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Unimolekulaarinen reaktio – Wikipedia
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Se voi olla <a href="/wiki/Alkeisreaktio" title="Alkeisreaktio">alkeisreaktio</a> tai kompleksinen reaktio, joka sopivissa olosuhteissa noudattaa 1. kertaluvun kinetiikkaa. Esimerkiksi <a href="/wiki/Radikaali_(kemia)" title="Radikaali (kemia)">radikaalin</a> <a href="/wiki/Kuivatislaus" title="Kuivatislaus">pyrolyysireaktio</a> on unimolekulaarinen kun reaktiopaine on suuri ja bimolekularinen kun reaktiopaine on pieni. Tämä vaihtuva reaktiomekanismi on selitettävissä kompleksisen reaktion paineriippuvuudella, kuten F. A. Lindemann ja J. A. Christiansen jo 1920-luvun alussa osoittivat toteen.<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><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> </p> <div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="fi" dir="ltr"><h2 id="mw-toc-heading">Sisällys</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Lindemann–Christiansen-mekanismi"><span class="tocnumber">1</span> <span class="toctext">Lindemann–Christiansen-mekanismi</span></a> <ul> <li class="toclevel-2 tocsection-2"><a href="#Molekyylin_sisäisen_vapausasteen_huomioon_ottaminen"><span class="tocnumber">1.1</span> <span class="toctext">Molekyylin sisäisen vapausasteen huomioon ottaminen</span></a></li> <li class="toclevel-2 tocsection-3"><a href="#Nopeusvakio_k2(E):n_energiariippuvuus"><span class="tocnumber">1.2</span> <span class="toctext">Nopeusvakio <i>k<sub>2</sub>(E)</i>:n energiariippuvuus</span></a></li> </ul> </li> <li class="toclevel-1 tocsection-4"><a href="#RRK-teoria"><span class="tocnumber">2</span> <span class="toctext">RRK-teoria</span></a></li> <li class="toclevel-1 tocsection-5"><a href="#QRRK-teoria"><span class="tocnumber">3</span> <span class="toctext">QRRK-teoria</span></a></li> <li class="toclevel-1 tocsection-6"><a href="#Huomautukset"><span class="tocnumber">4</span> <span class="toctext">Huomautukset</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#Katso_myös"><span class="tocnumber">5</span> <span class="toctext">Katso myös</span></a></li> <li class="toclevel-1 tocsection-8"><a href="#Lähteet"><span class="tocnumber">6</span> <span class="toctext">Lähteet</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Lindemann–Christiansen-mekanismi"><span id="Lindemann.E2.80.93Christiansen-mekanismi"></span>Lindemann–Christiansen-mekanismi</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=1" title="Muokkaa osiota Lindemann–Christiansen-mekanismi" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=1" title="Muokkaa osion lähdekoodia: Lindemann–Christiansen-mekanismi"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Pysyvän molekyylin unimolekulaarinen reaktio edellyttää tapahtuakseen aluksi, että molekyyli virittyy energeettisesti yli reaktion kynnysenergian <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 E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span>. Molekyylin virittyminen voi tapahtua <a href="/wiki/S%C3%A4hk%C3%B6magneettinen_s%C3%A4teily" title="Sähkömagneettinen säteily">sähkömagneettisen säteilyn</a> <a href="/wiki/Absorptio_(s%C3%A4hk%C3%B6magneettinen_s%C3%A4teily)" title="Absorptio (sähkömagneettinen säteily)">absorption</a> avulla. Reagoivat molekyylit vaihtavat energiaa ja virittyvät myös keskinäisten törmäysten seurauksena. Käytännössä kinetiikan mittaukseen kaasufaasissa tarvitaan <a href="/wiki/Reagenssi" title="Reagenssi">reagenssin</a> lisäksi kantokaasu, kuten <a href="/wiki/Helium" title="Helium">helium</a>. Kantokaasu, <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 {\ce {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdeb1f188c088c37acc8921c61145bb7f1e65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.131ex; height:2.176ex;" alt="{\displaystyle {\ce {M}}}"></span>, on reagoimaton, <a href="/wiki/Inertti" title="Inertti">inertti</a>, ja osallistuu kemialliseen reaktioon vain kineettisen energian absorboijana. Oletuksena reagenssimolekyylien ja kantokaasumolekyylien välisessä vuorovaikutuksessa on, että törmäys <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 {\ce {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdeb1f188c088c37acc8921c61145bb7f1e65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.131ex; height:2.176ex;" alt="{\displaystyle {\ce {M}}}"></span>:n kanssa on riittävän vahva virittyneen molekyylin, <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 {\text{A}}^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{A}}^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfa1625f9320b644949076f78ed98d12fc30cab9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle {\text{A}}^{*}}"></span>, muodostumiseksi, jonka seurauksena tasapainoreaktion palautuvan suunnan nopeusvakio <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 k_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c330fc841539e073ba8a335543dc8a8b0245574" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.544ex; height:2.509ex;" alt="{\displaystyle k_{-1}}"></span> voidaan ottaa <a href="/wiki/T%C3%B6rm%C3%A4ysteoria" title="Törmäysteoria">törmäysteorian</a> mukaisesti törmäyslukuna, <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 Z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>Z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1cc6b75e09a8aa3f04d8584b11db534f88fb56bd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.68ex; height:2.176ex;" alt="{\displaystyle Z}"></span>. Virittyneessä molekyylissä tapahtuu tämän jälkeen hyvin nopeita molekyylin sisäisiä energian siirtymisiä<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>a<span class="cite-bracket">]</span></a></sup> ja ylimääräenergia muuntuu <a href="/wiki/Molekulaarinen_jakaumafunktio#Vibraatiojakaumafunktio" title="Molekulaarinen jakaumafunktio">vibraatioenergiaksi</a>. Unimolekulaarisen reaktion Lindemann–Christiansen-mekanismi etenee aktivoinnin, sen purkautumisen, ja tuotteen muodostumisen kautta seuraavasti: </p> <dl><dd><dl><dd>(1)<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 \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>A + M</mtext> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo class="MJX-variant" stretchy="false">⇌<!-- ⇌ --></mo> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </munder> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mover> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>+ M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b6cb2acddc7a8179432d61d228dbead4771bb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.64ex; height:6.843ex;" alt="{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}"></span></dd></dl></dd></dl> <dl><dd><dl><dd>(2)<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 \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo stretchy="false">⟶<!-- ⟶ --></mo> <mrow /> </munder> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mover> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>tuotteet</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b1f478a923364a7d9bd8e82991331d73d07c095a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:20.677ex; height:5.676ex;" alt="{\displaystyle \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}"></span></dd></dl></dd></dl> <p>Reaktiovaiheineen (1) kinetiikka on 2. kertalukua ja reaktiovaiheen (2) kinetiikka on 1. kertalukua. Lähtöaineen häviämiselle voidaan kirjoittaa seuraava nopeuslaki: </p> <dl><dd><dl><dd>(3)<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 \qquad -{\frac {d[A]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>−<!-- − --></mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad -{\frac {d[A]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6dc2b7f4185ac260cf5ab8f6d5e5ed12f66e3107" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:38.664ex; height:5.843ex;" alt="{\displaystyle \qquad -{\frac {d[A]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]}"></span></dd></dl></dd></dl> <p>Virittynyt <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 A^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44e23745a51c2c2d8d91fd98c1cf721573747ece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle A^{*}}"></span> on reaktiossa lyhytaikainen välituote, joten siihen voi soveltaa <a href="/wiki/Alkeisreaktio#Peräkkäiset_1._kertaluvun_reaktiot" title="Alkeisreaktio">vakiotilaoletusta</a>: </p> <dl><dd><dl><dd>(4)<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 \qquad {\frac {d[A^{*}]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]-k_{2}[A^{*}]\,=\,0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>−<!-- − --></mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>−<!-- − --></mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\frac {d[A^{*}]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]-k_{2}[A^{*}]\,=\,0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/778db4b0e470693e53e5a2dad426ca328b11bbaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:52.142ex; height:5.843ex;" alt="{\displaystyle \qquad {\frac {d[A^{*}]}{dt}}=k_{1}[A][M]\,-\,k_{-1}[A^{*}][M]-k_{2}[A^{*}]\,=\,0}"></span></dd></dl></dd></dl> <p>Tästä seuraa, että <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 k_{-1}[A^{*}][M]=k_{1}[A][M]\,-\,k_{2}[A^{*}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>−<!