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Idealni rastvor - Wikipedia
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id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Početak</div> </a> </li> <li id="toc-Fizičko_porijeklo" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Fizičko_porijeklo"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Fizičko porijeklo</span> </div> </a> <ul id="toc-Fizičko_porijeklo-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Formalna_definicija" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Formalna_definicija"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Formalna definicija</span> </div> </a> <ul id="toc-Formalna_definicija-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Termodinamička_svojstva" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Termodinamička_svojstva"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Termodinamička svojstva</span> </div> </a> <button aria-controls="toc-Termodinamička_svojstva-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Uključi/isključi podsekciju Termodinamička svojstva</span> </button> <ul id="toc-Termodinamička_svojstva-sublist" class="vector-toc-list"> <li id="toc-Zapremina" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zapremina"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Zapremina</span> </div> </a> <ul id="toc-Zapremina-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Entalpija_i_toplotni_kapacitet" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Entalpija_i_toplotni_kapacitet"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Entalpija i toplotni kapacitet</span> </div> </a> <ul id="toc-Entalpija_i_toplotni_kapacitet-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Entropija_smjesa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Entropija_smjesa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.3</span> <span>Entropija smjesa</span> </div> </a> <ul id="toc-Entropija_smjesa-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Posljedice" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Posljedice"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Posljedice</span> </div> </a> <ul id="toc-Posljedice-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Neidealnost" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Neidealnost"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Neidealnost</span> </div> </a> <ul id="toc-Neidealnost-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Također_pogledajte" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Također_pogledajte"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Također pogledajte</span> </div> </a> <ul id="toc-Također_pogledajte-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Reference" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Reference"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Reference</span> </div> </a> <ul id="toc-Reference-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Sadržaj" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Uključi/isključi sadržaj" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Uključi/isključi sadržaj</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Idealni rastvor</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Idi na članak na drugom jeziku. Dostupno na 22 jezika" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-22" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">22 jezika</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D8%AD%D9%84%D9%88%D9%84_%D9%85%D8%AB%D8%A7%D9%84%D9%8A" title="محلول مثالي – arapski" lang="ar" hreflang="ar" data-title="محلول مثالي" data-language-autonym="العربية" data-language-local-name="arapski" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Dissoluci%C3%B3_ideal" title="Dissolució ideal – katalonski" lang="ca" hreflang="ca" data-title="Dissolució ideal" data-language-autonym="Català" data-language-local-name="katalonski" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%98%D0%B4%D0%B5%D0%B0%D0%BB%D0%BB%D0%B0_%D0%B8%D1%80%C4%95%D0%BB%D1%87%C4%95%D0%BA" title="Идеалла ирĕлчĕк – čuvaški" lang="cv" hreflang="cv" data-title="Идеалла ирĕлчĕк" data-language-autonym="Чӑвашла" data-language-local-name="čuvaški" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Ideale_L%C3%B6sung" title="Ideale Lösung – njemački" lang="de" hreflang="de" data-title="Ideale Lösung" data-language-autonym="Deutsch" data-language-local-name="njemački" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Ideal_solution" title="Ideal solution – engleski" lang="en" hreflang="en" data-title="Ideal solution" data-language-autonym="English" data-language-local-name="engleski" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Mezcla_ideal" title="Mezcla ideal – španski" lang="es" hreflang="es" data-title="Mezcla ideal" data-language-autonym="Español" data-language-local-name="španski" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C3%B5eline_lahus" title="Tõeline lahus – estonski" lang="et" hreflang="et" data-title="Tõeline lahus" data-language-autonym="Eesti" data-language-local-name="estonski" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%85%D8%AD%D9%84%D9%88%D9%84_%D8%A7%DB%8C%D8%AF%D9%87%E2%80%8C%D8%A2%D9%84" title="محلول ایدهآل – perzijski" lang="fa" hreflang="fa" data-title="محلول ایدهآل" data-language-autonym="فارسی" data-language-local-name="perzijski" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Ideaaliseos" title="Ideaaliseos – finski" lang="fi" hreflang="fi" data-title="Ideaaliseos" data-language-autonym="Suomi" data-language-local-name="finski" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Solution_id%C3%A9ale" title="Solution idéale – francuski" lang="fr" hreflang="fr" data-title="Solution idéale" data-language-autonym="Français" data-language-local-name="francuski" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Ide%C3%A1lis_oldat" title="Ideális oldat – mađarski" lang="hu" hreflang="hu" data-title="Ideális oldat" data-language-autonym="Magyar" data-language-local-name="mađarski" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Larutan_ideal" title="Larutan ideal – indonezijski" lang="id" hreflang="id" data-title="Larutan ideal" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonezijski" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Soluzione_ideale" title="Soluzione ideale – italijanski" lang="it" hreflang="it" data-title="Soluzione ideale" data-language-autonym="Italiano" data-language-local-name="italijanski" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E7%90%86%E6%83%B3%E6%BA%B6%E6%B6%B2" title="理想溶液 – japanski" lang="ja" hreflang="ja" data-title="理想溶液" data-language-autonym="日本語" data-language-local-name="japanski" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%9D%B4%EC%83%81_%EC%9A%A9%EC%95%A1" title="이상 