Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-08T22:43:32.605Z Has data issue: false hasContentIssue false
  • English
  • Français

A Molality-Based BET Equation for Modeling the Activity of Water Sorbed on Clay Minerals

Published online by Cambridge University Press:  01 January 2024

Jacob G. Reynolds ,
Cliff T. Johnston  and
Stephen F. Agnew
Jacob G. Reynolds*
Affiliation:
Washington River Protection Solutions, LLC, Richland, WA, 99352 USA
Cliff T. Johnston
Affiliation:
Crop, Soil and Environmental Sciences, Purdue University, West Lafayette, IN 47907 USA
Stephen F. Agnew
Affiliation:
Columbia Energy and Environmental Services, Inc., Richland, WA, 99354 USA
*
*E-mail address of corresponding author: reynoldsjacob@hotmail.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The Brunauer-Emmett-Teller (BET) theory models the effective specific surface area and water content of solids as a function of the relative vapor pressure of water. A modified form of the BET equation has been used successfully to model water activity in concentrated electrolyte solutions as a function of electrolyte concentration. This modified form, referred to here as the Stokes-Robinson BET model, is based on the electrolyte molality rather than on the mass of solute sorbed. The present study evaluates the Stokes-Robinson form of the BET equation to model water-sorption data on two smectites with different layer charges. One smectite was saturated with Na+ and another with Na+, Ca2+, or Mg2+. These results are compared to the Stokes-Robinson BET results of aqueous electrolyte solutions. Given published data on cation exchange capacities and water-vapor sorption isotherms for various clays, the molality of the aqueous phase in contact with the clay surface is calculated and related to water activity. The Stokes-Robinson BET model was found to describe accurately the water activity as a function of cation molality below water activities of 0.5 for the smectites. Good relative agreement was obtained between the number of water binding sites predicted by the model and the experimental data reported in the literature for other smectites. Water molecules were found to have a significantly greater affinity for montmorillonite than electrolyte solutions with the same cation molality as the montmorillonite interlayer. This modified BET approach simplifies water-activity modeling in highly saline environments because the same equation can be used for both the liquid- and mineral-surface phases.

Keywords

BET modelElectrolyte ThermodynamicsWater Activity
Type
Article
Information
Clays and Clay Minerals , Volume 60 , Issue 6 , December 2012 , pp. 599 - 609
Copyright
Copyright © Clay Minerals Society 2012

