{"id":2542,"date":"2026-10-14T16:45:40","date_gmt":"2026-10-14T15:45:40","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-prawa-avogadra\/"},"modified":"2026-10-14T16:45:40","modified_gmt":"2026-10-14T15:45:40","slug":"kalkulator-prawa-avogadra","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-prawa-avogadra\/","title":{"rendered":"Kalkulator prawa Avogadra"},"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\">Oblicz brakuj\u0105c\u0105 obj\u0119to\u015b\u0107 lub ilo\u015b\u0107 gazu<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"2542\" data-favorite-title=\"Prawo Avogadra\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-prawa-avogadra\/\" data-favorite-excerpt=\"Oblicz brakuj\u0105c\u0105 obj\u0119to\u015b\u0107 lub ilo\u015b\u0107 gazu z prawa Avogadra. Wpisz pocz\u0105tkow\u0105 obj\u0119to\u015b\u0107 i ilo\u015b\u0107 gazu, a tak\u017ce now\u0105 ilo\u015b\u0107 albo now\u0105 obj\u0119to\u015b\u0107 i otrzymaj wynik z pe\u0142nymi obliczeniami.\" aria-label=\"Dodaj do ulubionych\" 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\/pl\/chemia\/kalkulator-prawa-avogadra\/\" method=\"POST\" class=\"calculator\" id=\"calculator-2542\" data-post=\"2542\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Oblicz<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"oblicz\"><option value=\"v2\" selected>Ko\u0144cowa obj\u0119to\u015b\u0107 (V\u2082)<\/option><option value=\"n2\">Ko\u0144cowa ilo\u015b\u0107 gazu (n\u2082)<\/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><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Obj\u0119to\u015b\u0107 pocz\u0105tkowa (V\u2081)<\/label><div class=\"term\">V\u2081<\/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=\"objto_pocztkowa_v\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"0\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"L\" selected>L<\/option><option value=\"mL\">mL<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"m3\">m\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"gal\">gal (US)<\/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-2\">Obj\u0119to\u015b\u0107 gazu na pocz\u0105tku.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-4\">Pocz\u0105tkowa ilo\u015b\u0107 gazu (n\u2081)<\/label><div class=\"term\">n\u2081<\/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=\"pocztkowa_ilo_gazu_n\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.5\" min=\"0\" value=\"0.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mol\" selected>mol<\/option><option value=\"mmol\">mmol<\/option><option value=\"kmol\">kmol<\/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-4\">Ilo\u015b\u0107 gazu na pocz\u0105tku (w molach).<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-6\">Ko\u0144cowa ilo\u015b\u0107 gazu (n\u2082)<\/label><div class=\"term\">n\u2082<\/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=\"kocowa_ilo_gazu_n\" id=\"field-6\" aria-describedby=\"calc-info-6\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.5\" min=\"0\" value=\"1.5\"\/><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mol\" selected>mol<\/option><option value=\"mmol\">mmol<\/option><option value=\"kmol\">kmol<\/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\">Nowa ilo\u015b\u0107 gazu; obliczana jest obj\u0119to\u015b\u0107 ko\u0144cowa.<\/small><\/div><div class=\"field has-term\" id=\"input-5\" hidden><label for=\"field-8\">Obj\u0119to\u015b\u0107 ko\u0144cowa (V\u2082)<\/label><div class=\"term\">V\u2082<\/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=\"objto_kocowa_v\" id=\"field-8\" aria-describedby=\"calc-info-8\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 6\" min=\"0\" value=\"6\"\/><div class=\"grid grid-cols-1\"><select id=\"field-9\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"L\" selected>L<\/option><option value=\"mL\">mL<\/option><option value=\"cm3\">cm\u00b3<\/option><option value=\"m3\">m\u00b3<\/option><option value=\"ft3\">ft\u00b3<\/option><option value=\"gal\">gal (US)<\/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-8\">Nowa obj\u0119to\u015b\u0107 gazu; obliczana jest ko\u0144cowa ilo\u015b\u0107 gazu.