Henry’s Constants and Vapor–Liquid Distribution Constants for Gaseous Solutes in H2O and D2O at High Temperatures Roberto Ferna´ndez-Prinia… Unidad Actividad Quı´mica, Comisio´n Nacional de Energı´a Ato´mica, Av. Libertador 8250, 1429 Buenos Aires and INQUIMAE, Ftd. Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria, Pabello´n II, 1428 Buenos Aires, Argentina Jorge L. Alvarezb… Unidad Actividad Quı´mica, Comisio´n Nacional de Energı´a Ato´mica, Av. Libertador 8250, 1429 Buenos Aires and Universidad Technolo´gica Nacional, Ftd. Regional Bs. As., Medrano 951, 1179 Buenos Aires, Argentina Allan H. Harveyc… Physical and Chemical Properties Division, National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305 ͑Received 23 August 2002; revised manuscript received 29 January 2003; accepted 3 February 2003; published 23 May 2003͒ We have developed correlations for the Henry’s constant kH and the vapor–liquid distribution constant KD for 14 solutes in H2O and seven solutes in D2O. The solutes considered are common gases that might be encountered in geochemistry or the power industry. Solubility data from the literature were critically assessed and reduced to the appropriate thermodynamic quantities, making use of corrections for nonideality in the vapor and liquid phases as best they could be computed. While the correlations presented here cover the entire range of temperatures from near the freezing point of the solvent to high temperatures approaching its critical point, the main emphasis is on representation of the high-temperature behavior, making use of asymptotic relationships that constrain the temperature dependence of kH and KD near the critical point of the solvent. © 2003 by the U.S. Secretary of Commerce on behalf of the United States. All rights reserved. ͓DOI: 10.1063/1.1564818͔ Key words: distribution constant; gases; heavy water; Henry’s constant; solubility; vapor–liquid equilibrium; water. Contents 5.5. Solutes Excluded........................ 913 6. Conclusions................................ 913 7. Acknowledgments.......................... 913 1. Introduction................................ 904 8. Appendix A: Corrections to the Solute’s 2. Data Sources............................... 904 Chemical Potential in the Liquid Phase......... 913 3. Conversion of Data to k and K .............. 905 H D 9. Appendix B: Values of ln kH and ln KD Calculated 3.1. Thermodynamic Relations................ 905 from the Correlations........................ 915 3.2. Data Processing......................... 907 10. References................................. 915 3.3. Low-Temperature Data. ................. 908 3.4. Asymptotic Behavior and Consistency List of Tables Verification............................ 908 1. Data sources for gas solubility in H O.......... 906 4. Fitting Procedure........................... 909 2 2. Data sources for gas solubility in D O.......... 907 5. Results and Discussion....................... 910 2 3. Parameters for correlation of Henry’s constants 5.1. Noble Gases in H2O..................... 910 ͑ ͒ in H2O with Eq. 15 ........................ 910 5.2. Diatomic Gases in H2O.................. 911 4. Root-mean-square deviations in ln kH for solutes 5.3. Other Solutes in H2O.................... 911 in H2O and number of points in low-temperature 5.4. Solutes in D2O......................... 912 and high-temperature regions of fit............. 910 5. Parameters for correlation of equilibrium a͒ ͑ ͒ Member of Carrera del Investigador, CONICET, Argentina; Electronic distribution constants in H2O with Eq. 16 ...... 910 mail: [email protected] 6. Root-mean-square deviations in ln KD for solutes b͒Electronic mail: [email protected] ͒ in H O................................... 910 c Electronic mail: [email protected] 2 © 2003 by the U.S. Secretary of Commerce on behalf of the United States. 7. Parameters for correlation of Henry’s constants ͑ ͒ All rights reserved. in D2O with Eq. 15 ........................ 912 Õ Õ Õ Õ Õ 0047-2689 2003 32„2… 903 14 $37.50903 J. Phys. Chem. Ref. Data, Vol. 32, No. 2, 2003 904 FERNA´ NDEZ-PRINI, ALVAREZ, AND HARVEY 8. Root-mean-square deviations in ln kH for solutes to a polynomial. The correlations from that work were in D2O and number of points in low-temperature adopted as a Guideline by IAPWS, the International Asso- and high-temperature regions of fit............. 912 ciation for the Properties of Water and Steam ͑IAPWS, 9. Parameters for correlation of equilibrium 1995a͒. Several factors suggest the need for a revision at this ͑ ͒ distribution constants in D2O with Eq. 16 ...... 912 time. 10. Root-mean-square deviations in ln KD for solutes First, more is understood about the behavior of kH at high in D2O................................... 912 temperatures, particularly in the neighborhood of the critical ͑ ͒ 11. Calculated values of ln (kH/1 GPa) for solutes at point of the solvent. Japas and Levelt Sengers 1989 derived ͑ selected temperatures in H2O unless otherwise linear relationships, valid in the vicinity of the solvent criti- ͒ noted .................................... 