m
= = =
np
p
change of thermodynamic property upon mixing nonpolar portion of energy of vaporization polai. portion of energy of vaporization
literature Cited
American Petroleum Institute, Pittsburgh, Pa.: Project 44, ’Selected Values of Properties of Hydrocarbons and Related Compounds.” 1955. (2) Barker. J. A.. J . Chrm. Phps. 20, 1526 (1952). (3) Billmeyer, 1. \ V . > private communication. (4) Blanks. R. F., doctoral dissertation. University of California, Barkrlrv. Calif.. 1963 (5) Blanks: R. F.. Prausnitz. J. M., A.1.Ch.E. J . 8 , 86 (1962). ( 6 ) Bondi, A,. Z b i d . , 8, 610 (1962). (7) Bondi. A , . Simki’n: D. J., Ibid.. 3 , 473 (1957). (8) BristoLv. G.. \Vatson. \ V . F.. Trans. Faraday SOC.5 4 , 1731. 1742 (1958). (9) Brown, H. C. Pt ai...J. A m . Chem. SOC.7 5 , 1 (1953). (10) Brolvning. G . V.? Ferry, J. D., J . C h m . Phys. 17, 1107 (1
~
\
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,
i\ l- 9. 4 9.,.\
(11) Burrell, H.. Znterchem. Rei’. 14, 3; 31 (1955). (12) Conway. B. E.. Lakhanpal, M . L., J . Polymer Sci. 46, 75: 93, 111 (1960). (13) Delmas. G.. Patterson. D., Somcynsky, T., Zbid., 5 7 , 79 11062). (14) Doty. P. M.. Zablr. H. Z . . Zbid.: 1 , 90 (1946). (15) Dreisbach, R. R.; Adz,an. Chrni. Sei. No. 15 (1955). (16) Florv. P. J.. J . Chem. Phys. 1 0 , 51 (1942). (17) 1 b d . : ’ 1 8 , 108 (1950). (18) Flory. P. J.. “Principles of Polymer Chemistry,” Cornell University Press, N e w York. 1953. (19) Flory. P. J.. Fox. T. G., Jr., J . Am. Chem. Soc. 7 3 , 1904 (1951). (20) Florv. P. J.. Rehner, J.: J . Chpm. Phys. 1 1 , 521 (1943). (21) Fox.’T. G. et al.. Poiymer3, 71. 111 (1962). \ - -
--I
(22) Fox, T. G., Flory, P. J., J . Am. C h m . Soc. 73, 1909, 1915 (1951). (23) Gee, G.: Trans. Znst. Rubber Ind. 18, 266 (1943). (24) Hildebrand, J. H., Scott. R. L.. “Solubility of hTonelectrolytes,“ Reinhold. Nrw York: 1950. (25) Hirschfelder. J. 0 . .Curtiss, C. F., Bird, R. B., “Molecular Theory of Gases and Liquids.“ \Viley, New York: 1954. (26) Huggins, M. L.. Ann. .Y. I?, Acad. Scz. 4 3 , 1 (1942): J . Am. Chem. SOC.6 4 , 1712 (1942); 2nd. Eng. Chem. 3 5 , 216 (1943). . ig.Fedetation SOC.Paint Techno). (27) Lieberman: E. P., O ~ C D 34, No. 444. 30 (1962). (28) Munster. A , . J . C/zim. Phys. 49, 128 (1952). ( 2 9 ) Munster. A , . Trans. Faraday Soc. 46, 165 (1950). (30) Munster. A . Z. Physik. Chem. Leijrig 196, 106 (3950). (31) Nickerson. .T. K., doctoral dissartation. Texas University, Austin. ?’ex., 1960. (32) Pimentel, G. C.. McClellan: A. L., ’.The Hydrogen Bond,” LV. H. Freeman and Co., San Francisco, 1960. (33) Prausnitz. J. M . , Anderson, K . , ‘4.I.Ch.B. .7. 7 , 96 (1961). (34) Prausnitz, J. M., Shair, F. H.. Ibtd., p. 682. (35) Reid, R. C . . Sherwood. T. K.. “Properties of Gases and Liquids.” McGraw-Hill. New York, 1958. (36) Scatchard, G., Trans. Faraday SOC.33, 160 (1937): Chem. Rem. 8, 321 (1931); J . .4m. Chem. SOC. 56, 995 (1934). (37) Scott. R. L.: Magat. M.. J . Chem. Phys. 13, 172, 178 (1945). (38) Small. P. A , J . Appl. Chem. 3 , 71 (1953). (39) Timmermans. J.: “Physico-Chemical Constants of Pure Organic Compounds.” Elsevier. Amsterdam. 1950. (40) Tompa. H.. J . Chem. Phys. 21, 250 (1953). (41! Tompa. H., ”Polymer Solutions,” Acadrmic Press. New l o r k . 1956. (42) Van Arkel. .A. E.. Trans. Faraday Soc. 4 2 B , 81 (1946). (43) \Valkrr. E. E.. J . ‘4ppl. Chem. 2 , 470 (1952). (44) [Vatson, K . M . , Ind. Eng. Chem. 35, 398 (1943). RECEIVED for re\iew May 31. 1963 ACCEPTED October 14. 1963
DEW AND BUBBLE ISOTHERM CALCULATIONAL METHOD FOR BINARY .
