experimentally it is easier to measure time differences. Thus, at time t = tl, an aliquot of solute is injected which elutes at time tNl. Subsequentlyat t = t2,a second aliquot is injected which elutes at time tNz, Letting dtN = t ~-*t~~and d 19 = t2 - tl, then
where @J is the retention differential parameter, the nonsteady-state chromatographic parameter characteristic of a given solute and solvent at a given temperature. From eq 3, in the non-steady-state mode nrn
av,
ni
= -an1
(7)
PZ072-
Now the molar ratio, n,/n,, of the moles of volatilized solvent per unit volume of gas phase, n,, to moles of carrier gas per unit volume, n,, is the ratio of the solvent vapor pressure at the column temperature, pIo,to the partial pressure of carrier gas, pc, i.e. n, =
PlOnc
PC
The loss of moles of solvent with time, for constant carrier gas flow rate and temperature, is -dnl/d9 = F'n, combining eq 6-9
But since for an ideal carrier gas RTn,/p, = 1,solving for
(9)
ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984 2487 72- =
0
Pio dB R --= PZo d t N #'
where R is the ratio of solvent vapor pressure to solute vapor pressure. Thus knowing the solvent/solute vapor pressure ratio, and measuring the change in solute retention times between successive injections, one can easily determine 72m of a volatile solute in a volatile solvent by GC. The Henry's law constant, H, is simply related to 4, according to
Finally, the partial molar excess enthalpy can be determined from the temperature dependence of y2-:
a
1( 1
and since
the partial molar excess entropy can be estimated. EXPERIMENTAL SECTION A Perkin-Elmer Sigma 3 HWD, a dual-column,dual-TCD gas chromatograph,was used with identical 4 ft X 1/8 in. 0.d. stainless steel columns packed with 100/120 mesh Chromosorb G. Injection port and detector temperatures were set at 300 and 250 "C, respectively. Column temperatures were studied between 25 and 60 "C. The flow rate of helium was generally 20 mL/min through each column. No difference in retention volumes was observed over the range of 20-60 mL/min. The lower flow rate provides more precisely measurable retention times and prolongs column life. For peaks with long retention times, however, use of a higher flow rate sharpens up the peak and improves measurement precision. The attenuator must be set fairly high (64X or higher) to produce a steady base line when solvent is injected. To proceed, about 1-3 mL of the liquid solvent was injected into each of the columns. It is possible to inject solvent into just one of the columns, but it is easier to zero the recorder by injecting solvent into both columns. One can also inject different solvents into each column and thus be able to run two experiemntsalmost simultaneously. In any case, solvent is flash-evaporated in the injection port, and the vapors are swept into the column and condense to coat the packing. Equilibration of the solvent with the solid support requires only a few minutes, as evidenced by stabilization of the base line. Equilibration could be expedited by briefly raising the column temperature about 10 OC and then lowering it to the operating temperature or by briefly increasing the flow rate of carrier gas and then lowering it to the operational flow rate; in practice, however, equilibration is sufficiently rapid to obviate these procedures. Once the baseline has stabilized, the pen on the recorder chart is adjusted to the bottom of the scale and the chromatograph is ready for solute injection. For columns of the dimensionsused here, injection of more than about 3 mL of liquid solvent produces condensation of liquid droplets at the column outlet, which causes spiking by the detector until the excess has evaporated. Additional solvent can be injected at any time to reload the column. Since the change in retention time of a solute at different injection times is measured, injection of additional solvent merely resets the injection time clock. To clean a column, one need only raise the temperature above the solvent boiling point; once the recorder pen has equilibrated to the carrier gas base line, the column can be cooled and a new solvent injected. Solutes can be injected whenever the column has equilibrated with solvent. Less than 0.5 pL of solute gave half-scale peaks for short retention times; 2 p L may be required for a solute with a long retention time to produce an accurately measurable peak. No difference in retention time was observed if solutes were
A B C D Flgure 3. Non-steady-state chromatograms of methanol and ethanol on natane solvent, 45 O C . (a)Methanol, (b) ethanol. Injection times: (A) 0 s,(E) 2000 s, (C) 3000 s,(D) 4000 s. Aliquots of 1 pL of a 1:l mixture of methanol and ethanol injected. Helium carrier gas flow rate, 20 mL/mln. Recorder chart stopped after elution of ethanol peak until new sample injected. introduced neat, as mixtures, or as solutions. Variation of sample volume injected from 0.5 to 10 pL for solutes of polarity similar to that of the solvent had no effect on retention time. For different polarities, e.g., methanol solute in octane solvent or pentane solute in ethanol solvent, the absolute retention time decreased about 5% for a 1-10-pL change in volume injected, but the difference in retention times between injections, which is the parameter of interest here, was unaffected. Solutes were injected repetitively over at least a 1000-s range of injection times and over as much as 8000 s of the column life. Again, the slope of the plot of retention time vs. injection time is the retention differential parameter 4 = d t ~ / d 8(eq 6). RESULTS AND DISCUSSION The rate of solvent loss, dn,/dO, can be calculated by combining eq 8 and 9 and recognizing that RTn,/p, = 1:
