{"id":2133,"date":"2026-10-14T22:23:34","date_gmt":"2026-10-14T21:23:34","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-isoterma-langmuir\/"},"modified":"2026-10-14T22:23:34","modified_gmt":"2026-10-14T21:23:34","slug":"calculadora-isoterma-langmuir","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-isoterma-langmuir\/","title":{"rendered":"Calculadora da Isoterma de Adsor\u00e7\u00e3o de Langmuir"},"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\">Estime a cobertura superficial a partir da concentra\u00e7\u00e3o e da afinidade<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2133\" data-favorite-title=\"Isoterma de Adsor\u00e7\u00e3o de Langmuir\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-isoterma-langmuir\/\" data-favorite-excerpt=\"Calcule a fra\u00e7\u00e3o de cobertura superficial \u03b8 e a quantidade adsorvida q pela isoterma de Langmuir. Informe a concentra\u00e7\u00e3o ou press\u00e3o de equil\u00edbrio, a constante de afinidade KL e, opcionalmente, a capacidade m\u00e1xima qmax.\" aria-label=\"Adicionar aos favoritos\" 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\/pt\/quimica\/calculadora-isoterma-langmuir\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2133\" data-post=\"2133\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Campos de entrada<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Concentra\u00e7\u00e3o \/ Press\u00e3o (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=\"concentrao_presso_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=\"unidade\" aria-label=\"Unidade\"><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\">Concentra\u00e7\u00e3o de equil\u00edbrio do adsorbato em solu\u00e7\u00e3o, ou sua press\u00e3o parcial no caso de adsor\u00e7\u00e3o de gases.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Constante de afinidade de Langmuir (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=\"constante_de_afinidade_de_langmuir_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=\"unidade\" aria-label=\"Unidade\"><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\">Constante de equil\u00edbrio KL = ka\/kd. Sua unidade deve ser o inverso da unidade de concentra\u00e7\u00e3o\/press\u00e3o indicada acima (por exemplo, L\/mmol para 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\">Eu conhe\u00e7o a capacidade m\u00e1xima de adsor\u00e7\u00e3o (qmax)<\/label><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Capacidade m\u00e1xima de adsor\u00e7\u00e3o (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=\"capacidade_mxima_de_adsoro_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=\"unidade\" aria-label=\"Unidade\"><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\">Capacidade de monocamada: a quantidade adsorvida quando todos os s\u00edtios est\u00e3o ocupados (\u03b8 = 1).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2133\">Calcular<\/button><button type=\"reset\">Redefinir<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calcular automaticamente<\/label><small>Se ativado, o resultado \u00e9 atualizado automaticamente quando voc\u00ea altera qualquer valor.<\/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> Resultados da isoterma de Langmuir<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Fra\u00e7\u00e3o de cobertura superficial (\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=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Quantidade adsorvida (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=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Cobertura em outras concentra\u00e7\u00f5es<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Detalhes do c\u00e1lculo<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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>Sobre a isoterma de Langmuir<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copiar resultado\" aria-label=\"Copiar resultado\"><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\">Copiar link para este c\u00e1lculo<\/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>Deixar um coment\u00e1rio<\/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=\"2133\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">O que voc\u00ea achou deste resultado?