용액 – korejski" lang="ko" hreflang="ko" data-title="이상 용액" data-language-autonym="한국어" data-language-local-name="korejski" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Ideale_oplossing" title="Ideale oplossing – nizozemski" lang="nl" hreflang="nl" data-title="Ideale oplossing" data-language-autonym="Nederlands" data-language-local-name="nizozemski" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Roztw%C3%B3r_doskona%C5%82y" title="Roztwór doskonały – poljski" lang="pl" hreflang="pl" data-title="Roztwór doskonały" data-language-autonym="Polski" data-language-local-name="poljski" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Solu%C3%A7%C3%A3o_ideal" title="Solução ideal – portugalski" lang="pt" hreflang="pt" data-title="Solução ideal" data-language-autonym="Português" data-language-local-name="portugalski" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%98%D0%B4%D0%B5%D0%B0%D0%BB%D1%8C%D0%BD%D1%8B%D0%B9_%D1%80%D0%B0%D1%81%D1%82%D0%B2%D0%BE%D1%80" title="Идеальный раствор – ruski" lang="ru" hreflang="ru" data-title="Идеальный раствор" data-language-autonym="Русский" data-language-local-name="ruski" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Idealna_raztopina" title="Idealna raztopina – slovenski" lang="sl" hreflang="sl" data-title="Idealna raztopina" data-language-autonym="Slovenščina" data-language-local-name="slovenski" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%86%D0%B4%D0%B5%D0%B0%D0%BB%D1%8C%D0%BD%D0%B8%D0%B9_%D1%80%D0%BE%D0%B7%D1%87%D0%B8%D0%BD" title="Ідеальний розчин – ukrajinski" lang="uk" hreflang="uk" data-title="Ідеальний розчин" 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Wikipedije, slobodne enciklopedije</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="bs" dir="ltr"><figure typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Solution_Plot_Figure.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Solution_Plot_Figure.jpg/250px-Solution_Plot_Figure.jpg" decoding="async" width="250" height="191" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Solution_Plot_Figure.jpg/375px-Solution_Plot_Figure.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Solution_Plot_Figure.jpg/500px-Solution_Plot_Figure.jpg 2x" data-file-width="651" data-file-height="497" /></a><figcaption>Grafikon rastvaranja prema obrascu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \displaystyle y_{h}(x)=e^{-2x}[cos(3x)+{\frac {2}{3}}sin(3x)]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>h</mi> </mrow> </msub> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>2</mn> <mi>x</mi> </mrow> </msup> <mo stretchy="false">[</mo> <mi>c</mi> <mi>o</mi> <mi>s</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mrow> <mi>s</mi> <mi>i</mi> <mi>n</mi> <mo stretchy="false">(</mo> <mn>3</mn> <mi>x</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> </mstyle> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \displaystyle y_{h}(x)=e^{-2x}[cos(3x)+{\frac {2}{3}}sin(3x)]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/30c259bcf4d9c775965718e867882693d22dde02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:34.16ex; height:5.176ex;" alt="{\displaystyle \displaystyle y_{h}(x)=e^{-2x}[cos(3x)+{\frac {2}{3}}sin(3x)]}"></span></figcaption></figure> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Datoteka:Raoultov_zakon.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Raoultov_zakon.png/220px-Raoultov_zakon.png" decoding="async" width="220" height="200" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/47/Raoultov_zakon.png/330px-Raoultov_zakon.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/47/Raoultov_zakon.png/440px-Raoultov_zakon.png 2x" data-file-width="591" data-file-height="537" /></a><figcaption>Odnos parcijalnih i ukupnog pritiska idealnog rastvora komponenata A i B.</figcaption></figure> <p><b>Idealni rastvor</b> ili <b>idealna smjesa</b> – u <a href="/wiki/Hemija" title="Hemija">hemiji</a> – je <a href="/wiki/Rastvor" title="Rastvor">rastvor</a> u kojem plinska faza pokazuje termodinamička svojstva analogna svojstvima smjese <a href="/wiki/Idealni_plin" title="Idealni plin">idealnog plina</a>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> <a href="/wiki/Entalpija_mije%C5%A1anja" title="Entalpija miješanja">Entalpija miješanja</a> je nula <sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> kao što je promjena zapremine miješanjem po definiciji: što je entalpija miješanja bliža nuli, to je ponašanje rastvora "idealnije". Pritisak pare u rastvoru slijedi ili <a href="/w/index.php?title=Raoultov_zakon&action=edit&redlink=1" class="new" title="Raoultov zakon (stranica ne postoji)">Raoultov zakon</a> ili <a href="/w/index.php?title=Henryjev_zakon&action=edit&redlink=1" class="new" title="Henryjev zakon (stranica ne postoji)">Henryjev zakon</a> (ili oba)<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>, a <a href="/w/index.php?title=Koeficijent_aktivnosti&action=edit&redlink=1" class="new" title="Koeficijent aktivnosti (stranica ne postoji)">koeficijent aktivnosti</a> svake komponente (koja mjeri odstupanje od idealnosti) jednak je jedinici.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Koncept idealnog rastvora je osnovni za <a href="/w/index.php?title=Hemijska_termodinamika&action=edit&redlink=1" class="new" title="Hemijska termodinamika (stranica ne postoji)">hemijsku termodinamiku</a> i njenu primjenu, kao što je upotreba <a href="/w/index.php?title=Koligativna_svojstva&action=edit&redlink=1" class="new" title="Koligativna svojstva (stranica ne postoji)">koligativih svojstava</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Fizičko_porijeklo"><span id="Fizi.C4.8Dko_porijeklo"></span>Fizičko porijeklo</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=1" title="Uredi odlomak "Fizičko porijeklo"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=1" title="Edit section's source code: Fizičko porijeklo"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Idealnost rastvora analogna je <a href="/wiki/Idealni_plin" title="Idealni plin">idealnosti plinova</a>, s važnom razlikom što su intermolekulske interakcije u tekućinama jake i ne mogu se jednostavno zanemariti, kao što je to slučaj kod idealnih plinova. Umjesto toga, pretpostavlja se da je srednja snaga <a href="/w/index.php?title=Intermolekularne_sile&action=edit&redlink=1" class="new" title="Intermolekularne sile (stranica ne postoji)">interakcije</a> jednake između svih molekula rastvora. </p><p>Formalnije, za kombinaciju molekula A i B, interakcije između njih, za razliku od susjeda (U<sub>AB</sub>) i sličnih susjeda U<sub>AA</sub> i U<sub>BB</sub> moraju biti iste prosječne jačine, tj. 2 U<sub>AB</sub> = U<sub>AA</sub> + U<sub>BB</sub> i interakcije dužeg dometa moraju biti nula (ili barem nerazlučive). Ako su molekulske sile iste između AA, AB i