{"id":28649,"date":"2021-03-26T23:02:41","date_gmt":"2021-03-26T23:02:41","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=28649"},"modified":"2024-12-24T03:57:10","modified_gmt":"2024-12-24T03:57:10","slug":"mol-e-massa-molar-na-termodinamica","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/pt\/mol-e-massa-molar-na-termodinamica\/","title":{"rendered":"Mol e massa molar na Termodin\u00e2mica"},"content":{"rendered":"<h1 style=\"text-align:center;\">Mol e massa molar na Termodin\u00e2mica<\/h1>\n<p style=\"text-align:center;\"><em><strong>Resumo:<\/strong><br \/>\nA aula introduz o mol e a massa molar na termodin\u00e2mica, destacando a import\u00e2ncia das rela\u00e7\u00f5es entre as part\u00edculas em um objeto. Explica a necessidade de abordagens estat\u00edsticas para sistemas com muitas part\u00edculas. O mol \u00e9 definido com o N\u00famero de Avogadro e mostra como calcular a massa molar usando a tabela peri\u00f3dica.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Objetivos de Aprendizagem<\/strong><br \/>\nAo final desta aula, o estudante ser\u00e1 capaz de\n<\/p>\n<ol>\n<li><strong>Definir<\/strong> o que \u00e9 um mol e sua import\u00e2ncia para representar grandes quantidades de part\u00edculas em subst\u00e2ncias.<\/li>\n<li><strong>Aprender<\/strong> o valor e significado do N\u00famero de Avogadro como a quantidade de part\u00edculas em um mol.<\/li>\n<li><strong>Identificar<\/strong> a rela\u00e7\u00e3o entre a massa molar, o mol e o N\u00famero de Avogadro.<\/li>\n<li><strong>Calcular<\/strong> a massa molar de diferentes subst\u00e2ncias usando a tabela peri\u00f3dica.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>\u00cdNDICE DE CONTE\u00daDOS<\/strong><br \/>\n<a href=\"#1\">Introdu\u00e7\u00e3o<\/a><br \/>\n<a href=\"#2\">Os grandes n\u00fameros na termodin\u00e2mica<\/a><br \/>\n<a href=\"#3\">O que \u00e9 um mol?<\/a><br \/>\n<a href=\"#4\">O que \u00e9 a massa molar?<\/a>\n<\/p>\n<p><center><iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/c-EpWOSSQH8\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/center><br \/>\n<a name=\"1\"><\/a><\/p>\n<h2>Introdu\u00e7\u00e3o<\/h2>\n<p style=\"text-align: justify;\">Nosso estudo come\u00e7a com entender o que s\u00e3o o mol e a massa molar, mas primeiro precisamos revisar outra ideia: a de que <strong><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=85s\" rel=\"noopener\" target=\"_blank\">\u00abTodo objeto \u00e9 mais do que a soma de suas partes\u00bb<\/a><\/strong>. Porque a constitui\u00e7\u00e3o de um objeto vem de suas partes e \u00absua maneira de estar umas em rela\u00e7\u00e3o \u00e0s outras\u00bb. Essa \u00abmaneira de ser\u00bb vai al\u00e9m das qualidades de cada parte individualmente, porque se trata da rela\u00e7\u00e3o de todas com todas e n\u00e3o apenas em rela\u00e7\u00e3o a si mesmas. Como veremos, essa \u00e9 a raz\u00e3o pela qual diferentes objetos exibem qualidades diferentes, mesmo quando s\u00e3o feitos da mesma coisa. Por exemplo, mudando a temperatura transforma a \u00e1gua em gelo sem que se adicione, retire ou mude algo pr\u00f3prio da \u00e1gua. Assim nasce a \u00abTERMODIN\u00c2MICA\u00bb, <a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=292s\" rel=\"noopener\" target=\"_blank\"><strong>onde se estuda o comportamento dos sistemas com muitas part\u00edculas,<\/strong><\/a> tantas que uma abordagem estat\u00edstica \u00e9 necess\u00e1ria.