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"2542\">Oblicz<\/button><button type=\"reset\">Wyczy\u015b\u0107<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Obliczaj automatycznie<\/label><small>Po w\u0142\u0105czeniu wynik aktualizuje si\u0119 automatycznie po zmianie dowolnej warto\u015bci.<\/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> Wyniki \u2014 prawo Avogadra<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Obj\u0119to\u015b\u0107 ko\u0144cowa (V\u2082)<\/span><span class=\"result-term\">V\u2082<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Ko\u0144cowa ilo\u015b\u0107 gazu (n\u2082)<\/span><span class=\"result-term\">n\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>Kroki oblicze\u0144<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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>O prawie Avogadra<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Kopiuj wynik\" aria-label=\"Kopiuj wynik\"><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\">Kopiuj link do tego obliczenia<\/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>Zostaw komentarz<\/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=\"2542\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Jak oceniasz ten wynik?<\/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\">Lubi\u0119 to <\/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\">Pomocne <\/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\">Niejasne <\/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\">Rozczarowanie <\/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\">Niedok\u0142adne <\/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>Wz\u00f3r prawa Avogadra<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Wz\u00f3r<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\frac{V_1}{n_1} = \\frac{V_2}{n_2} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(V_1\\), \\(V_2\\) \u2014 pocz\u0105tkowa i ko\u0144cowa obj\u0119to\u015b\u0107 gazu<\/li>\n<li>\\(n_1\\), \\(n_2\\) \u2014 pocz\u0105tkowa i ko\u0144cowa ilo\u015b\u0107 gazu (mole)<\/li>\n<\/ul>\n<p>Wz\u00f3r m\u00f3wi, \u017ce przy sta\u0142ej temperaturze i ci\u015bnieniu obj\u0119to\u015b\u0107 gazu jest wprost proporcjonalna do liczby moli. Po przekszta\u0142ceniu pozwala od razu wyznaczy\u0107 szukan\u0105 warto\u015b\u0107: \\(V_2 = V_1 \\cdot \\frac{n_2}{n_1}\\) albo \\(n_2 = n_1 \\cdot \\frac{V_2}{V_1}\\).<\/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>Prawo Avogadra \u2013 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> gaz w elastycznym zbiorniku przy sta\u0142ej temperaturze i ci\u015bnieniu zajmuje 2 l i zawiera 0,5 mola gazu. Dodajemy kolejny gaz, a\u017c pr\u00f3bka osi\u0105gnie 1,5 mola. Jaka b\u0119dzie nowa obj\u0119to\u015b\u0107?<\/p>\n<p>\\[ V_2 = V_1 \\cdot \\frac{n_2}{n_1} = 2\\ \\text{L} \\cdot \\frac{1.5\\ \\text{mol}}{0.5\\ \\text{mol}} = 6\\ \\text{L} \\]<\/p>\n<p><strong>Wynik:<\/strong> ko\u0144cowa obj\u0119to\u015b\u0107 wynosi 6 l. Potrojenie ilo\u015bci gazu (z 0,5 do 1,5 mola) potraja obj\u0119to\u015b\u0107 \u2014 dok\u0142adnie tak, jak przewiduje prawo Avogadra.