Journal of Solution Chemistry

, Volume 47, Issue 5, pp 855–891 | Cite as

A Thermodynamic Model for ZrO2(am) Solubility at 25 °C in the Ca2+–Na+–H+–Cl–OH–H2O System: A Critical Review

  • Dhanpat Rai
  • Akira Kitamura
  • Marcus Altmaier
  • Kevin M. Rosso
  • Takayuki Sasaki
  • Taishi Kobayashi


Zirconium is an important element in the nuclear fuel cycle. Thermodynamic data and models to reliably predict Zr–OH system behavior in various conditions including high ionic strengths are required and currently are unavailable. Most available experimental data are rather old, obtained using inadequate methodologies, and provide equilibrium constant values that differ by many orders of magnitude. Previous reviews have recommended values based on available data. These reviews used all of the available data, including poor quality data, in a global fit to determine these values. This has resulted in recommended thermodynamic models with a large number of polynuclear species and a number of mononuclear species with values of thermodynamic constants for the solubility product of ZrO2(am) and Zr–OH hydrolysis constants that are many orders of magnitude different from those for the reliable analogous Hf reactions. In this critical review, we have evaluated the quality of the available data, selected only those data that are of high quality, and reinterpreted all of the high quality data using SIT and Pitzer models for applications to high ionic strength solutions. Herein for 25 °C we (1) present formation constant values for ZrOH3+, \( {\text{Zr}}\left( {\text{OH}} \right)_{2}^{2 + } \), Zr(OH)4(aq), \( {\text{Zr}}\left( {\text{OH}} \right)_{5}^{ - } \), and \( {\text{Zr}}\left( {\text{OH}} \right)_{6}^{2 - } \), and the solubility product for ZrO2(am) which are consistent with the Hf system, (2) report a revised value for the formation constant of \( {\text{Ca}}_{3} {\text{Zr}}\left( {\text{OH}} \right)_{6}^{4 + } \), (3) show that several hypothetical polynuclear species (\( {\text{Zr}}_{3} \left( {\text{OH}} \right)_{9}^{3 + } \), Zr4(OH) 15 + , and Zr4(OH)16(aq)) proposed in previous reviews are not needed, and (4) show that polynuclear species (\( {\text{Zr}}_{3} \left( {\text{OH}} \right)_{4}^{8 + } \) and \( {\text{Zr}}_{4} \left( {\text{OH}} \right)_{8}^{8 + } \)) are not important in a very extensive H+ concentration range (0.1–10−15.4 mol·kg−1). Our review has also resulted in SIT and Pitzer ion-interaction parameters applicable to as high ionic strength solutions as 5.6 mol·kg−1 in NaCl, 2.11 mol·kg−1 in CaCl2, and 23.5 mol·kg−1 in NaOH.


Solubility ZrO2(am) Solubility product Thermodynamic data Zirconium Hydrolyses constants 



We thank Japan Atomic Energy Agency for funding this research. Kevin Rosso acknowledges support from the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division through its Geosciences Program at Pacific Northwest National Laboratory.