-- − --></mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}[A^{*}][M]=k_{1}[A][M]\,-\,k_{2}[A^{*}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9aa0da5ef69b01ea77bb66cd6930bdfd6d8d0b52" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:33.479ex; height:2.843ex;" alt="{\displaystyle k_{-1}[A^{*}][M]=k_{1}[A][M]\,-\,k_{2}[A^{*}]}"></span>. Sijoittamalla tämä yhtälöön (3), saadaan <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 \qquad -{\frac {d[A]}{dt}}=k_{2}[A^{*}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad -{\frac {d[A]}{dt}}=k_{2}[A^{*}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/20d45dcce398973a65e3a6673b5dbab2b8ec6f95" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:20.997ex; height:5.843ex;" alt="{\displaystyle \qquad -{\frac {d[A]}{dt}}=k_{2}[A^{*}]}"></span>. </p><p>Sijoittamalla tähän yhtälöstä (4) ratkaistu <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 [A^{*}]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A^{*}]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79c5cdbf74ceff0ad7f1769ec737ef7832f24c5f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.091ex; height:2.843ex;" alt="{\displaystyle [A^{*}]}"></span> saadaan: </p> <dl><dd><dl><dd>(5)<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 \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]+k_{2}}}=k_{\text{uni}}[A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]+k_{2}}}=k_{\text{uni}}[A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f116e4bfd8f2f51249c670875626bb02e9a9cd4e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:37.726ex; height:6.509ex;" alt="{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]+k_{2}}}=k_{\text{uni}}[A]}"></span></dd></dl></dd></dl><p> Tästä on todettavissa, että <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 k_{\text{uni}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{uni}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f62e799f1a43389be2d20efcc2d260b45e4fbcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.729ex; height:2.509ex;" alt="{\displaystyle k_{\text{uni}}}"></span> riippuu puskurikaasun konsentraatiosta eli reaktiopaineesta. Oheisesta kuvasta on todettavissa, että nopeusvakiolla on paineriippuvuudessa kaksi rajatapausta:</p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:LCunimolek.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/LCunimolek.svg/250px-LCunimolek.svg.png" decoding="async" width="250" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/LCunimolek.svg/375px-LCunimolek.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/LCunimolek.svg/500px-LCunimolek.svg.png 2x" data-file-width="610" data-file-height="460" /></a><figcaption><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 [M]_{1/2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <msub> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]_{1/2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7b326b48454de0d3dd758668adcd7e53aeaba226" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:6.434ex; height:3.176ex;" alt="{\displaystyle [M]_{1/2}}"></span> on puskurikaasun konsentraatio, missä unimolekulaarisen nopeusvakion arvo on puolittunut sen arvosta korkeassa paineessa.</figcaption></figure><p> Kun reaktiolosuhteissa on <b>suuri</b> reaktiopaine,<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>b<span class="cite-bracket">]</span></a></sup> niin <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 k_{-1}[M]\gg k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>≫<!-- ≫ --></mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}[M]\gg k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c318e20015f6fd787a78900ed9292c226cad8ab7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.159ex; height:2.843ex;" alt="{\displaystyle k_{-1}[M]\gg k_{2}}"></span>, virityksen purkautuminen törmäysten seurauksena on paljon nopeampaa kuin virittyneen molekyylin unimolekulaarinen reaktio lopputuotteiksi. </p><p>Tällöin yhtälö (5) yksinkertaistuu muotoon: </p> <dl><dd><dl><dd>(6)<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 \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]}}\,\simeq \,{\frac {k_{1}k_{2}}{k_{-1}[A]}}=k_{\infty }[A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>≃<!-- ≃ --></mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]}}\,\simeq \,{\frac {k_{1}k_{2}}{k_{-1}[A]}}=k_{\infty }[A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9330937878fec3a6244deb62919936cc4b9d36e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:47.292ex; height:6.509ex;" alt="{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{-1}[M]}}\,\simeq \,{\frac {k_{1}k_{2}}{k_{-1}[A]}}=k_{\infty }[A]}"></span></dd></dl></dd></dl> <p>Tässä <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 k_{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/347b5465c2ce6e6f552a8686401cc428f451a66a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.087ex; height:2.509ex;" alt="{\displaystyle k_{\infty }}"></span> on unimolekulaarisen hajoamisen nopeusvakio kun reaktiopaine on suuri. Näissä olosuhteissa reaktio noudattaa <b>1. kertaluvun kinetiikkaa</b>. Toisaalta kun reaktiopaine on <b>pieni</b>, niin <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 k_{-1}[M]\ll k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>≪<!-- ≪ --></mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}[M]\ll k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6b15e5ebb6d96cb75fc0e54399f7e4d27eb18d15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:13.159ex; height:2.843ex;" alt="{\displaystyle k_{-1}[M]\ll k_{2}}"></span>. Tällöin yhtälö (5) voidaan kirjoittaa: </p> <dl><dd><dl><dd>(7)<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 \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{2}}}\,\simeq \,k_{1}[A][M]\,=\,k_{0}[A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>≃<!-- ≃ --></mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{2}}}\,\simeq \,k_{1}[A][M]\,=\,k_{0}[A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1ee8fbd2e55aaa74482e0415b1073f26bd63b899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:48.866ex; height:6.176ex;" alt="{\displaystyle \qquad -{\frac {d[A]}{dt}}={\frac {k_{1}k_{2}[A][M]}{k_{2}}}\,\simeq \,k_{1}[A][M]\,=\,k_{0}[A]}"></span></dd></dl></dd></dl> <p>Kun reaktiopaine on pieni, niin reaktionopeuden määräävä vaihe on molekyylin bimolekulaarinen reaktio, jonka nopeusvakio <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 k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376315fd4983f01dada5ec2f7bebc48455b14a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{1}}"></span> riippuu lineaarisesti <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 [M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ca74e595b2281c0aef1897ecafa282d1f182e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.736ex; height:2.843ex;" alt="{\displaystyle [M]}"></span>:sta. Reaktion kokonaiskertaluku on 2. Mittauksissa todettu 2. kertaluvun kinetiikka on ymmärrettävissä jos lähtöaineen konsentraatio on suuri, jolloin <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 [M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e5ca74e595b2281c0aef1897ecafa282d1f182e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.736ex; height:2.843ex;" alt="{\displaystyle [M]}"></span> voidaan merkitä <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 [A]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [A]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/79eaa334597b1861f1b08ca0c8fecb3858ebcb12" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.037ex; height:2.843ex;" alt="{\displaystyle [A]}"></span>:na. </p><p>Lindemann–Christiansen-mekanismin epätarkkuus on todettavissa sovitettaessa matalissa paineissa mitattuja nopeusvakioita teoriaan. Tätä varten <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 k_{\text{uni}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{uni}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f62e799f1a43389be2d20efcc2d260b45e4fbcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.729ex; height:2.509ex;" alt="{\displaystyle k_{\text{uni}}}"></span> otetaan yhtälöstä (5) ja sen osoittaja ja nimittäjä jaetaan <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 k_{-1}[M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}[M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9c91f07baf40a820e489daf68b43f54e5c1644d2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.28ex; height:2.843ex;" alt="{\displaystyle k_{-1}[M]}"></span>:llä: </p> <dl><dd><dl><dd>(8)<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 \qquad k_{\text{uni}}={\frac {k_{2}{\frac {k_{1}}{k_{-1}}}}{1+{\frac {k_{2}}{k_{-1}[M]}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\text{uni}}={\frac {k_{2}{\frac {k_{1}}{k_{-1}}}}{1+{\frac {k_{2}}{k_{-1}[M]}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dab845715c73805bcdd85a01a141e40ddfdb0c7b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:22.515ex; height:9.676ex;" alt="{\displaystyle \qquad k_{\text{uni}}={\frac {k_{2}{\frac {k_{1}}{k_{-1}}}}{1+{\frac {k_{2}}{k_{-1}[M]}}}}}"></span></dd></dl></dd></dl> <p>Otetaan yhtälöstä käänteisluku puolittain ja piirretään kuvaaja, jossa x-akselina on <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 {1}{[M]}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{[M]}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4c0590e9544d0602edca0af1b6ad25d5cc6d2881" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:4.572ex; height:6.009ex;" alt="{\displaystyle {\frac {1}{[M]}}}"></span> ja y-akselina on <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 {1}{k_{\text{uni}}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {1}{k_{\text{uni}}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/82b151565c800f096b8168155de016b7d31690d9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:4.565ex; height:5.676ex;" alt="{\displaystyle {\frac {1}{k_{\text{uni}}}}}"></span>. Teoria ennustaa lineaarista kuvaajaa, mutta käytännön mittaustulokset eivät tue tätä. </p><p>Siirtymistä korkeapainenopeusvakiosta <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 k_{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/347b5465c2ce6e6f552a8686401cc428f451a66a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.087ex; height:2.509ex;" alt="{\displaystyle k_{\infty }}"></span> mataliin paineisiin nopeusvakion saadessa yhä pienempiä arvoja sanotaan "fall-off"-painealueeksi. </p><p><br /> </p> <div class="mw-heading mw-heading3"><h3 id="Molekyylin_sisäisen_vapausasteen_huomioon_ottaminen"><span id="Molekyylin_sis.C3.A4isen_vapausasteen_huomioon_ottaminen"></span>Molekyylin sisäisen vapausasteen huomioon ottaminen</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=2" title="Muokkaa osiota Molekyylin sisäisen vapausasteen huomioon ottaminen" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=2" title="Muokkaa osion lähdekoodia: Molekyylin sisäisen vapausasteen huomioon ottaminen"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lindemann–Christiansen-mekanismissa