SYSTEM PHASE AND VOLUMETRIC BEHAVIOR N E W E L L C. R O D E W A L D , ’ J .
A . D A V I S , 2 A N D
F R E D
K U R A T A
CenfPr for Research zn Engineering Sctpnce. 1 *nzutrsit) of kansas. Laurence. Kan
A method for calculation of liquid and vapor compositions together with saturated volumetric properties of binary systems was developed and successfully used on the helium-nitrogen system. These calculations require only quantities measured in the determination of the dew and bubble points. The phose rule
Y, specifies that for an isothermally univariant system, if the pressure i s fixed, the intensive properties-X, $, #-are set, regardless of the amount of the phases present. Obviously a numerical solution for these variables requires four simultaneous equations. Since it i s possible to write two equations from material balances on nitrogen and helium at each volume per cent liquid, two independent runs are required-a dew isotherm and a bubble isotherm, The quantities which must be measured are the amount of known composition gas metered to the cell and the volume per cent liquid at cell conditions. In the limit, these equations go to the dew and bubble points. HE measurement of the solubility of light gases in liquids T p r e s r n t s man)i problems. jvhich arise primarily from the phase behavior peculiarities of these systems-i.e.. thr lo\v concentration of the gas component in the liquid phase and the low concentration of the liquid constituent in the vapor phase. For many industrially important binary systems such as a light hydrocarbon-\yarer. helium-methane. or helium--nitrogen, the solubility of the light gas in the liquid is less than 1 mole % over conqiderable ranges of pressure and temperature.
Prescnt addrrss. Continental Oil Co., Ponca City: Okla. Present address. Denver Rrsearch Crntrr. Marathon Oil Co.. Littleton. Colo. 1
2
6
I&EC FUNDAMENTALS
Methods frequently used to study the phase behavior of theae systems include the flowing-condensation method. the circulation method. and the static method. In these methods: samplrs of both phases must be \vithdra\vn for analyses either from circulation lines or directly from the equilibrium chamber. ,411 of thrse methods have bern used to study the liquid-vapor behavior of the helium--nitrogen system ( 7 . 1. 1-6. 7 0 ) . Surprisingly large difFerences exist among the data of these investigators. ranging from a maximum of 2.5 to a minimum of 0 to Syc, 7‘he primary source of disagreement is probably sampling error. This error ma); be reduced by taking a representative sample, by getting a single-phase sample. by purging leads adequately beforr sampling. and by sampling ivithout upset-
ring equilibrium in the .apparatus. T h e errors introduced by sampling are further increased by uncertainties in composition analy-sis. Concentration errors for mixtures containing less than 1 mole c/'c of the gas can range from 2 to 20% for analytical methods such as mass spectrometer, gas chromatograph, and thermal conductivih.. T h e de\< and bubble point method eliminate> all sampling and most analytical protilems. Mullhaupt and Di Paolo ( 7 2 ) used this method to fix the bubble point pressures of six heliumxenon mixtures containmg less than 0.500 mole % helium. Because the isothermal solution pressure increased steeply near complete condensation. the uncertainty in their graphically determined bubble point pressure \vas 1 5 to 10%. roughly corresponding to data scdtter due to sampling errors. Hence, all of the advantage gained in eliminating sampling and analyses is lost. In addition. the attainment of equilibrium conditions near the buhble point requires considerable time. Deiv point pressures, on the other hand, can be determined much more accurately. Llullhaupt and Di Paolo \