For example, with n-octane solvent, a carrier gas flow rate of 20 mL/min, and a column temperature of 45 "C, dnl/dO = 6.7 X lo-' mol/s. If 1mL of liquid octane wm initially injected, it would require over 2.5 h to elute it completely. All illustrative and typical set of chromatograms is shown in Figure 3. Injections of 1 p L of a 50/50 mixture of methanol and ethanol were made at arbitrarily chosen injection times: 0,2000,3000, and 4000 s. The net retention time of methanol varied from 52.8 s a t injection time 0 to 43.2 s after 4000 s had passed from the time of initial injection; the corresponding values for ethanol were 153.6 and 128.4 s, respectively. One might inquire regarding the effect of loss of solvent from the column during the elution of a long-retained solute; for ethanol, for example, after 4000 s there is about 3.3 X mol of octane left in the column, and in the 128-s retention time, about 3% of this is eluted. The point is, however, that this has no effect on the retention of ethanol at all, since the solute band moves faster than the solvent tail; what counts is the volume of solvent present in the column a t the time of injection. Clearly the limiting case is that of a solute of volatility (note that volatility is the product of solute vapor pressure and activity coefficient in the solvent, not vapor pressure alone) less than that of the solvent. Such a solute would move slower than the solvent and would elute as a discrete peak after
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ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984
Table 1. Limiting Activity Coefficients in Acetonitrile, 25 O C
72-
INJECTION
TIME,
SEC
x
Figure 4. Retention dlfferentials for various solutes in acetonitrile, 25 'C. (a) nPentane, (b) 2,2dimethylbutane,(c) 2-methylpentane, (d) 3-methylpentane, (e) 1-pentene, (f) n-hexane, (9) 1-hexene, (h) 2-
methylhexane, (I) cyclohexene, (i) 2,2,4trimethylpentane,(k)n-heptane, (I)cyclohexene, (m) l-heptene, and (n) noctane. IndivMual data points are not shown to retain clarity. the solvent tail had eluted. Note in the chromatograms that the peak heights increase in time, reflecting the shortening of retention time in time. As the solvent plug moves out of the column, the interstitial volume increases slightly. However, this has no effect on the parameter 9, which is related to the difference in solute net retention times. In Figure 4 is plotted the observed retention times of variou solutes in acetonitrile solvent at 25 OC with 20 mL/min of He carrier gas vs. the injection times. As should be expected, the lines intersect at a common point at 11150 s. This is the time that all the solvent has eluted from the column and agrees well with the column lifetime, 3 h, estimated by using eq 15. The retention time a t the common point corresponds, of course, to the retention time of air in the column packed with solid support alone, about 10 s. It can be noted in the diagram that for compounds with long retention times, such as n-octane on acetonitrile solvent, measurements of retention time can be made only in the latter stages of the life of the column, otherwise the peaks become too spread out and low to be accurately measured. In Tables I and I1 are listed limiting activity coefficients of a variety of solutes in acetonitrile and n-octane solvents, respectively. The values are not corrected for vapor-phase nonideality; given the uncertainty in the retention difference measurements, we believe the correction would not be significant. In the absence of automatic data handling capability, the overall accuracy is probably of the order of *lo%, which we hope to improve in the future by the computerization of the equipment. Comparison of the non-steady-state GC data with literature data for acetonitrile solvent shows fairly good agreement except for 1-pentene. Given the wide deviations from solution-phase ideality, the agreement is all the more remarkable. The literature values for pentane, hexane, and acetone were obtained by vapor-liquid equilibrium measurements; the others were derived from liquid-liquid chromatographic plus gas chromatographic data (20) and are of unknown accuracy. The activity coefficients in octane solvent were measured at 40 and 60 'C, for which no comparison data are available. As noted above, Thomas et al. (II), using normal GC, measured activity coefficients at 20 OC. As an aid to comparison, the present data were extrapolated linearly to 20 "C; we recognize that a priori it cannot be asserted that a linear extrapolation is justified for all solutes. In any case, given the uncertainties, the agreement between the normal GC and
compound"
non-steady-state GC
lit.