reaktiovaiheessa (1) tapahtuva lähtöainemolekyylin virittyminen otaksutaan tapahtuvan <a href="/wiki/T%C3%B6rm%C3%A4ysteoria" title="Törmäysteoria">törmäysteorian</a> mukaisesti kovien kuulien vahvana törmäyksenä yhdessä tapahtumassa. Törmäysteoriassa oletetaan, että vain kaksi vapausastetta (aiheutuvat liike-energiasta) vaikuttavat reaktion kinetiikkaan. Tällöin molekyylin virittymisen nopeusvakiolle voidaan kirjoittaa: </p> <dl><dd><dl><dd>(9)<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 \qquad k_{1}=Z_{1}e^{-{\frac {E_{0}}{k_{B}T}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{1}=Z_{1}e^{-{\frac {E_{0}}{k_{B}T}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14280eef10c7968ad46faeaabb818d9dbc51f510" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:18.862ex; height:4.843ex;" alt="{\displaystyle \qquad k_{1}=Z_{1}e^{-{\frac {E_{0}}{k_{B}T}}}}"></span></dd></dl></dd></dl> <p>Tässä <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 k_{B}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/70f38f7b73e53fd7b5d9ca64bec3a1438cc0eade" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.691ex; height:2.509ex;" alt="{\displaystyle k_{B}}"></span> on Boltzmannin vakio, <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> on absoluuttinen lämpötila, ja <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 E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span> vastaa kynnysenergiaa korkeapainerajalla so. <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 E_{\infty }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{\infty }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68cacbe04c10fce753db60f346f92a34e1567d1e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.591ex; height:2.509ex;" alt="{\displaystyle E_{\infty }}"></span>. Törmäysteorian mukaisesti laskettu kineettinen energia on vähintään kynnysenergian suuruinen eikä siinä oteta huomioon molekyylin sisäisiä vapausasteita (jotka ovat pääasiassa vibraatiovapausasteita). Todellisuudessa molekyyli on monimutkaisempi kuin kova kuula, joten sillä on konfiguraationsa mukaan runsaasti vapausasteita ja täten suuri todennäköisyys omata energiaa paljon yli klassisen kynnysenergian <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 E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span>. Tämän mukaan molekyylillä, jolla on <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>-kappaletta vapausasteita nopeusvakio pitäisi ilmaista:<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>c<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd>(10)<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 \qquad k_{1}={\frac {Z_{1}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{1}={\frac {Z_{1}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e0d940212b1810c15eab2ba1b204dc64af0df3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:36.554ex; height:8.009ex;" alt="{\displaystyle \qquad k_{1}={\frac {Z_{1}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"></span></dd></dl></dd></dl> <p>Tässä virittymisen nopeusvakio koostuu törmäysteorian törmäysluvusta <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 Z_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Z_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cea9e950915c77b3dcf9d4d54101820f538bc077" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.642ex; height:2.509ex;" alt="{\displaystyle Z_{1}}"></span> ja todennäköisyydestä sille, että törmäyksestä tullut viritysenergia jakaantuneena <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>-kappaleelle harmonisia värähtelijöitä on suurempi kuin kynnysenergia. Koska <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 E_{0}\gg k_{B}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>≫<!-- ≫ --></mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}\gg k_{B}T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d70eec638c6d100674e8421aa51b03c1376791bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.711ex; height:2.509ex;" alt="{\displaystyle E_{0}\gg k_{B}T}"></span>, niin yhtälössä (10) taajuustekijä on paljon suurempi kuin 1 verrattaessa tilannetta yhtälöön (9). Tämä törmäysteorian taajuustekijää vastaavan tekijän suuruus mahdollistaa monimutkaisten molekyylien värähdysvapausasteiden huomioimisen (suuri vibraatiotilatiheys). Tämä on parannus Lindemann–Christiansen-mekanismin teoriaan. </p><p>Korkeissa reaktiopaineissa se osuus reaktioista (ja niitä vastaavista nopeusvakioista), joilla on sisäistä energiaa törmäysten seurauksena välillä <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 E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span>:stä <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 E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fe293b7773fe2435d705864ed7a6c2eef092fca" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.608ex; height:2.343ex;" alt="{\displaystyle E+dE}"></span>:hen, on seuraava: </p> <dl><dd><dl><dd>(11)<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 \qquad {\frac {dk_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\frac {dk_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/709989ed6c77f1f26ab45f19a9955247f7929624" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:48.288ex; height:8.009ex;" alt="{\displaystyle \qquad {\frac {dk_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"></span></dd></dl></dd></dl> <p>Tämä yhtälö pätee tarkasti ottaen vain kun reaktiopaine on suuri. Jotta sitä voidaan käyttää myös muissa paineissa, on oletettava vahva törmäys lähtöainemolekyylin ja puskurikaasumolekyylin välillä. Tällöin suuri määrä energiaa siirtyy yhdessä tapahtumassa, siis virittymistä ja virittymisen purkautumista. Tämä olettama vaatii myös, että siirtynyt energia uudelleenjakautuu satunnaisesti molekyyleissä. Kun yhtälö (11) integroidaan raja-arvoilla <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 E=E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cb31b83e6a518f3c01b491199cad9a21c17a5829" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.644ex; height:2.509ex;" alt="{\displaystyle E=E_{0}}"></span> ja <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 E=\infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=\infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/19e52a47326dbb988c9c837c494fe92eaac023f8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.198ex; height:2.176ex;" alt="{\displaystyle E=\infty }"></span> ja otetaan <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 E_{0}\gg (s-1)k_{B}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>≫<!-- ≫ --></mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}\gg (s-1)k_{B}T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a03f2b6d0bdc6c3abdc45c9d53857229255c8a2a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.613ex; height:2.843ex;" alt="{\displaystyle E_{0}\gg (s-1)k_{B}T}"></span>, saadaan </p> <dl><dd><dl><dd>(12)<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 \qquad {\frac {k_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\frac {k_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d4aec99eb7b76644a5794004c9e62694478e2aa0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:39.443ex; height:8.009ex;" alt="{\displaystyle \qquad {\frac {k_{1}}{k_{-1}}}\,=\,{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"></span></dd></dl></dd></dl> <p>Tässä teorian mukaisesti <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 k_{-1}=Z_{1}\,=\,Z_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}=Z_{1}\,=\,Z_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/319e6409bde579a1e710382a6f743568a6f49764" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:17.077ex; height:2.509ex;" alt="{\displaystyle k_{-1}=Z_{1}\,=\,Z_{-1}}"></span>, jolloin nopeusvakio korkeissa paineissa on: </p> <dl><dd><dl><dd>(13)<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 \qquad k_{\infty }\,=\,{\frac {k_{2}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\infty }\,=\,{\frac {k_{2}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3daee497b9cfa0e0c01a2dd9cb18697fb9318b9e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:38.15ex; height:8.009ex;" alt="{\displaystyle \qquad k_{\infty }\,=\,{\frac {k_{2}}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}}"></span></dd></dl></dd></dl> <p>Tätä sanotaan Hinshelwood–Lindeman-teoriaksi.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>d<span class="cite-bracket">]</span></a></sup> Tällä teorialla voidaan mallintaa menestyksellä unimolekulaarisen reaktion fall-off -painealueen nopeusvakioiden arvot. Kuitenkaan teoria ei ole riittävän tarkka selittämään matalissa reaktiopaineissa tapahtuva kinetiikka. </p><p>Hinshelwood–Lindeman-teorian mukaisesti nopeusvakion <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 k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376315fd4983f01dada5ec2f7bebc48455b14a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{1}}"></span> arvo kasvaa, mutta <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span> pienenee kun vapausastemäärä <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> kasvaa. Täten virittyneen molekyylin elinaika pitenee. Mitä suurempi on vapausastelukumäärä sitä enemmän molekyyli voi varastoida energiaa sen eri vapausasteille. Tästä voi todeta, että teorian pitäisi mahdollistaa myös <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span>:n energiariippuvuus. Kuitenkin Hinshelwood–Lindeman-teoria pitää <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span>:n ja lisäksi <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 {k_{1}}{k_{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {k_{1}}{k_{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c92ef7150c97e3874e9737d11efcbdf257486da6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:4.38ex; height:5.843ex;" alt="{\displaystyle {\frac {k_{1}}{k_{-1}}}}"></span>:n energiasta riippumattomina. </p> <div class="mw-heading mw-heading3"><h3 id="Nopeusvakio_k2(E):n_energiariippuvuus"><span id="Nopeusvakio_k2.28E.29:n_energiariippuvuus"></span>Nopeusvakio <i>k<sub>2</sub>(E)</i>:n energiariippuvuus</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=3" title="Muokkaa