Inc., or the Matheson Company, Inc. (for purities see reference 15). The solvents .... (1) where V,O is the molar volume of pure solvent (subscript l), B, is the second virial .... Clever, H. L.; Battino, R.; Saylor, J. H.; Gross, P. M. J. Phys. Chem. 1957 ...
A-055 J. Chem. Thermodynamics 1978, 10, 8 17-822
Solubilities of gases in liquids II. The solubilities of He, Ne, Ar, Kr, O,, NZ, CO, CO,, CH,, CF,, and SF8 in n-octane I-octanol, n-decane, and I-decanol” ROBERT
J. WILCOCKb,
RUBIN
Department of Chemistry, WILLIAM
BATTINO,
Wright State University,
Dayton, Ohio 45431, U.S.A.
E‘. DANFORTH,
Department of Biology, Illinois Institute of Technology, Chicago, Illinois 60616, U.S.A. and EMMERICH WILHELM Institut fir Physikalische Wien. Austria
Chernie, Universitiit
Wien, WiihringerstraJe
42, A-1090
(Received 22 August 1977) The solubilities of 11 gases in n-octane, n-decane, I-octanol, and I-decanol have been determined at atmospheric pressure in the range 293 to 313 K. From the temperature variation of the experimental solubilities, partial molar enthalpies and entropies of solution for 1 atm partial pressure of gas and 298.15 K have been derived. Comparison with results obtained through application of scaled-particle theory showed satisfactory agreement.
1. Iutroduction As part of our continuing effort to obtain accurate gas solubihties in liquid systems of biological interest,“-3’ we have now started systematic studies in the homologous series of n-aikanes and I-alkanols, liquids which might serve as simple model substances for cell membranes. The solubilities of gases in lipid membranes arc related to at least two important physiological processes: membrane permeability and anesthesia.In those caseswhere substancespenetrate cell membranesby diffusion, theory and experiment strongly suggesta correlation between solubility in the membrane lipids and rate of transfer across the membrane.‘4-6’ A considerable amount of work has been devoted to the mechanism of anesthesia. Although there is still LICommunicated in part at the Fourth InternationaI Conference on Chemical Thermodynamics, Montpellier (France), 26 to 30 August 1975. b Current address: Dept. of Scientific and Industrial Research, Chemistry Division, Private Bag, Petone, New Zealand. 0021-9614/78/0901-0817 %01.00/O Q 1978 Academic Press Inc. (London) Ltd.
818
R. J. WILCOCK,
R. BATTINO,
W. F. DANFORTH,
AND
E. WILHELM
much controversy, it appears that anesthetic potency is closely related to lipid solubility. (‘-‘) In particular, Hansch et al. (lo) formulated a quantitative relation between the effective anesthetic pressure and the partition coefficients of 32 gaseous anesthetics in octanol + water (seealso references 11, 12). To see the effect of chain-length, both in alkanes and alkanols, upon solubility behaviour, we carried out a comparative study on the solubilities of the 11 gases He, Ne, Ar, Kr, Nz, 02, CO, COz, CH,, CF,, and SF, in n-octane, I-octanol, n-decane, and 1-decanol at partial gas pressures of 1 atm and in the temperature range 283 to 313 K.t
2. Experimental Details of the apparatus and procedures have been reported elsewhere.(‘3*‘4’ All measurements were carried out on thoroughly degassedsamples of liquids(14) with the aid of a modified Morrison-Billett apparatus.(l) Temperature control in the air thermostat was better than ) 10 mK. Absolute temperature measurements were performed with a platinum resistance thermometer calibrated by means of a water triple-point cell. The gaseswere obtained either from Air Products and Chemicals, Inc., or the Matheson Company, Inc. (for purities see reference 15). The solvents were either from Phillips Petroleum Company (alkanes) or from Eastman Organic Chemicals. They were fractionally distilled until their densities at 298.15 K were comparable to literature values: n-octane, 0.6988; n-decane, 0.7264; 1-octanol, 0.8247; and 1-decanol, 0.8206 g cme3. The imprecision of the reported solubilities is estimated to be Ifr 1.Oper cent or less, except for the gasesof very low solubility (He and Ne), where it is occasionally closer to +2.0 per cent.
