SOLUBILITIES OF HYDROCARBONS AKD CARBON DIOXIDEIN LIQUIDMETHANE
2345
Solubilities of Hydrocarbons and Carbon Dioxide in Liquid Methane and in Liquid Argon by G. T. Preston,*l E. W. Funk, and J. M. Prausnitz Department of Chemical Engineering, University of California, Berkeley, Berkeley, California 96720 (Received December 21, 1970) Publication costs borne completely by The Journal of Physical Chemistry
Solubility data in liquid methane and in liquid argon were obtained for carbon dioxide, n-pentane, cyclopentane, neopentane, 1,3-butadiene, and 2,3-dimethylbutane in the temperature region 90-125°K. Activity coefficients for the solutes, referred to the pure subcooled liquid, were interpreted with the Scatchard-Hildebrand equation allowing for deviations from the geometric-mean assumption for the cohesive energy density of unlike molecular pairs. Attention is given to the importance of pure-component solid transitions in solidliquid equilibrium calculations for binary mixtures. For saturated hydrocarbons, activity coefficients a t 120°K and “total” entropies of fusion decline sharply as the extent of hydrocarbon branching rises. Methane and cyclopentane form two liquid phases at about 123°K. The upper consolute point for this system is estimated to be 166°K and 76 mol % methane.
A recent review of solubility data for solids in cryogenic solvents2 showed that very little experimental information is available on solubilities in liquid argon. While solubility data in liquid methane are somewhat more plentiful, few measurements have been made a t low temperatures for hydrocarbons larger than propane. I n this work, we report solubility data for carbon dioxide and five hydrocarbons in liquid argon and in liquid methane. Particular attention is given to the effect of hydrocarbon molecular structure on solubility at low temperatures.
Experimental Section The experiments were carried out in a cylindrical stainless steel vacuum cryostat 3 ft high and 1 ft in diameter. Suspended from the cover plate of the cryostat was a massive heat sink assembly consisting of a copper bar partially immersed in a reservoir of liquid nitrogen boiling at atmospheric pressure. Figure 1 shows the basic features of the cryostat. The cryostat was evacuated to < l O - j mni pressure by a 4-in. oil diffusion pump, backed up by a large mechanical vacuum pump. The pumps were separated from the cryostat by a large liquid nitrogen cold trap. To minimize radiative heat transfer from the environment, two concentric heat shields made of copper sheet were located between the heat-sink assembly and the cryostat walls. The heat shields and the heat-sink assembly were highly poliehed and chrome plated. Thin cross-section stainless steel tubing and supports were used where large temperature gradients could exist in order to minimize conductive heat transfer. To permit visual observation of the mixtures, the equilibrium cell mas constructed from a thick-walled Pyrex tube 3 cm in diameter and 20 cm long. It was
located in a cylindrical cavity in the upper end of the copper bar. For good thermal contact \\-ith the copper bar, the ends of the cell were made of copper; they were sealed to the Pyrex tube by a pure indium soldering procedure. The upper end of the cell xyas bolted to the copper bar and the bolts were spring-loaded to allow for differences in thermal expansion. The cell contained a movable liquid-sampling probe, a pressure tap, an inlet and an outlet for recirculation of the vapor phase, and a thermocouple well. The cell construction is shown in Figure 2 . Temperatures in the liquid phase were measured Jvith a calibrated copper-constantan thermocouple, a Leeds and Xorthrup K-3 potentiometer, and a Honeywell galvanometer. The thermocouple and potentiometer leads were joined by soft-solder connections at a ceramic seal on the cryostat cover plate; the seal was elevated above the cover plate to decrease thermal gradients between the solder joints. Temperature control was maintained by a low gain, proportional mode temperature controller. Its platinum sensor was located in a cavity in the copper bar, just below the cell. To accelerate attainment of equilibrium between the liquid and solid phases and to assure a uniform temperature in the liquid phase, the vapor in the cell v a s recirculated at about 100 cm3/min with a peristaltic pump outside the cryostat. The returning vapor was cooled by countercurrent heat exchange with the vapor leaving the cell. The vapor reentered the cell near the bottom (1) Garrett Research & Development Co., La Verne, Calif. (2) G. T. Preston and J. R i . Prausnits, Ind. Eng. Chem., Process Des. Decelop., 9,264 (1970).