BB, tj. U<sub>AB</sub> = U<sub>AA</sub> = U<sub>BB</sub>, tada je rastvor automatski idealan. </p><p>Ako su molekule hemijski gotovo identične, npr. <a href="/wiki/N-butanol" class="mw-redirect" title="N-butanol">1-butanol</a> i <a href="/w/index.php?title=2-butanol&action=edit&redlink=1" class="new" title="2-butanol (stranica ne postoji)">2-butanol</a>, tada će rastvor biti gotovo idealan. Budući da su energije interakcije između A i B gotovo jednake, proizlazi da dolazi do vrlo male ukupne promjene energije (entalpije) kada se supstance miješaju. Što je priroda A i B različitija, to se očekuje da rastvor snažnije odstupa od idealnosti. </p> <div class="mw-heading mw-heading2"><h2 id="Formalna_definicija">Formalna definicija</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=2" title="Uredi odlomak "Formalna definicija"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=2" title="Edit section's source code: Formalna definicija"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Predložene su različite povezane definicije idealnog rastvora. Najjednostavnija definicija je da je idealni rastvor onaj kojem se svaka komponenta (i), za sve kompozicije, ponaša sukladno <a href="/w/index.php?title=Raoultov_zakon&action=edit&redlink=1" class="new" title="Raoultov zakon (stranica ne postoji)">Raoultovom zakonu</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}=x_{i}p_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}=x_{i}p_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77c8ce2e0ddf54bab0488920e31e544ef263d61e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:9.51ex; height:2.843ex;" alt="{\displaystyle p_{i}=x_{i}p_{i}^{*}}"></span> Tako <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bab39399bf5424f25d957cdc57c84a0622626d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.059ex; height:2.009ex;" alt="{\displaystyle p_{i}}"></span> je <a href="/w/index.php?title=Pritisak_pare&action=edit&redlink=1" class="new" title="Pritisak pare (stranica ne postoji)">pritisak pare</a> komponente i iznad rastvora, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"></span> je njegova <a href="/w/index.php?title=Molska_frakcija&action=edit&redlink=1" class="new" title="Molska frakcija (stranica ne postoji)">molska frakcija</a> i <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7a639fd7524a9d84c54a8f64a64afcdfa348eec4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; margin-left: -0.089ex; width:2.313ex; height:2.843ex;" alt="{\displaystyle p_{i}^{*}}"></span> je pritisak pare čiste supstance i, na istoj temperaturi.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p><p>Ova definicija ovisi o pritisku pare, koji je izravno mjerljivo svojstvo, barem za hlapljive komponente. Termodinamička svojstva se tada mogu dobiti iz <a href="/w/index.php?title=Hemijski_potencijal&action=edit&redlink=1" class="new" title="Hemijski potencijal (stranica ne postoji)">hemijskog potencijala</a> μ (ili <a href="/w/index.php?title=Parcijalno_molarno_svojstvo&action=edit&redlink=1" class="new" title="Parcijalno molarno svojstvo (stranica ne postoji)">delimične molarnosti</a> <a href="/wiki/Gibbsova_energija" class="mw-redirect" title="Gibbsova energija">Gibbsove energije</a> g) svake komponente, za koju se pretpostavlja da je data idealnim formulom idealnog plina </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (T,p_{i})=g(T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}}{p^{u}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ<!-- μ --></mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu (T,p_{i})=g(T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}}{p^{u}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cdbbe8771b40d5fee993e979c128721f06f159d1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.83ex; height:5.343ex;" alt="{\displaystyle \mu (T,p_{i})=g(T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}}{p^{u}}}}"></span>.</dd></dl> <p>Referentni pritisak <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p^{u}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{u}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2d977c5fbb8474380c7ea8f706e5178595a7b5e3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.431ex; height:2.676ex;" alt="{\displaystyle p^{u}}"></span> može biti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P^{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P^{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c3105fe6c995cfd258bdbb31e05fb67f3aaec3a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.876ex; height:2.676ex;" alt="{\displaystyle P^{0}}"></span> = 1 bar, ili kao pritisak smjese, radi olakšavanja rada. Supstitucijom vrijednosti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5bab39399bf5424f25d957cdc57c84a0622626d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.059ex; height:2.009ex;" alt="{\displaystyle p_{i}}"></span> Raoultovog zakona, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ<!-- μ --></mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msub> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>μ<!-- μ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu (T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/712ae0207aa2a61ab3689d0bbb9af5924c2efc28" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:59.888ex; height:6.009ex;" alt="{\displaystyle \mu (T,p_{i})=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {p_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}"></span>.</dd></dl> <p>Ova jednadžba za hemijski potencijal može se koristiti kao alternativna definicija za idealni rastvor. </p><p>Međutim, para iznad rastvora možda se zapravo ne ponaša kao mješavina idealnih plinova. Neki autori stoga definiraju idealni rastvor za koji se svaka komponenta ponaša analogno fugabilnosti Raoultovog zakona <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{i}=x_{i}f_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msubsup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{i}=x_{i}f_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1132038d5334ed40a1a094e4f2e74ef79bc4df6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:9.541ex; height:2.843ex;" alt="{\displaystyle f_{i}=x_{i}f_{i}^{*}}"></span>, </p><p>Ovdje je <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65da883ca3d16b461e46c94777b0d9c4aa010e79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.939ex; height:2.509ex;" alt="{\displaystyle f_{i}}"></span> komponenta <a href="/w/index.php?title=Fugasnost&action=edit&redlink=1" class="new" title="Fugasnost (stranica ne postoji)">fugasnosti</a> komponente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> u rastvoru I <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle f_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ed4795cb8f8175b2b7a0f450d98990fe1d46fcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.375ex; height:2.843ex;" alt="{\displaystyle f_{i}^{*}}"></span> je fugasnost <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> kao čiste supstance.