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Os grandes n\u00fameros na termodin\u00e2mica<\/h2>\n<p style=\"text-align: justify;\">Mas&#8230; O que queremos dizer com \u00abmuitas part\u00edculas\u00bb? Vemos grandes n\u00fameros com frequ\u00eancia: a <a href=\"https:\/\/www.google.com\/search?client=firefox-b-d&amp;q=popula%C3%A7%C3%A3o+da+terra\" rel=\"noopener\" target=\"_blank\">popula\u00e7\u00e3o da Terra<\/a> est\u00e1 por volta de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">(6-7)\\cdot 10^9<\/span><\/span> PESSOAS, e a <a href=\"https:\/\/cincodias.elpais.com\/cincodias\/2019\/11\/02\/economia\/1572730109_708795.html\" rel=\"noopener\" target=\"_blank\">d\u00edvida p\u00fablica dos Estados Unidos<\/a> est\u00e1 em torno de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">23 \\cdot 10^{12}<\/span><\/span> USD. Mas mesmo esses n\u00fameros empalidecem diante das magnitudes envolvidas na f\u00edsica t\u00e9rmica. Por exemplo, qualquer objeto ao seu alcance facilmente tem mais de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">10^{20}<\/span><\/span> PART\u00cdCULAS, e isso imp\u00f5e s\u00e9rios limites aos c\u00e1lculos que podemos realizar para compreend\u00ea-los.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #008000;\"><strong>Exemplo<\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;\">\n<p><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=402s\" rel=\"noopener\" target=\"_blank\"><strong>Um quilograma de g\u00e1s de Nitrog\u00eanio cont\u00e9m, aproximadamente<\/strong><\/a> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2\\cdot 10^{25}<\/span><\/span> MOL\u00c9CULAS DE <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N_2<\/span><\/span>. Suponhamos que temos um computador pessoal com um processador de <span dir=\"ltr\">3GHz<\/span> e, assumindo que ele usar\u00e1 toda a sua pot\u00eancia apenas para contar mol\u00e9culas, vejamos quanto tempo ele levar\u00e1 para contar todas as mol\u00e9culas do quilograma de Nitrog\u00eanio.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;\">\n<p><strong>Solu\u00e7\u00e3o:<\/strong> Como o computador usar\u00e1 toda a sua pot\u00eancia para contar mol\u00e9culas, ele contar\u00e1 uma mol\u00e9cula por cada ciclo do processador. Portanto, o tempo de contagem ser\u00e1:<\/p>\n<p style=\"text-align:center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\nt = \\dfrac{2\\cdot 10^{25}}{3\\cdot 10^9 \\left[\\dfrac{1}{s}\\right]} \\approx 6,\\overline{6} \\cdot 10^{15} [s]\n<\/span><\/span><\/p>\n<p>Agora, sabemos que cada ano tem <span dir=\"ltr\">356<\/span> dias, cada dia <span dir=\"ltr\">24<\/span> horas, e cada hora <span dir=\"ltr\">3600<\/span> segundos. Assim, se transformarmos os segundos em anos, obtemos a quantidade nada desprez\u00edvel de <span dir=\"ltr\">211.398.613,2<\/span> anos. Estamos falando de mais de <span dir=\"ltr\">200<\/span> milh\u00f5es de anos.<\/p>\n<p>Neste exemplo, s\u00f3 falamos sobre contar mol\u00e9culas e o tempo que levaria para faz\u00ea-lo, mas n\u00e3o dissemos nada sobre calcular a intera\u00e7\u00e3o entre as part\u00edculas. Se algo t\u00e3o simples leva tanto tempo, ent\u00e3o calcular a intera\u00e7\u00e3o combinada de todas elas \u00e9 inalcan\u00e7\u00e1vel.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Assim, para avan\u00e7ar no estudo da termodin\u00e2mica, \u00e9 necess\u00e1rio revisar algumas quest\u00f5es estat\u00edsticas, o <strong><a href=\"https:\/\/toposuranos.com\/limite-termodinamico-pressao-e-variaveis-extensivas-e-intensivas\/\" rel=\"noopener\" target=\"_blank\">limite termodin\u00e2mico<\/a><\/strong> e o conceito de mol. Come\u00e7aremos revisando este \u00faltimo.