3. Results Table 1 contains the experimental solubilities in the four liquids n-octane, 1-octanol, n-decane, and 1-decanol in terms of the Ostwald coefficient L at p2 = 1 atm partial TABLE
1. Solubilities
Gas He
Ne Ar Kr N2 02
t Throughout
of gases at 1 atm partial pressure of gas: thermodynamic Ostwald coefficient L, mole fraction x2 of gas (atm = 101325 Pa)
TIK
L
283.23 298.33 312.92 298.27 283.27 298.27 313.04 298.18 298.25 283.31 298.21 313.15
0.02797 0.03550 0.04221 0.05406 0.3616 0.3502 0.3700 1.053 0.1965 0.3127 0.3264 0.3356
1O’xz
Gas
Solvent : n-octane 1.933 co 2.370 2.733 3.609 CO2 24.96 23.36 23.92 CH, 70.01 13.11 CF, 21.59 21.77 SF, 21.70
this paper atm = 101.325 kPa; caltb = 4.184 J.
T/K
L
283.27 298.21 312.94 283.44 298.27 313.43 298.25 313.35 283.21 298.21 283.25 298.21 313.39
0.2569 0.2569 0.2620 2.108 1.806 1.614 0.7548 0.7353 0.2954 0.2989 1.631 1.401 1.225
temperature .104x2 17.74 17.14 16.95 144.4 119.8 103.8 50.26 47.44 20.47 20.00 113.0 93.80 79.44 ____-
T,
SOLUBILITIES
OF GASES
TABLE
GflS
L
1O’xa
283.18 298.23 313.35 298.24 283.20 298.05 313.54 298.16 283.18 298.11 313.19 283.15 298.11 313.48
0.02509 0.02959 0.03562 0.04288 0.3098 0.3055 0.3106 0.9242 0.1471 0.1518 0.1559 0.2658 0.2752 0.2823
2.081 2.367 2.756 3.430 25.67 24.42 23.99 73.61 12.20 12.14 12.06 22.04 22.00 21.81
282.45 298.17 298.08 283.28 298.10 313.57 298.06 283.32 298.15 313.60 283.35 298.13
0.01639 0.01866 0.02616 0.1890 0.1968 0.1984 0.5837 0.08514 0.09629 0.1019 0.1724 0.1749
T/K
-
819
IN LIQUIDS
l-continued Gas
~TIK
L
283.15 298.16 313.48 283.16 198.10 313.50 282.80 313.35 298.12 282.61 298.12 313.45
0.2047 0.2079 0.2228 1.748 1.583 1.409 0.6929 0.6218 0.2335 1.259 1.088 0.9716
16.98 16.62 17.22 143.9 125.8 108.3 57.37 47.98 18.73 105.0 87.36 75.37
282.94 298.05 282.66 298.12 313.64 283.23 298.08 313.46 282.66 298.15 313.48 282.61 298.15 313.48
0.1256 0.1312 1.720 1.443 1.263 0.4450 0.4154 0.4088 0.1038 0.1097 0.1167 0.5553 0.5035 0.4567
8.456 8.490 115.3 93.01 78.49 29.92 26.87 25.48 7.022 7.121 7.298 37.81 32.86 28.69
298.16 313.56 284.01 298.15 313.49 284.04 298.08 313.37 282.61 298.31 313.37 283.20 298.28 313.45
0.1232 0.1304 1.526 1.249 1.053 0.4143 0.4048 0.3856 0.09463 0.09996 0.1051 0.4740 0.4515 0.4005
9.640 9.827 123.2 97.33 79.14 33.62 31.66 29.05 7.747 7.845 7.948 38.98 35.62 30.42
1O’XZ
Solvent : n-decane He
Ne Ar
Kr N2
02
Solvent: He Ne Ar
Kr N&X
02
1.105 1.207 1.693 12.71 12.73 12.37 37.73 5.727 6.230 6.353 11.59 11.32
CO
co*
CH4 CFe SF6
I-octanol co CO*
CHI
CF,
SF6
Solvent : I-decanol He
Ne Ar
Kr NZ
02
282.64 298.11 313.49 298.09 282.60
298.10
313.54 298.06 282.57 298.08 313.42 282.74 298.10 313.56
0.01642 0.01932 0.02302 0.02527 0.1808 0.1910 0.1912 0.5439 0.07852 0.08536 0.09096 0.1549 0.1558 0.1641
1.338 1.512 1.736 1.978 14.74 14.94 14.41 42.50 6.403 6.681 6.859 12.63 12.19 12.37
co CO2
CHI
CF,
SF,
pressure of gas (subscript 2) and thermodynamic temperature T. In order to convert L to the corresponding equilibrium mole fraction x2, use was made of the relation:(‘*) x* = {(RT/p*+B,)/LV,“+l}-‘, (1) where V,Ois the molar volume of pure solvent (subscript l), B, is the second virial