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup> Budući da je fugabilnost definirana jednadžbom </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu (T,P)=g(T,P)=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {f_{i}}{p^{u}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>μ<!-- μ --></mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>=</mo> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">u</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> <mo stretchy="false">)</mo> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu (T,P)=g(T,P)=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {f_{i}}{p^{u}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/592d98a477674b372cf44b1360ea6e4ba7628422" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:42.383ex; height:5.843ex;" alt="{\displaystyle \mu (T,P)=g(T,P)=g^{\mathrm {u} }(T,p^{u})+RT\ln {\frac {f_{i}}{p^{u}}}}"></span></dd></dl> <p>ova definicija dovodi do idealnih vrijednosti hemijskog potencijala i drugih termodinamičkih svojstava, čak i kada pare komponenata iznad otopine nisu idealni plinovi. Ekvivalentna odrednica koristi termodinamičku <a href="/w/index.php?title=Aktivnost_(hemija)&action=edit&redlink=1" class="new" title="Aktivnost (hemija) (stranica ne postoji)">aktivnost</a> umjesto fugasnosti<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Termodinamička_svojstva"><span id="Termodinami.C4.8Dka_svojstva"></span>Termodinamička svojstva</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=3" title="Uredi odlomak "Termodinamička svojstva"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=3" title="Edit section's source code: Termodinamička svojstva"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Zapremina">Zapremina</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=4" title="Uredi odlomak "Zapremina"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=4" title="Edit section's source code: Zapremina"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Ako razlikujemo ovu posljednju jednadžbu s obzirom na <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4dc73bf40314945ff376bd363916a738548d40a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.745ex; height:2.176ex;" alt="{\displaystyle P}"></span> na konstantu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span> , dobija se: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=RT\left({\frac {\partial \ln f}{\partial P}}\right)_{T}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mi>T</mi> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=RT\left({\frac {\partial \ln f}{\partial P}}\right)_{T}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c57b9515f8b46a70b4e5e0dab0c73d8d70c55e3f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.761ex; height:6.343ex;" alt="{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=RT\left({\frac {\partial \ln f}{\partial P}}\right)_{T}}"></span></dd></dl> <p>ali iz jednadžbe Gibbsovog potencijala zna se da je: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5c9e16cb1d613f1c7a3bddaf4659fba3abf773fb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.532ex; height:6.343ex;" alt="{\displaystyle \left({\frac {\partial g(T,P)}{\partial P}}\right)_{T}=v}"></span></dd></dl> <p>Ove dvije posljednje jednačine sastavljene daju: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \ln f}{\partial P}}\right)_{T}={\frac {v}{RT}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mi>f</mi> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>v</mi> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \ln f}{\partial P}}\right)_{T}={\frac {v}{RT}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf06570d0c413e2312a30da915a824f091f1a3ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:18.292ex; height:6.176ex;" alt="{\displaystyle \left({\frac {\partial \ln f}{\partial P}}\right)_{T}={\frac {v}{RT}}}"></span></dd></dl> <p>Budući da je sve ovo, učinjeno za čistu supstancu, vrijedi I u smjesi, uz dodavanje indeksa <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> za sve <a href="/w/index.php?title=Intenzivna_varijabla&action=edit&redlink=1" class="new" title="Intenzivna varijabla (stranica ne postoji)">intenzivne varijable</a> i izmjenom <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>v</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e07b00e7fc0847fbd16391c778d65bc25c452597" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.128ex; height:1.676ex;" alt="{\displaystyle v}"></span> u <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {v_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {v_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98487fe462ce101bf156023e16b0cecd54e8d5de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.927ex; height:2.343ex;" alt="{\displaystyle {\bar {v_{i}}}}"></span>, što znači <a href="/w/index.php?title=Parcijalna_molarna_zapremina&action=edit&redlink=1" class="new" title="Parcijalna molarna zapremina (stranica ne postoji)">parcijalna molarna zapremina</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial \ln f_{i}}{\partial P}}\right)_{T,x_{i}}={\frac {\bar {v_{i}}}{RT}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>P</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>T</mi> <mo>,</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial \ln f_{i}}{\partial P}}\right)_{T,x_{i}}={\frac {\bar {v_{i}}}{RT}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/040ab78c34780d0e21e38681b6679865efd624b7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:20.974ex; height:6.509ex;" alt="{\displaystyle \left({\frac {\partial \ln f_{i}}{\partial P}}\right)_{T,x_{i}}={\frac {\bar {v_{i}}}{RT}}}"></span></dd></dl> <p>Primjenom prve jednadžbe ovog odjeljka na ovu posljednju jednadžbu koju smo dobili </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle v_{i}^{*}={\bar {v_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle v_{i}^{*}={\bar {v_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c04ccbb7d9d455e25500cd4a1def2ea4ccfc315" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.208ex; height:2.843ex;" alt="{\displaystyle v_{i}^{*}={\bar {v_{i}}}}"></span></dd></dl> <p>što znači da ee u idealnoj smjesi volumen dobija dodavanje volumena njegovih komponenata: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle V=\sum V_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>V</mi> <mo>=</mo> <mo>∑<!