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>O que \u00e9 um Mol?<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=760s\" rel=\"noopener\" target=\"_blank\"><strong>Um mol \u00e9 um nome usado para representar uma certa quantidade de coisas.<\/strong><\/a> Sua fun\u00e7\u00e3o \u00e9 semelhante \u00e0 da palavra \u00abd\u00fazia\u00bb quando voc\u00ea vai comprar ovos (1 d\u00fazia de ovos s\u00e3o <span dir=\"ltr\">12<\/span> ovos). O mol, no entanto, foi projetado para nos permitir lidar com n\u00fameros t\u00e3o grotescos quanto o n\u00famero de \u00e1tomos em certa subst\u00e2ncia. Sua defini\u00e7\u00e3o \u00e9 a seguinte:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #800000;\"><strong>Defini\u00e7\u00e3o<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\n<p>Um <strong>mol<\/strong> \u00e9 a quantidade de mat\u00e9ria que cont\u00e9m tantos objetos quanto o n\u00famero de \u00e1tomos em exatamente <span dir=\"ltr\">12[g]<\/span> de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">^{12}C<\/span><\/span><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">O mol tamb\u00e9m \u00e9 aproximadamente dito ser a quantidade de mat\u00e9ria que cont\u00e9m tantos objetos quanto o n\u00famero de \u00e1tomos em exatamente 1[g] de <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">^{1}H<\/span><\/span>, mas \u00e9 prefer\u00edvel usar o Carbono para a defini\u00e7\u00e3o porque, ao se apresentar em estado s\u00f3lido, \u00e9 muito mais f\u00e1cil de medir com precis\u00e3o.<\/p>\n<p style=\"text-align: justify;\">Um mol de \u00e1tomos \u00e9 equivalente a um <strong>N\u00famero de Avogadro<\/strong> <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">N_A<\/span><\/span> de \u00e1tomos. O N\u00famero de Avogadro, expresso com quatro algarismos significativos, \u00e9:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{N_A = 6.022 \\cdot 10^{23}}<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">O N\u00famero de Avogadro tamb\u00e9m costuma ser escrito com \u00abunidades\u00bb como <span class=\"katex-eq\" data-katex-display=\"false\">N_A = 6.022 \\cdot 10^{23} \\left[\\dfrac{1}{mol}\\right] <\/span> como um lembrete de sua defini\u00e7\u00e3o, embora seja uma magnitude adimensional (como [mol]).<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #008000;\"><strong>Exemplo<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\n<ul>\n<li><span dir=\"ltr\">1[mol]<\/span> de Carbono tem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span><\/span> \u00e1tomos de Carbono<\/li>\n<li><span dir=\"ltr\">1[mol]<\/span> de NaCl tem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span><\/span> mol\u00e9culas de NaCl<\/li>\n<li><span dir=\"ltr\">1[mol]<\/span> de elefantes tem <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span><\/span> elefantes<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/p>\n<h2>O que \u00e9 a Massa Molar?<\/h2>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=964s\" rel=\"noopener\" target=\"_blank\"><strong>A massa molar de uma subst\u00e2ncia \u00e9 a massa contida em um mol dessa subst\u00e2ncia.