{"id":66897,"date":"2026-10-13T10:09:03","date_gmt":"2026-10-13T07:09:03","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66897"},"modified":"2026-10-13T10:09:03","modified_gmt":"2026-10-13T07:09:03","slug":"debye-huckel-activity-coefficient-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/debye-huckel-activity-coefficient-calculator\/","title":{"rendered":"Debye\u2013H\u00fcckel Activity Coefficient Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Estimate an Ion Activity Coefficient from Ionic Strength<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66897\" data-favorite-title=\"Debye\u2013H\u00fcckel Activity Coefficient\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/debye-huckel-activity-coefficient-calculator\/\" data-favorite-excerpt=\"Estimate the activity coefficient of an ion in aqueous solution using the Debye\u2013H\u00fcckel limiting law, extended equation, or Davies equation. Enter the ionic strength, ion charge, and temperature to get \u03b3 and log\u2081\u2080 \u03b3.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/chemistry\/debye-huckel-activity-coefficient-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66897\" data-post=\"66897\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Model<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"model\"><option value=\"limiting\">Debye\u2013H\u00fcckel limiting law (I \u2264 0.01 M)<\/option><option value=\"extended\">Extended Debye\u2013H\u00fcckel equation (I \u2264 0.1 M)<\/option><option value=\"davies\" selected>Davies equation (I \u2264 0.5 M)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Ionic Strength (I)<\/label><div class=\"term\">I<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"ionic_strength_i\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.1\" min=\"0\" value=\"0.1\"\/><div class=\"unit\" id=\"calc-unit-2\">mol\/L<\/div><small id=\"calc-info-2\">I = \u00bd \u03a3 c\u1d62z\u1d62\u00b2 over all ions in the solution.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Ion Charge (z)<\/label><div class=\"term\">z<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"ion_charge_z\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. 1, 2 or -2\" step=\"any\" value=\"1\"\/><small id=\"calc-info-3\">Charge of the ion whose activity coefficient you need, e.g. +1 for Na\u207a, \u22122 for SO\u2084\u00b2\u207b. Only z\u00b2 is used, so the sign does not matter.<\/small><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-4\">Water Temperature<\/label><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"water_temperature\"><option value=\"t0\">0 \u00b0C<\/option><option value=\"t10\">10 \u00b0C<\/option><option value=\"t20\">20 \u00b0C<\/option><option value=\"t25\" selected>25 \u00b0C<\/option><option value=\"t30\">30 \u00b0C<\/option><option value=\"t40\">40 \u00b0C<\/option><option value=\"t50\">50 \u00b0C<\/option><option value=\"custom\">Custom A and B constants<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-5\">Constant A<\/label><div class=\"term\">A<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"constant_a\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.509\" min=\"0\" value=\"0.509\"\/><small id=\"calc-info-5\">Debye\u2013H\u00fcckel constant A for your solvent and temperature (0.509 for water at 25 \u00b0C).<\/small><\/div><div class=\"field has-term\" id=\"input-6\" hidden><label for=\"field-6\">Constant B<\/label><div class=\"term\">B<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"constant_b\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.328\" min=\"0\" value=\"0.328\"\/><small id=\"calc-info-6\">Debye\u2013H\u00fcckel constant B for your solvent and temperature (0.328 for water at 25 \u00b0C).<\/small><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-7\">Ion-Size Parameter (a)<\/label><div class=\"term\">a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"ionsize_parameter_a\" id=\"field-7\" aria-describedby=\"calc-unit-7 calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 4\" min=\"0\" value=\"4\"\/><div class=\"unit\" id=\"calc-unit-7\">\u00c5<\/div><small id=\"calc-info-7\">Effective hydrated-ion diameter in the extended equation: \u2248 3 \u00c5 for K\u207a\/Cl\u207b\/NO\u2083\u207b, 4\u20135 \u00c5 for Na\u207a\/Ca\u00b2\u207a, up to 9\u201311 \u00c5 for H\u207a\/Mg\u00b2\u207a.