{"id":2153,"date":"2026-10-14T23:33:55","date_gmt":"2026-10-14T22:33:55","guid":{"rendered":"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-livre-percurso-medio\/"},"modified":"2026-10-14T23:33:55","modified_gmt":"2026-10-14T22:33:55","slug":"calculadora-livre-percurso-medio","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-livre-percurso-medio\/","title":{"rendered":"Calculadora do livre percurso m\u00e9dio das mol\u00e9culas de g\u00e1s"},"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\">Calcule o caminho livre m\u00e9dio a partir da temperatura, da press\u00e3o e do di\u00e2metro de colis\u00e3o<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2153\" data-favorite-title=\"Livre percurso m\u00e9dio\" data-favorite-url=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-livre-percurso-medio\/\" data-favorite-excerpt=\"Calcule o livre percurso m\u00e9dio das mol\u00e9culas de um g\u00e1s a partir da temperatura, da press\u00e3o e do di\u00e2metro de colis\u00e3o. Informe as condi\u00e7\u00f5es do g\u00e1s em qualquer unidade comum e obtenha \u03bb em nm, \u00b5m, mm ou m.\" aria-label=\"Adicionar aos favoritos\" data-favorite-icon=\"icon icon-wind-2\">\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-livre-percurso-medio\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2153\" data-post=\"2153\"><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\">Temperatura (T)<\/label><div class=\"term\">T<\/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=\"number\" name=\"temperatura_t\" id=\"field-1\" aria-describedby=\"calc-info-1\" placeholder=\"e.g. 25\" min=\"-270\" step=\"any\" value=\"25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"C\" selected>\u00b0C<\/option><option value=\"K\">K<\/option><option value=\"F\">\u00b0F<\/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\">Temperatura absoluta do g\u00e1s. A temperatura ambiente (25 \u00b0C \u2248 298 K) \u00e9 um ponto de refer\u00eancia t\u00edpico.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Press\u00e3o (p)<\/label><div class=\"term\">p<\/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=\"presso_p\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"atm\" selected>atm<\/option><option value=\"kPa\">kPa<\/option><option value=\"Pa\">Pa<\/option><option value=\"bar\">bar<\/option><option value=\"mmHg\">mmHg (Torr)<\/option><option value=\"psi\">psi<\/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\">Press\u00e3o absoluta (n\u00e3o manom\u00e9trica) do g\u00e1s. Uma atmosfera \u00e9 a refer\u00eancia padr\u00e3o.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Di\u00e2metro de colis\u00e3o (d)<\/label><div class=\"term\">d<\/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=\"dimetro_de_coliso_d\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.37\" min=\"0\" value=\"0.37\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unidade\" aria-label=\"Unidade\"><option value=\"nm\" selected>nm<\/option><option value=\"pm\">pm<\/option><option value=\"A\">\u00c5<\/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-5\">Di\u00e2metro molecular efetivo admitido para uma colis\u00e3o no modelo de esferas r\u00edgidas. N\u2082 \u2248 0,37 nm, O\u2082 \u2248 0,36 nm, Ar \u2248 0,34 nm, He \u2248 0,26 nm.