The Journal of Physical Chemistry, Vol. 76, N o . 16, 1971
2346
G. T. PRESTON, E. W. FUNK, AND J. M. PRAUSNITZ SAMPLING AN0 RECIRCULATION L!NESl
N:+$$!FN FILL THREADED HANDLES
E
r b
TO VACUUM
\
QUICK-CONNECT FITTING FOR SAMPLE BULB
/ TO VACUUM PUMPS
-
WIRE
+-HEATING
Liauio N I T ROO EN
LVE STEM THERMOCOUPLE (NOT TO SCALE)
Figure 1. Schematic of cryostat,. 16) SPRING-
1-
Liauio
MIXTURE
Figure 3. Liquid-sampling valve.
OPPER TOP
END
I
COPPER BAR
Figure 2
NDIUM
SEALS
P1 ENSOR
7
solid-liquid equilibrium cell.
and bubbled up through the liquid, providing vigorous agitation. The probe used to sample the liquid phase was functionally equivalent t o a very tall vee-tip valve; it is shown schematically in Figure 3. The valve stem mas The Journal of Phusical Chemistry, Vol. 76, No. 16, 1971
raised or lowered, to open or close the valve, by turning a threaded handle at the top of the valve, outside the cryostat. Another threaded handle was used to raise and lower the entire probe in the cell. The valve body was wrapped with heating wire to achieve complete vaporization of the liquid sample as it entered the valve; a vacuum jacket served to decrease heat loss into the cell. The temperature in the valve was monitored by means of a thermocouple in the valve stem, near the tip. The inlet to the valve was a 0.006-in. i.d. needle extending down about 1 in. below the vacuum jacket. Thermal expansion or contraction was taken up by a kink in the needle between the valve seat and the vacuum jacket. The valve seat was copper. The valve stem tip was “Rulon” (Dixon Corp.), a filled Teflon which is elastic and thus does not cold-flow. All other parts of the valve were stainless steel. Analysis of the samples was carried out using a gas chromatograph equipped with a thermal conductivity detector and a hydrogen flame-ionization detector in series. Whereas the amount of the solvent component was determined from the response of the thermal conductivity detector, the amount of the solute component was determined from the response of the flame detector, which is several orders of magnitude more sensitive to hydrocarbons than the thermal conductivity detector. Both signals were observed on a 1-mV recorder and integrated by a ball-and-disk mechanical integrator.
SOLUBILITIES O F
2347
HYDROCARBONS AND CARBON DIOXIDEI N LIQUIDMETHANE
Details concerning the apparatus and its operation are given by Preston3and Funk.4
Materials The solvents and solutes were purchased from the suppliers listed in Table I ; the purities shown are the manufacturers’ specifications. A trace of carbon dioxide in the methane was removed by passing the methane through an Ascarite trap.
of the pure solid, f’ is the fugacity of the pure subcooled liquid, x is the mole fraction in solution, and y is the activity coefficient of the solute in the liquid, referred to the pure subcooled liquid, all at system temperature T. For temperatures not much below the melting temperature and for normal pressures, the fugacity ratio f2”f2’ can be estimated by
Table I Purity, Material
Supplier
%
Methane Argon n-Pentane 1,s-Butadiene Carbon dioxide Cyclopent ane Neopentane 2,3-Dimethylbutane
Matheson Co. Matheson Co. Phillips Petroleum Co. Phillips Petroleum Co. Matheson Co. Phillips Petroleum Co. Matheson Co. Phillips Petroleum Co.