osiota Nopeusvakio k2(E):n energiariippuvuus" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=3" title="Muokkaa osion lähdekoodia: Nopeusvakio k2(E):n energiariippuvuus"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Virittyneen molekyylin hajoamisen kinetiikkaa kuvaava nopeusvakio <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 k_{2}(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/db4999f7bf31b1b8f04bf32b5894e6d92df768b4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.85ex; height:2.843ex;" alt="{\displaystyle k_{2}(E)}"></span> voidaan arvioida tilastollisiin oletuksiin pohjautuen. Tätä lähestymistapaa edustaa RRK-teoria (Rice-Ramsperger-Kassel)<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>. Tämä teoria olettaa, että molekyyli koostuu joukosta kytkeytyneitä <a href="/wiki/Kvanttimekaaninen_harmoninen_v%C3%A4r%C3%A4htelij%C3%A4" title="Kvanttimekaaninen harmoninen värähtelijä">harmonisia värähtelijöitä</a>, jotka vaihtavat energiaa vapaasti jos </p> <dl><dd><dl><dd>a) kaikki <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 {\text{A}}^{\star }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{A}}^{\star }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3ae7028f0f5c33c8169fe0eb1a52734b4e6f2c4f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle {\text{A}}^{\star }}"></span>-molekyylit energialla <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 E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4232c9de2ee3eec0a9c0a19b15ab92daa6223f9b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.776ex; height:2.176ex;" alt="{\displaystyle E}"></span> ovat saatavilla ja niistä reaktio etenee tuotteisiin</dd></dl></dd></dl> <dl><dd><dl><dd>b) virittyneen molekyylin vibraatioenergian uudelleenjakaantuminen tapahtuu paljon nopeammin kuin itse unimolekulaarinen reaktio</dd></dl></dd></dl> <p>RRK-teoria olettaa, että reaktion alussa lähtöainemolekyylin vakio kokonaisenergia on jakaantunut tilastollisesti molekyylin energiatiloille. Tämmöisistä lähtöainemolekyyleistä koottua joukkoa sanotaan mikrokanoniseksi yhdelmäksi (engl. microcanonical ensemble)<sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">[</span>e<span class="cite-bracket">]</span></a></sup> Jokaiselta energiatilalta on sama todennäköisyys edetä reaktiossa lopputuotteisiin. Tämä mikrokanoninen yhdelmä säilyy kunnes lähtöainemolekyylit reagoivat lopputuotteiksi. </p> <div class="mw-heading mw-heading2"><h2 id="RRK-teoria">RRK-teoria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=4" title="Muokkaa osiota RRK-teoria" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=4" title="Muokkaa osion lähdekoodia: RRK-teoria"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Edellä on todettu, että unimolekulaaristen reaktioiden mitattu kinetiikka pienissä reaktiopaineissa ei aivan tarkasti ole selitettävissä Lindemann-Christiansen -mekanismilla vaan reaktion molekyylejä pitää tarkastella keskenään kytkeytyneinä värähtelijöinä. Tällöin viritysenergian voidaan olettaa jakaantuvan molekyylin sisäisesti niin, että se kerääntyy lopulta reaktion etenemisen kannalta katsoen erityisesti molekyylin katkeavalle sidokselle. Tällöin virittynyt <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 A^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44e23745a51c2c2d8d91fd98c1cf721573747ece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle A^{*}}"></span> voi muuttua aktivoiduksi kompleksiksi <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 A^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5937e9b61de17207053f263d23a26f6cc793340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.705ex; height:2.676ex;" alt="{\displaystyle A^{\ddagger }}"></span> ja energia voi keskittyä kuten esim. <i>cis</i>-<i>trans</i>-toisiintumisreaktiossa molekyylin kaksoissidoksen kiertoon (rotaatio). Tämä huomioiden reaktiovaiheet (1) ja (2) pitäisi kirjoittaa muotoon:<sup id="cite_ref-Laidler1987_11-0" class="reference"><a href="#cite_note-Laidler1987-11"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd>(1)<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 \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>A + M</mtext> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo class="MJX-variant" stretchy="false">⇌<!-- ⇌ --></mo> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </munder> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mover> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>+ M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65b6cb2acddc7a8179432d61d228dbead4771bb0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:23.64ex; height:6.843ex;" alt="{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle k_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }{\text{+ M}}}"></span></dd></dl></dd></dl> <dl><dd><dl><dd>(2)<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 \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo stretchy="false">⟶<!-- ⟶ --></mo> <mrow /> </munder> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mover> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo stretchy="false">⟶<!-- ⟶ --></mo> <mrow /> </munder> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mover> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>tuotteet</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/624eb4bc5907880afac03ed4aa2582fcc3bb82a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:27.833ex; height:5.676ex;" alt="{\displaystyle \qquad {\text{A}}^{\star }\;{\overset {\textstyle k_{2}}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{tuotteet}}}"></span></dd></dl></dd></dl> <p>Tässä <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 {\ce {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8cdeb1f188c088c37acc8921c61145bb7f1e65a9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.131ex; height:2.176ex;" alt="{\displaystyle {\ce {M}}}"></span> on puskurikaasumolekyyli tai lähtöainemolekyyli ja sen osuus on molekyylitörmäyksien aikana siirtää energiaa reagoiville <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 {\ce {A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7683201425b7130b4f6bc52be92b6de7ccbf648f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle {\ce {A}}}"></span>-molekyyleille. Yhtälössä <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 \nu ^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45631e9627f8b8b41b76ffd73f664e44075bbb5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.22ex; height:2.676ex;" alt="{\displaystyle \nu ^{\ddagger }}"></span> on kriittisen värähtelijän taajuus ja tyypillisesti <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 \nu ^{\ddagger }>k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo>></mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ^{\ddagger }>k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/558eb4ef9ded78d044b5a2e070413a7753b262ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.584ex; height:3.009ex;" alt="{\displaystyle \nu ^{\ddagger }>k_{2}}"></span>. Täten reaktion määräävä vaihe on virittyneen molekyylin muuntuminen aktivoiduksi kompleksiksi. Virittynyt molekyyli <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 A^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44e23745a51c2c2d8d91fd98c1cf721573747ece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle A^{*}}"></span> omaa kaiken tarvittavan energian muuntuakseen (värähtelemällä) aktivoiduksi kompleksiksi. Aktivoitunut kompleksi <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 A^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5937e9b61de17207053f263d23a26f6cc793340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.705ex; height:2.676ex;" alt="{\displaystyle A^{\ddagger }}"></span> on määritelmän mukaan se, joka hajoaa unimolekulaarisesti siirtymätilan kautta lopputuotteiksi reaktion <a href="/w/index.php?title=Potentiaalienergiapinta&action=edit&redlink=1" class="new" title="Potentiaalienergiapinta (sivua ei ole)">potentiaalienergiapinnalla</a>. Hinshelwood–Lindeman-teoriassa on mukana kynnysenergia <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 E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/411d268de7b1cf300d7481e3fe59f3b20887e0d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{0}}"></span>, mutta teoriassa ei oteta huomioon <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span>:n ja <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 {k_{1}}{k_{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {k_{1}}{k_{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c92ef7150c97e3874e9737d11efcbdf257486da6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:4.38ex; height:5.843ex;" alt="{\displaystyle {\frac {k_{1}}{k_{-1}}}}"></span>:n energiariippuvuutta. Sitävastoin RRK-teoriassa tämä on otettu huomioon. Yhtälöstä (8) saadaan huomioimalla energiariippuvuus RRK-teorian mukaan: </p> <dl><dd><dl><dd>(14)<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 \qquad dk_{\text{uni}}\,=\,{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad dk_{\text{uni}}\,=\,{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e4421f52691c262e3f05dc159f26e8f419b7111" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:59.895ex; height:9.343ex;" alt="{\displaystyle \qquad dk_{\text{uni}}\,=\,{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"></span></dd></dl></dd></dl> <p>Tämä on mikrokanoninen nopeusvakio, jossa molekyyleilla on energiaa välillä <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 E,E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>,</mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E,E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/04dab77e8c2df178a1ef5508ba1c065fc56f81d4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.417ex; height:2.509ex;" alt="{\displaystyle E,E+dE}"></span>. Unimolekulaarinen nopeusvakio saadaan integroimalla yhtälö (14): </p> <dl><dd><dl><dd>(15)<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 \qquad k_{\text{uni}}\,=\,\int _{E_{0}}^{\infty }{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msubsup> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msubsup> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\text{uni}}\,=\,\int _{E_{0}}^{\infty }{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02a74678eb531b58e7ff22fa2feb596203a839be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:63.406ex; height:9.343ex;" alt="{\displaystyle \qquad k_{\text{uni}}\,=\,\int _{E_{0}}^{\infty }{\frac {k_{2}(E)}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}{\frac {1}{(s-1)!