{"term":{"id":"01534","title":"Debye–Hückel equation","longtitle":"IUPAC Gold Book - Debye–Hückel equation","doi":"10.1351\/goldbook.D01534","code":"D01534","status":"current","mentioned":"<em>mentioned<\/em>: Bates–Guggenheim convention","definitions":[{"id":1,"text":"The chemical potential or activity of ions cannot be determined on a purely thermodynamic basis. This is due to the fact that the effects of an ion cannot be separated from the effects of the accompanying counter-ion, or in other terms, the electrochemical potential of the ion cannot be separated into the chemical and the electrical component. Such a separation must necessarily be based on a non-thermodynamic convention. The present convention is based on the assumption that the molal activity coefficient of the chloride ion in dilute aqueous solutions (\\(\\pu{I \\lt 0.10 mol kg-1}\\)) can be estimated by means of the Debye–Hückel equation: \\[-\\log_{10}\\gamma_{\\rm{B}}=\\frac{z_{\\rm{B}}^{2}\\ A\\ \\sqrt{I}}{1 + \\mathring{a}\\ B\\ \\sqrt{I}}\\] where \\(I\\) is ionic strength, \\(z\\) is the charge number of the ion, \\(\\mathring{a}\\) is ion size parameter and \\(A\\) and \\(B\\) are temperature-dependent constants. According to the Bates–Guggenheim convention \\(\\mathring{a}\\ B\\) is taken to be \\(1.5 \\sqrt{\\pu{mol kg-1}}\\) at all temperatures and for all compositions of the solutions.","links":[{"term":"Debye","url":"https:\/\/goldbook.iupac.org\/terms\/view\/D01533"},{"term":"charge number","url":"https:\/\/goldbook.iupac.org\/terms\/view\/C00993"},{"term":"chemical potential","url":"https:\/\/goldbook.iupac.org\/terms\/view\/C01032"},{"term":"coefficient","url":"https:\/\/goldbook.iupac.org\/terms\/view\/C01124"},{"term":"electrochemical potential","url":"https:\/\/goldbook.iupac.org\/terms\/view\/E01945"},{"term":"ionic strength","url":"https:\/\/goldbook.iupac.org\/terms\/view\/I03180"},{"term":"molal","url":"https:\/\/goldbook.iupac.org\/terms\/view\/M03969"},{"term":"pH","url":"https:\/\/goldbook.iupac.org\/terms\/view\/P04524"}],"sources":["PAC, 1984, 56, 567. 'Physicochemical quantities and units in clinical chemistry with special emphasis on activities and activity coefficients (Recommendations 1983)' on page 569 (https:\/\/doi.org\/10.1351\/pac198456050567)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/D01534\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/D01534\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/D01534\/plain"},"citation":"Citation: 'Debye–Hückel equation' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351\/goldbook.D01534","license":"The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https:\/\/creativecommons.org\/licenses\/by-sa\/4.0\/) for individual terms.","collection":"If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .","disclaimer":"The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using.","accessed":"2026-07-01T14:14:30+00:00"}}