<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Otw\u00f3rz list\u0119 rozwijan\u0105 <strong>Szukana warto\u015b\u0107<\/strong> i wybierz, czy chcesz obliczy\u0107 <strong>obj\u0119to\u015b\u0107 ko\u0144cow\u0105 (V\u2082)<\/strong>, czy <strong>ilo\u015b\u0107 ko\u0144cow\u0105 (n\u2082)<\/strong>. Pojawi si\u0119 pole dla warto\u015bci, kt\u00f3r\u0105 ju\u017c znasz; drugie zostanie ukryte.<\/li>\n<li>Wpisz <strong>obj\u0119to\u015b\u0107 pocz\u0105tkow\u0105 (V\u2081)<\/strong> i wybierz jej jednostk\u0119 (l, ml, cm\u00b3, m\u00b3, ft\u00b3 lub galony ameryka\u0144skie).<\/li>\n<li>Wpisz <strong>ilo\u015b\u0107 pocz\u0105tkow\u0105 (n\u2081)<\/strong> w molach, mmol lub kmol.<\/li>\n<li>Podaj znan\u0105 warto\u015b\u0107 ko\u0144cow\u0105: <strong>ilo\u015b\u0107 ko\u0144cow\u0105 (n\u2082)<\/strong>, je\u015bli obliczasz obj\u0119to\u015b\u0107, albo <strong>obj\u0119to\u015b\u0107 ko\u0144cow\u0105 (V\u2082)<\/strong> wraz z jednostk\u0105, je\u015bli obliczasz ilo\u015b\u0107.<\/li>\n<li>Odczytaj wynik, obliczenia krok po kroku oraz sprawdzenie, \u017ce \\(V_1\/n_1 = V_2\/n_2\\).<\/li>\n<\/ol>\n<p>Wszystkie przeliczenia jednostek odbywaj\u0105 si\u0119 automatycznie \u2014 mo\u017cesz poda\u0107 V\u2081 w litrach, a V\u2082 w stopach sze\u015bciennych, a wynik dla n\u2082 otrzymasz w jednostce wybranej dla n\u2081.<\/p>\n<h2>Czym jest prawo Avogadra?<\/h2>\n<p>Prawo Avogadra, sformu\u0142owane przez Amadeusza Avogadra w 1811 roku, m\u00f3wi, \u017ce <em>r\u00f3wne obj\u0119to\u015bci wszystkich gaz\u00f3w w tej samej temperaturze i pod tym samym ci\u015bnieniem zawieraj\u0105 t\u0119 sam\u0105 liczb\u0119 cz\u0105steczek<\/em>. R\u00f3wnowa\u017cnie: obj\u0119to\u015b\u0107 pr\u00f3bki gazu jest wprost proporcjonalna do jego ilo\u015bci (w molach), o ile temperatura i ci\u015bnienie pozostaj\u0105 sta\u0142e. Podwojenie liczby moli gazu podwaja obj\u0119to\u015b\u0107; odj\u0119cie po\u0142owy gazu zmniejsza obj\u0119to\u015b\u0107 o po\u0142ow\u0119.<\/p>\n<p>Jest to jedno z fundamentalnych praw wi\u0105\u017c\u0105cych si\u0119 z r\u00f3wnaniem <em>gazu idealnego<\/em>, \\(PV = nRT\\). Je\u015bli ci\u015bnienie \\(P\\) i temperatura \\(T\\) s\u0105 sta\u0142e, po przekszta\u0142ceniu wzgl\u0119dem \\(V\\) otrzymujemy \\(V = \\frac{nRT}{P}\\), a zatem \\(V\/n = \\text{sta\u0142a}\\). Prawo Avogadra to po prostu por\u00f3wnanie tego stosunku mi\u0119dzy dwoma stanami tego samego gazu w tych samych warunkach.<\/p>\n<p>Praktyczn\u0105 konsekwencj\u0105 jest <strong>obj\u0119to\u015b\u0107 molowa<\/strong>: jeden mol dowolnego gazu idealnego zajmuje przy danej temperaturze i ci\u015bnieniu t\u0119 sam\u0105 obj\u0119to\u015b\u0107. W warunkach normalnych (0 \u00b0C, 1 atm) wynosi ona 22,414 l, a w 25 \u00b0C przy 1 barze \u2014 24,789 l. Dzi\u0119ki temu mo\u017cna przelicza\u0107 obj\u0119to\u015bci gaz\u00f3w na mole bez wa\u017cenia gazu \u2014 to rutynowy krok w obliczeniach stechiometrycznych, przy zbieraniu gaz\u00f3w nad wod\u0105 i w przemys\u0142owych pomiarach gaz\u00f3w.<\/p>\n<p>Interpretuj\u0105c wynik, pami\u0119taj, \u017ce proporcjonalno\u015b\u0107 dzia\u0142a w obie strony: je\u015bli kalkulator poka\u017ce, \u017ce \\(n_2\\) jest trzykrotnie wi\u0119ksze od \\(n_1\\), obj\u0119to\u015b\u0107 r\u00f3wnie\u017c zmieni\u0142a si\u0119 trzykrotnie. Je\u015bli obliczona obj\u0119to\u015b\u0107 molowa \\(V\/n\\) odbiega od 22\u201325 l\/mol w warunkach zbli\u017conych do warunk\u00f3w otoczenia, sprawd\u017a wpisane dane \u2014 mo\u017ce to sygnalizowa\u0107 b\u0142\u0105d jednostki lub miejsca dziesi\u0119tnego.<\/p>\n<h2>Warto\u015bci odniesienia<\/h2>\n<table>\n<thead>\n<tr>\n<th>Warunki<\/th>\n<th>Obj\u0119to\u015b\u0107 molowa gazu idealnego<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0 \u00b0C, 1 atm (STP)<\/td>\n<td>22,414 l\/mol<\/td>\n<\/tr>\n<tr>\n<td>25 \u00b0C, 1 atm<\/td>\n<td>24,465 l\/mol<\/td>\n<\/tr>\n<tr>\n<td>25 \u00b0C, 1 bar (SATP)<\/td>\n<td>24,789 l\/mol<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Za\u0142o\u017cenia, ograniczenia i wskaz\u00f3wki<\/h2>\n<ul>\n<li><strong>Zachowanie gazu idealnego.