820
R. J. WILCOCK,
R. BATTlNO,
W. F. DANFORTH,
AND E. WILHELM
coefficient of pure gaseous solute, and R denotes the gas constant. For B, < RTIp.,, this reduces to the more customary form: x2 = {RT/LV;p,+
I>-‘.
(2)
Virial coefficients were taken from Dymond and Smith.“” The molar volumes at various temperatures were obtained by polynomial interpolation nf literature data 117~18) Whenever applicable, the resulting mole fractions x,(1 atm, 7) were fitted to AG,“=-RTlnx,=A+BT,
(3) which represents our results adequately over the temperature range investigated.(r2’ AC,0is the partial molar Gibbs energy of solution, and A and Bare constants related to the partial molar entropy and enthalpy of solution by ASi = -B and AH; = A. These quantities are contained in table 2, together with smoothed values of xz, all at 1 atm partial pressure of gas and 298.35 K. For n-octane and n-decane, several rather reliable literature values are available for comparison. (19) In the case of the rare gases, agreement with solubilities of reference 20 is satisfactory: generally, deviations are about 12.0 per cent or less, TABLE 2. Equilibrium solubility xp, partial molar enthalpy of solution AH;, and partial molar entropy of solution AS& in n-octane, n-decane, I-octanol, and I-decanol at 298.15 K and partial pressure of gasp2= 1 atm (atm = 101.325 kPa; calth = 4.184 J) AS; AH; AS; AH,” 10*x2 Gas 1O?uz Cal,,, K-r mol-’ calth mol-’ calt, K-l mol. 1 caltb mol-’
He Ne Ar Kr
2.33 3.61 24.05 70.0
ST: co co2 CHn CF, SF*
31.1 21.69 17.26 121.20 50.28 20.00 94.03
He Ne Ar Kr z:
2.39 3.43 24.66 73.6 21.95 12.13
CO co2 CH, CF, SF8
16.94 124.69 52.20 18.7 87.84
solvent: n-octane 2054 -9.7 -243 -12.8 -. -29 -12.1 -269 -1939 -709 -262 -2064 solvent: n-decane 1643 -389 -68 -62 88 -1654 -1031 -1891
1.21 1.69 12.60 37.7 11.32 6.10
-13.5 -15.3 --12.9 -13.2 -16.2
8.49 93.77 27.30 7.15 32.73
-11.1 -13.2 -13.6 -12.4 -12.4 -14.3 -13.9 -15.8
1.53 1.98 14.69 42.5 6.65 12.39 9.64 98.14 31.36 7.85 34.73
solvent: I-octanol 943 .--.14.8 - 164 -13.8 596 -12.7 --‘75 -- 14.4 46 -- 13.9 -2183 -16.6 -931 - 14.9 221 -13.7 -1574 -- 16.7 solvent: I-decanol 1486 -12.5 --I33 - 13.4 391 - 13.2 -112 -13.7 231 -13.0 - 2652 -18.1 -m880 - 14.4 147 -13.7 -14.54 16.1
SOLUBILITIES
821
OF GASES IN LIQUIDS
with the exception of He, where deviations up to 3.5 per cent occur. As for the entropy of solution, Clever et &‘20’ give - 10.1 cal,, K- ’ mol- ’ (He in n-octane), - 12.2cal,, K-’ mol-’ (Ar in n-octane), - 10.4Cal,, K-’ mol-’ (He in n-decane), and - 13.1 Cal,, K-’ mol- ’ (Ar in n-decane), in excellent accord with our results. The almost 50 per cent lower mole fraction solubility of CH, in n-octane of Onda, Sada, and Shinno must be due to experimental error, possibly incomplete degassing. For CF, and SF6 in n-octane, our results agree well with those of Wilhelm and Battino.(13’ No literature results could be found for any of the gasesin alcohols.
