{"id":3998,"date":"2026-10-14T22:25:04","date_gmt":"2026-10-14T21:25:04","guid":{"rendered":"https:\/\/wpcalc.com\/tr\/kimya\/langmuir-adsorpsiyon-izotermi-hesaplama\/"},"modified":"2026-10-14T22:25:04","modified_gmt":"2026-10-14T21:25:04","slug":"langmuir-adsorpsiyon-izotermi-hesaplama","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/tr\/kimya\/langmuir-adsorpsiyon-izotermi-hesaplama\/","title":{"rendered":"Langmuir Adsorpsiyon \u0130zotermi Hesaplama Arac\u0131"},"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\">Deri\u015fim ve afinite de\u011ferlerinden y\u00fczey kaplanma oran\u0131n\u0131 hesaplay\u0131n<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"3998\" data-favorite-title=\"Langmuir Adsorpsiyon \u0130zotermi\" data-favorite-url=\"https:\/\/wpcalc.com\/tr\/kimya\/langmuir-adsorpsiyon-izotermi-hesaplama\/\" data-favorite-excerpt=\"Langmuir izotermiyle kesirsel y\u00fczey kaplanmas\u0131n\u0131 \u03b8 ve adsorplanan miktar\u0131 q hesaplay\u0131n. Denge deri\u015fimini veya bas\u0131nc\u0131n\u0131, afinite sabitini KL ve isterseniz maksimum kapasiteyi qmax girin.\" aria-label=\"Favorilere ekle\" 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\/tr\/kimya\/langmuir-adsorpsiyon-izotermi-hesaplama\/\" method=\"POST\" class=\"calculator\" id=\"calculator-3998\" data-post=\"3998\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Giri\u015f alanlar\u0131<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Deri\u015fim \/ bas\u0131n\u00e7 (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=\"deriim_basn_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=\"birim\" aria-label=\"Birim\"><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\">\u00c7\u00f6zeltideki adsorbat\u0131n denge deri\u015fimi; gaz adsorpsiyonunda ise k\u0131smi bas\u0131nc\u0131.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Langmuir afinite sabiti (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_afinite_sabiti_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=\"birim\" aria-label=\"Birim\"><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\">Denge sabiti KL = ka\/kd. Birimi, yukar\u0131daki deri\u015fim\/bas\u0131n\u00e7 biriminin tersi olmal\u0131d\u0131r (\u00f6rn. mmol\/L i\u00e7in L\/mmol).<\/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\">Maksimum adsorpsiyon kapasitesini (qmax) biliyorum<\/label><\/div><div class=\"field has-term\" id=\"input-4\" hidden><label for=\"field-6\">Maksimum adsorpsiyon kapasitesi (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=\"maksimum_adsorpsiyon_kapasitesi_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=\"birim\" aria-label=\"Birim\"><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\">Tek tabaka (monolayer) kapasitesi: t\u00fcm aktif merkezler doluyken adsorbe edilen miktar (\u03b8 = 1).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Yeniden hesapla\" id=\"calculate-button\" data-post=\"3998\">Hesapla<\/button><button type=\"reset\">S\u0131f\u0131rla<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Otomatik hesapla<\/label><small>Etkinle\u015ftirilirse, herhangi bir de\u011feri de\u011fi\u015ftirdi\u011finizde sonu\u00e7 otomatik olarak g\u00fcncellenir.