99.97 99.995 99.90 99.89 99.8 99 90 99.90 99.95 I
Results The experimental results are summarized in Table 11. The solubility x2 is the mole fraction of solute in the liquid phase. Since it was only possible to maintain desired temperatures to .tO.5O0K, the temperatures given in Table I1 are averages calculated by
T
=
(CTJ/N i
where T, is the experimental temperature and N is the number of samples taken a t the desired temperature. For each average temperature, the average solubility in Table I1 was calculated by i
where xZ,( is the experimental solubility. The precision, or scatter, of the solubilities was calculated from precision = For the cyclopentane-methane system it was observed that a t about 123°K the system split into two liquid phases. Solubilities of carbon dioxide in methane shown in Table I1 are in good agreement with those reported by Davis5and by Cheung and Zander.6
Thermodynamics of Solid-Liquid Equilibria Assuming that the solid phase is pure solute and that the liquid phase is a saturated solution of the solute in the solvent, the equation of equilibrium is fzB = YZXZfi‘
(4)
where subscript 2 refers to the solute, f” is the fugacity
where R is the gas constant, T , is the melting temperature of the solute, and ASf is the molar entropy of fusion of the solute.’ Some substances undergo solid-phase transitions from one crystal structure t o another. For these solutes, if the temperature of interest is less than the transition temperature, Ttrans, the expression for the fugacity ratio fzs/fzl becomes
where AStrans is the molar entropy of transition. If there is more than one solid-phase transition above the temperature of interest, further terms must be added to eq 6. Table I11 gives the melting temperatures and entropies of fusion for carbon dioxide and 45 hydrocarbons. Also, transition temperatures and entropies of transition are given for those hydrocarbons for which experimental data are available. If no transition data are given for a particular hydrocarbon in Table 111, we cannot assume that the hydrocarbon does not exhibit transitions in the solid phase. For many hydrocarbons, the desired experimental information has not been obtained. The thermodynamics of solid-liquid equilibria becomes complicated if a solid solution is formed. I n this experimental work the solid-phase composition was not determined. However, there was no visual indication of any formation of a solid solution. Using semiquantitative calculations, Funk shows4 that the solubilities of the hydrocarbon solutes are negligible in solid methane or solid argon. Equation 5 was used in these calculations to estimate the ratio of the pure-component fugacities of methane in the liquid and solid phases, and regular solution theory’ was used to esti(3) G. T. Preston, Ph.D. Dissertation, University of California, Berkeley, 1970. (4) E. W. Funk, Ph.D. Dissertation, University of California, Berkeley, 1970. (5) J. A. Davis, N. Rodewald, and F. Kurata, A I C h E J . , 8, 537 (1962).
(6) H. Cheung and E. 64, N o . 88, 34 (1968).
H. Zander, Chem. Eng. Progr.,
Symp. Ser.,
(7) J. H. Hildebrand and R. L. Scott, “Solubility of Noneleotrolytes,” Dover Publications, New York, N. Y., 1964.
The Journal of Physical Chemistry, Vol, 76,No. 16, 1971
2348
G. T. PRESTON, E. W. FUNK, AND J. M. PRAUSNITZ
Table I1 : Summary of Experimental Results __-____System
No. of samples
Precision, re1 7c
9 7 8 7 7 8 9 14 8 7
6 3 13 6 5 8 7 26 7 9 4 4 6
I _ _ _ _
Solvent
Solute
Methane
n-Pentane
Argon
n-Pent ane
Methane
1,3-Butadiene
Argon
1,3-But adiene
Methane
Carbon dioxide
Argon
Carbon dioxide
Methane
Cyclopent ane
Argon
Cyclopentane
Methane
Xeopentane
Argon
Neopent ane
Methane
2,3-Dimethylbut ane
Argon
2,3-Dimethylbutane
T ,OK
108 x2
100.4 112.7 124.5 92.3 99.8 104.8 110.5 101.8 113.3 128.4 92.7 102.2 110.8 126.4 137.5 109.0 115.9 100.2 112.5 92.6 104.0 110.4 99.9 112.0 123.2 92.7 104.6 110.2 100.2 111.9 123.4 92.3 104.6 109.3
1.380 6.16 17.86 0.0158 0.0326 0.0563 0.1729 0.200 1.071 4.504 0,00147 0.00722 0.02241 0.732 2.366 0.0797 0.2059 3.52 12.9 0.151 0.328 0.651 10.1 16.9 26.5 0.901 1.30 1.51 3.98 10.0 43.1 0.278 0.638 0.801
mate the activity coefficients of methane in both liquid and solid phases.