Solubilities and thermodynamic functions pertaining to the solution process were calculated in the usual manner from the scaled-particle theory (SPT) formalism.(22-26’ Pertinent data for the gaseswere taken from reference 27 and the necessaryeffective Lennard-Jones potential parameters of the solvent were determined by standard methods.(‘3V25,27)Results are presented in table 3. Here the compactness of the TABLE 3. Physical properties and molecular parameters of the pure solvents at 298.15 K: molar volume Vy, thermal expansivity ap, effective hard-sphere diameter gl, energy parameter cl/k, and compactness factory 106Y;
m3 mol-’ n-octane n-decane I-octano1 1-decanol
163.48 195.89 158.36 191.55
5
a1
cllk
K-1
nm
K
J
1.17 1.04 0.854 0.829
0.654 0.707 0.662 0.711
601 673 662 680
0.539 0.568 0.577 0.592
solvent is denoted by y = Lna:/6V,“, where L is the Avogadro constant, and 6, is the effective hard-sphere diameter. For n-octane and n-decane the agreement with previously published values of cl is excellent. With respect to cl/k the new parameters are considered more reliable becauseof the larger number of gasesstudied. They are slightly larger than in reference 27. For the sake of brevity, we do not report detailed results of calculated thermodynamic quantities. Let it suffice that the pattern of agreement generally observed in applications of SPT to gas solubilities is preserved, with the exception of CO? in alkano1.t The enhanced solubility of CO2 in the alcohols is not surprising, if the relatively strong specific interaction between this gas and the hydroxyl group is considered.(2’ Interestingly, the entropy of cavity formation in both alkanols is only slightly smaller than in isobutanol :(‘) for example, for argon it is -2.63 cal,, K-.’ mole1 (in 1-octanol) and -2.56 Cal,, K-l mol-’ (in I-decanol) as compared with -2.89 Cal,, K-’ mol-’ in isobutanol (at 298.15 K). We tested the Hildebrand correlation (30-32) for the n-alknnes by plotting the difference between the partial molar entropy S2 of the gas in solution (equilibrium mole fraction x2) and the entropy of gas S,Bin its standard state against the solubility t Extensive tables are available upon request from the authors.
822
R. J. WILCOCK,
R. BATTINO,
W. F. DANFORTH,
AND E. WILHELM
expressedas -R In x2 (at 298.15 K). The usual linear plot is obtained with intercepts of -21.2 Cal,, K-* mol-’ (n-octane) and - 19.2 Cal,,,K-I mol-’ (n-decane), and with slopes 1.66 and 1.49. Whereas the intercepts are rather close to the theoretical value of -21.0 Cal,, K-’ mol- ’ ,(33) the slope for decane is somewhat lower than the value expected from its cohesive energy density.C32’ REFERENCES Battino, R.; Evans, F. D.; Danforth, W. F. J. Am. Oil Chem. Sot. 1968, 45, 830.