<\/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 izotermi sonu\u00e7lar\u0131<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Y\u00fczey kaplanma kesri (\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=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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>Adsorbe edilen miktar (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=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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>Di\u011fer deri\u015fimlerde kaplanma<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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>Hesaplama ayr\u0131nt\u0131lar\u0131<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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>Langmuir izotermi hakk\u0131nda<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Sonucu kopyala\" aria-label=\"Sonucu kopyala\"><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\">Bu hesaplaman\u0131n ba\u011flant\u0131s\u0131n\u0131 kopyala<\/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>Yorum b\u0131rak<\/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=\"3998\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Bu sonu\u00e7 hakk\u0131nda ne d\u00fc\u015f\u00fcn\u00fcyorsunuz?<\/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\">Be\u011fendim <\/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\">Faydal\u0131 <\/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\">Kafam kar\u0131\u015ft\u0131 <\/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\">Hayal k\u0131r\u0131kl\u0131\u011f\u0131 <\/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\">Hatal\u0131 <\/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 Adsorpsiyon \u0130zotermi Form\u00fcl\u00fc<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Form\u00fcl<\/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>G\u00f6sterimler:<\/strong><\/p>\n<ul>\n<li>\\(\\theta\\) \u2014 kesirsel y\u00fczey kaplanmas\u0131 (boyutsuz, 0 ile 1 aras\u0131nda)<\/li>\n<li>\\(K_L\\) \u2014 Langmuir afinite sabiti \\(= k_a \/ k_d\\); birimi, \\(C\\)'nin biriminin tersidir<\/li>\n<li>\\(C\\) \u2014 adsorbat\u0131n denge deri\u015fimi (gazlar i\u00e7in k\u0131smi bas\u0131n\u00e7)<\/li>\n<li>\\(q_{max}\\) \u2014 maksimum adsorpsiyon kapasitesi; t\u00fcm ba\u011flanma yerleri doldu\u011fundaki tek tabaka (monokatman) miktar\u0131<\/li>\n<li>\\(q\\) \u2014 denge halindeki adsorplanan miktar<\/li>\n<\/ul>\n<p>Form\u00fcl, sabit say\u0131da \u00f6zde\u015f ve birbirinden ba\u011f\u0131ms\u0131z ba\u011flanma yerine sahip bir y\u00fczeyde adsorpsiyon ile desorpsiyon aras\u0131ndaki dengeyi ifade eder: dolu yerlerin oran\u0131 deri\u015fimle birlikte hiperbolik bi\u00e7imde artar ve 1'e (tam tek tabaka) yaln\u0131zca asimptotik olarak yakla\u015f\u0131r.<\/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>Langmuir Adsorpsiyon \u0130zotermi \u2013 Hesaplama \u00d6rne\u011fi<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>\u00d6rnek:<\/strong> tek tabaka kapasitesi 100 mg\/g olan bir adsorban, 0,3 mmol\/L adsorbat i\u00e7eren bir \u00e7\u00f6zeltiyle dengelendiriliyor; Langmuir afinite sabiti \\(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>Sonu\u00e7:<\/strong> \u03b8 = 0,6 (ba\u011flanma yerlerinin %60'\u0131 dolu) ve adsorplanan miktar q = 60 mg\/g; kapasitenin 40 mg\/g'lik k\u0131sm\u0131 h\u00e2l\u00e2 kullan\u0131lmam\u0131\u015f durumda.<\/p>\n<p>\n\r\n<\/section>\n<h2>Hesaplama arac\u0131 nas\u0131l kullan\u0131l\u0131r?