EDN: VEWMIG
Authors & Affiliations
Kharitonova N.L.
National Research Nuclear University Moscow Engineering Physics Institute, Moscow, Russia
Kharitonova N.L. – Leading Researcher, Cand. Sci. (Tech.). Contacts: 31, Kashirskoe sh., Moscow, Russia, 115409. Tel.: +7 (499) 324-77-77; е-mail: This email address is being protected from spambots. You need JavaScript enabled to view it..
Abstract
The article is devoted to the analysis of thermodynamic data for calculating the dissociation constant of pure water (the ionic product of water) – Kw, which is a reference property in the chemistry of water and aqueous solutions. In 2024, the International Association for the Properties of Water and Steam (IAPWS) published updated recommendations for the equation for the ionization constant of water, Kw over a wide range of temperatures and densities. The article compares the correlation equations for calculating Kw recommended by IAPWS for the period from 1981 to 2024. The following equation are considered: (1) the correlation equation for calculation adopted by IAPWS in 1981 as recommended reference data for temperatures from 0 to 1000 °C and pressures from 1 to 10,000 bar; (2) a semi-empirical equation for calculating pKw (pKw ≡ −lg(Kw)), proposed by Lvov – Bandura in 2007 and then updated in 2019 (IAPWS R11-07(2019)); (3) IAPWS recommendations adopted in 2024 (IAPWS R11-24), providing for the calculation of pKw taking into account new experimental data – precision measurements of the electrical conductivity of high-purity water obtained in 2020–2024. An analysis of the experimental data used in the correlation equations for calculating pKw in a wide range of temperatures and densities was performed. It is demonstrated that even when processing the same set of experimental points, the empirical parameters in the equation for calculating pKw can differ depending on the method used to extrapolate the limiting conductivity at infinite dilution. It is shown that the refined equation IAPWS-2024 (IAPWS R11-24), obtained on the basis of the results of precision experiments using methods for measuring electrical conductivity in a flow cell, allows more accurate calculation of pKw values in the region of near-critical and supercritical parameters due to the inclusion of these experimental data in the regression analysis.
Keywords
water dissociation constant, ionic product of water, safety, supercritical water cooled reactor, water coolant, WWER-SKD, reference data, experimental data, physical and chemical properties of water and steam, aqueous solutions, specific electrical conductivity
Article Text (PDF, in Russian)
References
- Asmolov V.G. Perspektivy razvitiya tekhnologii VVER [Prospects for the Development of WWER Technology]. V sb.: Dollezhalevskie chteniya. VII–VIII tsikly: sbornik lektsiy i prezentatsiy [Proc. of the Dollezhal Readings. VII–VIII Cycles. Collection of lectures and presentations]. Moscow, AO NIKIET Publ., 2024. Pp. 71–102. Available at: https://www.nikiet.ru/page/news/files/dollezhall_chtenia_7_8c.pdf (accessed 08.05.2025).
- Revised Release on the Ionization Constant of H2O. IAPWS R11-24. International Association for the Properties of Water and Steam, 2024. Available at: http://www.iapws.org/relguide/Ionization.pdf (accessed 14.08.2025).
- Arcis H., Bachet M., Dickinson Sh., Duncanson I., Eaker R.W., Jarvis J., Johnson K., Lee Ch.A., Lord F., Marks Ch., Tremaine P.R. Revised Parameters for the IAPWS Formulation for the Ionization Constant of Water Over a Wide Range of Temperatures and Densities, Including Near-Critical Conditions. J. Phys. Chem. Ref. Data, 2024, vol. 53, рр. 023103-1–023103-23. doi: 10.1063/5.0198792.
- Arcis H., Ferguson J.P., Cox J.S., Tremaine P.R. The Ionization Constant of Water at Elevated Temperatures and Pressures: New Data from Direct Conductivity Measurements and Revised Formulations from T = 273 K to 674 K and p = 0.1 MPa to 31 MPa. J. Phys. Chem. Ref. Data, 2020, vol. 49, pр. 03310-31―03310-37. DOI: 10.1063/1.5127662.
- Revised Release on the Ionization Constant of H2O. IAPWS R11-07(2019). International Association for the Properties of Water and Steam, 2019.
- Bandura A.V., Lvov S.N. The Ionization Constant of Water over a Wide Range of Temperatures and Densities. J. Phys. Chem. Ref. Data, 2006, vol. 35, pp. 15–30. DOI: 0.1063/1.1928231.
- Bandura A.V., Lvov S.N. The ionization constant of water over a wide range of temperatures and densities. In: Steam, Water, and Hydrothermal Systems: Physics and Chemistry. Meeting the Needs of Industry, ed. by P.R. Tremaine, P.G. Hill, D.E. Irish, and P.V. Balakrishnan. Proceedings of the 13th International Conference on the Properties of Water and Steam. Ottawa: NRC Press, 2000. Pp. 96–103.
