{"id":66919,"date":"2026-10-13T10:15:00","date_gmt":"2026-10-13T07:15:00","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66919"},"modified":"2026-10-13T10:15:00","modified_gmt":"2026-10-13T07:15:00","slug":"kohlrauschs-law-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/kohlrauschs-law-calculator\/","title":{"rendered":"Kohlrausch's Law 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\">Predict the Electrolyte&#039;s Limiting Molar Conductivity from Its Ions<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66919\" data-favorite-title=\"Kohlrausch&#039;s Law\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/kohlrauschs-law-calculator\/\" data-favorite-excerpt=\"Calculate the limiting molar conductivity of any electrolyte at infinite dilution from its ionic conductivities and stoichiometric coefficients, using Kohlrausch&#039;s law of independent ion migration.\" 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\/kohlrauschs-law-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66919\" data-post=\"66919\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Cation (Positive Ion)<\/span><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Cation Name<\/label><input type=\"text\" name=\"cation_name\" id=\"field-2\" placeholder=\"e.g. Na\u207a\" step=\"any\" value=\"Na\u207a\"\/><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Limiting Molar Conductivity (\u03bb\u00b0\u208a)<\/label><div class=\"term\">\u03bb\u00b0\u208a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limiting_molar_conductivity_\" id=\"field-3\" aria-describedby=\"calc-unit-3 calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"50.11\"\/><div class=\"unit\" id=\"calc-unit-3\">S\u00b7cm\u00b2\/mol<\/div><small id=\"calc-info-3\">Ionic limiting molar conductivity at infinite dilution and 25 \u00b0C (Na\u207a = 50.11, K\u207a = 73.5, Ca\u00b2\u207a = 119.0).<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Stoichiometric Coefficient (\u03bd\u208a)<\/label><div class=\"term\">\u03bd\u208a<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"stoichiometric_coefficient_\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"1\"\/><small id=\"calc-info-4\">Number of cations per formula unit, e.g. 1 in NaCl, 2 in Ca(OH)\u2082.<\/small><\/div><div class=\"field is-checkbox is-single\" id=\"input-5\"><input type=\"checkbox\" id=\"field-5\" value=\"1\"\/><label for=\"field-5\">Add a second cation<\/label><\/div><div class=\"field\" id=\"input-6\" hidden><label for=\"field-6\">Second Cation Name<\/label><input type=\"text\" name=\"second_cation_name\" id=\"field-6\" placeholder=\"e.g. Ca\u00b2\u207a\" step=\"any\" value=\"Ca\u00b2\u207a\"\/><\/div><div class=\"field has-term\" id=\"input-7\" hidden><label for=\"field-7\">Limiting Molar Conductivity (\u03bb\u00b0\u208a\u2082)<\/label><div class=\"term\">\u03bb\u00b0\u208a\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limiting_molar_conductivity_\" id=\"field-7\" aria-describedby=\"calc-unit-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"119\"\/><div class=\"unit\" id=\"calc-unit-7\">S\u00b7cm\u00b2\/mol<\/div><\/div><div class=\"field has-term\" id=\"input-8\" hidden><label for=\"field-8\">Stoichiometric Coefficient (\u03bd\u208a\u2082)<\/label><div class=\"term\">\u03bd\u208a\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"stoichiometric_coefficient_\" id=\"field-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"1\"\/><\/div><div class=\"is-single field\" id=\"input-9\"><span class=\"font-semibold\">Anion (Negative Ion)<\/span><\/div><div class=\"field\" id=\"input-10\"><label for=\"field-10\">Anion Name<\/label><input type=\"text\" name=\"anion_name\" id=\"field-10\" placeholder=\"e.g. Cl\u207b\" step=\"any\" value=\"Cl\u207b\"\/><\/div><div class=\"field has-term\" id=\"input-11\"><label for=\"field-11\">Limiting Molar Conductivity (\u03bb\u00b0\u208b)<\/label><div class=\"term\">\u03bb\u00b0\u208b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limiting_molar_conductivity_\" id=\"field-11\" aria-describedby=\"calc-unit-11 calc-info-11\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"76.35\"\/><div class=\"unit\" id=\"calc-unit-11\">S\u00b7cm\u00b2\/mol<\/div><small id=\"calc-info-11\">Ionic limiting molar conductivity at infinite dilution and 25 \u00b0C (Cl\u207b = 76.35, OH\u207b = 198.3, SO\u2084\u00b2\u207b = 160.0).