-- ∑ --></mo> <msub> <mi>V</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle V=\sum V_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e066ecdbb8897057b852ec2cfaf0af7f8e72fba2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.783ex; height:3.843ex;" alt="{\displaystyle V=\sum V_{i}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Entalpija_i_toplotni_kapacitet">Entalpija i toplotni kapacitet</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=5" title="Uredi odlomak "Entalpija i toplotni kapacitet"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=5" title="Edit section's source code: Entalpija i toplotni kapacitet"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Postupajući na sličan način, ali izveden u odnosu na<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}"></span>, do sličnog rezultata dolazimo sa <a href="/wiki/Entalpija" title="Entalpija">entalpijom</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {g(T,P)-g^{\mathrm {gas} }(T,p^{u})}{RT}}=\ln {\frac {f}{p^{u}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>g</mi> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <mi>P</mi> <mo stretchy="false">)</mo> <mo>−<!-- − --></mo> <msup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msup> <mo stretchy="false">(</mo> <mi>T</mi> <mo>,</mo> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>R</mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>f</mi> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {g(T,P)-g^{\mathrm {gas} }(T,p^{u})}{RT}}=\ln {\frac {f}{p^{u}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59093f37b5e30645dd2979d9ed7b5ba334ec91e9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:30.084ex; height:6.176ex;" alt="{\displaystyle {\frac {g(T,P)-g^{\mathrm {gas} }(T,p^{u})}{RT}}=\ln {\frac {f}{p^{u}}}}"></span></dd></dl> <p>izvedenica s obzirom na T i pamćenje toga da je ona <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \left({\frac {\partial {\frac {g}{T}}}{\partial T}}\right)_{P}=-{\frac {h}{T^{2}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>g</mi> <mi>T</mi> </mfrac> </mrow> </mrow> <mrow> <mi mathvariant="normal">∂<!-- ∂ --></mi> <mi>T</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>P</mi> </mrow> </msub> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>h</mi> <msup> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left({\frac {\partial {\frac {g}{T}}}{\partial T}}\right)_{P}=-{\frac {h}{T^{2}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/61415e89ab77c44addaedb7d790b341f447174df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:17.812ex; height:7.676ex;" alt="{\displaystyle \left({\frac {\partial {\frac {g}{T}}}{\partial T}}\right)_{P}=-{\frac {h}{T^{2}}}}"></span> pa dobijamo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {{\bar {h_{i}}}-h_{i}^{\mathrm {gas} }}{R}}=-{\frac {h_{i}^{*}-h_{i}^{\mathrm {gas} }}{R}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>−<!-- − --></mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <mi>R</mi> </mfrac> </mrow> <mo>=</mo> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>−<!-- − --></mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> </mrow> <mi>R</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {{\bar {h_{i}}}-h_{i}^{\mathrm {gas} }}{R}}=-{\frac {h_{i}^{*}-h_{i}^{\mathrm {gas} }}{R}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/960f49c76a7280b816712de077463cc212ccfaa3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:26.326ex; height:6.176ex;" alt="{\displaystyle -{\frac {{\bar {h_{i}}}-h_{i}^{\mathrm {gas} }}{R}}=-{\frac {h_{i}^{*}-h_{i}^{\mathrm {gas} }}{R}}}"></span></dd></dl> <p>što je opet <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {h_{i}}}=h_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>=</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {h_{i}}}=h_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1fffb7c001bab329fc088ebe9e7b2a481e71bb5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.63ex; height:3.176ex;" alt="{\displaystyle {\bar {h_{i}}}=h_{i}^{*}}"></span>. </p><p>To znači da je entalpija smjese jednaka zbroju njezinih komponenata. </p><p>Od <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {u_{i}}}={\bar {h_{i}}}-p{\bar {v_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>−<!-- − --></mo> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {u_{i}}}={\bar {h_{i}}}-p{\bar {v_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5875197e971a7514101f2d9003465964b0aff954" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.304ex; height:2.843ex;" alt="{\displaystyle {\bar {u_{i}}}={\bar {h_{i}}}-p{\bar {v_{i}}}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{i}^{*}=h_{i}^{*}-pv_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>−<!-- − --></mo> <mi>p</mi> <msubsup> <mi>v</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{i}^{*}=h_{i}^{*}-pv_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79bd69efc7f844b8fb9844006ae635b780e322be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.067ex; height:2.843ex;" alt="{\displaystyle u_{i}^{*}=h_{i}^{*}-pv_{i}^{*}}"></span>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle u_{i}^{*}={\bar {u_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>u</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle u_{i}^{*}={\bar {u_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f907b0cd2e90919eed4ee8eae75cd60ea7091151" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.612ex; height:2.843ex;" alt="{\displaystyle u_{i}^{*}={\bar {u_{i}}}}"></span></dd></dl> <p>To je također lahko provjerljivo: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle C_{pi}^{*}={\bar {C_{pi}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>C</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle C_{pi}^{*}={\bar {C_{pi}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b0df94ddbf8b92447f21bb222eb954e891d0e528" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:9.675ex; height:3.676ex;" alt="{\displaystyle C_{pi}^{*}={\bar {C_{pi}}}}"></span></dd></dl> <div class="mw-heading mw-heading3"><h3 id="Entropija_smjesa">Entropija smjesa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=6" title="Uredi odlomak "Entropija smjesa"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=6" title="Edit section's source code: Entropija smjesa"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konačno, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {g_{i}}}=\mu _{i}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}}{p^{u}}}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>=</mo> <msub> <mi>μ<!-- μ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> <mo>=</mo> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">g</mi> <mi mathvariant="normal">a</mi> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msubsup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msubsup> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>u</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>μ<!