- Marshall W.L., Franck E.U. Ion product of water substance, 0–1000 °C, 1–10,000 bars. New international formulation and its background. J. Phys. Chem. Ref. Data, 1981, vol. 10, p. 295.
- Marshall W.L. Consideration of Present Knowledge of the Ionization Behavior of Water as a Function of Temperature and Pressure. Minutes of IAPWS Meeting, Ottawa, Canada, September 15–9, 1975.
- Marshall W.L. Further Evaluation of the Ionization Constant of Water. Description from 0 to 1000 °C and from 1 to above 10,000 Bars. Minutes of IAPWS Meeting, Kyoto, Japan, September 5–10, 1976.
- Marshall W.L. Revised Evaluation of the Ion Product of Water. Description from 0 to 1000 °C and from 1 to above 10,000 Bars. Minutes of IAPWS Meeting, Moscow, USSR, September 10–16, 1977.
- Chase M.W. JANAF Thermochemical Tables. 4th ed. J. Phys. Chem. Ref. Data, 1998, Monograph 9.
- Revised Release on the IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. (IAPWS, R6-95). International Association for the Properties of Water and Steam, 2018. Available at: http://www.iapws.org/relguide/IAPWS-95.html (accessed 14.08.2025).
- Wagner W., Pruß A. The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use. J. Phys. Chem. Ref. Data, 2002, vol. 31, pp. 387–535.
- Kharitonova N.L., Gurbanova Sh.A. Termodinamicheskie dannye dlya rascheta vysokotemperaturnogo vodorodnogo pokazatelya рНt vodnogo teplonositelya reaktornykh ustanovok sverkhkriticheskikh parametrov [Thermodynamic data for calculating the high-temperature hydrogen index pH of the water coolant of reactor installations with supercritical parameters]. Voprosy atomnoy nauki i tekhniki. Ceriya: Yaderno-reaktornye konstanty – Problems of Atomic Science and Technology. Series: Nuclear and Reactor Constants, 2022, no. 4, pp. 201–213. Available at: https://vant.ippe.ru/images/pdf/2022/issue2022-4-201-213.pdf (accessed 14.08.2025).
- Noyes A.A., Kato Y., Sosman R.B. The hydrolysis of ammonium acetate and the ionization of water at high temperatures. J. Am. Chem. Soc., 1910, vol. 32, рр. 159–178.
- Holzapfel W.B., Franck E.U. Leitfahigkeit und Ionendissoziation des Wassers bis 1000 °C und 100 kBar, Ber. Bunsenges. Phys. Chem., 1966, vol. 70, pp. 1105–1112.
- Quist A.S. Ionization constant of water to 800 °C and 4000 Bars. J. Phys. Chem., 1970, vol. 74, pp. 3396–3402.
- Fisher J.R., Barnes H.L. Ion-product constant of water to 350 °C. J. Phys. Chem., 1972, vol. 76, pp. 90–99.
- Svistunov E.P., Smirnov S.N., Komissarov K.B. Ionic distribution factors of electrolytes and ionic product of water at saturation line. Therm. Eng., 1977, vol. 24, pp. 45–47.
- Svistunov E.P., Golubev B.P., Smirnov S.N., Sevastjanov V.P. Ionic product for water for wide range of state parameters. Therm. Eng., 1978, vol. 25, p. 70.
- Helgeson H.C., Kirkham D.H. Theoretical prediction of the thermodynamic properties of aqueous electrolytes at high pressures and temperatures. III. Equation of state for aqueous species at infinite dilution. American Journal of Science, 1976, vol. 276, no. 2, pp. 97–240.
- Arcis H., Lee C.A., Zimmerman G.H., Tremaine P.R. Critical review of transport properties of HCl, KOH, and NaOH in high temperature water and correlations for H3O+ and OH−. J. Phys. Chem. Ref. Data, 2023, vol. 52(2), p. 023103. DOI: 10.1063/5.0138262.
- Zimmerman G.H., Staros D.J., Arcis H. Critical review of transport and equilibrium properties of potassium chloride in high temperature water. J. Chem. Eng. Data, 2022, vol. 67, pp. 533–544. DOI: 10.1021/acs.jced.1c00814.
- Zimmerman G.H., Gruszkiewicz M.S., Wood R.H. New apparatus for conductance measurements at high temperatures: Conductance of aqueous solutions of LiCl, NaCl, NaBr, and CsBr at 28 MPa and water densities from 700 to 260 kg m–3. J. Phys. Chem., 1995, vol. 99, pp. 11612–11625.