References

Abraham, M. and Abraham, N.C., 2000 Electrolyte and water activities in very concentrated solutions Electrochimica Acta 46 137–142.CrossRefGoogle Scholar
Ally, M.R. and Braunstein, J., 1993 BET model for calculating activities of salts and water, molar enthalpies, molar volumes and liquid-solid phase behavior in concentrated electrolyte solutions Fluid Phase Equilibria 87 213–236.CrossRefGoogle Scholar
Ally, M.R. and Braunstein, J., 1998 Statistical mechanics of multilayer adsorption: electrolyte and water activities in concentrated solutions Journal of Chemical Thermodynamics 30 49–58.CrossRefGoogle Scholar
Barshad, I., 1949 The nature of lattice expansion and its relation to the hydration in montmorillonite and vermiculite American Mineralogist 34 675–684.Google Scholar
Borchardt, G., Dixon, J.B. and Weed, S.B., 1989 Smectities Minerals in Soil Environments 2nd edition Wisconsin, USA Soil Science Society of America Madison 675–718.Google Scholar
Brunauer, S. Emmett, P.H. and Teller, E., 1938 Adsorption of gases in multimolecular layers Journal of The American Chemical Society 60 309–319.CrossRefGoogle Scholar
Cariati, F. Erre, L. Micera, G. Piu, P. and Gessa, C., 1981 Water molecules and hydroxyl groups in montmorillonites as studied by near infrared spectroscopy Clays and Clay Minerals 29 157–159.CrossRefGoogle Scholar
Cases, J.M. Berend, I. Bessen, G. Francois, M. Uriot, J.P. Thomas, F. and Poirier, J.E., 1992 Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 1. The sodium-exchanged form Langmuir 8 2730–2739.CrossRefGoogle Scholar
Cases, J.M. Berend, I. Francois, M. Uriot, J.P. Michot, L.J. and Thomas, F., 1997 Mechanism of adsorption and desorption of water vapor by homoionic montmorillonite. 3. The Mg2+, Ca2+, Sr2+ and Ba2+ exchanged forms Clays and Clay Minerals 45 8–22.CrossRefGoogle Scholar
Costanzo, P.M. and Guggenheim, S., 2001 Baseline studies of the Clay Minerals Society source clays Clays and Clay Minerals 49 371–452.CrossRefGoogle Scholar
Dalton, R.W. McClanahan, J.L. and Maatman, R.W., 1962 The partial exclusion of electrolytes from the pores of silica gel Journal of Colloid Science 17 207–219.CrossRefGoogle Scholar
Denis, J.H., 1991 Compaction and swelling of Ca-smectite in water and in CaCl2 solutions: Water activity measurements and matrix resistance to compaction Clays and Clay Minerals 39 35–42.CrossRefGoogle Scholar
Dontsova, K.M. Norton, L.D. and Johnston, C.T., 2005 Calcium and magnesium effects on ammonia adsorption by soil clays Soil Science Society of America Journal 69 1225–1232.CrossRefGoogle Scholar
Edwards, D.G. and Quirk, J.P., 1962 Repulsion of chloride by montmorillonite Journal of Colloid Science 17 872–882.CrossRefGoogle Scholar
Farmer, V.C. and Russell, J.D., 1971 Interlayer complexes in layer silicates: The structure of water in lamellar ionic solutions Transactions of the Faraday Society 67 2737–2749.CrossRefGoogle Scholar
Goldberg, R.N. and Nuttall, R.L., 1978 Evaluated activity and osmotic coefficients for aqueous solutions: The alkaline earth metal halides Journal of Physical and Chemical Reference Data 7 263–310.CrossRefGoogle Scholar
Hatch, C.D. Wieset, J.S. Crane, C.C. Harris, K.J. Kloss, H.G. and Baltrusaitis, J., 2012 Water adsorption on clay minerals as a function of relative humidity: application of BET and Freundlich adsorption models Langmuir 28 1790–1803.CrossRefGoogle Scholar
Hill, R.C.P. Reynolds, J.G. and Rutland, P.L., 2011 A comparison of Hanford and Savannah River site high-level wastes Proceedings of the 13th International High-Level Waste Management Conference 114–117.Google Scholar
Hillel, D., 1982 Introduction to Soil Physics San Diego CA, USA Academic Press, Inc..Google Scholar
Johnston, C.T., 2010 Probing the nanoscale architecture of clay minerals Clay Minerals 45 245–279.CrossRefGoogle Scholar
Johnston, C.T. Sposito, G. and Erickson, C., 1992 Vibrational probe studies of water interaction with montmorillonite Clays and Clay Minerals 40 722–730.CrossRefGoogle Scholar
Keren, R. and Shainberg, I., 1975 Water vapor isotherms and heat of immersion of Na/Ca-montmorillonite systems — I: Homoionic clay Clays and Clay Minerals 23 193–200.CrossRefGoogle Scholar
Laird, D.A., 1996 Model for crystalline swelling of 2:1 phyllosilicates Clays and Clay Minerals 44 553–559.CrossRefGoogle Scholar
Laird, D.A., 1999 Layer charge influences on the hydration of expandable 2:1 phyllosilicates Clays and Clay Minerals 47 630–636.CrossRefGoogle Scholar
Laird, D.A., 2006 Influence of layer charge on swelling of smectites Applied Clay Science 34 74–87.CrossRefGoogle Scholar
Laudelout, H. Van Bladel, R. and Robeyns, J., 1971 The effect of water activity on ion exchange selectivity in clays Soil Science 111 211–213.CrossRefGoogle Scholar
Laudelout, H. Van Bladel, R. and Robeyns, J., 1972 Hydration of cations on a clay surface from the effects of water activity on ion exchange selectivity Soil Science Society of America Proceedings 36 30–34.CrossRefGoogle Scholar
Lobo, V.M.M., 1989 Handbook of Electrolyte Solutions Oxford, UK Elsevier.Google Scholar
Malikova, N. Cadene, A. Dubois, E. Marry, V. Durand-Vidal, S. Turq, P. Breu, J. Longeville, S. and Zanotti, J.M., 2007 Water diffusion in a synthetic hectorite clay studied by quasi-elastic neutron scattering Journal of Physical Chemistry C 111 17603–17611.CrossRefGoogle Scholar