<\/small><\/div><div class=\"field has-term\" id=\"input-12\"><label for=\"field-12\">Stoichiometric Coefficient (\u03bd\u208b)<\/label><div class=\"term\">\u03bd\u208b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"stoichiometric_coefficient_\" id=\"field-12\" aria-describedby=\"calc-info-12\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"1\"\/><small id=\"calc-info-12\">Number of anions per formula unit, e.g. 2 in CaCl\u2082 or Na\u2082SO\u2084.<\/small><\/div><div class=\"field is-checkbox is-single\" id=\"input-13\"><input type=\"checkbox\" id=\"field-13\" value=\"1\"\/><label for=\"field-13\">Add a second anion<\/label><\/div><div class=\"field\" id=\"input-14\" hidden><label for=\"field-14\">Second Anion Name<\/label><input type=\"text\" name=\"second_anion_name\" id=\"field-14\" placeholder=\"e.g. SO\u2084\u00b2\u207b\" step=\"any\" value=\"SO\u2084\u00b2\u207b\"\/><\/div><div class=\"field has-term\" id=\"input-15\" hidden><label for=\"field-15\">Limiting Molar Conductivity (\u03bb\u00b0\u208b\u2082)<\/label><div class=\"term\">\u03bb\u00b0\u208b\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"limiting_molar_conductivity_\" id=\"field-15\" aria-describedby=\"calc-unit-15\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"160\"\/><div class=\"unit\" id=\"calc-unit-15\">S\u00b7cm\u00b2\/mol<\/div><\/div><div class=\"field has-term\" id=\"input-16\" hidden><label for=\"field-16\">Stoichiometric Coefficient (\u03bd\u208b\u2082)<\/label><div class=\"term\">\u03bd\u208b\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"stoichiometric_coefficient_\" id=\"field-16\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1\" value=\"1\"\/><\/div><div class=\"field is-single\" id=\"input-17\"><label for=\"field-17\">Output Unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-17\" name=\"output_unit\"><option value=\"scm2\" selected>S\u00b7cm\u00b2\/mol (common in tables)<\/option><option value=\"m2\">S\u00b7m\u00b2\/mol (SI)<\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66919\">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> Kohlrausch&#039;s Law Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Limiting Molar Conductivity (\u039b\u00b0\u2098)<\/span><span class=\"result-term\">\u039b\u00b0\u2098<\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>Ion Contributions<\/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>Calculation Details<\/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>About Kohlrausch&#039;s Law of Independent Ion Migration<\/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><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=\"66919\" 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>Kohlrausch's Law 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\">\n\\[ \\Lambda^\\circ_m = \\nu_+ \\lambda^\\circ_+ + \\nu_- \\lambda^\\circ_- \\quad \\text{or, in general,} \\quad \\Lambda^\\circ_m = \\sum_i \\nu_i \\lambda^\\circ_i \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\Lambda^\\circ_m\\) \u2014 limiting molar conductivity of the electrolyte at infinite dilution (S\u00b7cm\u00b2\/mol)<\/li>\n<li>\\(\\lambda^\\circ_i\\) \u2014 limiting molar conductivity (ionic conductivity) of ion \\(i\\) at infinite dilution (S\u00b7cm\u00b2\/mol)<\/li>\n<li>\\(\\nu_i\\) \u2014 stoichiometric coefficient of ion \\(i\\) in the formula unit (e.g. 2 for the Cl\u207b in CaCl\u2082)<\/li>\n<\/ul>\n<p>The formula expresses Kohlrausch's law of independent migration of ions: at infinite dilution each ion contributes to the total conductivity independently of every other ion, so the electrolyte's limiting molar conductivity is just the sum of the ionic conductivities weighted by their stoichiometric coefficients.<\/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>Kohlrausch's Law \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an electrolyte whose formula unit contains one Na\u207a ion, one Ca\u00b2\u207a ion, one Cl\u207b ion and one SO\u2084\u00b2\u207b ion. All four ions have a stoichiometric coefficient of 1, and their limiting molar conductivities at 25 \u00b0C are \u03bb\u00b0(Na\u207a) = 50.11, \u03bb\u00b0(Ca\u00b2\u207a) = 119.0, \u03bb\u00b0(Cl\u207b) = 76.35 and \u03bb\u00b0(SO\u2084\u00b2\u207b) = 160.0 S\u00b7cm\u00b2\/mol \u2014 exactly the calculator's default values.<\/p>\n<p>\\[ \\Lambda^\\circ_m = 1 \\times 50.11 + 1 \\times 119.0 + 1 \\times 76.35 + 1 \\times 160.0 = 405.46 \\ \\text{S\u00b7cm}^2\\!\/\\text{mol} \\]<\/p>\n<p><strong>Result:<\/strong> \\(\\Lambda^\\circ_m = 405.46\\) S\u00b7cm\u00b2\/mol (equivalently 0.040546 S\u00b7m\u00b2\/mol).<\/p>\n<p>If instead you uncheck both \"Add a second cation\" and \"Add a second anion\" boxes, the same inputs reduce to NaCl: \\(\\Lambda^\\circ_m(\\text{NaCl}) = 50.11 + 76.35 = 126.46\\) S\u00b7cm\u00b2\/mol, the accepted tabulated value.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Cation Name<\/strong> (optional, used for labeling) and its <strong>Limiting Molar Conductivity (\u03bb\u00b0\u208a)<\/strong> in S\u00b7cm\u00b2\/mol, e.g. 50.11 for Na\u207a.<\/li>\n<li>Set the cation's <strong>Stoichiometric Coefficient (\u03bd\u208a)<\/strong> \u2014 the number of such cations per formula unit, e.g. 2 for Na\u207a in Na\u2082SO\u2084.<\/li>\n<li>If the salt has two different cations (e.g. KAl(SO\u2084)\u2082), tick <strong>Add a second cation<\/strong> and fill in the second cation's name, \u03bb\u00b0 and coefficient; otherwise leave the box unticked.<\/li>\n<li>Repeat the same steps for the anion: <strong>Anion Name<\/strong>, <strong>Limiting Molar Conductivity (\u03bb\u00b0\u208b)<\/strong>, <strong>Stoichiometric Coefficient (\u03bd\u208b)<\/strong>, and optionally <strong>Add a second anion<\/strong>.<\/li>\n<li>Choose the <strong>Output Unit<\/strong> \u2014 S\u00b7cm\u00b2\/mol (the unit used in most data tables) or S\u00b7m\u00b2\/mol (the SI unit).<\/li>\n<li>Read the result: the <strong>Limiting Molar Conductivity (\u039b\u00b0\u2098)<\/strong>, a per-ion breakdown of contributions, and the full substitution are shown immediately.<\/li>\n<\/ol>\n<h2>What is Kohlrausch's law of independent ion migration?<\/h2>\n<p>When an electric field is applied to an electrolyte solution, both the cations and the anions migrate and carry current. Friedrich Kohlrausch discovered (around 1875) that at <em>infinite dilution<\/em> \u2014 where the ions are so far apart that they no longer interact \u2014 each ion migrates independently of its counter-ion. The molar conductivity of the whole electrolyte is therefore simply the sum of the individual ionic conductivities, each multiplied by how many of that ion the formula unit produces on dissociation.<\/p>\n<p>A classic experimental proof is the difference rule: \\(\\Lambda^\\circ_m(\\text{KCl}) - \\Lambda^\\circ_m(\\text{NaCl})\\) equals \\(\\Lambda^\\circ_m(\\text{KBr}) - \\Lambda^\\circ_m(\\text{NaBr})\\), because the anion's contribution cancels out and only the difference between K\u207a and Na\u207a remains. This additivity is exactly what the calculator reproduces.<\/p>\n<p>The law is most valuable for <strong>weak electrolytes<\/strong> such as acetic acid. Strong electrolytes obey Kohlrausch's square-root law \\(\\Lambda_m = \\Lambda^\\circ_m - K\\sqrt{c}\\), so their limiting conductivity can be found by extrapolating measured values to zero concentration. Weak electrolytes are almost fully associated even at low concentration, so extrapolation fails \u2014 but Kohlrausch's law gives the answer directly: \\(\\Lambda^\\circ_m(\\text{CH}_3\\text{COOH}) = \\lambda^\\circ(\\text{H}^+) + \\lambda^\\circ(\\text{CH}_3\\text{COO}^-) = 349.65 + 40.9 \\approx 390.6\\) S\u00b7cm\u00b2\/mol.<\/p>\n<p>Once you know \\(\\Lambda^\\circ_m\\), comparing it with a measured molar conductivity \\(\\Lambda_m\\) at concentration \\(c\\) gives the degree of dissociation \\(\\alpha = \\Lambda_m \/ \\Lambda^\\circ_m\\) \u2014 the standard route in dissociation-constant and solubility problems. Our <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/molar-conductivity-calculator\/\">Molar Conductivity Calculator<\/a> handles the \\(\\Lambda_m = \\kappa \/ c\\) step, and the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/solubility-product-ksp-calculator\/\">Solubility Product Calculator<\/a> covers the sparingly-salt applications.<\/p>\n<h2>Assumptions and limitations<\/h2>\n<ul>\n<li><strong>Infinite dilution:<\/strong> the law strictly holds only as \\(c \\to 0\\). At real concentrations, ion\u2013ion interactions (ion atmospheres) lower \\(\\Lambda_m\\) below \\(\\Lambda^\\circ_m\\); for strong electrolytes this follows \\(\\Lambda_m = \\Lambda^\\circ_m - K\\sqrt{c}\\). For how activities deviate at finite concentration, see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/debye-huckel-activity-coefficient-calculator\/\">Debye\u2013H\u00fcckel Activity Coefficient Calculator<\/a>.<\/li>\n<li><strong>Temperature:<\/strong> tabulated \u03bb\u00b0 values refer to 25 \u00b0C in water. Conductivity rises roughly 2\u20133 % per degree, so use values measured at your temperature if high accuracy matters.<\/li>\n<li><strong>Per mole of ions:<\/strong> \u03bb\u00b0 is defined per mole of the ion as written, not per unit charge. For Ca\u00b2\u207a, \u03bb\u00b0 = 119.0 S\u00b7cm\u00b2\/mol already accounts for the double charge \u2014 do not multiply by 2 again.<\/li>\n<li><strong>Charge neutrality:<\/strong> the stoichiometric coefficients must describe a neutral formula unit (\\(\\sum \\nu_+ z_+ = \\sum \\nu_- z_-\\)), otherwise the entered \"salt\" cannot exist and the sum is meaningless.<\/li>\n<li><strong>Complete dissociation at infinite dilution:<\/strong> even weak electrolytes are treated as fully dissociated in the limit \\(c \\to 0\\); partial dissociation only matters at finite concentration.<\/li>\n<li><strong>Unit conversion:<\/strong> 1 S\u00b7cm\u00b2\/mol = 10\u207b\u2074 S\u00b7m\u00b2\/mol. Data tables almost always use S\u00b7cm\u00b2\/mol, which is the calculator's default input unit.<\/li>\n<\/ul>\n<h2>Reference: limiting molar conductivities of common ions (25 \u00b0C, S\u00b7cm\u00b2\/mol)<\/h2>\n<table>\n<thead>\n<tr>\n<th>Cation<\/th>\n<th>\u03bb\u00b0<\/th>\n<th>Anion<\/th>\n<th>\u03bb\u00b0<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>H\u207a<\/td>\n<td>349.65<\/td>\n<td>OH\u207b<\/td>\n<td>198.3<\/td>\n<\/tr>\n<tr>\n<td>Li\u207a<\/td>\n<td>38.7<\/td>\n<td>Cl\u207b<\/td>\n<td>76.35<\/td>\n<\/tr>\n<tr>\n<td>Na\u207a<\/td>\n<td>50.11<\/td>\n<td>Br\u207b<\/td>\n<td>78.1<\/td>\n<\/tr>\n<tr>\n<td>K\u207a<\/td>\n<td>73.5<\/td>\n<td>I\u207b<\/td>\n<td>76.8<\/td>\n<\/tr>\n<tr>\n<td>NH\u2084\u207a<\/td>\n<td>73.5<\/td>\n<td>NO\u2083\u207b<\/td>\n<td>71.5<\/td>\n<\/tr>\n<tr>\n<td>Ag\u207a<\/td>\n<td>61.9<\/td>\n<td>HCO\u2083\u207b<\/td>\n<td>44.5<\/td>\n<\/tr>\n<tr>\n<td>Mg\u00b2\u207a<\/td>\n<td>106.1<\/td>\n<td>CH\u2083COO\u207b<\/td>\n<td>40.9<\/td>\n<\/tr>\n<tr>\n<td>Ca\u00b2\u207a<\/td>\n<td>119.0<\/td>\n<td>SO\u2084\u00b2\u207b<\/td>\n<td>160.0<\/td>\n<\/tr>\n<tr>\n<td>Ba\u00b2\u207a<\/td>\n<td>127.2<\/td>\n<td>\u00bdSO\u2084\u00b2\u207b (per equivalent)<\/td>\n<td>80.0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Use these values directly in the calculator's \u03bb\u00b0 fields. Note the remarkably high values for H\u207a and OH\u207b \u2014 a consequence of the Grotthuss proton-hopping mechanism in water, which also explains why strong acids and bases conduct so much better than their salts.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the limiting molar conductivity of any electrolyte at infinite dilution from its ionic conductivities and stoichiometric coefficients, using Kohlrausch's law of independent ion migration.<\/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-66919","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\/66919","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=66919"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66919\/revisions"}],"predecessor-version":[{"id":66920,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66919\/revisions\/66920"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66919"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}