-- μ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {g_{i}}}=\mu _{i}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}}{p^{u}}}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/137b5ebe607fa0514c79cf30062eebdb8c46b5f5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:72.709ex; height:6.176ex;" alt="{\displaystyle {\bar {g_{i}}}=\mu _{i}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}}{p^{u}}}=g_{i}^{\mathrm {gas} }+RT\ln {\frac {f_{i}^{*}}{p^{u}}}+RT\ln x_{i}=\mu _{i}^{*}+RT\ln x_{i}}"></span></dd></dl> <p>Što znači da: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta g_{i,\mathrm {mix} }=RT\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta g_{i,\mathrm {mix} }=RT\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f3134ce560dd6c281e030452c324431306d21c6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.338ex; height:2.843ex;" alt="{\displaystyle \Delta g_{i,\mathrm {mix} }=RT\ln x_{i}}"></span> a budući da je Gibbsova slobodna energija po molu smjese <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/99269e24e8109b604cc42cd4d3d94941c0a54aa5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.502ex; height:2.509ex;" alt="{\displaystyle G_{m}}"></span> </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle G_{m}=\sum _{i}x_{i}{g_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>=</mo> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G_{m}=\sum _{i}x_{i}{g_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/21aec69449c8079c0ea31e01521c109911cdbe40" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:14.38ex; height:5.509ex;" alt="{\displaystyle G_{m}=\sum _{i}x_{i}{g_{i}}}"></span> tada </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}{x_{i}\ln x_{i}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>,</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mi>T</mi> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}{x_{i}\ln x_{i}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/019f606696c68d101e6595c793bd7bbc7b2e9249" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.116ex; height:5.509ex;" alt="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}{x_{i}\ln x_{i}}}"></span></dd></dl> <p>Napokon možemo izračunati molarnu <a href="/w/index.php?title=Entropija_smjese&action=edit&redlink=1" class="new" title="Entropija smjese (stranica ne postoji)">entropiju smjese</a>, po obrascima <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle g_{i}^{*}=h_{i}^{*}-Ts_{i}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msubsup> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>=</mo> <msubsup> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>−<!-- − --></mo> <mi>T</mi> <msubsup> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}^{*}=h_{i}^{*}-Ts_{i}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2008013b0d5077f78213b06bed08c8c6f26e5e8b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:14.285ex; height:2.843ex;" alt="{\displaystyle g_{i}^{*}=h_{i}^{*}-Ts_{i}^{*}}"></span> and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {g_{i}}}={\bar {h_{i}}}-T{\bar {s_{i}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>h</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> <mo>−<!-- − --></mo> <mi>T</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">¯<!-- ¯ --></mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {g_{i}}}={\bar {h_{i}}}-T{\bar {s_{i}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dab09d195fa735746ca5b253f96b57be019508ca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.513ex; height:2.843ex;" alt="{\displaystyle {\bar {g_{i}}}={\bar {h_{i}}}-T{\bar {s_{i}}}}"></span> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta s_{i,\mathrm {mix} }=-R\sum _{i}\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>,</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−<!-- − --></mo> <mi>R</mi> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta s_{i,\mathrm {mix} }=-R\sum _{i}\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44342012cc17272632c4b74b688d0183710cd7ad" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:22.233ex; height:5.509ex;" alt="{\displaystyle \Delta s_{i,\mathrm {mix} }=-R\sum _{i}\ln x_{i}}"></span></dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta S_{\mathrm {m,mix} }=-R\sum _{i}x_{i}\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>S</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>,</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mo>−<!-- − --></mo> <mi>R</mi> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta S_{\mathrm {m,mix} }=-R\sum _{i}x_{i}\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6398a1d45f4ac52612840c45460cf1b218838411" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:25.886ex; height:5.509ex;" alt="{\displaystyle \Delta S_{\mathrm {m,mix} }=-R\sum _{i}x_{i}\ln x_{i}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Posljedice">Posljedice</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=7" title="Uredi odlomak "Posljedice"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=7" title="Edit section's source code: Posljedice"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Interakcije rastvarač-rastvorena supstanca slične su interakcijama rastvorene supstance i druge rastvorene supstance </p><p>Budući da je entalpija miješanja (rastvora) jednaka nuli, promjena <a href="/wiki/Gibbsova_slobodna_energija" title="Gibbsova slobodna energija">Gibbsove slobodne energije</a> pri miješanju određuje se isključivo pomoću <a href="/w/index.php?title=Entropija_mije%C5%A1anja&action=edit&redlink=1" class="new" title="Entropija miješanja (stranica ne postoji)">entropije miješanja</a>. Stoga je molarna Gibbsova slobodna energija miješanja je </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}x_{i}\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>,</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mi>T</mi> <munder> <mo>∑<!-- ∑ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </munder> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}x_{i}\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c86e404b97bbfe49174715fda0389029e18bdd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:26.116ex; height:5.509ex;" alt="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT\sum _{i}x_{i}\ln x_{i}}"></span></dd></dl> <p>ili dvokomponentnog rastvora: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT(x_{A}\ln x_{A}+x_{B}\ln x_{B})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ<!