  1. 1.
    Brown, P.L., Curti, E., Grambow, B.: Chemical Thermodynamics of Zirconium. Chemical Thermodynamics, vol. 8. Elsevier B. V., Amsterdam (2005)Google Scholar
  2. 2.
    Guillaumont, R., Fanghänel, Th, Fuger, J., Grenthe, I., Neck, V., Palmer, D.A., Rand, M.H.: Update on the Chemical Thermodynamics of Uranium, Plutonium, Americium, and Technetium. Chemical Thermodynamics, vol. 5. Elsevier B.V, Amsterdam (2003)Google Scholar
  3. 3.
    Rai, D., Yui, M., Schaef, H.R., Kitamura, A.: Thermodynamic model for SnO2(cr) and SnO2(am) solubility in the aqueous Na+–H+–OH–Cl–H2O system. J. Solution Chem. 40, 1155–1172 (2011)CrossRefGoogle Scholar
  4. 4.
    Rai, D., Xia, Y., Hess, N.J., Strachan, D.M., McGrail, B.P.: Hydroxo and chloro complexes/ion-interactions of Hf4+ and the solubility product of HfO2(am). J. Solution Chem. 30, 949–967 (2001)CrossRefGoogle Scholar
  5. 5.
    Shannon, R.D.: Revised effective ionic radii and systematic studies of interatomic distances in halides and chaleogenides. Acta Cryst. A32, 751–767 (1976)CrossRefGoogle Scholar
  6. 6.
    Bilinski, H., Branica, M., Sillén, L.G.: Precipitation and hydrolysis of metallic ions II. Studies on the solubility of zirconium hydroxide in dilute solutions and in 1 M NaClO4. Acta Chem. Scand. 20, 853–861 (1966)CrossRefGoogle Scholar
  7. 7.
    Chekmarev, A.M., Chibrikin, V.V., Yagodin, V.G.: Study of the hydrolysis of Zr4+ and Hf4+ ions in sulfate solutions by the method of paper chromatography. Radiokhimiya 17, 165–168 (1975)Google Scholar
  8. 8.
    Connick, R.E., McVey, W.H.: The aqueous chemistry of zirconium. J. Am. Chem. Soc. 71, 3182–3191 (1949)CrossRefGoogle Scholar
  9. 9.
    Davydov, Y.P., Zabrodskii, V.N.: Hydrolysis of zirconium(IV) with the formation of mono- and polynuclear hydroxy complexes in solutions. Vestsi Akad. Navuk BSSR, Ser. Khim. Navuk. 2, 3–8 (1987)Google Scholar
  10. 10.
    Ekberg, C., Brown, P.L., Comarmond, M.J., Albinsson, Y.: On the hydrolysis of tetravalent metal ions. Mater. Res. Soc. Symp. Proc. 663, 1091–1100 (2001)CrossRefGoogle Scholar
  11. 11.
    Nazarenko, V.A., Mandzhgaladze, O.V.: Determination of the formation constants of hydroxo-complexes of zirconium by the method of competing reactions. Russ. J. Inorg. Chem. 14, 639–643 (1969)Google Scholar
  12. 12.
    Norén, B.: The hydrolysis of Zr4+ and Hf4+. Acta Chem. Scand. 27, 1369–1384 (1973)CrossRefGoogle Scholar
  13. 13.
    Paramonova, V.I., Sergeev, A.N.: The application of ion-exchange in the investigation of the substance in solution—V. The study of the process of complex formation by zirconium in nitric acid. Zh. Neorg. Khim. 3, 215–221 (1958)Google Scholar
  14. 14.
    Peshkova, V.M., Mel’chakova, N.V., Zhemchuzhin, S.G.: Complex formation in the benzoyl–acetone [1-phenylbutane-1,3-dione]-zirconium–benzene–water system and the hydrolysis of zirconium ions. Russ. J. Inorg. Chem. 6, 630–634 (1961)Google Scholar
  15. 15.
    Solovkin, A.S., Ivantsov, A.I.: Hydrolysis constants of the Zr4+ ion in perchlorate media. Russ. J. Inorg. Chem. 11, 1013–1016 (1966)Google Scholar
  16. 16.
    Tribalat, S., Schriver, L.: Polymérisation du zirconium(IV) en solution acide. Bull. Soc. Chim. Fr. 9, 2012–2014 (1975)Google Scholar
  17. 17.
    Veyland, A.: Propriétés Thermodynamiques, Cinétiques et Structurales de Complexes Simples et Mixtes du Zirconium(IV) avec les Ions Hydroxyle et Carbonate. University of Reims Champagne-Ardenne, Reims (1999)Google Scholar
  18. 18.
    Zielen, A.J.: The Hydrolytic Polymerization of Zirconium, in Radiation Laboratory. University of California, Berkeley (1953)Google Scholar
  19. 19.
    Zielen, A.J., Connic, R.E.: The hydrolytic polymerization of zirconium in perchloric acid solutions. J. Am. Chem. Soc. 78, 5785–5792 (1956)CrossRefGoogle Scholar
  20. 20.
    Larsen, E.M., Gamhill, A.M.: Electrometric titration of zerconium and hafnium solutions. J. Am. Chem. Soc. 72, 3615–3619 (1950)CrossRefGoogle Scholar