- Gruszkiewicz M.S., Wood R.H. Conductance of dilute LiCl, NaCl, NaBr, and CsBr solutions in supercritical water using a flow conductance cell. J. Phys. Chem., 1997, vol. 101, pp. 6549–6559.
- Hnedkovsky L., Wood R.H., Balashov V.N. Electrical conductances of aqueous Na2SO4, H2SO4, and their mixtures: Limiting equivalent ion conductances, dissociation constants, and speciation to 673 K and 28 MPa. J. Phys. Chem., 2005, vol. 109, pp. 9034–9046.
- Ho P.C., Palmer D.A., Wood R.H. Conductivity measurements of dilute aqueous LiOH, NaOH, and KOH solutions to high temperatures and pressures using a flow-through cell. J. Phys. Chem., 2000, vol. 104, pp. 12084–12089.
- Zimmerman G.H., Arcis H., Tremaine P.R. Limiting conductivities and ion association constants of aqueous NaCl under hydrothermal conditions: Experimental data and correlations. J. Chem. Eng. Data, 2012, vol. 57, pp. 2415–2429.
- Arcis H., Zimmerman G.H., Tremaine P.R. Ion-pair formation in aqueous strontium chloride and strontium hydroxide solutions under hydrothermal conditions by AC conductivity measurements. Phys. Chem. Chem. Phys., 2014, vol. 16, pp. 17688–17704.
- Arcis H., Ferguson J.P., Zimmerman G.H., Tremaine P.R. The limiting conductivity of the borate ion and its ion-pair formation constants with sodium and potassium under hydrothermal conditions. Phys. Chem. Chem. Phys., 2016, vol. 18, pp. 24081–24094.
- Arcis H., Ferguson J.P., Applegarth L.M., Zimmerman G.H., Tremaine P.R. Ionization of boric acid in water from 298 K to 623 K by AC conductivity and Raman spectroscopy. J. Chem. Thermodyn., 2017, vol. 106, pp. 187–198.
- Conrad J.K., Arcis H., Ferguson J.P., Tremaine P.R. Second ionization constant of sulfuric acid in H2O and D2O from 150 to 300 °C at p = 11.5 MPa using flow AC conductivity. Phys. Chem. Chem. Phys., 2023, vol. 25, pp. 1659–1676.
- Arcis H., Plumridge J., Tremaine P.R. Limiting conductivities of strong acids and bases in D2O and H2O: Deuterium isotope effects on proton hopping over a wide temperature range. J. Phys. Chem., 2022, vol. 126, pp. 8791–8803.
- Arcis H., Conrad J.K., Ferguson J.P., Erickson K.M., Tremaine P.R. First ionization constant of phosphoric acid and of acetic acid in H2O and D2O from T = 373 K to 573 K at p = 11.5 and 20 MPa by AC conductivity methods. J. Solution Chem., 2024, vol. 53, pp. 91–125.
- Marshall W.L. Electrical conductance of liquid and supercritical water evaluated from 0 °C and 0.1 MPa to high temperatures and pressures. Reduced-state relationships. J. Chem. Eng. Data, 1987, vol. 32, pp. 221–226.
- Styrikovich M.A., Martynova O.I., Miropol'skij Z.L. Protsessy generatsii para na elektrostantsiyakh. Ucheb. dlya energeticheskikh spetsial'nostey vuzov. Pod obshchey red. M.A. Styrikovicha [Steam generation processes at power plants. Textbook for power engineering specialties of higher education institutions]. Moscow, Energiya Publ., 1969. 312 p.
- Kharitonova N.L., Tyapkov V.F. Water Chemistries of VVER-SCW Nuclear Power Plants: The Choice and Justification (Review). Therm. Eng., 2024, vol. 71, issue 8, pp. 675–688. DOI: https://doi.org/10.1134/S0040601524700204.
- Cohen E.R., Cvitaˇs T., Frey J.G., Holmstrom B., Kuchitsu K., Marquardt R., Mills I., Pavese F., Quack M., Stohner J., Strauss H.L., Takami M., Thor A.J. Quantities, Units and Symbols in Physical Chemistry: IUPAC Green Book. 3rd ed. Cambridge: RSC Publishing, 2007.
- GOST 34100.3-2017. Neopredelennost' izmereniya. Chast' 3. Rukovodstvo po vyrazheniyu neopredelennosti izmereniya (ISO/IEC Guide 98-3:2008 IDT) [GOST 34100.3-2017. Uncertainty of measurement. Part 3. Guide to the expression of uncertainty in measurement (ISO/IEC Guide 98-3:2008 IDT]. Moscow, Standartinform Publ., 2018.
UDC 621.039.58
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