}}{\Bigg (}{\frac {E_{0}}{k_{B}T}}{\Bigg )}^{s-1}e^{-{\frac {E_{0}}{k_{B}T}}}{\Bigg (}{\frac {dE}{k_{B}T}}{\Bigg )}}"></span></dd></dl></dd></dl> <p>RRK-teorian mukaan molekyyli koostuu löyhästi kytkeytyneistä varähtelijöistä, jotka voivat vaihtaa energiaa vapaasti. Olennnaista RRK-teorian olettamuksessa on, että virittyneillä molekyyleillä, <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 A^{*}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>∗<!-- ∗ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{*}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/44e23745a51c2c2d8d91fd98c1cf721573747ece" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.797ex; height:2.343ex;" alt="{\displaystyle A^{*}}"></span>, on eri pituisia elinaikoja, joten virittyneen molekyylin muuntuminen aktivoiduksi kompleksiksi, <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 A^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle A^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b5937e9b61de17207053f263d23a26f6cc793340" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.705ex; height:2.676ex;" alt="{\displaystyle A^{\ddagger }}"></span>, riippuu täysin tilastollisista tekijöistä. Kasselin mukaan reaktio tapahtuu kun kynnysenergia kasaantuu riittävän määrän värähtelyjen aikana molekyylin yhteen vibraationmoodiin, joka johtaa lopputuotteisiin.<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>f<span class="cite-bracket">]</span></a></sup> RRK-teorian mukaan kuten myös Hinshelwood-Lindemann -teoriassa molekyyli virittyy vahvan törmäyksen seurauksena. Tällöin suuri määrä energiaa (enemmän kuin <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 k_{B}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{B}T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c3b4baed050c25a0d97fc74e8da32d37dcecaf50" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:4.327ex; height:2.509ex;" alt="{\displaystyle k_{B}T}"></span>) siirtyy, joten virittyminen tapahtuu suurella todennäköisyydellä yhden törmäyksen aikana. RRK-teorian mukaan nopeusvakio <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span> riippuu energiasta tilastollisesti. Yleisesti <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>-kappaletta vibraatiokvantteja voidaan jakaa kahdelle värähtelijälle <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 j+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5baf2ec9e436e9309065133555e3cb2ecd88f87e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:4.988ex; height:2.509ex;" alt="{\displaystyle j+1}"></span>-kertaa<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">[</span>g<span class="cite-bracket">]</span></a></sup>, ja vibraatioenergiatasolla <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>:llä erotettavien energiatilojen lukumäärä (degeneraatio) on täten <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 j+1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5baf2ec9e436e9309065133555e3cb2ecd88f87e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:4.988ex; height:2.509ex;" alt="{\displaystyle j+1}"></span> kappaletta. Molekyylille, jolla on <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>-kappaletta värähtelijöitä, tämä tilastollinen paino <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 W(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c22e7d910286376b2f4ee66a401fde88e3950f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.02ex; height:2.843ex;" alt="{\displaystyle W(E)}"></span> (so. degeneraatio) <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span>:llä vibraatioenergiatasolla on:<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">[</span>h<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Steinfeld1998_14-1" class="reference"><a href="#cite_note-Steinfeld1998-14"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd>(16)<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 \qquad W(E)={\frac {(j+s-1)!}{j!(s-1)!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>j</mi> <mo>+</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> <mrow> <mi>j</mi> <mo>!</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad W(E)={\frac {(j+s-1)!}{j!(s-1)!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/43b3d8023b3122418faf85d3deef48518d98a6be" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:25.948ex; height:6.509ex;" alt="{\displaystyle \qquad W(E)={\frac {(j+s-1)!}{j!(s-1)!}}}"></span></dd></dl></dd></dl> <p>Oletetaan reaktion kannalta, että virittyneen molekyylin hajoaminen (dissosiaatio) vaatii <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span>-kappaletta vibraatiokvantteja aktivoidussa kompleksissa. Tällöin jäljellä olevat vapaat vibraatiokvantit voidaan jakaa <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 s-1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s-1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b027c8c033c9ca80d57161107c464eca1000e47f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.093ex; height:2.343ex;" alt="{\displaystyle s-1}"></span> -tiloille seuraavasti: </p> <dl><dd><dl><dd>(17)<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 \qquad W(E)'={\frac {(j-m+s-1)!}{(j-m)!(s-1)!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <msup> <mo stretchy="false">)</mo> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>j</mi> <mo>−<!-- − --></mo> <mi>m</mi> <mo>+</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>j</mi> <mo>−<!-- − --></mo> <mi>m</mi> <mo stretchy="false">)</mo> <mo>!</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad W(E)'={\frac {(j-m+s-1)!}{(j-m)!(s-1)!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8a47f78d1d39ae7988117bcb9b0475ea29f636de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:31.513ex; height:6.509ex;" alt="{\displaystyle \qquad W(E)'={\frac {(j-m+s-1)!}{(j-m)!(s-1)!}}}"></span></dd></dl></dd></dl> <p>Todennäköisyys sille, että <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 m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> vibraatiokvanttia on sijoittunut dissosiaation kannalta oikein on <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 {W(E)'}{W(E)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <msup> <mo stretchy="false">)</mo> <mo>′</mo> </msup> </mrow> <mrow> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {W(E)'}{W(E)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/222603347d61babc66a79ae4ff380970a20e65cf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:7.541ex; height:6.509ex;" alt="{\displaystyle {\frac {W(E)'}{W(E)}}}"></span>. Kokonaisenergia <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 E=jh\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>j</mi> <mi>h</mi> <mi>ν<!-- ν --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=jh\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e820052df998924ea94753f8008ce95855c87b55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.403ex; height:2.509ex;" alt="{\displaystyle E=jh\nu }"></span> ja reaktion etenemisen kannalta katsoen kriittisellä värähtelijän energia on <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 E_{0}=mh\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mi>h</mi> <mi>ν<!-- ν --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}=mh\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9ab12e559b0eded2bec2d32cf1e901c9d54e72c8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.479ex; height:2.509ex;" alt="{\displaystyle E_{0}=mh\nu }"></span>.<sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">[</span>i<span class="cite-bracket">]</span></a></sup><a href="/wiki/Kertoma#Stirlingin_approksimaatio" title="Kertoma">Stirlingin approksimaatiota</a> soveltaen unimolekulaarinen nopeusvakio on tämän todennäköisyyden ja aktivoidun kompleksin hajoamisen värähdystaajuuden tulo. Klassisella rajalla <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 j\gg s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>≫<!-- ≫ --></mo> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j\gg s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a9d0383799acd56ad20bc1efddfec3c2241ed7ac" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:5.689ex; height:2.509ex;" alt="{\displaystyle j\gg s}"></span> ja <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 j-m\gg s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> <mo>−<!-- − --></mo> <mi>m</mi> <mo>≫<!-- ≫ --></mo> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j-m\gg s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/77361dbdf868bc0f28fa83a55850276a6c6586f1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:10.57ex; height:2.509ex;" alt="{\displaystyle j-m\gg s}"></span> ja kertomalla saadun yhtälön osoittaja ja nimittäjä <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 (h\nu )^{s-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>h</mi> <mi>ν<!-- ν --></mi> <msup> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (h\nu )^{s-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3954139de14697e8c7305c24a250e908a90218a6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.484ex; height:3.176ex;" alt="{\displaystyle (h\nu )^{s-1}}"></span>:llä, saadaan nopeusvakioksi: </p> <dl><dd><dl><dd>(18)<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 \qquad k_{2}(E)\,=\,k(E=jh\nu )\,=\,\nu ^{\ddagger }{\Bigg (}{\frac {E-E_{0}}{E}}{\Bigg )}^{s-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mi>k</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo>=</mo> <mi>j</mi> <mi>h</mi> <mi>ν<!-- ν --></mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mo>−<!