THE SOLUBILITY OF GASES IN LIQUIDS RUBIN BATTINO' Department of Chewistry, Illinois Institute of Technology, Chicago, Illinois 60616 AXD H. LAWRENCE CLEVER Department of Chemistry, Etnory University, Atlanta, Georgia 30392 Received October 2.5, 1965 CONTENTS I. Introduction ..........................................................395 11. Nomencl ...... .. ............ ....... ....... 396 111. Methods ratus. ........ ... ............................. 397 A. Manome&-Volumetric Methods. ....................................397 1. The Solubility of Oxygen in Rater as a Comparison Standard.. .............. 397 2. Degassing the Solvent ................................................ 398 3. The Effect of Temperature on Solubility Measurements .................. 399 4. The Apparatus of Cook and Hanson. ................ .............. 399 5. Saturation Metho ...... .............. 400 13. Mass Spectrometric b .......... ................. 402 ............................ 403 .......................... 404 ........... ....................... 406 ..........................406 ................ ...... 407 ................ ........ 407 ... ............. ....... 407 ............................... 407 s. .................. ...... 407 .............................408 ............................. 408 1. Regular Solution Theory ..................... ....... 408 2. Cell Potential and Cavity Models.. .. .................... 410 3. Ot,her Contributions to Theory. .... ........................ 411 4. Special Studies. .................... ..................... 411 B. Temperahre Coefficient of Gas Solubility. ...............................412 C. Partial Molal Volumes of Gases Dissolved in Liquids .............. 413 D. GM ,Solubilities in Mixed Nonelectrolyte Solvents. ........ .... ...... 413 E. Solvent Surface Tension and Gas Solubility ............. ....... 415 F. SaltEffects ............................................... .... 416 G. Solubility of Gases in Biological Fluids. .... ..................... 419 H. Effect, of Pressure on Gas Solubility. ......... .................... 421 I. Solubility of Gases in Molten Salts and Glasses. ...... .... ........ 424 J. The Solubility of Gases in Molten Metals and Alloys.. .......... ..... 426 VI. Solribilit,y Data. ........................................... ........ 453 VII. References.. .............. ..................... ..... 453 I. IKTRODUCTION the solubility of gases in hunian tissues to the solubility The solubility of gases in liquids has been under of gases in molten salts and metals. quantitative investigation since the beginning of the This review brings up to date the earlier comprehen- nineteenth century. The last decade has seen some sive review of Pllarkham and Kobe (393). An annotated remarkable advances in theory, empirical correlations, bibliography (1907-1941) on the solubility of Ar, COZ, systems studied, and apparatus. Much of the earlier He, and Nz in organic liquids was prepared by Croxton work was more qualitative than quantitative. Gas (115). The two books by Hildebrand and Scott solubilities have become increasingly more important (243, 244) contain chapters on gas solubility and many for both the theoretical understanding of the liquid references. There are other papers containing either state and solutions, and for practical applications from general correlations or many references (170, 206, 247, 248, 282, 353, 373, 485, 670). The review by Him- (1) Department of Chemistry. Wright State College. Dayton, Ohio 4j431. melblau (249) on the diffusion of dissolved gases in 395 396 RUBINBATTINO AND H. LAWRENCECLEVER liquids is of interest, and the review by Rowlinson and K Henry's law constant or Setschenow equation param- Richardson (509) on the solubility of solids in com- eter Henry's law constant (to fit Eq 5) pressed gases may interest some readers. The limited Ki KP Henry's law constant (to fit Eq 6) literature on the solubility of liquids in compressed KO Henry's law constant (to fit Eq 7) gases has yet to be reviewed. K' Henry's law constant, modified The literature since Varkham and Kobe was searched K, Henry's law constant, reduced and critically evaluated. The principal medium of the K", K." limiting Henry's law constants in water and in salt solution search was Chemical Abstracts through Vol. 59, or the L Ostwald coefficient (see section IVB) end of 1963. All pertinent articles abstracted through M molecular weight the end of 1963 were included, although many articles P pressure which were published in 1964 and 1965 were also included. P., Po solvent vapor pressure Where the original paper was not examined, a Chemical PT total pressure Pi partial pressure or vapor pressure Abstracts reference is supplied in the list of references. S Kuenen coefficient (see