{"id":34632,"date":"2021-03-26T13:00:24","date_gmt":"2021-03-26T13:00:24","guid":{"rendered":"https:\/\/toposuranos.com\/material\/?p=34632"},"modified":"2025-09-19T23:02:40","modified_gmt":"2025-09-19T23:02:40","slug":"mol-et-massa-molaris-in-thermodynamica","status":"publish","type":"post","link":"http:\/\/toposuranos.com\/material\/la\/mol-et-massa-molaris-in-thermodynamica\/","title":{"rendered":"Mol et massa molaris in Thermodynamica"},"content":{"rendered":"<h1 style=\"text-align:center;\">Mol et massa molaris in Thermodynamica<\/h1>\n<p style=\"text-align:center;\"><em><strong>Summarium:<\/strong><br \/>\nHaec lectio introducit mol et massam molarem in thermodynamica, illustrans momentum relationum inter particulas in obiecto. Explicat necessitatem rationum statisticarum pro systematibus cum multis particulis. Definitur mol cum Numero Avogadro et ostenditur quomodo massa molaris per tabulam periodicam computetur.<\/em><\/p>\n<p style=\"text-align:center;\"><strong>Proposita Discendi<\/strong><br \/>\nIn fine huius lectionis discipulus poterit\n<\/p>\n<ol>\n<li><strong>Definire<\/strong> quid sit mol eiusque momentum ad magnas copias particularum in substantiis repraesentandas.<\/li>\n<li><strong>Discere<\/strong> valorem et significationem Numeri Avogadro ut quantitatem particularum in uno mole.<\/li>\n<li><strong>Ag\u00adnoscere<\/strong> relationem inter massam molarem, mol et Numerum Avogadro.<\/li>\n<li><strong>Computare<\/strong> massam molarem diversarum substantiarum utens tabula periodica.<\/li>\n<\/ol>\n<p style=\"text-align:center;\"><strong>INDEX CONTENTORUM<\/strong><br \/>\n<a href=\"#1\">Introductio<\/a><br \/>\n<a href=\"#2\">Numeri magni in thermodynamica<\/a><br \/>\n<a href=\"#3\">Quid est mol?<\/a><br \/>\n<a href=\"#4\">Quid est massa molaris?<\/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>Introductio<\/h2>\n<p style=\"text-align: justify;\">Studium nostrum incipit intellegendo quid sint mol et massa molaris, sed prius necesse est aliam notionem recognoscere: eam scilicet quod <strong><a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=85s\" rel=\"noopener\" target=\"_blank\">\u00abOmne obiectum plus est quam summa partium suarum\u00bb<\/a><\/strong>. Constitutio enim obiecti provenit ex partibus eius et ex \u00abmodo quo inter se positae sunt\u00bb. Hic \u00abmodus essendi\u00bb ultra proprietates cuiusque partis singillatim extenditur, quia agitur de relatione omnium ad omnia et non solum ad se ipsas. Ut videbimus, haec est causa cur diversa obiecta qualitates diversas exhibeant etiamsi ex eisdem rebus constant. Exempli gratia, mutata temperatura aqua in glaciem vertitur, nihil addito, sublato aut mutato quod aquae proprium sit. Sic nascitur \u00abTHERMODYNAMICA\u00bb, <a href=\"https:\/\/www.youtube.com\/watch?v=c-EpWOSSQH8&amp;t=292s\" rel=\"noopener\" target=\"_blank\"><strong>ubi investigatur se gerere systemata ex multis particulis constantia,<\/strong><\/a> tot ut ratio statistica necessaria sit.<\/p>\n<p><a name=\"2\"><\/a><\/p>\n<h2>Numeri magni in thermodynamica<\/h2>\n<p style=\"text-align: justify;\">Sed&#8230; quid significamus cum dicimus \u00abmultas particulas\u00bb? Magnos numeros saepe videmus: <a href=\"https:\/\/www.google.com\/search?client=firefox-b-d&amp;q=poblaci%C3%B3n+de+la+tierra\" rel=\"noopener\" target=\"_blank\">populatio Terrae<\/a> est circa <span class=\"katex-eq\" data-katex-display=\"false\">(6-7)\\cdot 10^9<\/span> HOMINES, et <a href=\"https:\/\/cincodias.elpais.com\/cincodias\/2019\/11\/02\/economia\/1572730109_708795.html\" rel=\"noopener\" target=\"_blank\">debitum publicum Civitatum Foederatarum Americae<\/a> est circa <span class=\"katex-eq\" data-katex-display=\"false\">23 \\cdot 10^{12}<\/span> USD. Sed etiam hi numeri pallescunt coram magnitudinibus quae in physica thermica occurrunt. Exempli gratia, quodlibet obiectum prope te facile habet plus quam <span class=\"katex-eq\" data-katex-display=\"false\">10^{20}<\/span> PARTICULAS, quod graves limites imponit calculis quos ad intellegendum facere possumus.