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66897\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Activity Coefficient Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Activity Coefficient (\u03b3)<\/span><span class=\"result-term\">\u03b3<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>log\u2081\u2080 \u03b3<\/span><span class=\"result-term\">log \u03b3<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Model Range and Applicability<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>About the Debye\u2013H\u00fcckel Theory<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66897\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Debye\u2013H\u00fcckel Activity Coefficient Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\\[ \\log_{10}\\gamma = -A z^2 \\sqrt{I} \\qquad \\text{(limiting law)} \\\\[4pt] \\log_{10}\\gamma = \\frac{-A z^2 \\sqrt{I}}{1 + B a \\sqrt{I}} \\qquad \\text{(extended)} \\\\[4pt] \\log_{10}\\gamma = -A z^2 \\left( \\frac{\\sqrt{I}}{1+\\sqrt{I}} - 0.3\\,I \\right) \\qquad \\text{(Davies)} \\]\n\\[ \\gamma = 10^{\\log_{10}\\gamma} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\gamma\\) \u2014 activity coefficient of the ion (dimensionless)<\/li>\n<li>\\(z\\) \u2014 charge of the ion (only \\(z^2\\) is used, so the sign does not matter)<\/li>\n<li>\\(I\\) \u2014 ionic strength of the solution in mol\/L, \\(I = \\tfrac{1}{2}\\sum c_i z_i^2\\)<\/li>\n<li>\\(A\\), \\(B\\) \u2014 Debye\u2013H\u00fcckel constants of the solvent, set by temperature (0.509 and 0.328 for water at 25 \u00b0C)<\/li>\n<li>\\(a\\) \u2014 ion-size parameter in \u00e5ngstr\u00f6ms (extended equation only)<\/li>\n<\/ul>\n<p>Each variant gives the base-10 logarithm of the activity coefficient; raising 10 to that power returns \\(\\gamma\\) itself, which converts an analytical concentration into an effective thermodynamic activity via \\(a = \\gamma c\\).<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Debye\u2013H\u00fcckel Activity Coefficient \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> estimate the activity coefficient of Na\u207a (z = +1) in a 0.1 M ionic-strength solution at 25 \u00b0C, using the Davies equation.<\/p>\n<p>\\[ \\sqrt{I} = \\sqrt{0.1} = 0.3162 \\]<\/p>\n<p>\\[ \\frac{\\sqrt{I}}{1+\\sqrt{I}} - 0.3I = \\frac{0.3162}{1.3162} - 0.3(0.1) = 0.2403 - 0.0300 = 0.2103 \\]<\/p>\n<p>\\[ \\log_{10}\\gamma = -0.509 \\times 1^2 \\times 0.2103 = -0.1070 \\]<\/p>\n<p>\\[ \\gamma = 10^{-0.1070} = 0.782 \\]<\/p>\n<p><strong>Result:<\/strong> \u03b3 \u2248 0.782 (log\u2081\u2080 \u03b3 \u2248 \u22120.107). The effective concentration of Na\u207a is only about 78% of its analytical concentration \u2014 a sizable correction at 0.1 M.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Pick a <strong>Model<\/strong>: the limiting law for I up to 0.01 M, the extended Debye\u2013H\u00fcckel equation up to 0.1 M, or the Davies equation up to 0.5 M when no ion-size parameter is known.<\/li>\n<li>Enter the <strong>Ionic Strength (I)<\/strong> in mol\/L. If you only know the composition, compute \\(I = \\tfrac{1}{2}\\sum c_i z_i^2\\) over all ions first.<\/li>\n<li>Enter the <strong>Ion Charge (z)<\/strong> of the ion in question, e.g. 2 for Ca\u00b2\u207a or \u22122 for SO\u2084\u00b2\u207b. The sign is irrelevant because only \\(z^2\\) enters the equations.<\/li>\n<li>Select the <strong>Water Temperature<\/strong> (0\u201350 \u00b0C) to set the constants A and B automatically, or choose \"Custom A and B constants\" and type them in for another solvent.<\/li>\n<li>If you chose the extended equation, enter the <strong>Ion-Size Parameter (a)<\/strong> in \u00e5ngstr\u00f6ms \u2014 about 3 \u00c5 for K\u207a, Cl\u207b, NO\u2083\u207b; 4\u20135 \u00c5 for Na\u207a or Ca\u00b2\u207a; up to 9\u201311 \u00c5 for H\u207a or Mg\u00b2\u207a.<\/li>\n<li>Read the <strong>Activity Coefficient (\u03b3)<\/strong> and <strong>log\u2081\u2080 \u03b3<\/strong> in the results, together with the applicable range and a step-by-step substitution.<\/li>\n<\/ol>\n<h2>What is the Debye\u2013H\u00fcckel activity coefficient?