section IVA) The emphasis in this review was placed on physical Si", Si solubility of gas in pure solvent, or sdt solution methods of determining solubilities and on reporting 32 partial molar entropy of gas in solution and discussing only equilibrium or saturation solubili- S: molar entropy of gas in gas phase ties. Thus, the vast literature on the analysis of gases AS" molar entropy of solution T temperature, "K absorbed in liquids was ignored. Since most of these To critical temperature analyses involve Chemical methods, the latter was Ti reduced temperature also ignored except for oxygen in water. The extensive v, V volume, molar volume literature on the solubility of gases in ponds, streams, VS volume of solvent and ground waters was not included because of the volume of gas equilibrium criterion. molar volume of gas in cc/mole at 0' partial molar volume at infinite dilution of gas There is an almost nonexistent dividing line between partial molar volume at infinite dilution of electro- gas solubility (in liquids) and vapor-liquid equilibrium, lyte especially at elevated pressures. The solubility of the XP, XI mole fraction solubility of gas in solution vapors of some substances was included where the XPi ideal mole fraction solubility of gas in solution experimental conditions were such that the pressure Y vapor phase mole fraction was lower than the normal vapor pressure. Also in- Lower Case Symbols cluded are: (a) solubilities of gases in molten metals, arbitrary constants salt concentration, moles per liter alloys, salts, and glasses; (b) solubilities of gas mix- gas concentration, moles per liter tures; (c) solubility in tissues and some biological activity coefficient of dissolved gas in salt-free solu- systems; (d) solubility nomographs; and (e) partial tion molal volumes of gases in liquids. activity coefficient of dissolved gas in salt solution The large body of literature on the solubility of gases gravitational constant in plastic materials was excluded since much of this excess Gibbs free energy Boltzmann constant data is for plastic films. The solubility of gases in solids salting-out parameter and substances whose composition would tend to be salting-out parameter for salt x indeterminable (like molten slags) was also excluded. nonelectrolyte self-interaction parameter salt-effect parameter 11. NOMENCLATURE molality The system of notation used in this review follows. pressure Some specialized symbols which apply to a particular radius of spherical gas atom temperature, "C approach, and where we wished use the author's to decimal fraction of solute in solution own notation for clarity, are defined where they are volume used. Greek Letter Symbols Upper Case Symbols Bunsen coefficient (see section IVA) A arbitrary constant interaction parameters C1, Cd concentration of gas dissolved in the liquid phase absorption coefficient (see section IVB) c, concentration of gas dissolved in the gas phase compressibility of pure solvent CW weight solubility (see section IVD) activity coefficient heat capacity change on solution AC, Hildebrand solubility parameter AEV molar energy of vaporization Q molar Gibbs free energy LennardJones force constant Hz Henry's law constant (see section VD) volume fraction or vapor phase activity coefficient AH, AB" molar heat of solution density AHy molar heat, of vaporization surface tension SOLUBILITYOF GASESIN LIQUIDS 397 111. METHODSAND APPARATUS the physical properties of pressure, volume, and tem- The variety of approaches which have been used to perature are usually adequately determined. The determine the solubility of gases in liquids is an ade- discrepancies, often large, between published values quate testimonial to man’s ingenuity. The equipment which appear in the literature (for example, the solu- used ranges in complexity and cost from mass spec- bility of atmospheric gases in water and sea water con- trometers to the simple van Slyke apparatus, in time tinues to be measured and debated) are most probably from minutes to many hours, and in precision from the due to other factors. Cook and Hanson (104) list purely qualitative to the highly precise. these as being one or more of the folIowing: (a) failure Primarily physical methods will be discussed in to attain equilibrium; (b) failure to completely degas this section, although, in specific instances chemical the solvent; (c) failure to ascertain the true amount of methods are sometimes more precise. There are several gas dissolved; and (d) failure to make certain that the reasons for omitting chemical methods (except for transfer of gas from a primary container to the ap- oxygen in water). First, they are normally specific for paratus does not involve contamination. The last two a particular gas and thus do not