-- − --></mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mi>E</mi> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="2.470em" minsize="2.470em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{2}(E)\,=\,k(E=jh\nu )\,=\,\nu ^{\ddagger }{\Bigg (}{\frac {E-E_{0}}{E}}{\Bigg )}^{s-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/241cdfaee528b41e72a280acacc8d431093aafbc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.171ex; width:46.891ex; height:8.009ex;" alt="{\displaystyle \qquad k_{2}(E)\,=\,k(E=jh\nu )\,=\,\nu ^{\ddagger }{\Bigg (}{\frac {E-E_{0}}{E}}{\Bigg )}^{s-1}}"></span></dd></dl></dd></dl><p> Oheisesta kuvaajasta selviää nopeusvakion riippuvuus energiasta eri vapausastemäärillä.</p><figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Tiedosto:RRKnopeusvakio.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/RRKnopeusvakio.svg/250px-RRKnopeusvakio.svg.png" decoding="async" width="250" height="189" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d1/RRKnopeusvakio.svg/375px-RRKnopeusvakio.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d1/RRKnopeusvakio.svg/500px-RRKnopeusvakio.svg.png 2x" data-file-width="610" data-file-height="460" /></a><figcaption>Unimolekulaarisen nopeusvakion riippuvuus energiasta, <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 E_{0}=40\,{\text{ kcal mol}}^{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>40</mn> <mspace width="thinmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext> kcal mol</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E_{0}=40\,{\text{ kcal mol}}^{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2176dffb9a5eea2aee73c93f18f7a222f3548add" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.888ex; height:3.009ex;" alt="{\displaystyle E_{0}=40\,{\text{ kcal mol}}^{-1}}"></span>. LC on Lindemann–Christiansen-mekanismi.</figcaption></figure><p> Kuvaajasta on todettavissa nopeusvakion arvon suureneminen kun energia kasvaa ja toisaalta vakioenergia-arvolla nopeusvakion arvo pienenee kun värähtelijöiden määrä kasvaa. Tämä tapahtuu, koska tällöin energia jakaantuu yhä useammille värähtelijöille (yhä suurempi molekyyli) ja kriittiselle värähtelijälle jää yhä vähemmän energiaa. </p><p>Sijoitettaessa yhtälö (18) yhtälöön (15) ja merkitsemällä <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={\frac {E-E_{0}}{k_{B}T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>E</mi> <mo>−<!-- − --></mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x={\frac {E-E_{0}}{k_{B}T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2c8c02769cd02cea0d3d827b31c9e05a3c681988" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.65ex; height:5.843ex;" alt="{\displaystyle x={\frac {E-E_{0}}{k_{B}T}}}"></span> ja <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 b={\frac {E_{0}}{k_{B}T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b={\frac {E_{0}}{k_{B}T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5fb55e59eeb96e99b5089a574a44221aa3f2d590" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:9.259ex; height:5.843ex;" alt="{\displaystyle b={\frac {E_{0}}{k_{B}T}}}"></span> ja merkitsemällä <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 dx={\frac {dE}{k_{B}T}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>x</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dx={\frac {dE}{k_{B}T}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7cb54465cdd936322489f93917f218423350e709" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.807ex; height:5.843ex;" alt="{\displaystyle dx={\frac {dE}{k_{B}T}}}"></span> saadaan:<sup id="cite_ref-Steinfeld1998_14-2" class="reference"><a href="#cite_note-Steinfeld1998-14"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd>(19)<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 \qquad k_{\text{uni}}\,=\,{\frac {\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}{(s-1)!}}\int \limits _{0}^{\infty }{\frac {x^{s-1}e^{-x}dx}{1+{\frac {\nu ^{\ddagger }}{\omega }}{\Big (}{\frac {x}{b+x}}{\Big )}^{s-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mrow> <mrow> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mi>x</mi> </mrow> </msup> <mi>d</mi> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mi>ω<!-- ω --></mi> </mfrac> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">(</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>x</mi> <mrow> <mi>b</mi> <mo>+</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mo maxsize="1.623em" minsize="1.623em">)</mo> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msup> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\text{uni}}\,=\,{\frac {\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}{(s-1)!}}\int \limits _{0}^{\infty }{\frac {x^{s-1}e^{-x}dx}{1+{\frac {\nu ^{\ddagger }}{\omega }}{\Big (}{\frac {x}{b+x}}{\Big )}^{s-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a655d722c9ec72b2c2a117929a23c24e6c8c706" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -5.005ex; width:41.753ex; height:10.676ex;" alt="{\displaystyle \qquad k_{\text{uni}}\,=\,{\frac {\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}{(s-1)!}}\int \limits _{0}^{\infty }{\frac {x^{s-1}e^{-x}dx}{1+{\frac {\nu ^{\ddagger }}{\omega }}{\Big (}{\frac {x}{b+x}}{\Big )}^{s-1}}}}"></span></dd></dl></dd></dl> <p>Kun reaktiopaine suurenee, niin <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 \omega (=k_{-1}[M])\to \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> <mo stretchy="false">(</mo> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo stretchy="false">)</mo> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega (=k_{-1}[M])\to \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b676c69b136805b0001822f7551ff050c18cd407" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:18.926ex; height:2.843ex;" alt="{\displaystyle \omega (=k_{-1}[M])\to \infty }"></span>. Tällöin yhtälö (19) supistuu <a href="/wiki/Arrheniuksen_yht%C3%A4l%C3%B6" title="Arrheniuksen yhtälö">Arrheniuksen yhtälön</a> muotoon: </p> <dl><dd><dl><dd>(20)<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 \qquad k_{\infty }\,=\,\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\infty }\,=\,\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/86d96faeb5ff839039091ffa17a4fa10b9a3980c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:20.035ex; height:4.843ex;" alt="{\displaystyle \qquad k_{\infty }\,=\,\nu ^{\ddagger }e^{-{\frac {E_{0}}{k_{B}T}}}}"></span></dd></dl></dd></dl> <p>Nopeusvakio <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 k_{\text{uni}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{\text{uni}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7f62e799f1a43389be2d20efcc2d260b45e4fbcf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.729ex; height:2.509ex;" alt="{\displaystyle k_{\text{uni}}}"></span>:n laskemiseksi tarvitaan tieto parametreista <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 \nu ^{\ddagger },s,E_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo>,</mo> <mi>s</mi> <mo>,</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ^{\ddagger },s,E_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f7f0a9d444ca774b344b2437765f320c97e5959d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.147ex; height:3.009ex;" alt="{\displaystyle \nu ^{\ddagger },s,E_{0}}"></span>. RRK-teorian puutteena voidaan pitää sitä, että jotta saadaan nopeusvakioiden RRK-laskennollisista arvoista kokeellisesti mitattujen nopeusvakioiden arvojen kanssa yhteneviä, pitää <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>:lle ottaa kokonaisnormaalimoodilukumäärästä noin puolet laskuihin. Lisäksi RRK-teorian mahdollistama arvo <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 \nu ^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu ^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/45631e9627f8b8b41b76ffd73f664e44075bbb5a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.22ex; height:2.676ex;" alt="{\displaystyle \nu ^{\ddagger }}"></span>:lle on useimmille reaktioille liian pieni. Korjauksen tähän antaa RRK-teoriasta pidemmälle kehitetty <a href="/wiki/RRKM-teoria" title="RRKM-teoria">RRKM-teoria</a>. </p> <div class="mw-heading mw-heading2"><h2 id="QRRK-teoria">QRRK-teoria</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=5" title="Muokkaa osiota QRRK-teoria" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=5" title="Muokkaa osion lähdekoodia: QRRK-teoria"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Kuten edellä on todettavissa, että unimolekulaarisen reaktion Lindemann–Christiansen-mekanismissa ei oteta huomioon <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 k_{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c51b4ba57ee596d8435fc4ed76703ca3a2fc444a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{2}}"></span>:n ja <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 {k_{1}}{k_{-1}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {k_{1}}{k_{-1}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c92ef7150c97e3874e9737d11efcbdf257486da6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:4.38ex; height:5.843ex;" alt="{\displaystyle {\frac {k_{1}}{k_{-1}}}}"></span>:n energiariippuvuutta kuten RRK-teoriassa. Tämä sama voidaan tuoda esiin RRK-teorian tilastollisessa käsittelyssä (quantumRRK). Tällöin Lindemann–Christiansen-mekanismin yhtälöt (1) ja (2) kirjoitetaan:<sup id="cite_ref-Steinfeld1998_14-3" class="reference"><a href="#cite_note-Steinfeld1998-14"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><dl><dd>(1)<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 \qquad {\text{A + M}}\;{\overset {\textstyle dk_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }(E){\text{+ M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>A + M</mtext> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo class="MJX-variant" stretchy="false">⇌<!-- ⇌ --></mo> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </munder> <mstyle displaystyle="false" scriptlevel="0"> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mover> </mrow> <mspace width="thickmathspace" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mtext>+ M</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle dk_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }(E){\text{+ M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/74e39af96940c198a9051fcfbf7417b6a95362ba" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:27.225ex; height:6.843ex;" alt="{\displaystyle \qquad {\text{A + M}}\;{\overset {\textstyle dk_{1}}{\underset {\textstyle k_{-1}}{\rightleftharpoons }}}\;{\text{A}}^{\star }(E){\text{+ M}}}"></span></dd></dl></dd></dl> <dl><dd><dl><dd>(2)<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 \qquad {\text{A}}^{\star }(E)\;{\overset {\textstyle k_{2}(E)}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }(E)\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo stretchy="false">⟶<!