<\/h2>\n<ol>\n<li>Adsorbat\u0131n denge <strong>deri\u015fimini veya bas\u0131nc\u0131n\u0131 (C)<\/strong> girin ve birimini se\u00e7in \u2014 \u00e7\u00f6zeltilerde molar ya da k\u00fctle deri\u015fimi, gaz adsorpsiyonunda bir bas\u0131n\u00e7 birimi (atm, kPa, bar, Pa, mmHg).<\/li>\n<li><strong>Langmuir afinite sabitini (KL)<\/strong> girin ve buna kar\u015f\u0131l\u0131k gelen ters birimi se\u00e7in (\u00f6r. mmol\/L i\u00e7in L\/mmol, atm i\u00e7in 1\/atm). \\(K_L\\)'nin birimi, \\(C\\)'nin biriminin tersi olmal\u0131d\u0131r.<\/li>\n<li>Tek tabaka kapasitesini biliyorsan\u0131z <strong>\"Maksimum adsorpsiyon kapasitesini (qmax) biliyorum\"<\/strong> onay kutusunu i\u015faretli b\u0131rak\u0131n ve <strong>maksimum adsorpsiyon kapasitesini (qmax)<\/strong> birimiyle birlikte girin; i\u015fareti kald\u0131r\u0131rsan\u0131z yaln\u0131zca kaplanma derecesi \u03b8 hesaplan\u0131r.<\/li>\n<li><strong>Kesirsel y\u00fczey kaplanmas\u0131n\u0131 (\u03b8)<\/strong> ve <strong>adsorplanan miktar\u0131 (q)<\/strong> okuyun. Sonu\u00e7larda ayr\u0131ca ba\u015fka deri\u015fimlerdeki kaplanmay\u0131 g\u00f6steren bir tablo ve ad\u0131m ad\u0131m hesaplama da yer al\u0131r.<\/li>\n<\/ol>\n<h2>Langmuir adsorpsiyon izotermi nedir?<\/h2>\n<p>Langmuir izotermi, Irving Langmuir taraf\u0131ndan 1918'de yay\u0131mlanan, dengedeki adsorpsiyonun en basit nicel modelidir. Sabit say\u0131da \u00f6zde\u015f ve birbirinden ba\u011f\u0131ms\u0131z ba\u011flanma yerinden olu\u015fan, her yerin en fazla bir molek\u00fcl ba\u011flayabildi\u011fi bir y\u00fczeyi tan\u0131mlar. Bo\u015f yerlere adsorpsiyon \\(k_a C (1-\\theta)\\) h\u0131z\u0131nda, desorpsiyon ise \\(k_d\\,\\theta\\) h\u0131z\u0131nda ger\u00e7ekle\u015fir; dengede iki h\u0131z e\u015fit olur ve bu da \\(K_L = k_a\/k_d\\) ile \\(\\theta = K_L C\/(1 + K_L C)\\) hiperbolik kaplanma ifadesini verir.<\/p>\n<p>\\(K_L\\) parametresi adsorbat\u0131n y\u00fczeye olan afinitesini \u00f6l\u00e7er. B\u00fcy\u00fck bir \\(K_L\\) g\u00fc\u00e7l\u00fc ba\u011flanma demektir: \\(C = 1\/K_L\\) oldu\u011funda (yar\u0131 doyma noktas\u0131) yerlerin yar\u0131s\u0131 dolmu\u015ftur ve y\u00fcksek kaplanma \u00e7ok d\u00fc\u015f\u00fck deri\u015fimlerde bile sa\u011flan\u0131r. \\(q_{max}\\) kapasitesi tam tek tabaka kaplanmas\u0131n\u0131 temsil eder; buna yaln\u0131zca asimptotik olarak yakla\u015f\u0131l\u0131r, yani y\u00fczey sonlu bir deri\u015fimde hi\u00e7bir zaman tam olarak \"dolu\" olmaz.<\/p>\n<p>Ayn\u0131 matematik kimyan\u0131n di\u011fer alanlar\u0131ndaki doyma e\u011frilerini de tan\u0131mlar \u2014 Langmuir izotermi bi\u00e7imsel olarak <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/michaelis-menten-calculator\/\">Michaelis\u2013Menten<\/a> h\u0131z denklemiyle \u00f6zde\u015ftir \u2014 ve <a href=\"https:\/\/wpcalc.com\/tr\/kimya\/bet-yuzey-alani-hesaplama\/\">BET y\u00fczey alan\u0131<\/a> y\u00f6ntemi gibi \u00e7ok tabakal\u0131 modellerin temelini olu\u015fturur. Uygulamada \\(K_L\\) ve \\(q_{max}\\), \u00f6l\u00e7\u00fclm\u00fc\u015f denge verileri \u00fczerinden ya do\u011frusal olmayan regresyonla ya da do\u011frusalla\u015ft\u0131r\u0131lm\u0131\u015f \u00e7izimlerle bulunur; \u00f6rne\u011fin e\u011fimi \\(1\/q_{max}\\) ve kesi\u015fimi \\(1\/(K_L q_{max})\\) olan \\(C\/q\\)'ya kar\u015f\u0131 \\(C\\) grafi\u011fi \u00e7izilir.