<\/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\">Curti <\/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\">\u00datil <\/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\">Confuso <\/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\">Decepcionado <\/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\">Impreciso <\/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>F\u00f3rmula da isoterma de adsor\u00e7\u00e3o de Langmuir<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">F\u00f3rmula<\/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>Onde:<\/strong><\/p>\n<ul>\n<li>\\(\\theta\\) \u2014 fra\u00e7\u00e3o de cobertura superficial (adimensional, de 0 a 1)<\/li>\n<li>\\(K_L\\) \u2014 constante de afinidade de Langmuir \\(= k_a \/ k_d\\), com unidades inversas \u00e0s de \\(C\\)<\/li>\n<li>\\(C\\) \u2014 concentra\u00e7\u00e3o de equil\u00edbrio (ou press\u00e3o parcial, no caso de gases) do adsorbato<\/li>\n<li>\\(q_{max}\\) \u2014 capacidade m\u00e1xima de adsor\u00e7\u00e3o, isto \u00e9, a quantidade de monocamada quando todos os s\u00edtios est\u00e3o ocupados<\/li>\n<li>\\(q\\) \u2014 quantidade adsorvida no equil\u00edbrio<\/li>\n<\/ul>\n<p>A f\u00f3rmula expressa o equil\u00edbrio entre adsor\u00e7\u00e3o e dessor\u00e7\u00e3o em uma superf\u00edcie com um n\u00famero fixo de s\u00edtios id\u00eanticos e independentes: a fra\u00e7\u00e3o de s\u00edtios ocupados cresce de forma hiperb\u00f3lica com a concentra\u00e7\u00e3o e s\u00f3 se aproxima de 1 (monocamada completa) de maneira assint\u00f3tica.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.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>Isoterma de adsor\u00e7\u00e3o de Langmuir \u2013 exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> um adsorvente com capacidade de monocamada de 100 mg\/g \u00e9 colocado em equil\u00edbrio com uma solu\u00e7\u00e3o contendo 0,3 mmol\/L de adsorbato, e a constante de afinidade de Langmuir \u00e9 \\(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>Resultado:<\/strong> \u03b8 = 0,6 (60% dos s\u00edtios de adsor\u00e7\u00e3o est\u00e3o ocupados) e a quantidade adsorvida \u00e9 q = 60 mg\/g, restando ainda 40 mg\/g de capacidade n\u00e3o utilizada.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe a <strong>concentra\u00e7\u00e3o\/press\u00e3o de equil\u00edbrio (C)<\/strong> do adsorbato e escolha a unidade \u2014 concentra\u00e7\u00e3o molar ou m\u00e1ssica para solu\u00e7\u00f5es, ou uma unidade de press\u00e3o (atm, kPa, bar, Pa, mmHg) para adsor\u00e7\u00e3o de gases.<\/li>\n<li>Informe a <strong>constante de afinidade de Langmuir (KL)<\/strong> e selecione a unidade rec\u00edproca correspondente (por exemplo, mmol\/L combina com L\/mmol, atm com 1\/atm). A unidade de \\(K_L\\) deve ser o inverso da unidade de \\(C\\).<\/li>\n<li>Se voc\u00ea conhece a capacidade de monocamada, mantenha marcada a caixa <strong>\"Eu conhe\u00e7o a capacidade m\u00e1xima de adsor\u00e7\u00e3o (qmax)\"<\/strong> e informe a <strong>capacidade m\u00e1xima de adsor\u00e7\u00e3o (qmax)<\/strong> com sua unidade; caso contr\u00e1rio, desmarque-a e apenas a cobertura \u03b8 ser\u00e1 calculada.<\/li>\n<li>Leia a <strong>fra\u00e7\u00e3o de cobertura superficial (\u03b8)<\/strong> e a <strong>quantidade adsorvida (q)<\/strong>. Os resultados tamb\u00e9m incluem uma tabela com a cobertura em outras concentra\u00e7\u00f5es e o c\u00e1lculo passo a passo.<\/li>\n<\/ol>\n<h2>O que \u00e9 a isoterma de adsor\u00e7\u00e3o de Langmuir?<\/h2>\n<p>A isoterma de Langmuir, publicada por Irving Langmuir em 1918, \u00e9 o modelo quantitativo mais simples de adsor\u00e7\u00e3o no equil\u00edbrio. Ela descreve uma superf\u00edcie composta por um n\u00famero fixo de s\u00edtios id\u00eanticos e independentes, cada um dos quais pode ligar-se no m\u00e1ximo a uma mol\u00e9cula. A adsor\u00e7\u00e3o ocorre a uma velocidade \\(k_a C (1-\\theta)\\) sobre os s\u00edtios vazios, enquanto a dessor\u00e7\u00e3o ocorre a uma velocidade \\(k_d\\,\\theta\\); no equil\u00edbrio, as duas velocidades se igualam, o que leva a \\(K_L = k_a\/k_d\\) e \u00e0 express\u00e3o hiperb\u00f3lica da cobertura \\(\\theta = K_L C\/(1 + K_L C)\\).