<\/h2>\n<p>In any solution that is not extremely dilute, each ion is surrounded by an <em>ion atmosphere<\/em> of opposite charge. This cloud screens the ion's electrostatic interactions, so the ion behaves thermodynamically as if its concentration were lower than the value you measure analytically. The effective concentration is called the <strong>activity<\/strong>, \\(a = \\gamma c\\), and the proportionality factor \\(\\gamma\\) is the <strong>activity coefficient<\/strong>. Debye\u2013H\u00fcckel theory derives \\(\\gamma\\) purely from electrostatics: the correction grows with the square of the ion's charge and with the square root of the solution's ionic strength.<\/p>\n<p>Activity coefficients matter whenever equilibrium constants are applied to real solutions. A <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/solubility-product-ksp-calculator\/\">solubility product<\/a> is written in activities, not concentrations, so a salt can appear far more soluble in a 0.1 M NaCl background than in pure water purely because \u03b3 drops. The same correction enters <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/standard-cell-potential-calculator\/\">Nernstian cell potentials<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/van-t-hoff-equation-calculator\/\">equilibrium-shift calculations<\/a>: ignoring \u03b3 is the most common source of error when comparing measured and predicted values in moderately concentrated solutions.<\/p>\n<p>The three variants of the theory trade accuracy for input requirements. The <strong>limiting law<\/strong> is exact only as I \u2192 0 and needs nothing beyond I and z. The <strong>extended equation<\/strong> adds the finite ion size \\(a\\), extending the reliable range to about 0.1 M. The <strong>Davies equation<\/strong> replaces \\(a\\) with an empirical \u22120.3I term, so it needs no size parameter yet stays useful up to roughly 0.5 M \u2014 which is why it is the default choice in geochemistry and speciation software. The calculator flags it clearly when your ionic strength exceeds the recommended range of the selected model.<\/p>\n<p>To interpret the result: \u03b3 = 1 means the ion behaves ideally (essentially only at infinite dilution); \u03b3 = 0.782 as in the example means the ion's activity is 78% of its analytical concentration. Because \\(z^2\\) appears in every formula, divalent ions are corrected roughly four times as strongly as monovalent ones at the same ionic strength.<\/p>\n<h2>Assumptions, limitations, and practical tips<\/h2>\n<ul>\n<li><strong>Dilute solutions only.<\/strong> The theory treats the solvent as a dielectric continuum with point-charge (limiting law) or fixed-size ions. Above the stated limits, ion pairing, specific ion\u2013solvent interactions and finite ion concentrations dominate; SIT or Pitzer models are then required.<\/li>\n<li><strong>Complete dissociation<\/strong> is assumed. Weak electrolytes should first be speciated \u2014 only free ions contribute to I and to the \u03b3 of a given ion.<\/li>\n<li><strong>Water as the solvent.<\/strong> The built-in A and B constants apply to water between 0 and 50 \u00b0C. For other solvents, look up A and B for that medium and use the \"Custom\" option.<\/li>\n<li><strong>Molarity vs molality.<\/strong> The equations are rigorously defined on the molal scale; the difference from molarity is negligible below ~0.5 M, which matches the models' valid range.<\/li>\n<li><strong>Tip:<\/strong> if you do not know the ion-size parameter for your ion, use the Davies equation \u2014 it was designed precisely to avoid that input.<\/li>\n<li><strong>Tip:<\/strong> to build I yourself, sum over every ion in solution: for 0.01 M MgCl\u2082, \\(I = \\tfrac{1}{2}(0.01 \\times 2^2 + 0.02 \\times 1^2) = 0.03\\) M.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Estimate the activity coefficient of an ion in aqueous solution using the Debye\u2013H\u00fcckel limiting law, extended equation, or Davies equation. Enter the ionic strength, ion charge, and temperature to get \u03b3 and log\u2081\u2080 \u03b3.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[56],"class_list":["post-66897","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-stoichiometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66897","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66897"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66897\/revisions"}],"predecessor-version":[{"id":66898,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66897\/revisions\/66898"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}