ref
n-pentane 2,2-dimethylbutane 2-methylpentane 3-methylpentane n-hexane 2-methylhexane 2,3-dimethylpentane n-heptane 2,2,4-trimethylpentane n-octane 1-pentene 1-hexene 1-heptene cyclohexane cyclohexene acetone CHCls
17.2 19.3 21.9 20.4 24.0 29.8 23.2 31.6 32.4 46.9 6.08 12.7 21.7 19.1 12.1 1.04 1.29
20.4
18
25.5
19
9.47 14.3
20 20
12.1 1.10 1.21
20 11 20
" Vapor pressure data: hydrocarbons except cyclohexene and 1heptene from ref 13; cyclohexene, ref 14; 1-heptene, estimated from data in ref 13; acetone, ref 15; CHCl,, ref 16; acetonitrile, ref 17. Table 11. Limiting Activity Coefficients in n -Octane70 and 60 OC 72-
compound"
40 "C
60 'C
20
acetone acetonitrile chloroform methanol ethanol ethyl acetate nitromethane n-pentane
5.92 26.1 1.55 65.0 36.2 2.94 24.6 1.00
5.79 18.3 1.43 51.9 27.7 2.81 21.4 1.05
6.07 39.1 1.69 83.8 49.1 3.09 28.8 0.97
OCb
lit. 20 *CC 7.3 31.3 1.43 80 50.5 3.25 29.5 0.95
'Vapor pressure data: same as Table I, plus methanol and ethanol, ref 21; ethyl acetate, ref 22; and nitromethane, ref 16. bValues at 20 OC calculated by using a linear extrapolation from the data at 40 and 60 "C. "Data from ref 11.
non-steady-state GC is quite reasonable, especially in view of the wide range of solute polarities and wide range of magnitudes of the values. The question may well be asked whether the values reported are truly infinite dilution values. Although the reduced detector sensitivity requires relatively large sample sizes, there is a relatively large amount of solvent in the column. Following the calculation of maximum permissible sample size given by Conder and Young (8),we assume our 4 ft X l/s in. 0.d. column contains 5 g of solid support onto which a maximum of 2 mL of acetonitrile solvent is deposited. A peak with a 50-s retention time and a 10-s base-line width will be dissolved in about 2 X loT2mol of solvent. If the partition isotherm can be considered linear over a maximum solute concentration range of 0.01 mol fraction, the amount of solute injected, allowing for the distribution of solute within the peak, should not exceed about 1 x 10". mol; i.e., for a solute with a molecular weight of 100, the maximum sample size should be 10 mg or 10 p L . Thus, the injection volume generally used here, 0.5 pL, should produce solutions effectively at infinite dilution, i.e., derived activity coefficients are y2- values. Only in the very last stages of the column life, when the solute bandwidth in the column exceeds the length of column occupied by the solvent, will insufficient solvent be available. As noted above, a completely independent set of data on retention volume decrease with loss of the stationary phase
ANALYTICAL CHEMISTRY, VOL. 56, NO. 13, NOVEMBER 1984
Table 111. Limiting Activity Coefficients in n -Octadecane, 60 OC"
compound
Y 2-
lit.
ref
ben 2ene
0.82 0.82
0.86
7
n-heptane "Data
from ref 2. See text.