<\/p>\n<p>O par\u00e2metro \\(K_L\\) mede a afinidade do adsorbato pela superf\u00edcie. Um \\(K_L\\) grande significa liga\u00e7\u00e3o forte: metade dos s\u00edtios j\u00e1 est\u00e1 ocupada quando \\(C = 1\/K_L\\) (o ponto de meia-satura\u00e7\u00e3o), e coberturas elevadas s\u00e3o alcan\u00e7adas em concentra\u00e7\u00f5es baixas. A capacidade \\(q_{max}\\) representa a cobertura completa da monocamada; ela s\u00f3 \u00e9 alcan\u00e7ada de forma assint\u00f3tica, de modo que uma superf\u00edcie nunca fica perfeitamente \"cheia\" em concentra\u00e7\u00f5es finitas.<\/p>\n<p>A mesma matem\u00e1tica descreve curvas de satura\u00e7\u00e3o em outros contextos da qu\u00edmica \u2014 a isoterma de Langmuir \u00e9 formalmente id\u00eantica \u00e0 equa\u00e7\u00e3o de velocidade de <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/michaelis-menten-calculator\/\">Michaelis\u2013Menten<\/a> \u2014 e \u00e9 a base sobre a qual foram constru\u00eddos modelos de multicamadas, como o m\u00e9todo de <a href=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-area-superficial-bet\/\">\u00e1rea superficial BET<\/a>. Na pr\u00e1tica, \\(K_L\\) e \\(q_{max}\\) s\u00e3o obtidos pelo ajuste de dados experimentais de equil\u00edbrio, seja por regress\u00e3o n\u00e3o linear, seja por gr\u00e1ficos linearizados, como o de \\(C\/q\\) em fun\u00e7\u00e3o de \\(C\\), cuja inclina\u00e7\u00e3o \u00e9 \\(1\/q_{max}\\) e cujo intercepto \u00e9 \\(1\/(K_L q_{max})\\).<\/p>\n<h2>Hip\u00f3teses, limita\u00e7\u00f5es e dicas pr\u00e1ticas<\/h2>\n<ul>\n<li><strong>Adsor\u00e7\u00e3o em monocamada:<\/strong> cada s\u00edtio comporta no m\u00e1ximo uma mol\u00e9cula. Se houver adsor\u00e7\u00e3o em multicamadas ou condensa\u00e7\u00e3o capilar, o modelo de Langmuir subestima a quantidade retida.<\/li>\n<li><strong>Superf\u00edcie homog\u00eanea:<\/strong> assume-se que todos os s\u00edtios s\u00e3o energeticamente id\u00eanticos. Adsorventes reais (carv\u00f5es ativados, argilas, biomateriais) costumam ser heterog\u00eaneos, e nesses casos os modelos de Freundlich, Sips ou Toth geralmente se ajustam melhor aos dados.<\/li>\n<li><strong>Sem intera\u00e7\u00f5es laterais:<\/strong> as mol\u00e9culas adsorvidas n\u00e3o interagem entre si; o calor de adsor\u00e7\u00e3o \u00e9 constante e independente da cobertura.<\/li>\n<li><strong>Equil\u00edbrio e comportamento ideal:<\/strong> o sistema precisa ter atingido o equil\u00edbrio, a solu\u00e7\u00e3o deve ser dilu\u00edda e os gases devem se comportar de forma ideal nas press\u00f5es utilizadas.<\/li>\n<li><strong>Depend\u00eancia da temperatura:<\/strong> \\(K_L\\) \u00e9 uma constante de equil\u00edbrio, portanto varia com a temperatura \u2014 na adsor\u00e7\u00e3o exot\u00e9rmica usual, ela diminui conforme a temperatura aumenta. Use sempre um \\(K_L\\) medido na temperatura de interesse.<\/li>\n<li><strong>Consist\u00eancia de unidades:<\/strong> como o produto \\(K_L C\\) deve ser adimensional, confira se as unidades de \\(C\\) e \\(K_L\\) s\u00e3o rec\u00edprocas antes de confiar em qualquer valor publicado.<\/li>\n<\/ul>\n<p>Uma verifica\u00e7\u00e3o r\u00e1pida ao interpretar os resultados: se \\(K_L C \\ll 1\\), voc\u00ea est\u00e1 no regime linear de Henry (\\(\\theta \\approx K_L C\\)), no qual a cobertura cresce em propor\u00e7\u00e3o direta \u00e0 concentra\u00e7\u00e3o; se \\(K_L C \\gg 1\\), a superf\u00edcie est\u00e1 praticamente saturada e novos aumentos de \\(C\\) quase n\u00e3o alteram \\(q\\). A tabela de cobertura da calculadora permite ver de relance em qual regime voc\u00ea est\u00e1.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calcule a fra\u00e7\u00e3o de cobertura superficial \u03b8 e a quantidade adsorvida q pela isoterma de Langmuir. Informe a concentra\u00e7\u00e3o ou press\u00e3o de equil\u00edbrio, a constante de afinidade KL e, opcionalmente, a capacidade m\u00e1xima qmax.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[3],"tags":[67],"class_list":["post-2133","post","type-post","status-publish","format-standard","hentry","category-quimica","tag-reacoes"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2133","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/comments?post=2133"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2133\/revisions"}],"predecessor-version":[{"id":2226,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2133\/revisions\/2226"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2133"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2133"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2133"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}