<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #008000;\"><strong>Exemplum<\/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>Unum kilogramma gasi Nitrogenii continet, circiter<\/strong><\/a> <span class=\"katex-eq\" data-katex-display=\"false\">2\\cdot 10^{25}<\/span> MOLECULAS <span class=\"katex-eq\" data-katex-display=\"false\">N_2<\/span>. Ponamus nos habere computatrum personale cum processore 3GHz et, si totam potentiam suam solum ad numerandas moleculas dedicet, videamus quantum temporis necessarium sit ad omnes moleculas kilogrammi Nitrogenii numerandas.<\/p>\n<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: justify;\">\n<p><strong>Solutio:<\/strong> Cum computatrum totam potentiam ad numerandas moleculas adhibeat, numerabit unam moleculam per unum cyclum processoris. Ergo tempus numerandi erit:<\/p>\n<p style=\"text-align:center;\"><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>\n<p>Nunc scimus unumquemque annum 356 dies habere, unumquemque diem 24 horas, unamquamque horam 3600 secundos. Quare, si secundos in annos convertimus, obtinemus non parvam quantitatem 211.398.613,2 annorum. Loquimur de plus quam ducentis milionibus annorum.<\/p>\n<p>In hoc exemplo tantum egimus de numerandis moleculis et de tempore quod id facere requireret, nihil autem diximus de computanda interactione inter particulas. Si res tam simplex tantum temporis sumit, tum computare interactionem coniunctam omnium earum prorsus inaccessibile est.<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Itaque, ut in studio thermodynamicae progrediamur, necesse est quaestiones quasdam statisticas recognoscere, <strong><a href=\"https:\/\/toposuranos.com\/limite-termodinamico-presion-y-variables-extensivas-e-intensivas\/\" rel=\"noopener\" target=\"_blank\">limitem thermodynamicum<\/a><\/strong> atque notionem molis. Nos autem hanc postremam primum recognoscere incipiemus.<\/p>\n<p><a name=\"3\"><\/a><\/p>\n<h2>Quid est 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>Mol est nomen adhibitum ad certam quantitatem rerum repraesentandam.<\/strong><\/a> Officium eius simile est vocabulo \u00abduodena\u00bb cum ova emere velis (1 duodena ovorum sunt 12 ova). Mol tamen excogitatus est ut nobis liceat magnitudines tam immanes tractare quam numerum atomorum in aliqua substantia. Definitio eius haec est:<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #800000;\"><strong>Definitio<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\n<p><strong>Mol<\/strong> est quantitas materiae quae tot res continet quot sunt atomi in exacte 12[g] <span class=\"katex-eq\" data-katex-display=\"false\">^{12}C<\/span>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: justify;\">Mol etiam proxime exprimitur dicendo eam esse quantitatem materiae quae tot res continet quot sunt atomi in exacte 1[g] <span class=\"katex-eq\" data-katex-display=\"false\">^{1}H<\/span>, sed praestat Carbonem ad definitionem adhiberi quia, cum in statu solido comparet, multo facilius est eum accurate metiri.