Hostname: page-component-848d4c4894-8kt4b Total loading time: 0 Render date: 2024-06-20T16:56:18.876Z Has data issue: false hasContentIssue false

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*
Washington River Protection Solutions, LLC, Richland, WA, 99352 USA
Cliff T. Johnston
Crop, Soil and Environmental Sciences, Purdue University, West Lafayette, IN 47907 USA
Stephen F. Agnew
Columbia Energy and Environmental Services, Inc., Richland, WA, 99354 USA
*E-mail address of corresponding author:


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.

Copyright © Clay Minerals Society 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)


Abraham, M. and Abraham, N.C., 2000 Electrolyte and water activities in very concentrated solutions Electrochimica Acta 46 137142.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 213236.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 4958.CrossRefGoogle Scholar
Barshad, I., 1949 The nature of lattice expansion and its relation to the hydration in montmorillonite and vermiculite American Mineralogist 34 675684.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 675718.Google Scholar
Brunauer, S. Emmett, P.H. and Teller, E., 1938 Adsorption of gases in multimolecular layers Journal of The American Chemical Society 60 309319.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 157159.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 27302739.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 45 822.CrossRefGoogle Scholar
Costanzo, P.M. and Guggenheim, S., 2001 Baseline studies of the Clay Minerals Society source clays Clays and Clay Minerals 49 371452.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 207219.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 3542.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 12251232.CrossRefGoogle Scholar
Edwards, D.G. and Quirk, J.P., 1962 Repulsion of chloride by montmorillonite Journal of Colloid Science 17 872882.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 27372749.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 263310.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 17901803.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 114117.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 245279.CrossRefGoogle Scholar
Johnston, C.T. Sposito, G. and Erickson, C., 1992 Vibrational probe studies of water interaction with montmorillonite Clays and Clay Minerals 40 722730.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 193200.CrossRefGoogle Scholar
Laird, D.A., 1996 Model for crystalline swelling of 2:1 phyllosilicates Clays and Clay Minerals 44 553559.CrossRefGoogle Scholar
Laird, D.A., 1999 Layer charge influences on the hydration of expandable 2:1 phyllosilicates Clays and Clay Minerals 47 630636.CrossRefGoogle Scholar
Laird, D.A., 2006 Influence of layer charge on swelling of smectites Applied Clay Science 34 7487.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 211213.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 3034.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 1760317611.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 153181.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 297306.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 34543463.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 18321839.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 13671371.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 393398.CrossRefGoogle Scholar
Ohtaki, H., 2001 Ionic solvation in aqueous and nonaqueous solutions Monatshefte für Chemie 132 12371268.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 260265.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 131140.CrossRefGoogle Scholar
Orchitson, H.D., 1955 Adsorption of water vapor: III. Homoionic montmorillonites at 25°C Soil Science 79 7178.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 9 117.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 376377.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 175179.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 798812.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 3556.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. 87112.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 337373.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 659661.Google Scholar
Sposito, G. and Prost, R., 1982 Structure of water adsorbed on smectites Chemical Reviews 82 553573.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 155174.CrossRefGoogle Scholar
Staples, B.R., 1981 Activity and osmotic coefficients of aqueous alkali metal nitrites Journal of Physical and Chemical Reference Data 10 765777.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 385407.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 16891691.CrossRefGoogle Scholar
Stokes, R.H. and Robinson, R.A., 1948 Ionic hydration and activity in electrolyte solutions Journal of the American Chemical Society 70 18701878.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 120131.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 6851003.CrossRefGoogle Scholar