-- ⟶ --></mo> <mrow /> </munder> <mstyle displaystyle="false" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mover> </mrow> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mover> <munder> <mo stretchy="false">⟶<!-- ⟶ --></mo> <mrow /> </munder> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mover> </mrow> <mspace width="thickmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\text{A}}^{\star }(E)\;{\overset {\textstyle k_{2}(E)}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }(E)\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c835094d5103fc3a279c46c33410b2fb2fbde351" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:30.652ex; height:6.176ex;" alt="{\displaystyle \qquad {\text{A}}^{\star }(E)\;{\overset {\textstyle k_{2}(E)}{\underset {}{\longrightarrow }}}{\text{A}}^{\ddagger }(E)\;{\overset {\nu ^{\ddagger }}{\underset {}{\longrightarrow }}}\;{\text{H}}}"></span></dd></dl></dd></dl> <p>Tässä <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 {\text{H}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{H}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8109aaddd1080d2d96db8687afd0fa27bcd41acf" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle {\text{H}}}"></span> on reaktion lopputuote. Reaktion lopputuotteelle saadaan käyttäen vakiotilaoletusta sekä <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 {\text{A}}^{\ddagger }(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{A}}^{\ddagger }(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c253d1406abce6ac800df1093b1d6bf25310fdc8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.29ex; height:3.343ex;" alt="{\displaystyle {\text{A}}^{\ddagger }(E)}"></span>:lle että <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 {\text{A}}^{\star }(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{A}}^{\star }(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/88d44a03a51e975b8b6ace79c3cd43d6b6f72576" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.382ex; height:2.843ex;" alt="{\displaystyle {\text{A}}^{\star }(E)}"></span>:lle muodostumisnopeudeksi (<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^{\ddagger }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p^{\ddagger }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/083845de13c685d0caf86da1912e1041e401e96d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:2.221ex; height:3.009ex;" alt="{\displaystyle p^{\ddagger }}"></span> on ekvivalettisten mekanismipolkujen lukumäärä): </p> <dl><dd><dl><dd>(21)<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 \qquad {\frac {d[H]}{dt}}\,=\,{\frac {1}{p^{\ddagger }}}\nu ^{\ddagger }[A^{\ddagger }(E)]\,=\,k_{2}(E)[A^{\star }(E)]\,=\,{\frac {k_{2}(E)\,dk_{1}(E)\,[A][M]}{k_{-1}[M]+k_{2}(E)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <mo stretchy="false">[</mo> <mi>H</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <mi>d</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msup> <mi>p</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> </mfrac> </mrow> <msup> <mi>ν<!-- ν --></mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>‡<!-- ‡ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo stretchy="false">[</mo> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>⋆<!-- ⋆ --></mo> </mrow> </msup> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo stretchy="false">]</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mi>A</mi> <mo stretchy="false">]</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\frac {d[H]}{dt}}\,=\,{\frac {1}{p^{\ddagger }}}\nu ^{\ddagger }[A^{\ddagger }(E)]\,=\,k_{2}(E)[A^{\star }(E)]\,=\,{\frac {k_{2}(E)\,dk_{1}(E)\,[A][M]}{k_{-1}[M]+k_{2}(E)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c996a1b0c2c4ec70a690a950ca4cfff00182f0de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:69.27ex; height:6.509ex;" alt="{\displaystyle \qquad {\frac {d[H]}{dt}}\,=\,{\frac {1}{p^{\ddagger }}}\nu ^{\ddagger }[A^{\ddagger }(E)]\,=\,k_{2}(E)[A^{\star }(E)]\,=\,{\frac {k_{2}(E)\,dk_{1}(E)\,[A][M]}{k_{-1}[M]+k_{2}(E)}}}"></span></dd></dl></dd></dl> <p><br /> Unimolekulaariselle nopeusvakiolla (ks. yhtälö (5)) on energiariippuvuus välillä <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 E\to E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">→<!-- → --></mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\to E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d755a2fc4df35209833fcd34a866fd2be151d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.997ex; height:2.343ex;" alt="{\displaystyle E\to E+dE}"></span>: </p> <dl><dd><dl><dd>(22)<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 \qquad k_{\text{uni}}(E)\,=\,{\frac {k_{2}(E)\,dk_{1}(E)[M]}{k_{-1}[M]+k_{2}(E)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\text{uni}}(E)\,=\,{\frac {k_{2}(E)\,dk_{1}(E)[M]}{k_{-1}[M]+k_{2}(E)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b193517ea184f8ad0c289b0c48ed77738deb6edd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:33.707ex; height:6.509ex;" alt="{\displaystyle \qquad k_{\text{uni}}(E)\,=\,{\frac {k_{2}(E)\,dk_{1}(E)[M]}{k_{-1}[M]+k_{2}(E)}}}"></span></dd></dl></dd></dl> <p>Termisen nopeusvakio laskemiseksi yhtälö (22) on integroitava </p> <dl><dd><dl><dd>(23)<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 \qquad k_{\text{uni}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,dk_{1}(E)\,[M]}{k_{-1}[M]+k_{2}(E)}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}\,=\,\omega \int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,P(E)dE}{\omega +k_{2}(E)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mtext>uni</mtext> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mrow> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mi>ω<!-- ω --></mi> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>P</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>E</mi> </mrow> <mrow> <mi>ω<!-- ω --></mi> <mo>+</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\text{uni}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,dk_{1}(E)\,[M]}{k_{-1}[M]+k_{2}(E)}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}\,=\,\omega \int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,P(E)dE}{\omega +k_{2}(E)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/65f68553fa0eb55a6adbd39d3bde13dac32075e6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.505ex; width:76.762ex; height:10.009ex;" alt="{\displaystyle \qquad k_{\text{uni}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,dk_{1}(E)\,[M]}{k_{-1}[M]+k_{2}(E)}}\,=\,\int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}}{1+{\frac {k_{2}(E)}{k_{-1}[M]}}}}\,=\,\omega \int \limits _{E_{0}}^{\infty }{\frac {k_{2}(E)\,P(E)dE}{\omega +k_{2}(E)}}}"></span></dd></dl></dd></dl> <p>Tässä <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 \omega =k_{-1}[M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ω<!-- ω --></mi> <mo>=</mo> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega =k_{-1}[M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3901ca87a55ff09a83801d03c5ee9afae9e31d6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.824ex; height:2.843ex;" alt="{\displaystyle \omega =k_{-1}[M]}"></span>. Korkeissa paineissa <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 [M]\to \infty }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo stretchy="false">→<!-- → --></mo> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]\to \infty }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f0ad87496b668417c7dbf966038e6a1d933076c5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.674ex; height:2.843ex;" alt="{\displaystyle [M]\to \infty }"></span>, joten nopeusvakiolle saadaan </p> <dl><dd><dl><dd>(24)<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 \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}\,=\,k_{2}(E)\,dK(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mi>d</mi> <mi>K</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}\,=\,k_{2}(E)\,dK(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/101b03eb735beae4c8cf0fd9e3bdd598ac115738" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:45.225ex; height:9.176ex;" alt="{\displaystyle \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E){\frac {dk_{1}(E)}{k_{-1}}}\,=\,k_{2}(E)\,dK(E)}"></span></dd></dl></dd></dl> <p>Tasapainovakio <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 dK(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>K</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dK(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/562155e3cfbcdbbe70f8da5379558666499ffcfd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.867ex; height:2.843ex;" alt="{\displaystyle dK(E)}"></span> voidaan antaa tilastollisen mekaniikan mukaisesti todennäköisyytenä <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(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/687fe7f4688af755503fd00e7538f285e2a9954b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.33ex; height:2.843ex;" alt="{\displaystyle P(E)}"></span>, koska <a href="/wiki/Alkeisreaktio#Lisätieto" title="Alkeisreaktio">Boltzmannin jakaumafunktion</a> mukaan voidaan kirjoittaa: </p> <dl><dd><dl><dd>(25)<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 \qquad {\frac {N_{i}(E_{i})}{N}}\,=\,P(E_{i})\,=\ {\frac {g_{i}\,e^{-{\frac {E_{i}}{k_{B}T}}}}{Q_{v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>N</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">(</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> </mrow> <mi>N</mi> </mfrac> </mrow> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mi>P</mi> <mo stretchy="false">(</mo> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="thinmathspace" /> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad {\frac {N_{i}(E_{i})}{N}}\,=\,P(E_{i})\,=\ {\frac {g_{i}\,e^{-{\frac {E_{i}}{k_{B}T}}}}{Q_{v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59a7f2c16fba4123afaa057766fe3f0f59b1849a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:35.823ex; height:8.176ex;" alt="{\displaystyle \qquad {\frac {N_{i}(E_{i})}{N}}\,=\,P(E_{i})\,=\ {\frac {g_{i}\,e^{-{\frac {E_{i}}{k_{B}T}}}}{Q_{v}}}}"></span></dd></dl></dd></dl> <p>Tässä <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 Q_{v}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle Q_{v}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/138e2e2b18d08e567eda703007eac1cd6908eceb" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.868ex; height:2.509ex;" alt="{\displaystyle Q_{v}}"></span> on lähtöainemolekyylin <a href="/wiki/Molekulaarinen_jakaumafunktio" title="Molekulaarinen jakaumafunktio">vibraatiojakaumafunktio</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(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/687fe7f4688af755503fd00e7538f285e2a9954b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.33ex; height:2.843ex;" alt="{\displaystyle P(E)}"></span> on todennäköisyys sille, että molekyyli löytyy energiavälillä <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 E\to E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">→<!