{"id":1977,"date":"2026-10-07T06:37:19","date_gmt":"2026-10-07T05:37:19","guid":{"rendered":"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-clausiusa-clapeyrona\/"},"modified":"2026-10-07T06:37:19","modified_gmt":"2026-10-07T05:37:19","slug":"kalkulator-clausiusa-clapeyrona","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-clausiusa-clapeyrona\/","title":{"rendered":"Kalkulator r\u00f3wnania Clausiusa\u2013Clapeyrona"},"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\">Oszacowanie pr\u0119\u017cno\u015bci pary w nowej temperaturze<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"1977\" data-favorite-title=\"Clausius\u2013Clapeyron\" data-favorite-url=\"https:\/\/wpcalc.com\/pl\/chemia\/kalkulator-clausiusa-clapeyrona\/\" data-favorite-excerpt=\"Oszacuj pr\u0119\u017cno\u015b\u0107 par cieczy w dowolnej temperaturze na podstawie jednej znanej pary ci\u015bnienie\u2013temperatura oraz entalpii parowania, korzystaj\u0105c ze sca\u0142kowanego r\u00f3wnania Clausiusa\u2013Clapeyrona. Wprowad\u017a znane warunki, temperatur\u0119 docelow\u0105 i \u0394Hpar.\" aria-label=\"Dodaj do ulubionych\" 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\/pl\/chemia\/kalkulator-clausiusa-clapeyrona\/\" method=\"POST\" class=\"calculator\" id=\"calculator-1977\" data-post=\"1977\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Pola danych<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Znana pr\u0119\u017cno\u015b\u0107 pary (P\u2081)<\/label><div class=\"term\">P\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=\"znana_prno_pary_p\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 760\" min=\"0\" value=\"760\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"mmhg\" selected>mmHg<\/option><option value=\"kpa\">kPa<\/option><option value=\"atm\">atm<\/option><option value=\"pa\">Pa<\/option><option value=\"bar\">bar<\/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\">Pr\u0119\u017cno\u015b\u0107 pary cieczy w znanej temperaturze<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Znana temperatura (T\u2081)<\/label><div class=\"term\">T\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=\"number\" name=\"znana_temperatura_t\" id=\"field-3\" aria-describedby=\"calc-info-3\" placeholder=\"e.g. 100\" step=\"0.01\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><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-3\">Temperatura, w kt\u00f3rej zmierzono znan\u0105 pr\u0119\u017cno\u015b\u0107 pary<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Temperatura docelowa (T\u2082)<\/label><div class=\"term\">T\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=\"number\" name=\"temperatura_docelowa_t\" id=\"field-5\" aria-describedby=\"calc-info-5\" placeholder=\"e.g. 25\" step=\"0.01\" value=\"25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"jednostka\" aria-label=\"Jednostka\"><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-5\">Temperatura, w kt\u00f3rej chcesz oszacowa\u0107 pr\u0119\u017cno\u015b\u0107 pary<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-7\">Entalpia parowania (\u0394Hvap)<\/label><div class=\"term\">\u0394Hvap<\/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=\"entalpia_parowania_hvap\" id=\"field-7\" aria-describedby=\"calc-info-7\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 40.7\" min=\"0.0001\" value=\"40.7\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"jednostka\" aria-label=\"Jednostka\"><option