<\/p>\n<p style=\"text-align: justify;\">Unus mol atomorum aequivalet <strong>Numero Avogadro<\/strong> <span class=\"katex-eq\" data-katex-display=\"false\">N_A<\/span> atomorum. Numerus Avogadro, quattuor digitis significantibus expressus, est:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\boxed{N_A = 6.022 \\cdot 10^{23}}<\/span>\n<p style=\"text-align: justify;\">Numerus Avogadro etiam scribi solet cum \u00abunitatibus\u00bb ut <span class=\"katex-eq\" data-katex-display=\"false\">N_A = 6.022 \\cdot 10^{23} \\left[\\dfrac{1}{mol}\\right] <\/span> quasi admonitio definitionis eius, quamvis sit magnitudo adimensionis (sicut [mol]).<\/p>\n<table>\n<tbody>\n<tr>\n<td style=\"color: #008000;\"><strong>Exemplum<\/strong><\/td>\n<\/tr>\n<tr>\n<td>\n<ul>\n<li>1[mol] Carbonis habet <span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span> atomos Carbonis<\/li>\n<li>1[mol] NaCl habet <span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span> moleculas NaCl<\/li>\n<li>1[mol] elephantorum habet <span class=\"katex-eq\" data-katex-display=\"false\">6.022 \\cdot 10^{23}<\/span> elephantes<\/li>\n<\/ul>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><a name=\"4\"><\/a><\/p>\n<h2>Quid est massa molaris?<\/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>Massa molaris substantiae est massa contenta in uno mole substantiae.<\/strong><\/a> Ita, massa molaris Carbonis 12 est 12[g], massa molaris aquae est circa 18[g]. Una via ad bonam approximationem massae molaris obtinendam est per summam numerorum massicorum elementorum quae compositum constituunt. Exempli gratia, pro aqua habemus:<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">H_2 O = {}^{1}H + {}^{1}H + {}^{16}O<\/span>\n<p style=\"text-align: justify;\">Id est, duo isotopi Hydrogenii cum uno tantum protone et unus Oxygenii, qui 8 protones et 8 neutrones continet. Quare massa molaris erit 18[g].<\/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>Alia ratio accuratior idem faciendi est adiuvando tabula periodica,<\/strong><\/a> quae considerat massam molarem atomorum rationem habens tenuis differentiae inter massas protonum et neutronum.<\/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=\"tabula periodica elementorum\" 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=\"tabula periodica elementorum\" class=\" aligncenter lazyload\" width=\"1148\" height=\"631\" \/><\/noscript><\/p>\n<p style=\"text-align: justify;\">Si determinamus massam molarem aquae utens datis ex tabula periodica, habebimus quod unus mol aquae ponderabit <span class=\"katex-eq\" data-katex-display=\"false\">2\\cdot 1,00794 + 15,9994 [g]=18,01448[g]<\/span>.<\/p>\n<p style=\"text-align: justify;\">Massa particulae (moleculae vel atomi) substantiae est igitur massa molaris divisa per Numerum Avogadro<\/p>\n<p style=\"text-align: center;\"><span class=\"katex-eq\" data-katex-display=\"false\">\\textnormal{Massa Particulae} = \\dfrac{\\textnormal{Massa Molaris}}{\\text{Numerus Avogadro}}<\/span>\n","protected":false},"excerpt":{"rendered":"<p>Mol et massa molaris in Thermodynamica Summarium: Haec lectio introducit mol et massam molarem in thermodynamica, illustrans momentum relationum inter particulas in obiecto. Explicat necessitatem rationum statisticarum pro systematibus cum multis particulis. Definitur mol cum Numero Avogadro et ostenditur quomodo massa molaris per tabulam periodicam computetur. Proposita Discendi In fine huius lectionis discipulus poterit Definire [&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":1,"footnotes":""},"categories":[1250,1292],"tags":[],"class_list":["post-34632","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-physica","category-thermodynamica"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Mol et massa molaris in Thermodynamica - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Mol est unitas quae repraesentat 6.022 x 10^23 particulas, ut atomos vel moleculas. 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