:: Battino, R.; Evans, F. D.; Danforth, W. F.; Wilhelm, E. J. Chem. Thermodynamics 1971, 3, 743. 3. Byrne, J. E.; Battino, R.; Danforth, W. F. J. Chem. Thermodynamics 1974, 6, 245. 4. Davson, H.; Danielli, J. F. The Permeability of Natural Membranes, 2nd edition. Cambridge University Press: Cambridge, 1952, pp. 80, 294. 5. Waartiovaara, V. ; Collander, R. Permeabifitiilstheorien. Protoplasmatologia II/cd. SprinprVerlag: Wien. 1960. 6. Lieb, W. R.; Stein, W. D. The Molecular Basis of Membrane Function. Tosteson, D. C.; editor. Prentice-Hall: Englewood Cliffs, N.J. 1969, p. 445. 7. Dawe, R. A. ; Miller, K. W.; Smith, E. B. Nature London 1964, 204, 789. 8. Miller, K. W.; Paton, W. D. M.; Smith, E. B.; Nature London 1965, 206, 574. 9. Miller, K. W.; Paton, W. D. M.; Smith, E. B.; Smith, R. A. Anesthesiology 1972, 36, 339. 10. Hansch, C.; Vittoria, A.; Silipo, A.; Jow, P. Y. C. J. Med. Chem. 1975, 18, 546. 11. Leo, A.; Hansch, C. ; Elkins, D. Chem. Rev. 1971, 71, 525. 12. Wilhelm, E.; Battino, R.; Wilcock, R. J. Chem. Rev. 1977, 77, 219. 13. Wilhelm, E.; Battino, R. J. Chem. Thermodynamics 1971, 3, 379. 14. Battino, R. ; Bar&of, M.; Bogan, M.; Wilhelm, E. Anal. Chem. 1971, 43, 806. 15. Wilcock, R. J.; Battino, R.; Wilhelm, E. J. Chem. Thermodynamics 1977, 9, 111. 16. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Gases. Clarendon Press: Oxford, 1969. 17. Selected Values of Properties of Hydrocarbons and Related Compounds, A.P.I. Research Project 44, Thermodynamics Research Center Texas A & M University, College Station, Texas. 1%7. 18. Selected Vahtes of Properties of Chemical Compounds, Thermodynamics Research Center Data Project, Texas A & M University: College Station, Texas, 1%8. 19. Wilhelm, E.; Battino, R. Chem. Rev. 1974, 73, 1. 20. Clever, H. L.; Battino, R.; Saylor, J. H.; Gross, P. M. J. Phys. Chem. 1957, 61, 1078. 21. Onda, K.; Sada, E. ; Shinno, S. Kogyo Kagaku Zasshi 1958, 61. 702. 22. Reiss, H.; Frisch, H. L.; Lebowitz, J. L. J. Chem. Phys. 1959, 31, 369. 23. Reiss, H.; Frisch, H. L.; Helfand, E.; Lebowitz, J. L. J. Chem. Phys. 1960, 32, 119. 24. Pierotti, R. A. J. Phys. Chem. 1963, 67, 1840. 25. Pierotti, R. A. J. Phys. Chem. 1%5, 69, 281. 26. Pierotti, R. A. Chem. Rev. 1976, 76, 717. Wilhelm. E.: Battino. R. J. Chem. Phvs. 1971. 55. 4012. Z: Field, RI L. f Wilhelm, E.; Battino, RI J. Chem. Thermodynamics 1974, 6, 237. 29. Geller, E. B.; Battino, R.; Wilhelm, E. J. Chem. Thermodynamics 1976, 8, 197. 30. Jolley, J. E.; Hildebrand, J. H. J. Am. Chem. Sot. 1958, 80, 1050. 31. Dvmond. J. H. J. Phvs. Chem. 1967. 71. 1829. 32. Hildebrand, J. H.; Piausnitz, J. M.;‘Scdtt, R. L. Regular and Related Solutions, Van Nostrand Reinhold Company: New York, 1970, p. 116. 33. Hermsen, R. W.; Prausnitz, J. M. J. Chem. Phys. 1961, 34, 108.