<\/small><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-7\">Exibir o caminho livre m\u00e9dio em<\/label><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"exibir_o_caminho_livre_mdio_em\"><option value=\"nm\" selected>nan\u00f4metros (nm)<\/option><option value=\"um\">micr\u00f4metros (\u00b5m)<\/option><option value=\"mm\">mil\u00edmetros (mm)<\/option><option value=\"m\">metros (m)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalcular\" id=\"calculate-button\" data-post=\"2153\">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 do caminho livre m\u00e9dio<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Caminho livre m\u00e9dio (\u03bb)<\/span><span class=\"result-term\">\u03bb<\/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 is-column\" id=\"output-2\"><span class=\"field-title\"><span>Em outras unidades<\/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>Detalhes do c\u00e1lculo<\/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>Sobre o caminho livre m\u00e9dio<\/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><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=\"2153\" 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>Livre percurso m\u00e9dio<\/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\\[ \\lambda = \\frac{k\\,T}{\\sqrt{2}\\,\\pi\\,d^{2}\\,p} = \\frac{1}{\\sqrt{2}\\,\\sigma\\,n} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Onde:<\/strong><\/p>\n<ul>\n<li>\\(\\lambda\\) \u2014 livre percurso m\u00e9dio, a dist\u00e2ncia m\u00e9dia que uma mol\u00e9cula percorre entre colis\u00f5es (m)<\/li>\n<li>\\(k = 1.380649\\times10^{-23}\\) J\/K \u2014 constante de Boltzmann (valor exato no SI)<\/li>\n<li>\\(T\\) \u2014 temperatura absoluta do g\u00e1s (K)<\/li>\n<li>\\(d\\) \u2014 di\u00e2metro de colis\u00e3o molecular, modelo de esferas r\u00edgidas (m)<\/li>\n<li>\\(p\\) \u2014 press\u00e3o absoluta do g\u00e1s (Pa)<\/li>\n<li>\\(\\sigma = \\pi d^{2}\\) \u2014 se\u00e7\u00e3o de choque (m\u00b2)<\/li>\n<li>\\(n = p\/(kT)\\) \u2014 densidade num\u00e9rica de mol\u00e9culas (m\u207b\u00b3)<\/li>\n<\/ul>\n<p>A f\u00f3rmula vem da teoria cin\u00e9tica de um g\u00e1s dilu\u00eddo: a cada unidade de dist\u00e2ncia percorrida, uma mol\u00e9cula varre um volume de colis\u00e3o \\(\\sigma\\), e o fator \\(\\sqrt{2}\\) leva em conta o movimento relativo dos pares que colidem.<\/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>Livre percurso m\u00e9dio \u2013 Exemplo de c\u00e1lculo<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemplo:<\/strong> g\u00e1s nitrog\u00eanio \u00e0 temperatura ambiente e press\u00e3o atmosf\u00e9rica (25 \u00b0C, 1 atm), com di\u00e2metro de colis\u00e3o de 0,37 nm \u2014 os valores padr\u00e3o desta calculadora.<\/p>\n<p>\\[ T = 25 + 273.15 = 298.15\\ \\text{K}, \\quad p = 1\\ \\text{atm} = 101{,}325\\ \\text{Pa}, \\quad d = 0.37\\ \\text{nm} = 3.7\\times10^{-10}\\ \\text{m} \\]<\/p>\n<p>\\[ \\sigma = \\pi d^{2} = \\pi \\times (3.7\\times10^{-10})^{2} = 4.30\\times10^{-19}\\ \\text{m}^{2} \\]<\/p>\n<p>\\[ \\lambda = \\frac{1.380649\\times10^{-23} \\times 298.15}{\\sqrt{2} \\times \\pi \\times (3.7\\times10^{-10})^{2} \\times 101{,}325} = \\frac{4.116\\times10^{-21}}{6.162\\times10^{-14}} \\]<\/p>\n<p><strong>Resultado:<\/strong> \\(\\lambda \\approx 6.68\\times10^{-8}\\) m \u2248 <strong>66,8 nm<\/strong>. Em condi\u00e7\u00f5es ambientes, uma mol\u00e9cula de nitrog\u00eanio percorre em m\u00e9dia cerca de 67 nan\u00f4metros \u2014 aproximadamente 180 di\u00e2metros moleculares \u2014 antes de colidir com outra mol\u00e9cula.<\/p>\n<p>\n\r\n<\/section>\n<h2>Como usar a calculadora<\/h2>\n<ol>\n<li>Informe a <strong>Temperatura (T)<\/strong> do g\u00e1s e escolha a unidade (\u00b0C, K ou \u00b0F). Use as escalas absolutas de temperatura corretamente \u2014 25 \u00b0C \u00e9 convertido automaticamente para 298,15 K.<\/li>\n<li>Informe a <strong>Press\u00e3o (p)<\/strong> com sua unidade (atm, kPa, Pa, bar, mmHg\/Torr ou psi). Certifique-se de que se trata da press\u00e3o absoluta, e n\u00e3o da press\u00e3o manom\u00e9trica.