has been published (2). Using their tabulated values of dVN/dV,,,, where V,,, is the accumulated flow rate, and recognizing that this ratio is identical with our retention differential parameter 4, we can calculate the limiting activity Coefficients of benzene and heptane in n-octadecane at 60 OC, as given in Table 111. The values listed are the averages determined from their five sets of data taken at different flow rates. The benzene activity coefficient agrees well with GLC-determined data tabulated by Locke (7). Although no literature data were found for n-heptane in n-octadecane, the value found, 0.82, appears quite reasonable when compared with the available data for normal paraffin solutes in normal paraffin solvents. The principal source of error in the non-steady-state GC data is the determination of change in retention time with time. These changes are relatively small, requiring that GC conditions be maintained constant over an extended period of time. Short-term column temperature and flow fluctuations, however, will therefore tend to average out, although long-term thermal drift will introduce uncertainty. Derived activity coefficients are of course sensitive also to the vapor pressure values selected. Measurement precision would be improved by automating the data handling; in fact, the whole process would seem to be amenable to automation with an autosampler and microprocessor control and calculation. Compared to normal GC, and especially that using volatile solvents, the non-steady-state technique has certain advantages. In particular, the weight of solvent in the column need not be known. It is difficult to determine exactly what this weight is with ordinary nonvolatile solvents, so that the indirect method adopted by Eckert et al. (11)for volatile solvents is probably as accurate as any method. The present technique, however, is applicable to exactly the same systems. In addition, in non-steady-state GC, to need not be known, which can be a problem in normal GC. It is probably the case that in our technique, the effects on retention of liquid surface and solid support adsorption tend to cancel, since a retention difference is measured. This cancellation will be more likely when successive retention measurements are made closely
2489
together in time. Another advantage of non-steady-state GC is that to change solvents, one need not pack a new column; all one has to do is evaporate off the old solvent and introduce a new one. This would eliminate any problems arising from solid support or packing structure effects. We are in the process of refining the technique and applying it to a diversity of solvents and solutes of practical engineering interest. Registry No. B,B-Dimethylbutane,75-83-2;2-methylpentane, 107-83-5;3-methylpentane,96-14-0; 2-methylhexane, 591-76-4; 2,3-dimethylpentane,565-59-3; n-heptane, 142-82-5; 2,2,4-trimethylpentane, 540-84-1;n-octane, 111-65-9;1-heptene,592-76-7; cyclohexane, 110-82-7; acetone, 67-64-1; acetonitrile, 75-05-8; chloroform, 67-66-3; methanol, 67-56-1;ethanol, 64-17-5;ethyl acetate, 141-78-6;nitromethane, 75-52-5; n-pentane, 109-66-0. LITERATURE CITED Belfer, A. I. Neftekhimiya 1972, 12, 435; Chem. Abstr. 1973, 78, 20591. Oisson, A.-M.; Mathiasson, L.; Jonsson, J. A.; Haraldson, L. J. Chromatogr. 1976, 128, 35. Null, H. R. "Phase Equllibria in Process Design"; Wiley: New York, 1970. Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. Am. Inst. Chem. Engr. J . 1975, 2 1 , 1086. Kojima, K.; Tochigi, K. "Predlctlons of Vapor-Liquid Equilibria by the ASOG Method"; Elsevier: New York, 1979. Porter, P. E.; Deai, C. H.; Stross, F. H. J. Am. Chem. SOC.1956, 78, 2999. Locke, D. C. Adv. Chromatogr. (N. V . ) 1976, 14, 87. Conder, J. R.; Young, C. L. "Physicochemical Measurement by Gas Chromatography"; Wiiey: New York, 1979. Laub, R. 3.; Pecsok, R. L. "Physicochemical Applications of Gas Chromatography"; Wiiey: New York, 1978. Meyer, E. F.; Baiocchl, J. A. Ami. Chem. 1977, 49, 1029. Thomas, E. R.; Newman, B. A.; Long, T. C.; Wood, D. A.; Eckert, C. A. J. Chem. Eng. Data 1982, 2 7 , 399. Eckert, C. A.; Newman, B. A.; Nicoiaides, G. L.; Long, T. C. Am. Inst. Chem. Engr. J. 1981, 2 7 , 33. Rossini, F. D. "Selected Values of Physical and Thermodynamic Propertles of Hydrocarbons and Related Compounds"; American Petroleum Instttute: Pittsburgh, 1953. Letcher, T. M.; Marslcano, F. J. Chem. Thermodyn. 1974, 6 , 509. Diaz-Pena, M.; Crespo-Colin, A.; Compostlro, A. J. Chem. Thermodyn. 1978, 10, 1101. Boublik, T.; Fried, V.; Hala, E. "The Vapor Pressures of Pure Substances"; Elsevier: Amsterdam, 1973. Brown, I.; Smith, F. Aust. J. Chem. 1854, 7 , 269. Gerster, J. A.; Gorton, J. A.; Eklund, R. B. J. Chem. Eng. Data 1960, 5 . 423. Deal, C. H.; Derr, E. L. Ind. Eng. Chem. Prod. Res. Dev. 1964, 3 , 394
iicke, D. C. J. Chromatogr. 1868, 3 5 , 24. Ambrose, D.; Sprake, C. H. S. J. Chem. Thermodyn. 1970, 2 , 631. Ambrose, D.; Eliender, J. H.; Gundry, H. A.; Lee, D. A,; Townsend, R. J. Chem. Thermodyn. 1881, 13, 795.
RECEIVED for review May 10, 1984. Accepted July 2, 1984. Research supported by a PSC-CUNY Grant.