<\/strong> Prawo Avogadra zak\u0142ada, \u017ce cz\u0105steczki gazu maj\u0105 pomijaln\u0105 obj\u0119to\u015b\u0107 i nie oddzia\u0142uj\u0105 ze sob\u0105. Gazy rzeczywiste spe\u0142niaj\u0105 je dobrze przy niskim ci\u015bnieniu i temperaturach znacznie wy\u017cszych od temperatury wrzenia, natomiast odbiegaj\u0105 od niego przy wysokim ci\u015bnieniu lub blisko punktu skraplania. Dla gaz\u00f3w g\u0119stych dok\u0142adniejszy opis daje <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-rownania-van-der-waalsa\/\">kalkulator r\u00f3wnania van der Waalsa<\/a>.<\/li>\n<li><strong>Sta\u0142a temperatura i ci\u015bnienie.<\/strong> Prawo obowi\u0105zuje tylko wtedy, gdy zar\u00f3wno \\(T\\), jak i \\(P\\) s\u0105 takie same przed i po zmianie. Typowym uk\u0142adem jest elastyczny zbiornik (t\u0142ok lub balon) otwarty na sta\u0142e ci\u015bnienie zewn\u0119trzne. Je\u015bli zmienia si\u0119 tak\u017ce temperatura, u\u017cyj zamiast tego r\u00f3wnania po\u0142\u0105czonego albo r\u00f3wnania gazu idealnego.<\/li>\n<li><strong>Ilo\u015b\u0107 to tylko mole gazu.<\/strong> Dodanie do zbiornika cieczy lub cia\u0142a sta\u0142ego nie zmienia \\(n\\); licz\u0105 si\u0119 wy\u0142\u0105cznie substancje gazowe. Gaz rozpuszczony, kt\u00f3ry wydziela si\u0119 z roztworu, ju\u017c tak.<\/li>\n<li><strong>Sp\u00f3jne jednostki.<\/strong> Poniewa\u017c prawo opiera si\u0119 na stosunku, \\(V_1\\) i \\(V_2\\) wystarczy poda\u0107 w tej samej jednostce, podobnie \\(n_1\\) i \\(n_2\\) \u2014 kalkulator zadba o to za ciebie, r\u00f3wnie\u017c przy jednostkach mieszanych.<\/li>\n<li><strong>Liczba cz\u0105steczek.<\/strong> Pomno\u017cenie ko\u0144cowej ilo\u015bci przez sta\u0142\u0105 Avogadro, \\(N_A = 6.02214076 \\times 10^{23}\\ \\text{mol}^{-1}\\), pokazuje, ile cz\u0105steczek zawiera ko\u0144cowa pr\u00f3bka \u2014 kalkulator podaje t\u0119 warto\u015b\u0107 automatycznie.<\/li>\n<\/ul>\n<p>Je\u015bli Twoje zadanie dotyczy por\u00f3wnywania szybko\u015bci dyfuzji dw\u00f3ch gaz\u00f3w, a nie zajmowanego przez nie miejsca, zajrzyj do <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-prawa-grahama\/\">kalkulatora prawa Grahama<\/a>. Z kolei dla reakcji, w kt\u00f3rych ilo\u015b\u0107 gazu zmienia si\u0119 w czasie, <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/okres-poltrwania-reakcji-kalkulator\/\">kalkulator okresu p\u00f3\u0142trwania reakcji<\/a> pomo\u017ce \u015bledzi\u0107 \\(n\\), zanim zastosujesz prawo Avogadra.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oblicz brakuj\u0105c\u0105 obj\u0119to\u015b\u0107 lub ilo\u015b\u0107 gazu z prawa Avogadra. Wpisz pocz\u0105tkow\u0105 obj\u0119to\u015b\u0107 i ilo\u015b\u0107 gazu, a tak\u017ce now\u0105 ilo\u015b\u0107 albo now\u0105 obj\u0119to\u015b\u0107 i otrzymaj wynik z pe\u0142nymi obliczeniami.<\/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":[4],"tags":[39],"class_list":["post-2542","post","type-post","status-publish","format-standard","hentry","category-chemia","tag-gazy"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2542","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/comments?post=2542"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2542\/revisions"}],"predecessor-version":[{"id":2774,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/2542\/revisions\/2774"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=2542"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=2542"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=2542"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}