<\/li>\n<li>Informe o <strong>Di\u00e2metro de colis\u00e3o (d)<\/strong> das mol\u00e9culas em nm, pm ou \u00c5. Valores t\u00edpicos: N\u2082 \u2248 0,37 nm, O\u2082 \u2248 0,36 nm, Ar \u2248 0,34 nm, He \u2248 0,26 nm.<\/li>\n<li>Escolha a unidade de sa\u00edda em <strong>Exibir livre percurso m\u00e9dio em<\/strong> \u2014 nan\u00f4metros servem para press\u00f5es pr\u00f3ximas da atmosf\u00e9rica; micr\u00f4metros ou metros, para condi\u00e7\u00f5es de v\u00e1cuo.<\/li>\n<li>Leia o livre percurso m\u00e9dio (\u03bb), seu valor em todas as unidades de comprimento comuns e o passo a passo do c\u00e1lculo.<\/li>\n<\/ol>\n<h2>O que \u00e9 o livre percurso m\u00e9dio?<\/h2>\n<p>O livre percurso m\u00e9dio \\(\\lambda\\) \u00e9 a dist\u00e2ncia m\u00e9dia que uma mol\u00e9cula de g\u00e1s percorre entre duas colis\u00f5es sucessivas com outras mol\u00e9culas. No ar ao n\u00edvel do mar, ele \u00e9 de apenas cerca de 70 nm \u2014 uma mol\u00e9cula colide bilh\u00f5es de vezes por segundo. Numa c\u00e2mara de alto v\u00e1cuo, o mesmo g\u00e1s pode ter um livre percurso m\u00e9dio de cent\u00edmetros ou metros, o que significa que as mol\u00e9culas voam praticamente sem impedimento at\u00e9 atingir as paredes da c\u00e2mara.<\/p>\n<p>O valor resulta de dois efeitos que competem entre si. A densidade num\u00e9rica \\(n = p\/(kT)\\) diz o qu\u00e3o cheio est\u00e1 o g\u00e1s: mais mol\u00e9culas por metro c\u00fabico significam trajetos mais curtos. A se\u00e7\u00e3o de choque \\(\\sigma = \\pi d^2\\) diz o tamanho do alvo que cada mol\u00e9cula apresenta. Combinando os dois, obt\u00e9m-se \\(\\lambda = 1\/(\\sqrt{2}\\,\\sigma\\,n)\\), o que equivale \u00e0 forma em fun\u00e7\u00e3o da press\u00e3o usada por esta calculadora.<\/p>\n<p>O resultado varia de maneiras intuitivas: <strong>reduzir a press\u00e3o \u00e0 metade dobra \\(\\lambda\\)<\/strong>; aumentar a temperatura com a press\u00e3o fixa aumenta \\(\\lambda\\) proporcionalmente; e <strong>dobrar o di\u00e2metro molecular divide \\(\\lambda\\) por quatro<\/strong>, pois a se\u00e7\u00e3o de choque cresce com \\(d^2\\). \u00c9 por isso que o livre percurso m\u00e9dio \u00e9 o par\u00e2metro-chave da tecnologia do v\u00e1cuo: ele determina se o g\u00e1s escoa como um cont\u00ednuo ou no regime molecular livre (regime de Knudsen).<\/p>\n<p>Se voc\u00ea tamb\u00e9m quiser saber a que velocidade as mol\u00e9culas se deslocam entre essas colis\u00f5es, combine este resultado com a <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/molecular-speed-of-a-gas-calculator\/\">calculadora de velocidade molecular de um g\u00e1s<\/a> \u2014 dividindo a velocidade m\u00e9dia pelo livre percurso m\u00e9dio, obt\u00e9m-se a frequ\u00eancia de colis\u00f5es.<\/p>\n<h2>Como interpretar o resultado<\/h2>\n<p>O bloco \"Em outras unidades\" tamb\u00e9m informa a densidade num\u00e9rica \\(n\\) e o espa\u00e7amento m\u00e9dio entre as mol\u00e9culas, \\(n^{-1\/3}\\). Uma verifica\u00e7\u00e3o \u00fatil de sanidade: o livre percurso m\u00e9dio deve ser muito maior que tanto o di\u00e2metro molecular quanto o espa\u00e7amento entre as mol\u00e9culas (no ar, cerca de 180 espa\u00e7amentos). Se \\(\\lambda\\) se tornar compar\u00e1vel ao tamanho do seu equipamento, voc\u00ea est\u00e1 no regime de escoamento molecular, no qual conceitos como viscosidade e press\u00e3o de cont\u00ednuo perdem o significado usual.<\/p>\n<p>Outras propriedades de gases que voc\u00ea pode calcular com nossas ferramentas incluem a <a href=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-densidade-de-gases\/\">calculadora de densidade de g\u00e1s<\/a> e a <a href=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-lei-de-avogadro-2\/\">calculadora da Lei de Avogadro<\/a>, que relaciona o n\u00famero de mol\u00e9culas ao volume em temperatura e press\u00e3o constantes.