<\/strong><\/a> Assim, a massa molar do Carbono 12 \u00e9 de <span dir=\"ltr\">12[g]<\/span>, a massa molar da \u00e1gua \u00e9 pr\u00f3xima a 18[g]. Uma maneira de obter uma boa aproxima\u00e7\u00e3o da massa molar \u00e9 atrav\u00e9s da soma dos n\u00fameros de massa dos elementos que comp\u00f5em o composto. Por exemplo, para a \u00e1gua temos:<\/p>\n<p style=\"text-align: center;\"><span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">H_2 O = {}^{1}H + {}^{1}H + {}^{16}O<\/span><\/span><\/p>\n<p style=\"text-align: justify;\">Ou seja, dois is\u00f3topos de Hidrog\u00eanio com um \u00fanico pr\u00f3ton e um de Oxig\u00eanio, que cont\u00e9m 8 pr\u00f3tons e 8 n\u00eautrons. Assim, a massa molar ser\u00e1 de <span dir=\"ltr\">18[g]<\/span>.<\/p>\n<p style=\"text-align: justify;\"><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=1068s\" rel=\"noopener\" target=\"_blank\"><strong>Outra maneira mais precisa de fazer o mesmo \u00e9 utilizando a tabela peri\u00f3dica,<\/strong><\/a> que considera a massa molar dos \u00e1tomos levando em conta a ligeira diferen\u00e7a de massa que existe entre pr\u00f3tons e n\u00eautrons.<\/p>\n<p><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAIAAAAAAAP\/\/\/yH5BAEAAAAALAAAAAABAAEAAAIBRAA7\" data-src=\"https:\/\/1.bp.blogspot.com\/-ESRV4m1EHMI\/YGTErvT1CDI\/AAAAAAAAExQ\/d1LGTs2jqyIlJ7sUBmKED36I2Lhdzm57ACLcBGAsYHQ\/s0\/2000px-Periodic_table_large-es-updated-2018.svg.png\" alt=\"tabela peri\u00f3dica dos elementos\" class=\" aligncenter lazyload\" width=\"1148\" height=\"631\" \/><noscript><img decoding=\"async\" src=\"https:\/\/1.bp.blogspot.com\/-ESRV4m1EHMI\/YGTErvT1CDI\/AAAAAAAAExQ\/d1LGTs2jqyIlJ7sUBmKED36I2Lhdzm57ACLcBGAsYHQ\/s0\/2000px-Periodic_table_large-es-updated-2018.svg.png\" alt=\"tabela peri\u00f3dica dos elementos\" class=\" aligncenter lazyload\" width=\"1148\" height=\"631\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">Se determinarmos a massa molar da \u00e1gua usando os dados da tabela peri\u00f3dica, teremos que cada mol de \u00e1gua pesa <span dir=\"ltr\"><span class=\"katex-eq\" data-katex-display=\"false\">2\\cdot 1,00794 + 15,9994 [g]=18,01448[g]<\/span><\/span>.<\/p>\n<p style=\"text-align: justify;\">A massa de uma part\u00edcula (mol\u00e9cula ou \u00e1tomo) de uma subst\u00e2ncia \u00e9, portanto, a massa molar dividida pelo N\u00famero de Avogadro<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\textnormal{Massa da Part\u00edcula} = \\dfrac{\\textnormal{Massa Molar}}{\\text{N\u00famero de Avogadro}}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>Mol e massa molar na Termodin\u00e2mica Resumo: A aula introduz o mol e a massa molar na termodin\u00e2mica, destacando a import\u00e2ncia das rela\u00e7\u00f5es entre as part\u00edculas em um objeto. Explica a necessidade de abordagens estat\u00edsticas para sistemas com muitas part\u00edculas. O mol \u00e9 definido com o N\u00famero de Avogadro e mostra como calcular a massa [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":28637,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":17,"footnotes":""},"categories":[637,921],"tags":[],"class_list":["post-28649","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fisica-pt","category-termodinamica-pt"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.4 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Mol e massa molar na Termodin\u00e2mica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"O mol \u00e9 uma unidade que representa 6,022 x 10^23 part\u00edculas, como \u00e1tomos ou mol\u00e9culas. 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