value=\"kj_mol\" selected>kJ\/mol<\/option><option value=\"j_mol\">J\/mol<\/option><option value=\"kcal_mol\">kcal\/mol<\/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-7\">Ciep\u0142o potrzebne do odparowania jednego mola cieczy (40,7 kJ\/mol dla wody w pobli\u017cu punktu wrzenia)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Przelicz ponownie\" id=\"calculate-button\" data-post=\"1977\">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 pr\u0119\u017cno\u015bci pary<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Pr\u0119\u017cno\u015b\u0107 pary w T\u2082 (w jednostce P\u2081)<\/span><span class=\"result-term\">P\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>Pr\u0119\u017cno\u015b\u0107 pary w T\u2082<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"kPa\"><\/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-3\"><span class=\"field-title\"><span>Pr\u0119\u017cno\u015b\u0107 pary w T\u2082<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"atm\"><\/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-4\"><span class=\"field-title\"><span>Pr\u0119\u017cno\u015b\u0107 pary w T\u2082<\/span><\/span><span class=\"field-value\" id=\"result-4\" data-unit=\"mmHg\"><\/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=\"1977\" 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 Clausiusa\u2013Clapeyrona<\/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\\[ \\ln\\!\\left(\\frac{P_2}{P_1}\\right) = -\\frac{\\Delta H_{vap}}{R}\\left(\\frac{1}{T_2} - \\frac{1}{T_1}\\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Gdzie:<\/strong><\/p>\n<ul>\n<li>\\(P_1\\) \u2014 pr\u0119\u017cno\u015b\u0107 par w znanej temperaturze (dowolna jednostka ci\u015bnienia)<\/li>\n<li>\\(P_2\\) \u2014 pr\u0119\u017cno\u015b\u0107 par w temperaturze docelowej (ta sama jednostka co \\(P_1\\))<\/li>\n<li>\\(T_1\\) \u2014 znana temperatura (w kelwinach)<\/li>\n<li>\\(T_2\\) \u2014 temperatura docelowa (w kelwinach)<\/li>\n<li>\\(\\Delta H_{vap}\\) \u2014 entalpia parowania (J\/mol)<\/li>\n<li>\\(R\\) \u2014 sta\u0142a gazowa, \\(8.314\\ \\text{J\/(mol\u00b7K)}\\)<\/li>\n<\/ul>\n<p>Jest to sca\u0142kowana posta\u0107 r\u00f3wnania Clausiusa\u2013Clapeyrona. Zak\u0142ada, \u017ce para zachowuje si\u0119 jak gaz doskona\u0142y, a entalpia parowania jest sta\u0142a w ca\u0142ym zakresie temperatur, i pozwala przewidzie\u0107, jak pr\u0119\u017cno\u015b\u0107 par zmienia si\u0119 wyk\u0142adniczo wraz z temperatur\u0105.<\/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>Clausius\u2013Clapeyron \u2014 przyk\u0142ad obliczenia<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Przyk\u0142ad:<\/strong> woda wrze w 100 \u00b0C przy ci\u015bnieniu 760 mmHg (1 atm). Oszacuj pr\u0119\u017cno\u015b\u0107 par wody w 25 \u00b0C, przyjmuj\u0105c \\(\\Delta H_{vap} = 40.7\\ \\text{kJ\/mol}\\).<\/p>\n<p>Zamie\u0144 temperatury na kelwiny: \\(T_1 = 373.15\\ \\text{K}\\), \\(T_2 = 298.15\\ \\text{K}\\) oraz \\(\\Delta H_{vap} = 40\\,700\\ \\text{J\/mol}\\).<\/p>\n<p>\\[ \\ln\\!\\left(\\frac{P_2}{760}\\right) = -\\frac{40\\,700}{8.314}\\left(\\frac{1}{298.15} - \\frac{1}{373.15}\\right) = -4894.9 \\times 0.000674 = -3.300 \\]<\/p>\n<p>\\[ P_2 = 760 \\times e^{-3.300} \\]<\/p>\n<p><strong>Wynik:<\/strong> \\(P_2 \\approx 28.04\\ \\text{mmHg}\\), czyli oko\u0142o 3,74 kPa lub 0,0369 atm. (Zmierzona warto\u015b\u0107 to 23,76 mmHg \u2014 r\u00f3\u017cnica wynika z tego, \u017ce \u0394Hpar nie jest w pe\u0142ni sta\u0142a; patrz uwagi poni\u017cej.)<\/p>\n<p>\n\r\n<\/section>\n<h2>Jak korzysta\u0107 z kalkulatora<\/h2>\n<ol>\n<li>Wprowad\u017a <strong>znan\u0105 pr\u0119\u017cno\u015b\u0107 par (P\u2081)<\/strong> cieczy i wybierz jej jednostk\u0119 (mmHg, kPa, atm, Pa lub bar). Dobrze sprawdza si\u0119 tu temperatura wrzenia przy znanym ci\u015bnieniu.<\/li>\n<li>Wprowad\u017a <strong>znan\u0105 temperatur\u0119 (T\u2081)<\/strong>, przy kt\u00f3rej zmierzono to ci\u015bnienie, w \u00b0C, K lub \u00b0F.<\/li>\n<li>Wprowad\u017a <strong>temperatur\u0119 docelow\u0105 (T\u2082)<\/strong>, dla kt\u00f3rej chcesz oszacowa\u0107 pr\u0119\u017cno\u015b\u0107 par, w dowolnej z tych samych jednostek temperatury.<\/li>\n<li>Wprowad\u017a <strong>entalpi\u0119 parowania (\u0394Hpar)<\/strong> i wybierz kJ\/mol, J\/mol lub kcal\/mol. Warto\u015b\u0107 t\u0119 podaj\u0105 tabele dla typowych cieczy.<\/li>\n<li>Odczytaj wyniki: szacowana pr\u0119\u017cno\u015b\u0107 par w temperaturze T\u2082 jest wy\u015bwietlana w wybranej jednostce ci\u015bnienia, wraz z przeliczeniami na kPa, atm i mmHg.<\/li>\n<\/ol>\n<h2>Co to jest r\u00f3wnanie Clausiusa\u2013Clapeyrona?<\/h2>\n<p>R\u00f3wnanie Clausiusa\u2013Clapeyrona opisuje zale\u017cno\u015b\u0107 mi\u0119dzy pr\u0119\u017cno\u015bci\u0105 par cieczy a temperatur\u0105. Pr\u0119\u017cno\u015b\u0107 par ro\u015bnie gwa\u0142townie wraz z temperatur\u0105, poniewa\u017c wi\u0119cej cz\u0105steczek ma wystarczaj\u0105c\u0105 energi\u0119, aby opu\u015bci\u0107 faz\u0119 ciek\u0142\u0105. R\u00f3wnanie to ujmuje rzecz ilo\u015bciowo: wykres \\(\\ln P\\) w funkcji \\(1\/T\\) jest lini\u0105 prost\u0105 o wsp\u00f3\u0142czynniku kierunkowym \\(-\\Delta H_{vap}\/R\\). Ciecze o wysokiej entalpii parowania, takie jak woda, wykazuj\u0105 silniejsz\u0105 zale\u017cno\u015b\u0107 od temperatury ni\u017c ciecze lotne, np. aceton czy eter.<\/p>\n<p>Sca\u0142kowana posta\u0107 u\u017cywana w tym kalkulatorze wymaga tylko jednego punktu odniesienia \u2014 zwykle temperatury wrzenia \u2014 aby oszacowa\u0107 pr\u0119\u017cno\u015b\u0107 par w ka\u017cdej innej temperaturze. Jest to standardowa metoda \u201ena szybkiego\u201d w chemii i in\u017cynierii chemicznej do interpolacji, poniewa\u017c bezpo\u015brednie pomiary nie zawsze s\u0105 dost\u0119pne w interesuj\u0105cej nas temperaturze.<\/p>\n<p>Interpretacja wyniku jest prosta: je\u015bli \\(T_2  T_1\\), pr\u0119\u017cno\u015b\u0107 ro\u015bnie. Na przyk\u0142ad obliczenie powy\u017cej wyja\u015bnia, dlaczego woda paruje w temperaturze pokojowej, cho\u0107 wrze dopiero w 100 \u00b0C \u2014 jej pr\u0119\u017cno\u015b\u0107 par w 25 \u00b0C to nadal oko\u0142o 0,037 atm. Pr\u0119\u017cno\u015b\u0107 par decyduje te\u017c o wrzeniu: ciecz wrze, gdy jej pr\u0119\u017cno\u015b\u0107 par r\u00f3wna si\u0119 ci\u015bnieniu otoczenia, dlatego woda wrze poni\u017cej 100 \u00b0C na du\u017cych wysoko\u015bciach.<\/p>\n<p>Je\u015bli og\u00f3lnie zajmujesz si\u0119 problemami zwi\u0105zanymi z gazami, przydatne mog\u0105 by\u0107 r\u00f3wnie\u017c nasze kalkulatory <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/polaczone-prawo-gazowe\/\">po\u0142\u0105czonego prawa gazowego<\/a> i <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/prawo-daltona\/\">prawa Daltona<\/a>. Ta sama wyk\u0142adnicza zale\u017cno\u015b\u0107 od temperatury pojawia si\u0119 w kinetyce \u2014 zobacz kalkulator <a href=\"https:\/\/wpcalc.com\/pl\/chemia\/rownanie-arrheniusa-2\/\">r\u00f3wnania Arrheniusa<\/a>.<\/p>\n<h2>Za\u0142o\u017cenia, ograniczenia i wskaz\u00f3wki praktyczne<\/h2>\n<ul>\n<li><strong>Sta\u0142a \u0394Hpar.<\/strong> Entalpia parowania w rzeczywisto\u015bci maleje wraz z temperatur\u0105 i osi\u0105ga zero w punkcie krytycznym. Przy r\u00f3\u017cnicach 20\u201350 K b\u0142\u0105d jest zwykle ma\u0142y, ale przy setkach kelwin\u00f3w ro\u015bnie \u2014 przyk\u0142ad z wod\u0105 powy\u017cej zawy\u017ca wynik o oko\u0142o 18%, poniewa\u017c w rzeczywisto\u015bci \u0394Hpar wzrasta z 40,7 kJ\/mol przy 100 \u00b0C do oko\u0142o 44 kJ\/mol w pobli\u017cu 25 \u00b0C. Dla lepszej dok\u0142adno\u015bci u\u017cyj warto\u015bci \u0394Hpar zmierzonej blisko \u015brodka Twojego zakresu temperatur.<\/li>\n<li><strong>Para jako gaz doskona\u0142y.<\/strong> Wyprowadzenie pomija obj\u0119to\u015b\u0107 molow\u0105 cieczy i zak\u0142ada, \u017ce para spe\u0142nia prawa gaz\u00f3w doskona\u0142ych. Jest to bardzo dobre przybli\u017cenie przy niskich ci\u015bnieniach (poni\u017cej kilku atmosfer).<\/li>\n<li><strong>Tylko dla r\u00f3wnowagi para\u2013ciecz.<\/strong> R\u00f3wnanie dotyczy substancji czystej. Nie opisuje roztwor\u00f3w, gdzie potrzebne jest prawo Raoulta lub wsp\u00f3\u0142czynniki aktywno\u015bci, i nie nale\u017cy nim ekstrapolowa\u0107 powy\u017cej temperatury krytycznej.<\/li>\n<li><strong>Wybierz wiarygodny punkt odniesienia.<\/strong> Dobrym punktem odniesienia jest normalna temperatura wrzenia (1 atm) z podr\u0119cznika; r\u00f3wnie dobrze sprawdzi si\u0119 dowolna tablicowana warto\u015b\u0107 pr\u0119\u017cno\u015bci par.<\/li>\n<li><strong>Uwa\u017caj na jednostki.<\/strong> W samej metodzie temperatura musi by\u0107 wyra\u017cona w kelwinach; kalkulator przelicza za Ciebie \u00b0C i \u00b0F. Zachowaj sp\u00f3jno\u015b\u0107 \u0394Hpar i R \u2014 kalkulator sam dokonuje wewn\u0119trznie przeliczenia na J\/mol.<\/li>\n<\/ul>\n<p>Dla przypomnienia, entalpie parowania w normalnej temperaturze wrzenia obejmuj\u0105 m.in.: wod\u0119 (40,7 kJ\/mol), etanol (38,6 kJ\/mol), metanol (35,2 kJ\/mol), aceton (29,1 kJ\/mol) i benzen (30,8 kJ\/mol).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Oszacuj pr\u0119\u017cno\u015b\u0107 par cieczy w dowolnej temperaturze na podstawie jednej znanej pary ci\u015bnienie\u2013temperatura oraz entalpii parowania, korzystaj\u0105c ze sca\u0142kowanego r\u00f3wnania Clausiusa\u2013Clapeyrona. Wprowad\u017a znane warunki, temperatur\u0119 docelow\u0105 i \u0394Hpar.<\/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":[63],"class_list":["post-1977","post","type-post","status-publish","format-standard","hentry","category-chemia","tag-reakcje"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/1977","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=1977"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/1977\/revisions"}],"predecessor-version":[{"id":2053,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/posts\/1977\/revisions\/2053"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/media?parent=1977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/categories?post=1977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/pl\/wp-json\/wp\/v2\/tags?post=1977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}