-- Δ --></mi> <msub> <mi>G</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> <mo>,</mo> <mi mathvariant="normal">m</mi> <mi mathvariant="normal">i</mi> <mi mathvariant="normal">x</mi> </mrow> </mrow> </msub> <mo>=</mo> <mi>R</mi> <mi>T</mi> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>+</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta G_{\mathrm {m,mix} }=RT(x_{A}\ln x_{A}+x_{B}\ln x_{B})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edee8390935eeabfd2aa0180e3497031c7a529ef" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:36.298ex; height:3.009ex;" alt="{\displaystyle \Delta G_{\mathrm {m,mix} }=RT(x_{A}\ln x_{A}+x_{B}\ln x_{B})}"></span></dd></dl> <p>gdje m označava molarnost, tj. promjenu Gibbsove slobodne energije po molu otopine, i </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e87000dd6142b81d041896a30fe58f0c3acb2158" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.129ex; height:2.009ex;" alt="{\displaystyle x_{i}}"></span> je <a href="/w/index.php?title=Molna_frakcija&action=edit&redlink=1" class="new" title="Molna frakcija (stranica ne postoji)">molna frakcija</a> komponente <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span>.</dd></dl> <p>Ova slobodna energija miješanja uvijek je negativna (budući da je svaki <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}\in [0,1]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>∈<!-- ∈ --></mo> <mo stretchy="false">[</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}\in [0,1]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a32830173af0dc0eaf16f580cc75ef2f78b4f15e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.623ex; height:2.843ex;" alt="{\displaystyle x_{i}\in [0,1]}"></span>, svaki <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0722112a359701cfbf69c0ad59042a6e99141696" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.456ex; height:2.509ex;" alt="{\displaystyle \ln x_{i}}"></span> ili njegovo ograničenje <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}\rightarrow 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">→<!-- → --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}\rightarrow 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/892bbdb99fb50c02627568aaaf135c208522716d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:6.906ex; height:2.509ex;" alt="{\displaystyle x_{i}\rightarrow 0}"></span> mora biti negativno (beskonačno), tj. „Idealni rastvori uvijek se u potpunosti miješaju“. </p><p>Gornja jednadžba može se izraziti u terminima <a href="/w/index.php?title=Hemijski_potencijal&action=edit&redlink=1" class="new" title="Hemijski potencijal (stranica ne postoji)">hemijskog potencijala</a> pojedinačnih je </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mu _{i}=\mu _{i}^{*}+RT\ln x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>μ<!-- μ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <msubsup> <mi>μ<!-- μ --></mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msubsup> <mo>+</mo> <mi>R</mi> <mi>T</mi> <mi>ln</mi> <mo>⁡<!-- --></mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mu _{i}=\mu _{i}^{*}+RT\ln x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d06120fb4c1f1a56aa858f136e07d29e0c5a019c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:18.839ex; height:2.843ex;" alt="{\displaystyle \mu _{i}=\mu _{i}^{*}+RT\ln x_{i}}"></span></dd></dl> <p>Bilo koja komponenta <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle i}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>i</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle i}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/add78d8608ad86e54951b8c8bd6c8d8416533d20" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.802ex; height:2.176ex;" alt="{\displaystyle i}"></span> idealnog rastvor poštuje <a href="/w/index.php?title=Raoultov_zakon&action=edit&redlink=1" class="new" title="Raoultov zakon (stranica ne postoji)">Raoultov zakon</a> u cijelom rasponu sastava: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \P _{i}=(P_{i})_{pure}x_{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mo>¶</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mo stretchy="false">(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>u</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \P _{i}=(P_{i})_{pure}x_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fb5f5578f2802b0ce973c2bd518868bf04296fa6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:15.052ex; height:3.509ex;" alt="{\displaystyle \P _{i}=(P_{i})_{pure}x_{i}}"></span></dd></dl> <p>gdje </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (P_{i})_{pure}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>P</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <msub> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mi>u</mi> <mi>r</mi> <mi>e</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (P_{i})_{pure}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c682545f50308cf775a5a3390ee974bbbecc9f0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:7.995ex; height:3.009ex;" alt="{\displaystyle (P_{i})_{pure}\,}"></span> je ravnoteža <a href="/w/index.php?title=Pritisak_pare&action=edit&redlink=1" class="new" title="Pritisak pare (stranica ne postoji)">pritiska pare</a> čiste komponente</dd> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{i}\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{i}\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7beb41cde977577a7aa598a9defd58dc8d529bb8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.516ex; height:2.009ex;" alt="{\displaystyle x_{i}\,}"></span> je <a href="/w/index.php?title=Molna_frakcija&action=edit&redlink=1" class="new" title="Molna frakcija (stranica ne postoji)">molna frakcija</a> komponente u rastvoru.</dd></dl> <p>Također se može pokazati da su, za idealne rastvor, količine strogo aditivne. </p> <div class="mw-heading mw-heading2"><h2 id="Neidealnost">Neidealnost</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=8" title="Uredi odlomak "Neidealnost"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=8" title="Edit section's source code: Neidealnost"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Odstupanja od idealnosti mogu se opisati upotrebom <a href="/w/index.php?title=Margulesova_funkcija&action=edit&redlink=1" class="new" title="Margulesova funkcija (stranica ne postoji)">Margulesovih funkcija</a> ili <a href="/w/index.php?title=Koeficijent_aktivnosti&action=edit&redlink=1" class="new" title="Koeficijent aktivnosti (stranica ne postoji)">koeficijenata aktivnosti</a>. Jedan Margulesov parametar može biti dovoljan da opiše svojstva rastvora, ako su odstupanja od idealnosti skromna; takvi rastvori nazivaju se <i><a href="/w/index.php?title=Pravi_rastvor&action=edit&redlink=1" class="new" title="Pravi rastvor (stranica ne postoji)">pravi rastvor</a> </i>. </p><p>Za razliku od idealnih rastvora, gdje su količine strogo aditivne i miješanje je uvijek potpuno, volumen neidealnog rastvora, općenito, nije jednostavni zbir zapremina komponentnih čistih tekućina i <a href="/w/index.php?title=Topljivost&action=edit&redlink=1" class="new" title="Topljivost (stranica ne postoji)">topljivost</a> nije