<\/p>\n<h2>Varsay\u0131mlar, s\u0131n\u0131rlamalar ve pratik ipu\u00e7lar\u0131<\/h2>\n<ul>\n<li><strong>Tek tabaka adsorpsiyonu:<\/strong> her ba\u011flanma yeri en fazla bir molek\u00fcl tutar. \u00c7ok tabakal\u0131 adsorpsiyon veya k\u0131lcal yo\u011fu\u015fma s\u00f6z konusuysa Langmuir modeli adsorplanan miktar\u0131 oldu\u011fundan k\u00fc\u00e7\u00fck g\u00f6sterir.<\/li>\n<li><strong>Homojen y\u00fczey:<\/strong> t\u00fcm ba\u011flanma yerleri enerjik a\u00e7\u0131dan \u00f6zde\u015f varsay\u0131l\u0131r. Ger\u00e7ek adsorbanlar (aktif karbonlar, killer, biyomalzemeler) \u00e7o\u011funlukla heterojendir; bu t\u00fcr verilerde Freundlich, Sips veya Toth modelleri genellikle daha iyi uyum sa\u011flar.<\/li>\n<li><strong>Yanal etkile\u015fim yok:<\/strong> adsorplanm\u0131\u015f molek\u00fcller birbirini etkilemez; adsorpsiyon \u0131s\u0131s\u0131 sabittir ve kaplanmadan ba\u011f\u0131ms\u0131zd\u0131r.<\/li>\n<li><strong>Denge ve ideal davran\u0131\u015f:<\/strong> sistem dengeye ula\u015fm\u0131\u015f olmal\u0131, \u00e7\u00f6zelti seyreltik olmal\u0131 ve kullan\u0131lan bas\u0131n\u00e7larda gazlar ideal davran\u0131\u015f g\u00f6stermelidir.<\/li>\n<li><strong>S\u0131cakl\u0131k ba\u011f\u0131ml\u0131l\u0131\u011f\u0131:<\/strong> \\(K_L\\) bir denge sabiti oldu\u011fundan s\u0131cakl\u0131kla de\u011fi\u015fir \u2014 ola\u011fan ekzotermik adsorpsiyonda s\u0131cakl\u0131k artt\u0131k\u00e7a azal\u0131r. \\(K_L\\) de\u011ferini her zaman ilgilendi\u011finiz s\u0131cakl\u0131kta \u00f6l\u00e7\u00fclm\u00fc\u015f olan\u0131ndan kullan\u0131n.<\/li>\n<li><strong>Birim tutarl\u0131l\u0131\u011f\u0131:<\/strong> \\(K_L C\\) \u00e7arp\u0131m\u0131 boyutsuz olmak zorunda oldu\u011fundan, yay\u0131mlanm\u0131\u015f bir de\u011fere g\u00fcvenmeden \u00f6nce \\(C\\) ve \\(K_L\\) birimlerinin birbirinin tersi oldu\u011funu kontrol edin.<\/li>\n<\/ul>\n<p>Sonu\u00e7lar\u0131 yorumlarken h\u0131zl\u0131 bir ak\u0131l kontrol\u00fc: \\(K_L C \\ll 1\\) ise do\u011frusal Henry b\u00f6lgesindesinizdir (\\(\\theta \\approx K_L C\\)) ve kaplanma deri\u015fimle do\u011fru orant\u0131l\u0131 artar; \\(K_L C \\gg 1\\) ise y\u00fczey neredeyse doymu\u015ftur ve \\(C\\)'nin artmas\u0131 \\(q\\)'yu neredeyse hi\u00e7 de\u011fi\u015ftirmez. Hesaplama arac\u0131n\u0131n kaplanma tablosu, hangi b\u00f6lgede oldu\u011funuzu bir bak\u0131\u015fta g\u00f6rmenizi sa\u011flar.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Langmuir izotermiyle kesirsel y\u00fczey kaplanmas\u0131n\u0131 \u03b8 ve adsorplanan miktar\u0131 q hesaplay\u0131n. Denge deri\u015fimini veya bas\u0131nc\u0131n\u0131, afinite sabitini KL ve isterseniz maksimum kapasiteyi qmax girin.<\/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":[65],"class_list":["post-3998","post","type-post","status-publish","format-standard","hentry","category-kimya","tag-reaksiyonlar"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/3998","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/comments?post=3998"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/posts\/3998\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/media?parent=3998"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/categories?post=3998"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/tr\/wp-json\/wp\/v2\/tags?post=3998"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}