-- → --></mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\to E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d755a2fc4df35209833fcd34a866fd2be151d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.997ex; height:2.343ex;" alt="{\displaystyle E\to E+dE}"></span> Boltzmannin jakaumassa. Jos energia oletetaan jatkuvaksi niin vibraatiotilojen lukumäärä energiavälillä <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 E\to E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">→<!-- → --></mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\to E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6d755a2fc4df35209833fcd34a866fd2be151d71" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.997ex; height:2.343ex;" alt="{\displaystyle E\to E+dE}"></span> on <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 W(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c22e7d910286376b2f4ee66a401fde88e3950f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.02ex; height:2.843ex;" alt="{\displaystyle W(E)}"></span> ja se on sama kuin tilastollinen paino <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}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>g</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle g_{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2ce36142a0a1c6660e82bdf3ef3f1551317efe0c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.909ex; height:2.009ex;" alt="{\displaystyle g_{i}}"></span>. <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 W(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c22e7d910286376b2f4ee66a401fde88e3950f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.02ex; height:2.843ex;" alt="{\displaystyle W(E)}"></span> on suhteutettu tilojen tiheyteen, joten yleisesti pätee </p> <dl><dd><dl><dd>(26)<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 \qquad P(E)\,=\ N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mi>P</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mtext> </mtext> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mi>d</mi> <mi>E</mi> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad P(E)\,=\ N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9640d360d5e7cc0d1667c4cc42afcb729e4b5fc6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:30.116ex; height:7.676ex;" alt="{\displaystyle \qquad P(E)\,=\ N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"></span></dd></dl></dd></dl> <p>Tämä voidaan sijoittaa yhtälöön (24), jolloin saadaan </p> <dl><dd><dl><dd>(27)<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 \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E)N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mi>d</mi> <mi>E</mi> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E)N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1536927267eea7244c73ed4bbc640dd92ab75402" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:36.421ex; height:9.676ex;" alt="{\displaystyle \qquad k_{\infty }\,=\,\int \limits _{E_{0}}^{\infty }k_{2}(E)N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"></span></dd></dl></dd></dl> <p>Toisaalta matalissa paineissa <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 [M]\to 0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <mo stretchy="false">→<!-- → --></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle [M]\to 0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58838b99bc3f96e4a3eb7c70929c12d0b2e1afe9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:8.512ex; height:2.843ex;" alt="{\displaystyle [M]\to 0}"></span>, joten yhtälöstä (23) saadaan </p> <dl><dd><dl><dd>(28)<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 \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }dk_{1}(E)\,[M]}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mi>d</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }dk_{1}(E)\,[M]}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32cb696e0ba960f57fc0aa5cd6b4229f2386759d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:24.864ex; height:9.176ex;" alt="{\displaystyle \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }dk_{1}(E)\,[M]}"></span></dd></dl></dd></dl> <p>Kun otetaan ns. vahva törmäys, niin <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 k_{-1}=Z_{-1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{-1}=Z_{-1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a2c59b2ce4f238b0b51a2b1086d752e88ea963b5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.563ex; height:2.509ex;" alt="{\displaystyle k_{-1}=Z_{-1}}"></span>, niin voidaan kirjoittaa aktivoidun kompleksin rakenteesta riippumaton nopeusvakio. </p> <dl><dd><dl><dd>(29)<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 \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }[M]Z_{-1}N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <munderover> <mo>∫<!-- ∫ --></mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi>E</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞<!-- ∞ --></mi> </mrow> </munderover> <mo stretchy="false">[</mo> <mi>M</mi> <mo stretchy="false">]</mo> <msub> <mi>Z</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mn>1</mn> </mrow> </msub> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msup> <mi>e</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−<!-- − --></mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>E</mi> <mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mrow> </mfrac> </mrow> </mrow> </msup> <mi>d</mi> <mi>E</mi> </mrow> <msub> <mi>Q</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>v</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }[M]Z_{-1}N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6cff5524d46ef3c6b12653cf107e3064db72d856" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.338ex; width:37.018ex; height:9.676ex;" alt="{\displaystyle \qquad k_{0}\,=\,\int \limits _{E_{0}}^{\infty }[M]Z_{-1}N(E)\,{\frac {e^{-{\frac {E}{k_{B}T}}}dE}{Q_{v}}}}"></span></dd></dl></dd></dl> <p>Yhtälön (29) mukaisesti <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 k_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eafdfeca4ead3960fca92311910970eba7ec48a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{0}}"></span> on sitä suurempi mitä kookkaampi molekyyli on, koska sillä on tällöin myös suuri energiatilatiheys. Huomioitavaa on se, että <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 k_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eafdfeca4ead3960fca92311910970eba7ec48a1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{0}}"></span>:n riippumattomuus aktivoidun kompleksin (so. siirtymätila) spektroskooppisesta rakenteesta mahdollistaa verrata laskennollisia ja kokeellisia nopeusvakioiden arvoja toisiinsa. </p> <div class="mw-heading mw-heading2"><h2 id="Huomautukset">Huomautukset</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=6" title="Muokkaa osiota Huomautukset" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=6" title="Muokkaa osion lähdekoodia: Huomautukset"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="viitteet-malline" class="viitteet-malline" style="list-style-type:lower-alpha;"><ol class="references"> <li id="cite_note-3"><span class="mw-cite-backlink"><a href="#cite_ref-3">↑</a></span> <span class="reference-text">Virittyneessä molekyylissä tapahtuu energian sisäsiirtymä (engl. internal conversion) elektroniselle perustilalle <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 {\text{S}}_{0}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{S}}_{0}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8e652cb3cde40d987e8f3319ffcb820788b57f8f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.347ex; height:2.509ex;" alt="{\displaystyle {\text{S}}_{0}}"></span> (<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 {\text{S}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>S</mtext> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{S}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f8ac4b87e90f3fac374b245e9c404f8efc4addd6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.293ex; height:2.176ex;" alt="{\displaystyle {\text{S}}}"></span> on singlettitila).</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><a href="#cite_ref-4">↑</a></span> <span class="reference-text">Kineettisessä mittauksessa reaktiopaineen määrään vaikutetaan muuttamalla puskurikaasun (M), joka on tuotteiden muodostumisen kannalta katsoen reagoimaton, konsentraatiota.</span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><a href="#cite_ref-5">↑</a></span> <span class="reference-text"><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 (1-s)!\,=\,1\cdot 2\cdot 3\cdot ...\cdot (1-s)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−<!-- − --></mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>!</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mn>1</mn> <mo>⋅<!-- ⋅ --></mo> <mn>2</mn> <mo>⋅<!-- ