{"id":66925,"date":"2026-10-13T10:15:48","date_gmt":"2026-10-13T07:15:48","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66925"},"modified":"2026-10-13T10:15:48","modified_gmt":"2026-10-13T07:15:48","slug":"langmuir-adsorption-isotherm-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/langmuir-adsorption-isotherm-calculator\/","title":{"rendered":"Langmuir Adsorption Isotherm 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 Surface Coverage from Concentration and Affinity<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66925\" data-favorite-title=\"Langmuir Adsorption Isotherm\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/langmuir-adsorption-isotherm-calculator\/\" data-favorite-excerpt=\"Calculate fractional surface coverage \u03b8 and adsorbed amount q from the Langmuir isotherm. Enter the equilibrium concentration or pressure, the affinity constant KL, and optionally the maximum capacity qmax.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry-1\">\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\/langmuir-adsorption-isotherm-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66925\" data-post=\"66925\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Concentration \/ Pressure (C)<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"concentration_pressure_c\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.3\" min=\"0\" value=\"0.3\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"mM\" selected>mmol\/L (mM)<\/option><option value=\"uM\">\u00b5mol\/L (\u00b5M)<\/option><option value=\"M\">mol\/L (M)<\/option><option value=\"mg_L\">mg\/L<\/option><option value=\"atm\">atm<\/option><option value=\"kPa\">kPa<\/option><option value=\"bar\">bar<\/option><option value=\"Pa\">Pa<\/option><option value=\"mmHg\">mmHg (Torr)<\/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><small id=\"calc-info-1\">Equilibrium concentration of the adsorbate in solution, or its partial pressure for gas adsorption.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Langmuir Affinity Constant (KL)<\/label><div class=\"term\">KL<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"langmuir_affinity_constant_kl\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 5\" min=\"0\" value=\"5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"mM\" selected>L\/mmol (mM\u207b\u00b9)<\/option><option value=\"uM\">L\/\u00b5mol (\u00b5M\u207b\u00b9)<\/option><option value=\"M\">L\/mol (M\u207b\u00b9)<\/option><option value=\"mg_L\">L\/mg<\/option><option value=\"atm\">1\/atm<\/option><option value=\"kPa\">1\/kPa<\/option><option value=\"bar\">1\/bar<\/option><option value=\"Pa\">1\/Pa<\/option><option value=\"mmHg\">1\/mmHg<\/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><small id=\"calc-info-3\">Equilibrium constant KL = ka\/kd. Its unit must be the reciprocal of the concentration\/pressure unit above (e.g. L\/mmol for mmol\/L).<\/small><\/div><div class=\"field is-checkbox is-single\" id=\"input-3\"><input type=\"checkbox\" id=\"field-5\" value=\"1\" checked=\"checked\"\/><label for=\"field-5\">I know the maximum adsorption capacity (qmax)<\/label><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Maximum Adsorption Capacity (qmax)<\/label><div class=\"term\">qmax<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"maximum_adsorption_capacity_qmax\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 100\" min=\"0\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"unit\" aria-label=\"Unit\"><option value=\"mg_g\" selected>mg\/g<\/option><option value=\"mmol_g\">mmol\/g<\/option><option value=\"umol_g\">\u00b5mol\/g<\/option><option value=\"g_kg\">g\/kg<\/option><option value=\"mol_kg\">mol\/kg<\/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><small id=\"calc-info-6\">Monolayer capacity: the adsorbed amount when every site is occupied (\u03b8 = 1).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66925\">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> Langmuir Isotherm Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Fractional Surface Coverage (\u03b8)<\/span><span class=\"result-term\">\u03b8<\/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>Adsorbed Amount (q)<\/span><span class=\"result-term\">q<\/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>Coverage at Other Concentrations<\/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 Langmuir Isotherm<\/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=\"66925\" 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>Langmuir Adsorption Isotherm 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\\[ \\theta = \\frac{K_L \\, C}{1 + K_L \\, C} \\qquad q = q_{max} \\cdot \\theta = \\frac{q_{max} \\, K_L \\, C}{1 + K_L \\, C} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\theta\\) \u2014 fractional surface coverage (dimensionless, 0 to 1)<\/li>\n<li>\\(K_L\\) \u2014 Langmuir affinity constant \\(= k_a \/ k_d\\), with units reciprocal to those of \\(C\\)<\/li>\n<li>\\(C\\) \u2014 equilibrium concentration (or partial pressure for gases) of the adsorbate<\/li>\n<li>\\(q_{max}\\) \u2014 maximum adsorption capacity, the monolayer amount when every site is occupied<\/li>\n<li>\\(q\\) \u2014 adsorbed amount at equilibrium<\/li>\n<\/ul>\n<p>The formula expresses the equilibrium between adsorption and desorption on a surface with a fixed number of identical, independent sites: the fraction of occupied sites rises hyperbolically with concentration and approaches 1 (complete monolayer) only asymptotically.<\/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>Langmuir Adsorption Isotherm \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an adsorbent with a monolayer capacity of 100 mg\/g is equilibrated in a solution containing 0.3 mmol\/L of adsorbate, and the Langmuir affinity constant is \\(K_L = 5\\) L\/mmol.<\/p>\n<p>\\[ K_L \\, C = 5 \\ \\tfrac{\\text{L}}{\\text{mmol}} \\times 0.3 \\ \\tfrac{\\text{mmol}}{\\text{L}} = 1.5 \\]<\/p>\n<p>\\[ \\theta = \\frac{1.5}{1 + 1.5} = 0.6 \\]<\/p>\n<p>\\[ q = q_{max} \\cdot \\theta = 100 \\ \\tfrac{\\text{mg}}{\\text{g}} \\times 0.6 = 60 \\ \\tfrac{\\text{mg}}{\\text{g}} \\]<\/p>\n<p><strong>Result:<\/strong> \u03b8 = 0.6 (60% of the adsorption sites are occupied) and the adsorbed amount is q = 60 mg\/g, with 40 mg\/g of capacity still unused.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the equilibrium <strong>Concentration \/ Pressure (C)<\/strong> of the adsorbate and choose its unit \u2014 molar or mass concentration for solutions, or a pressure unit (atm, kPa, bar, Pa, mmHg) for gas adsorption.<\/li>\n<li>Enter the <strong>Langmuir Affinity Constant (KL)<\/strong> and pick the matching reciprocal unit (e.g. mmol\/L goes with L\/mmol, atm with 1\/atm). The unit of \\(K_L\\) must be the inverse of the unit of \\(C\\).<\/li>\n<li>If you know the monolayer capacity, keep the checkbox <strong>\"I know the maximum adsorption capacity (qmax)\"<\/strong> ticked and enter <strong>Maximum Adsorption Capacity (qmax)<\/strong> with its unit; otherwise untick it and only the coverage \u03b8 will be computed.<\/li>\n<li>Read the <strong>Fractional Surface Coverage (\u03b8)<\/strong> and the <strong>Adsorbed Amount (q)<\/strong>. The results also include a table of coverage at other concentrations and a step-by-step calculation.<\/li>\n<\/ol>\n<h2>What Is the Langmuir Adsorption Isotherm?<\/h2>\n<p>The Langmuir isotherm, published by Irving Langmuir in 1918, is the simplest quantitative model of adsorption at equilibrium. It describes a surface composed of a fixed number of identical, independent sites, each of which can bind at most one molecule. Adsorption proceeds at a rate \\(k_a C (1-\\theta)\\) onto empty sites, while desorption proceeds at a rate \\(k_d\\,\\theta\\); at equilibrium the two rates are equal, which gives \\(K_L = k_a\/k_d\\) and the hyperbolic coverage expression \\(\\theta = K_L C\/(1 + K_L C)\\).<\/p>\n<p>The parameter \\(K_L\\) measures the affinity of the adsorbate for the surface. A large \\(K_L\\) means strong binding: half of the sites are already occupied when \\(C = 1\/K_L\\) (the half-saturation point), and high coverage is achieved at low concentrations. The capacity \\(q_{max}\\) represents complete monolayer coverage; it is approached only asymptotically, so a surface is never perfectly \"full\" at finite concentration.<\/p>\n<p>The same mathematics describes saturation curves elsewhere in chemistry \u2014 the Langmuir isotherm is formally identical to the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/michaelis-menten-calculator\/\">Michaelis\u2013Menten<\/a> rate equation \u2014 and it is the foundation on which multilayer models such as the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/bet-surface-area-calculator\/\">BET surface area<\/a> method are built. In practice, \\(K_L\\) and \\(q_{max}\\) are obtained by fitting measured equilibrium data, either by non-linear regression or by linearised plots such as \\(C\/q\\) versus \\(C\\), whose slope is \\(1\/q_{max}\\) and whose intercept is \\(1\/(K_L q_{max})\\).<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Monolayer adsorption:<\/strong> each site holds one molecule at most. If multilayer adsorption or capillary condensation occurs, the Langmuir model underestimates the uptake.<\/li>\n<li><strong>Homogeneous surface:<\/strong> all sites are assumed energetically identical. Real sorbents (activated carbons, clays, biomaterials) are often heterogeneous, and the Freundlich, Sips or Toth models usually fit such data better.<\/li>\n<li><strong>No lateral interactions:<\/strong> adsorbed molecules do not affect one another; the heat of adsorption is constant and independent of coverage.<\/li>\n<li><strong>Equilibrium and ideal behaviour:<\/strong> the system must have reached equilibrium, the solution must be dilute, and gases must behave ideally at the pressures used.<\/li>\n<li><strong>Temperature dependence:<\/strong> \\(K_L\\) is an equilibrium constant, so it changes with temperature \u2014 for the usual exothermic adsorption it decreases as temperature rises. Always use a \\(K_L\\) measured at the temperature of interest.<\/li>\n<li><strong>Unit consistency:<\/strong> because the product \\(K_L C\\) must be dimensionless, check that the units of \\(C\\) and \\(K_L\\) are reciprocals before trusting any published value.<\/li>\n<\/ul>\n<p>A quick sanity check when interpreting results: if \\(K_L C \\ll 1\\) you are in the linear Henry regime (\\(\\theta \\approx K_L C\\)), where coverage grows in direct proportion to concentration; if \\(K_L C \\gg 1\\) the surface is nearly saturated and further increases in \\(C\\) barely change \\(q\\). The calculator's coverage table makes it easy to see which regime you are in at a glance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate fractional surface coverage \u03b8 and adsorbed amount q from the Langmuir isotherm. Enter the equilibrium concentration or pressure, the affinity constant KL, and optionally the maximum capacity qmax.<\/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":[57],"class_list":["post-66925","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-reactions"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66925","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=66925"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66925\/revisions"}],"predecessor-version":[{"id":66926,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66925\/revisions\/66926"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66925"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66925"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66925"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}