<\/p>\n<h2>Premissas e limita\u00e7\u00f5es<\/h2>\n<ul>\n<li><strong>Modelo de esferas r\u00edgidas:<\/strong> as mol\u00e9culas s\u00e3o tratadas como esferas r\u00edgidas de um \u00fanico di\u00e2metro. Mol\u00e9culas reais interagem por meio de potenciais suaves e de longo alcance, de modo que os di\u00e2metros de colis\u00e3o tabelados s\u00e3o valores efetivos, geralmente ajustados a dados de viscosidade \u2014 espere resultados com precis\u00e3o de aproximadamente \u00b120%.<\/li>\n<li><strong>G\u00e1s dilu\u00eddo e ideal:<\/strong> a f\u00f3rmula assume \\(\\lambda \\gg d\\), ou seja, que as colis\u00f5es s\u00e3o eventos bin\u00e1rios breves. Ela falha em gases densos e perto da condensa\u00e7\u00e3o; para condi\u00e7\u00f5es densas ou n\u00e3o ideais, consulte a <a href=\"https:\/\/wpcalc.com\/pt\/quimica\/calculadora-equacao-de-van-der-waals\/\">calculadora da equa\u00e7\u00e3o de Van der Waals<\/a>.<\/li>\n<li><strong>G\u00e1s de componente \u00fanico:<\/strong> assume-se um di\u00e2metro uniforme. Para misturas de gases, \u00e9 preciso estimar um di\u00e2metro efetivo (por exemplo, a partir de dados de viscosidade da mistura).<\/li>\n<li><strong>Distribui\u00e7\u00e3o de Maxwell\u2013Boltzmann:<\/strong> o fator \\(\\sqrt{2}\\) depende da distribui\u00e7\u00e3o de velocidades em equil\u00edbrio, que vale na maioria das condi\u00e7\u00f5es pr\u00e1ticas.<\/li>\n<li><strong>Press\u00e3o absoluta obrigat\u00f3ria:<\/strong> um man\u00f4metro marca zero a 1 atm, mas a f\u00edsica depende da press\u00e3o absoluta. N\u00e3o subtraia nada \u2014 se o seu man\u00f4metro marca 0 bar na press\u00e3o ambiente, informe ~1 atm, e n\u00e3o 0 (press\u00e3o zero \u00e9 rejeitada de qualquer forma).<\/li>\n<\/ul>\n<h2>Valores t\u00edpicos a 25 \u00b0C<\/h2>\n<table>\n<thead>\n<tr>\n<th>Press\u00e3o<\/th>\n<th>\u03bb para o N\u2082 (d = 0,37 nm)<\/th>\n<th>Regime<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1 atm (101 325 Pa)<\/td>\n<td>\u2248 67 nm<\/td>\n<td>Escoamento cont\u00ednuo<\/td>\n<\/tr>\n<tr>\n<td>1\/100 atm \u2248 1 013 Pa<\/td>\n<td>\u2248 6,7 \u00b5m<\/td>\n<td>Transi\u00e7\u00e3o<\/td>\n<\/tr>\n<tr>\n<td>1 Pa<\/td>\n<td>\u2248 6,8 \u00b5m<\/td>\n<td>In\u00edcio do escoamento de Knudsen<\/td>\n<\/tr>\n<tr>\n<td>10\u207b\u2076 atm (alto v\u00e1cuo)<\/td>\n<td>\u2248 6,7 cm<\/td>\n<td>Escoamento molecular<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Veja como \u03bb cresce rapidamente quando a press\u00e3o cai \u2014 um fator 10 na press\u00e3o corresponde a um fator 10 no livre percurso m\u00e9dio, em temperatura constante.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calcule o livre percurso m\u00e9dio das mol\u00e9culas de um g\u00e1s a partir da temperatura, da press\u00e3o e do di\u00e2metro de colis\u00e3o. Informe as condi\u00e7\u00f5es do g\u00e1s em qualquer unidade comum e obtenha \u03bb em nm, \u00b5m, mm ou m.<\/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":[41],"class_list":["post-2153","post","type-post","status-publish","format-standard","hentry","category-quimica","tag-gases"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2153","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=2153"}],"version-history":[{"count":0,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/posts\/2153\/revisions"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/media?parent=2153"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/categories?post=2153"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pt\/wp-json\/wp\/v2\/tags?post=2153"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}