Activity Coefficients For many nonpolar systems, the theory of regular solutions’ can be used to estimate the activity coefficients. For a binary system, the equation of Scatchard’ for the activity coefficient of the solute is
RT In y2 =
V2.412@12
(7)
where v2 is the molar volume of the subcooled liquid solute, Alzis the exchange energy density, and @I is the volume fraction of the solvent in solution, defined by @1
XlZ’1
= XlV1
+
x2v2
(8)
The exchange energy density is related to the cohesive energy densities, C4j,by A12
=
c11 +
c22
- 2c12
(9)
where C11 is the cohesive energy density of the solvent, CZzis the cohesive energy density of the subcooled liquid solute, and Clz is the cohesive energy density The Journal of Physical Chemistry, Vol. 76, No. 16,1071
7 6 7 3 7 10 9 6
7 7 8 8 6
7 4 7 8 4 7 5 5 0
5 4
7 15 46 11 6 9
7
Recommended 11%
0.03
0.07
0.05
0.11
-0.02 -0.04 0.007 0.023
3
8 8 8 12 8 4 10 10 9 9 15 9 11
0.015
0.036
0.025
0.045
characterizing the interaction between solute and solvent. The most serious weakness of regular solution theory, as with most solution theories, lies in its inability to relate accurately interactions between unlike molecules to those between like molecules. The Scatchard-Hildebrand theory’ makes the assumption that the cohesive energy density for unlike-molecule interactions is given by the geometric mean of the cohesive energy densities of the like molecules. c 1 2
= [cllc2211’2
(10)
Since results are very sensitive to this mixing rule, for quantitative application. the geometric-mean mixing rule is relaxed by writing ClZ
=
[cllc2*11’*(l - 112)
(11)
where Zl2 is a binary constant, whose magnitude is of the order of characteristic of the solute-solvent pair. This constant, t o a good approximation, is independent of composition and varies little with temperature. From London’s theory of dispersion forces, an approximate expression for 112 can be derived; this expression shows that 112 can be positive or negative, but it seldom
SOLUBILITIES OF
HYDROCARBONS AND CARBON DIOXIDE IN LIQUID
2349
R’lETHANE
Table 111: Temperatures and Entropies for Fusion and Other Solid-Phase Transitions’ Hydrocarbon
1. Methane
2. Butane 3. 4. 5. 6.
2-Methylpropane Pentane Isopentane Neopentane
7. Cyclopent ane
8. Hexane 9. 2-Methylpentane 10. 2,2-Dimethylbutane
11. 2,3-Dimethylbutane
12. Cyclohexane 13. 14. 15. 16. 17. 18. 19.
Methylcyclopentane Heptane 2-Methylhexane 2,2-Dimethylpentane 2,4-Dimethylpentane 3,3-Dimethylpentane 2,2,3-Trimethylbut ane
Tm, OK
A&, cal/mol-OK
90.6 (20 * 5)* 134.8 (107.6) 113.5 143.5 113.2 256.5 (140.0)c 179 3 (138.0) (122.4) 177.8 119.5 173.4 (141.1) (127.1) 144.7 (136.1) 279.8 (186.1) 130.7 182.6 154.9 149.4 153.9 138.7 248.2
2.26 (0. 8.32 (4.62) 9.55 14.02 10.88 3.03 (4.43)c 0.81 (0,60) (9.53) 17.51 12.55 0.80 (0.57) (10.16) 1.34 (11.40) 2.28 (8.59) 12.67 18.39 13.69 9.38 10.40 12.18 2.12d
I
Hydrocarbon
20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33.
3-Ethylpentane hlethylcyclohexane Octane 2-Methylheptane 3-Methylheptane 4-Methylheptane 2,2-Dimethylhexane 2,5-Dimethylhexane 3,3-Dimethylhexane 2,2,3-Trimethylpentane 2,2,4-Trimethylpentane 2,3,3-Trimethylpentane 2,3,4-Trimethylpentane
34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46.