914 cal point, relating both kH and KD to the solvent density. The ͑ 12. Calculated values of ln KD for solutes at selected relationship for kH was exploited Harvey and Levelt Sen- ͑ ͒ ͒ temperatures in H2O unless otherwise noted .... 914 gers, 1990; Harvey, 1996 to produce correlations that were better able to fit Henry’s constant data at high temperatures List of Figures and that had superior extrapolation behavior. Revised formu- ͓␳ 1. T ln KD for H2 in H2O as a function of 1*(1) lations should take advantage of this advance rather than Ϫ␳ c1͔.................................... 908 relying on polynomials with little physical basis. ͓␳ Ϫ␳ ͔ 2. T ln KD as a function of 1*(1) c1 for the Second, better methods are available for reducing high- CO2 –H2O system.......................... 909 temperature solubility data to Henry’s constants. These meth- ods, some of which have been presented previously 1. Introduction ͑Ferna´ndez-Prini et al., 1992; Alvarez et al., 1994͒, will be discussed in a subsequent section. The solubilities of gases in water, and their distribution Third, additional data exist for some aqueous systems, in- between coexisting vapor and liquid phases, are important in cluding a few systems not included in the original work of a variety of contexts. Aqueous gas solubilities are needed for Ferna´ndez-Prini and Crovetto ͑1989͒. We are now able to design calculations in chemical processing and for many produce correlations for four additional solutes in H2O. geochemical studies. In steam power plants, the distribution Fourth, new standards have been adopted for the represen- of solutes between water and steam is important. In hydro- tation of both the thermodynamic temperature scale ͑Preston- thermal systems, corrosion often depends on the concentra- Thomas, 1990͒ and the thermodynamic properties of pure tion of solutes. For many gases, accurate measurements of water ͑IAPWS, 2000a; Wagner and Pruß, 2002͒. While nei- solubility exist at temperatures near 25 °C, but data at higher ther of these changes is likely to make a significant differ- temperatures are much more sparse and scattered. Since ence within the uncertainty to which high-temperature Hen- many of the important applications are at high temperatures, ry’s constants are known, it is still desirable to be consistent there is a need for evaluated data and careful correlation to with the latest standards. provide scientists and engineers with the best possible data at Finally, we mention that correlations for KD for ten solutes ͑ ͒ high-temperature conditions. in H2O were produced by Alvarez et al. 1994 and later The fundamental thermodynamic quantity describing the adopted as an IAPWS Guideline ͑IAPWS, 2000b͒. This work solubility of a gas in a liquid is the Henry’s constant kH , did take advantage of the theoretical advance of Japas and defined by Levelt Sengers ͑1989͒, and is therefore less in need of revi- ϭ ͒ ͑ ͒ sion. However, we revise it here in order to add more solutes kH lim ͑ f 2 /x2 , 1 ! and reevaluate some data for the old solutes, and to produce x2 0 correlations for kH and KD that are based on the same data. where f 2 and x2 are, respectively, the liquid-phase fugacity The purpose of this work is to provide reliable values for and mole fraction of the solute. While this definition can be kH and KD for applications at high temperatures. The highly applied at any state of the solvent, in this work we restrict precise kH data available for many aqueous solutes between our attention to vapor–liquid equilibrium conditions in single approximately 0 and 60 °C are not described to within their solvents, so that kH is a function only of temperature along uncertainty by the correlations presented in this work. Those the saturation curve of the solvent. A related quantity is the whose interest is confined to this temperature range should vapor–liquid distribution constant KD , defined by not use our correlations; instead they should use the smooth- ϭ ͒ ͑ ͒ ing equations for k in the papers ͑referenced in the next KD lim ͑y 2 /x2 , 2 H ! ͒ x2 0 section where these high-quality measurements are reported. where y 2 is the vapor-phase solute mole fraction in equilib- rium with the liquid. 2. Data Sources Ferna´ndez-Prini and Crovetto ͑1989͒ examined solubility data as a function of temperature for ten nonpolar gases in For many solutes, there have been numerous studies, of ͑ ordinary water which we will call H2O, despite the fact that widely varying quality, of their solubility in water near ͒ it is not isotopically pure and seven in heavy water (D2O). 25 °C. In the past 30 years, techniques have been developed They converted the data to Henry’s constants and fitted them ͑Battino, 1989͒ for highly accurate measurement of solubili- J. Phys. Chem. Ref. Data, Vol. 32, No. 2, 2003 HENRY’S CONSTANTS AND VAPOR-LIQUID DISTRIBUTION CONSTANTS 905 ties of gases in water at low temperature and near- due to its high vapor pressure; this is especially true of aque- atmospheric pressure, rendering most earlier work obsolete.