Malikova, N. Dubois, E. Marry, V. Rotenberg, B. and Turq, P., 2010 Dynamics in clays — combining neutron scattering and microscopic simulation Zeitschrift für Physikalische Chemie — International Journal of Research in Physical Chemistry and Chemical Physics 224 153–181.Google Scholar
Marcus, Y., 2005 BET modeling of solid-liquid phase diagrams of common ion binary salt hydrate mixtures. I. The BET parameters Journal of Solution Chemistry 34 297–306.CrossRefGoogle Scholar
Marry, V. Turq, P. Cartailler, T. and Levesque, D., 2002 Microscopic simulation of structure and dynamics of water and counterions in a monohydrated montmorillonite Journal of Chemical Physics 117 3454–3463.CrossRefGoogle Scholar
Marry, V. and Turq, P., 2003 Microscopic simulations of interlayer structure and dynamics in bihydrated heteroionic montmorillonites Journal of Physical Chemistry B 107 1832–1839.CrossRefGoogle Scholar
Mooney, R.W. Keenan, A.G. and Wood, L.A., 1952 Adsorption of water vapor by montmorillonite. I. Heat of desorption and application of BET theory Journal of the American Chemical Society 74 1367–1371.CrossRefGoogle Scholar
Mortland, M.M. and Raman, K.V., 1968 Surface acidity of smectites in relation to hydration, exchangeable cation, and structure Clays and Clay Minerals 16 393–398.CrossRefGoogle Scholar
Ohtaki, H., 2001 Ionic solvation in aqueous and nonaqueous solutions Monatshefte für Chemie 132 1237–1268.CrossRefGoogle Scholar
Olson, R.A. and Robbins, J.E., 1971 The cause of the suspension effect in resin-water systems Soil Science Society of America Proceedings 35 260–265.CrossRefGoogle Scholar
Onodera, Y. Iwasaki, T. Ebina, T. Hayashi, H. Torii, K. Chatterjee, A. and Mimura, H., 1998 Effect of layer charge on fixation of cesium ions in smectites Journal of Contaminant Hydrology 35 131–140.CrossRefGoogle Scholar
Orchitson, H.D., 1955 Adsorption of water vapor: III. Homoionic montmorillonites at 25°C Soil Science 79 71–78.Google Scholar
Pashley, R.M. and Quirk, P.M., 1984 The effect of cation valency on DLVO and hydration forces between macroscopic sheets of muscovite mica in relation to clay swelling Colloids and Surfaces 9 1–17.CrossRefGoogle Scholar
Pearce, J.N., 1936 The vapor pressures and activity coefficients of aqueous solutions of calcium and aluminum nitrate at 25° (correction) Journal of the American Chemical Society 58 376–377.CrossRefGoogle Scholar
Polubesova, T. and Borisover, M., 2009 Two components of chloride anion exclusion volume in montmorillonitic soils Colloids and Surfaces A — Physicochemical and Engineering Aspects 347 175–179.Google Scholar
Posner, A.M. and Quirk, J.P., 1964 Changes in basal spacing of montmorillonite in electrolyte solutions Journal of of Colloid Science 19 798–812.CrossRefGoogle Scholar
Posner, A.M. and Quirk, J.P., 1964 The adsorption of water from concentrated electrolyte solutions by montmorillonite and illite Proceedings of the Royal Society A278 35–56.Google Scholar
Schoonheydt, R.A. Johnston, C.T., Bergaya, F. Theng, B.K.G. and Lagaly, G., 2007 Surface and interface chemistry of clay minerals Handbook of Clay Science Amsterdam Elsevier Science Ltd. 87–112.Google Scholar
Schoonheydt, R.A. and Johnston, C.T., 2011 The surface properties of clay minerals Layered Structures and their Application in Advanced Technologies 11 337–373.Google Scholar
Shpigel, L.P. and Mishchenko, K.P., 1967 Activities and rational activity coefficients of water in potassium nitrate and sodium nitrate solutions at 1, 25, 50, and 75° over a wide concentration range Journal of Applied Chemistry USSR 40 659–661.Google Scholar
Sposito, G. and Prost, R., 1982 Structure of water adsorbed on smectites Chemical Reviews 82 553–573.CrossRefGoogle Scholar
Środoń, J. and McCarty, D.K., 2008 Surface area and layer charge of smectite from CEC and EGME/H2O-retention measurements Clays and Clay Minerals 56 155–174.CrossRefGoogle Scholar
Staples, B.R., 1981 Activity and osmotic coefficients of aqueous alkali metal nitrites Journal of Physical and Chemical Reference Data 10 765–777.CrossRefGoogle Scholar
Staples, B.R. and Nuttall, R.L., 1977 The activity and osmotic coefficients of aqueous calcium chloride at 298.15 K Journal of Physical and Chemical Reference Data 6 385–407.CrossRefGoogle Scholar
Stokes, R.H., 1945 Isopiestic vapor pressure measurements on concentrated solutions of sodium hydroxide at 25°C Journal of the American Chemical Society 67 1689–1691.CrossRefGoogle Scholar
Stokes, R.H. and Robinson, R.A., 1948 Ionic hydration and activity in electrolyte solutions Journal of the American Chemical Society 70 1870–1878.CrossRefGoogle ScholarPubMed
Woodruff, W.F. and Revil, A., 2011 CEC-normalized claywater sorption isotherm Water Resources Research 47 w11502.CrossRefGoogle Scholar
Xu, W. Johnston, C.T. Parker, P. and Agnew, S.F., 2000 Infrared study of water sorption on Na-, Li-, Ca- and Mg-exchanged (SWy-1 and SAz-1) montmorillonites Clays and Clay Minerals 48 120–131.CrossRefGoogle Scholar
Zachara, J.M. Serne, J. Freshley, M. Mann, F. Anderson, F. Wood, M. Jones, T. and Myers, D., 2007 Geochemical processes controlling migration of tank waste in Hanford’s vadose zone Vadose Zone Journal 6 685–1003.CrossRefGoogle Scholar