Decane Dodecane Eicosane l-Butene 2-Methylpropene l-Pentene 2-Methylbutene-2 Heptene-1 Butadiene-1,3 Pent adiene-1,4 2-Methylbutadiene-l,3 1,2-Dimethylacetylene Carbon dioxide
2,Z13,3-Tetramethylbutane
Tm, OK
ASf, cal/mol-°K
154.5 146.6 216.3 164.1 152.6 172,2 152.0 181.9 147.0 160.9 165.8 172.4 163.9 373.8 (148.0) 243.1 263.5 309.5 87.8 132.8 105.8 139.4 154.1 164.2 125.0 126.3 140.6 216.5
14.63 11.00 22.80 14.94 17.81 15.05 18.20 16.89 11.58 12,82 13.28 2.12d 13.51 4.55 (2.56) 28.26 33.15 47 46 10.47 10.67 11.14 13.02 19.64 11.62 11.73 9.05 15.70 4.86 I
a J. Timmermans, “Physico-Chemical Constants of Pure Organic Compounds,” Elsevier, Amsterdam, 1950; R. H. Perry, C. H. Chilton, and S. D. Kirkpatrick, Ed., “Chemical Engineers’ Handbook,” 4th ed, McGraw-Hill, New York, N. Y., 1963; J. SolidG. Aston and G. H . Messerley, J . Amer. Chem. Soc., 58, 2354 (1936). b Parentheses denote solid-phase transition data. phase transition data determined by indirect experiment (data of Aston and Messerly). d These low entropies of fusion suggest the possibility of transitions t o more stable solid forms at temperatures below the melting temperature.
gives good quantitative results. Preston and Prausnitz2 and Cheung and Zander6 discuss methods for obtaining rough estimates of 112 for use in solid-liquid equilibria. If we introduce the solubility parameter 6 into eq 7, 9, and 11, the expression for the activity coefficient of the solute is
RT In
+
yz = v ~ i p 1 ~ [ ( 61 6 ~ ) ~211281621
(12)
where a1 = Clll/*and 62 = C221/2.When lI2 = 0, eq 12 reduces to the familiar Scatchard-Hildebrand equation. Experimental solubility data were used t o calculate 112 for each binary system. the results are shown in Table 11. I n these calculations, solubility parameters and liquid molar volumes were obtained from a corresponding-states correlation. Equation 12, coupled with eq 4 and 6, enables us to estimate the fugacity of each component in the binary liquid mixtures as a function of temperature and composition. I n such calculations, solubility parameters and liquid molar volumes are functions of temperature
as indicated in the corresponding-states correlation,2 but’ 112 is considered t’o be independent of temperature.
Correlation of Activity Coefficients and Entropies of Fusion The values of 112 given in Table I1 show that 112 generally increases with difference in molecular size and chemical nature. It is impractical, however, t o attempt any quantitative correlation of 112 because the values of Ll2 are sensitive to the extrapolation of solubility parameters to low temperatures. We attempt to correlate instead the activity coefficients of the saturated hydrocarbon solutes at infinite dilution in the solvent. Activity coefficients a t infinite dilution in methane and argon were first calculated a t 120°K for a variety of saturated hydrocarbons using eq 12 and assuming 112 = 0. These calculated activity coefficients are given in Table IV. Figure 4 shows the activity coefficients plotted against a solute parameter r , which is a measure of the extent of branching in the hydrocarbon. The Journal of Physical Chemistry, Vol. 7 6 , N o . 16,1971
G. T. PRESTON, E. W. FUNK, AND J. &I. PRAUSNITZ
2350
~-
Table IV : Activity Coefficients at 120'K of Hydrocarbons at Infinite Dilution in Liquid Methane and in Liquid Argon Solute
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16.
Cyclohexane Cyclopentane Methylcyclohexane Methylcyclopentane Octane Heptane Hexane Pentane 3-Methylhexane 2-Methylpentane 3-Methylpentane Isopentane Isooctane 2,3-Dimethylbutane Xeopentane 1,3-Butadiene
9.60 9.92 9.25 9.15 8.80 8.70 8.63 8.60 8.58 8.52 8.52 8.49 8.48 8.46 8.26 9.45
41.2 46.1 29.7 15.4 17.4 10.5 6.7 5.2 7.9 5.6 5.4 4.4 8.6 5.2 3.2 21.2
597.6 538.1 492.9 164.0 329.0 134.7 57.4 35.7 88.1 46.5 45.7 27.8 126.0 40.5 16.5 136.0
62.1
21.5
19.4 6.42 140.0
1291.0
602.0
311.0 64.1 8000.0
a Solubility parameters calculated using the correlation given in G. T. Preston and J. M. Prausnita, Ind. Eng. Chern., Process Des. Develop., 9,264 (1970). * At 120"K, the solubility parameter of methane is 6.61 and that for argon is 5.68 (cal/cm8)'/2.