  21. 21.
    Brown, P.L., Ekberg, C.: Hydrolysis of Metal Ions. Wiley-VCH Verlag GmbH and Co. KGaA, Weinheim (2016)CrossRefGoogle Scholar
  22. 22.
    Cho, H.-R., Walther, C., Rothe, J., Neck, V., Denecke, M.A., Dardenne, K., Fanghänel, Th: Combined LIBD and XAFS investigation of the formation and structure of Zr(IV) colloids. Anal. Bioanal. Chem. 383, 28–40 (2005)CrossRefPubMedGoogle Scholar
  23. 23.
    Sasaki, T., Kobayashi, T., Takagi, I., Moriama, H.: Solubility measurement of zirconium(IV) hydrous oxide. Radiochim. Acta 94, 489–494 (2006)CrossRefGoogle Scholar
  24. 24.
    Altmaier, M., Neck, V., Fanghänel, Th.: Solubility of Zr(IV), Th(IV) and Pu(IV) hydrous oxides in CaCl2 solutions and the formation of ternary Ca–M(IV)–OH complexes. Radiochim. Acta 96, 541–550 (2008)CrossRefGoogle Scholar
  25. 25.
    Sheka, I.A., Pevzner, T.V.: Solubility of zirconium and hafnium hydroxides in sodium hydroxide solutions. Russ. J. Inorg. Chem. 5, 1119–1121 (1960)Google Scholar
  26. 26.
    Ekberg, C., Källvenius, G., Albinsson, Y., Brown, P.L.: Studies on the hydrolytic behavior of zirconium(IV). J. Solution Chem. 33, 47–79 (2004)CrossRefGoogle Scholar
  27. 27.
    Kovalenko, P.N., Bagdasarov, K.N.: The solubility of zirconium hydroxide. Russ. J. Inorg. Chem. 6, 272–275 (1961)Google Scholar
  28. 28.
    Becking, L.B., Kaplan, I.R., Moore, D.: Limits of the natural environment in terms of pH and oxidation–reduction potentials. J. Geol. 68, 243–284 (1960)CrossRefGoogle Scholar
  29. 29.
    Sterner, S.M., Felmy, A.R., Rustad, J.R., Pitzer, K.S.: Thermodynamic Analysis of Aqueous Solutions Using INSIGHT. Pacific Northwest National Laboratory, Richland (1997)Google Scholar
  30. 30.
    Rai, D.: Solubility product of Pu(IV) hydrous oxide and equilibrium constants of Pu(IV)/Pu(V), Pu(IV)/Pu(VI), and Pu(V)/Pu(VI) couples. Radiochim. Acta 35, 97–108 (1984)CrossRefGoogle Scholar
  31. 31.
    Rai, D., Swanson, J.L.: Properties of plutonium (IV) polymer of environmental importance. Nucl. Tech. 54, 107–112 (1981)CrossRefGoogle Scholar
  32. 32.
    Rai, D., Felmy, A.R., Juracich, S.P., Rao, L.: Estimating the Hydrogen Ion Concentration in Concentrated NaCl and Na2SO4 Electrolytes. Sandia National Laboratories, Albuquerque NM (1995)CrossRefGoogle Scholar
  33. 33.
    Rand, M., Fuger, J., Grenthe, I., Neck, V., Rai, D.: Chemical Thermodynamics of Thorium. Chemical Thermodynamics, vol. 11. OECD Publishing, Paris (2008)Google Scholar
  34. 34.
    Felmy, A.R.: GMIN: A Computerized Chemical Equilibrium Model Using a Constrained Minimization of the Gibbs Free Energy. Pacific Northwest National Laboratory, Richland (1990)CrossRefGoogle Scholar
  35. 35.
    Harvie, C.E., Moller, N., Weare, J.H.: The prediction of mineral solubilities in natural waters: the Na–K–Mg–Ca–H–Cl–SO4–OH–HCO3–CO2–H2O system to high ionic strengths at 25 °C. Geochim. Cosmochim. Acta 48, 723–751 (1984)CrossRefGoogle Scholar
  36. 36.
    Latimer, W.M.: The Oxidation States of the Elements and Their Potentials in Aqueous Solutions, 2nd edn. Prentice-Hall Inc., Englewood Cliffs (1952)Google Scholar
  37. 37.
    Sasaki, T., Kobayashi, T., Takagi, I., Moriyama, H.: Hydrolysis constant and coordination geometry of zirconium(IV). Nucl. Sci. Technol. 45, 735–739 (2008)CrossRefGoogle Scholar
  38. 38.
    Baes Jr., C.F., Mesmer, R.E.: The Hydrolysis of Cations. Wiley, New York (1976)Google Scholar
  39. 39.
    Rai, D., Felmy, A.R., Ryan, J.L.: Uranium(IV) hydrolysis constants and solubility product of UO2·xH2O(am). Inorg. Chem. 29, 260–264 (1990)CrossRefGoogle Scholar
  40. 40.
    Ryan, J.L., Rai, D.: Thorium(IV) hydrous oxide solubility. Inorg. Chem. 26, 4140–4142 (1987)CrossRefGoogle Scholar
  41. 41.
    Weast, R.C.: Handbook of Chemistry and Physics, 53rd edn., 1972–1973. CRC Press, Cleveland (1972)Google Scholar
  42. 42.