zagarantovana u cijelom rasponu sastava. Može se odrediti mjerenjem gustina <a href="/w/index.php?title=Termodinami%C4%8Dka_aktivnost&action=edit&redlink=1" class="new" title="Termodinamička aktivnost (stranica ne postoji)">termodinamičke aktivnosti</a> komponenata. </p> <div class="mw-heading mw-heading2"><h2 id="Također_pogledajte"><span id="Tako.C4.91er_pogledajte"></span>Također pogledajte</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=9" title="Uredi odlomak "Također pogledajte"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=9" title="Edit section's source code: Također pogledajte"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Koeficijent_aktivnosti&action=edit&redlink=1" class="new" title="Koeficijent aktivnosti (stranica ne postoji)">Koeficijent aktivnosti</a></li> <li><a href="/w/index.php?title=Entropija_mije%C5%A1anja&action=edit&redlink=1" class="new" title="Entropija miješanja (stranica ne postoji)">Entropija miješanja</a></li> <li><a href="/w/index.php?title=Margulesova_funkcija&action=edit&redlink=1" class="new" title="Margulesova funkcija (stranica ne postoji)">Margulesova funkcija</a></li> <li><a href="/w/index.php?title=Normalni_rastvor&action=edit&redlink=1" class="new" title="Normalni rastvor (stranica ne postoji)">Normalni rastvor</a></li> <li><a href="/w/index.php?title=Pravi_rastvor&action=edit&redlink=1" class="new" title="Pravi rastvor (stranica ne postoji)">Pravi rastvor</a></li> <li><a href="/w/index.php?title=Prividno_molarno_svojstvo&action=edit&redlink=1" class="new" title="Prividno molarno svojstvo (stranica ne postoji)">Prividno molarno svojstvo</a></li> <li><a href="/w/index.php?title=Jednad%C5%BEba_razbla%C5%BEivanja&action=edit&redlink=1" class="new" title="Jednadžba razblaživanja (stranica ne postoji)">Jednadžba razblaživanja</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Reference">Reference</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Idealni_rastvor&veaction=edit&section=10" title="Uredi odlomak "Reference"" class="mw-editsection-visualeditor"><span>uredi</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Idealni_rastvor&action=edit&section=10" title="Edit section's source code: Reference"><span>uredi izvor</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r3312388">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r3303350">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFFelderRousseauBullard2005" class="citation book cs1">Felder, Richard M.; Rousseau, Ronald W.; Bullard, Lisa G. (2005). <span class="cs1-lock-limited" title="Dostupan probni rok, a inače je potrebna pretplata"><a rel="nofollow" class="external text" href="https://archive.org/details/elementaryprinci00feld"><i>Elementary Principles of Chemical Processes</i></a></span>. Wiley. str. <a rel="nofollow" class="external text" href="https://archive.org/details/elementaryprinci00feld/page/n322">293</a>. <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:Knji%C5%BEni_izvori/978-0471687573" title="Posebno:Knjižni izvori/978-0471687573"><bdi>978-0471687573</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Principles+of+Chemical+Processes&rft.pages=293&rft.pub=Wiley&rft.date=2005&rft.isbn=978-0471687573&rft.aulast=Felder&rft.aufirst=Richard+M.&rft.au=Rousseau%2C+Ronald+W.&rft.au=Bullard%2C+Lisa+G.&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Felementaryprinci00feld&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AIdealni+rastvor" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><i>A to Z of Thermodynamics</i> Pierre Perrot <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Posebno:Knji%C5%BEni_izvori/0-19-856556-9" title="Posebno:Knjižni izvori/0-19-856556-9">0-19-856556-9</a></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r3303350"><cite id="CITEREFFelderRousseauBullard" class="citation book cs1">Felder, Richard M.; Rousseau, Ronald W.; Bullard, Lisa G. <i>Elementary Principles of Chemical Processes</i>. Wiley. str. 293. <a href="/wiki/ISBN_(identifikator)" class="mw-redirect" title="ISBN (identifikator)">ISBN</a> <a href="/wiki/Posebno:Knji%C5%BEni_izvori/978-0471687573" title="Posebno:Knjižni izvori/978-0471687573"><bdi>978-0471687573</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Elementary+Principles+of+Chemical+Processes&rft.pages=293&rft.pub=Wiley&rft.isbn=978-0471687573&rft.aulast=Felder&rft.aufirst=Richard+M.&rft.au=Rousseau%2C+Ronald+W.&rft.au=Bullard%2C+Lisa+G.&rfr_id=info%3Asid%2Fbs.wikipedia.org%3AIdealni+rastvor" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">Gold Book, FileI02938 <a rel="nofollow" class="external text" href="https://goldbook.iupac.org/terms/view/I02938">GoldBookRef:mixture,file:I02938</a></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">P. Atkins and J. de Paula, <i>Atkins’ Physical Chemistry</i> (8th edn, W.H.Freeman 2006), p.144</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text">T. Engel and P. Reid <i>Physical Chemistry</i> (Pearson 2006), p.194</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text">K.J. Laidler and J.H. Meiser <i>Physical Chemistry</i> (Benjamin-Cummings 1982), p.180</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text">R.S. Berry, S.A. Rice and J. Ross, <i>Physical Chemistry</i> (Wiley 1980) p.750</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text">I.M. Klotz, <i>Chemical Thermodynamics</i> (Benjamin 1964) p.322</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-10">^</a></b></span> <span class="reference-text">P.A. Rock, <i>Chemical Thermodynamics: Principles and Applications</i> (Macmillan 1969), p.261</span> </li> </ol></div></div></div><!--esi <esi:include src="/esitest-fa8a495983347898/content" /> --><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Preuzeto iz "<a dir="ltr" href="https://bs.wikipedia.org/w/index.php?title=Idealni_rastvor&oldid=3231901">https://bs.wikipedia.org/w/index.php?title=Idealni_rastvor&oldid=3231901</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Posebno:Kategorije" title="Posebno:Kategorije">Kategorije</a>: <ul><li><a href="/wiki/Kategorija:Rastvori" title="Kategorija:Rastvori">Rastvori</a></li><li><a href="/wiki/Kategorija:Termodinamika" title="Kategorija:Termodinamika">Termodinamika</a></li><li><a href="/w/index.php?title=Kategorija:Hemijska_termodinamika&action=edit&redlink=1" class="new" title="Kategorija:Hemijska termodinamika (stranica ne postoji)">Hemijska termodinamika</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Ova stranica je posljednji put izmijenjena na datum 30 oktobar 2020 u 20:10.</li> <li id="footer-info-copyright">Tekst je dostupan pod <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/">slobodnom licencom Autorstvo-Dijeliti pod istim uvjetima</a>; mogu se primijeniti i dodatni uvjeti. 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