Kumber of CH, groups in saturated hydrocarbon r= Total number of carbon atoms in saturated hydrocarbon
l0,000
Figure 4 shows that there is a strong decrease in the predicted activity coefficient at infinite dilution with an increase in the extent of branching in the saturated hydrocarbon; Figure 5 shows results when argon is the solvent.
2000
1
6ooo~ 4000
I-
-
60 2
I
I
1
-
600
8;
1
NUMBERS AS GIVEN IN T A B L E I V
I
NUMBERS AS GIVEN IN TABLE I V
\ 1000 -' \
1
I
0
1
PREDICTED WITH P,, = 0 CALCULATED USING EXPERIMENTAL
2
400 1001 80
o
200
'.
''
30
05
40 60
100 I
60 40 20 '
O
I
0
0.2 0.4 r , D E G R E E OF
0.6
0.8
BRANCHING
Figure 5 . Activity coefficients at 120°K of saturated hydrocarbons at infinite dilution in argon. PREDICTED WITH P,,= 0 CALCULATED USING EXPERIMENTAL 1 1 2
o 0
0
0.2 r
,
0.4
0.6
0.8
D E G R E E OF B R A N C H I N G
Figure 4. Activity coefficients a t 120°K of saturated hydrocarbons at infinite dilution in methane. The Journal
of
Physical Chemistry,Vol. 76,N o . 16, 1971
i
Using experimental values of lI2, activity coefficients a t infinite dilution were again calculated at 120°1< using eq 12, and these are also given in Table IV. Figure 4 shows experimental activity coefficients of the saturated hydrocarbons at infinite dilution in methane and Figure 5 shows similar results in argon. For both solvents, the experimental activity coefficients define a line above that predicted with ZI2 = 0 and with a smaller
SOLUBILITIES OF HYDROCARBONS AND CARBON DIOXIDEIN LIQUIDMETHANE
fusion, it is seldom possible to predict what part of the “total” entropy appears a t the transition temperature, and it is almost never possible to give an accurate prediction of transition temperatures. Figure 6 can be used to obtain reasonable estimates of the “total” entropy of fusion of saturated and unsaturated aliphatic hydrocarbons. With an estimated entropy of fusion from Figure 6, the fugacity ratio can be estimated by
I
036
1
035 034
In
’ ‘1 =
-0
fis -
fi‘
6
-I
2351
NUMBERS AS G I V E N IN TABLE I l l
=
[
AS(t’ota1) 1 - -
R
F]
(14)
where AS(tota1) is the “total” entropy of fusion. This approximate equation tends to underestimate the fugacity ratio for two reasons. First, the effect of considering that the “total” entropy change occurs at the melting point is to predict a fugacity ratio which is too small; this effect becomes large only when the temperature of interest and the transition temperatures are far below the melting temperature. For example, the fugacity ratio predicted for neopentane (melting temperature 256.5”K and transition temperature 140°K) at 120°K using eq 14 is 0.014 and the value predicted using transition data from Table I11 in eq 6 is 0.120. Second, eq 14 gives an unrealistically low value of the fugacity ratio if the transition temperature is below the temperature of interest. The uncertainty in the fugacity ratio can be estimated by taking as a lower limit the fugacity ratio calculated by eq 14 and as an upper limit the value calculated by eq 5 , which neglects the lowering of the fugacity ratio due to phase transitions.
mm 4
0
0.6
0.2 0.4 r , DEGREE O F BRANCHING
0.0
Figure 6. Total entropies of fusion (from most stable solid to liquid) for aliphatic hydrocarbons.
slope. (The experimental activity coefficients of 1,3butadiene a t infinite dilution in liquid methane and in liquid argon are much larger than those predicted by Figures 4 and 5 . ) Figures 4 and 5 can be used to obtain estimates of activity coefficients a t infinite dilution for those saturated hydrocarbons that have not been determined experimentally. For temperatures not far removed from 120”1