    Lemire, R.J., Fuger, J., Nitsche, H., Potter, P., Rand, M.H., Rydberg, J., Spahiu, K., Sullivan, J.C., Ullman, W.J., Vitorge, P., Wanner, H.: Chemical Thermodynamics of Neptunium and Plutonium. Chemical Thermodynamics, vol. 4. Elsevier, Amsterdam (2001)Google Scholar
  43. 43.
    Rai, D., Moore, D.A., Felmy, A.R., Rosso, K.M., Bolton Jr., H.: PuPO4(cr, hyd.) solubility product and Pu3+ complexes with phosphate and ethylenediaminetetraacetic acid. J. Solution Chem. 39, 778–807 (2010)CrossRefGoogle Scholar
  44. 44.
    Rai, D., Moore, D.A., Hess, N.J., Rosso, K.M., Rao, L., Heald, S.M.: Chromium(III) hydroxide solubility in the aqueous K+–H+–OH–CO2–HCO3 – CO3 2−–H2O system: a thermodynamic model. J. Solution Chem. 36, 1261–1285 (2007)CrossRefGoogle Scholar
  45. 45.
    Rai, D., Moore, D.A., Rosso, K.M., Felmy, A.R., Bolton Jr., H.: Environmental mobility of Pu(IV) in the presence of ethtylenediaminetetraacetic acid: myth or reality. J. Solution Chem. 37, 957–986 (2008)CrossRefGoogle Scholar
  46. 46.
    Rai, D., Yui, M., Moore, D.A., Lumetta, G.J., Rosso, K.M., Xia, Y., Felmy, A.R., Skomurski, F.N.: Thermodynamic model for ThO2(am) solubility in alkaline-silica solutions. J. Solution Chem. 37, 1725–1746 (2008)CrossRefGoogle Scholar
  47. 47.
    Mak, T.C.W.: Refinement of the crystal structure of zirconyl chloride octahydrate. Can. J. Chem. 46, 3491–3497 (1968)CrossRefGoogle Scholar
  48. 48.
    Ryabchikov, D.I., Marov, I.N., Ermakov, A.N., Belyaeva, V.K.: Stability of some inorganic and organic complex compounds of zirconium and hafnium. J. Inorg. Nucl. Chem. 26, 965–980 (1964)CrossRefGoogle Scholar
  49. 49.
    Karlysheva, K.F., Chumakova, L.S., Malinko, L.A., Sheka, I.A.: Reaction of zirconium and hafnium oxide chlorides with sodium carbonate in solution. Russ. J. Inorg. Chem. 27, 1582–1585 (1982)Google Scholar
  50. 50.
    João, A., Bigot, S., Fromage, F.: Etude des carbonates complexes des éléments IVB II—Détermination des constants d’équilibre de formamtion des tétracarbonatozirconate (IV) et -hafnate (IV). Bull. Soc. Chim. Fr. 6, 943–947 (1987)Google Scholar
  51. 51.
    Rai, D., Kitamura, A., Rosso, K.M., Sasaki, T., Kobayashi, T.: Issues concerning the determination of solubility products of sparingly soluble crystalline solids: solubility of HfO2(cr). Radiochim. Acta 104, 583–592 (2016)CrossRefGoogle Scholar
  52. 52.
    Kobayashi, T., Sasaki, T., Takagi, I., Moriyama, H.: Solubility of zirconium(IV) hydrous oxides. J. Nucl. Sci. Technol. 44, 90–94 (2007)CrossRefGoogle Scholar
  53. 53.
    Pitzer, K.S.: Activity Coefficients in Electrolyte Solutions, 2nd edn. CRC Press Inc., Boca Raton (1991)Google Scholar
  54. 54.
    Becke, A.D.: A new mixing of Hartree-Fock and local density functional theories. J. Chem. Phys. 98, 1372–1377 (1993)CrossRefGoogle Scholar
  55. 55.
    Binkley, J.S., Pople, J.A., Hehre, W.J.: Self-consistent molecular orbital methods. 21. Small split-valence basis sets for 1st row elements. J. Am. Chem. Soc. 102, 939–947 (1980)CrossRefGoogle Scholar
  56. 56.
    Dobbs, K.D., Hehre, W.J.: Molecular-orbital theory of the properties of inorganic and organometallic compounds. 6. Extended basis sets for 2nd-row transition metals. J. Comput. Chem. 8, 880–893 (1987)CrossRefGoogle Scholar
  57. 57.
    Valiev, M., Bylaska, E.J., Govind, N., Kowalski, K., Straatsma, T.P., van Dam, H.J.J., Wang, D., Nieplocha, J., Apra, E., Windus, T.L., de Jong, W.A.: NWChem: a comprehensive and scalable open-source solution for large scale molecular simulations. Comput. Phys. Commun. 181, 1477–1489 (2010)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Rai Enviro-Chem, LLCYachatsUSA
  2. 2.Japan Atomic Energy AgencyTokai-muraJapan
  3. 3.Karlsruhe Institute of Technology, Institute for Nuclear Waste DisposalKarlsruheGermany
  4. 4.Pacific Northwest National LaboratoryRichlandUSA
  5. 5.Kyoto UniversityKyotoJapan

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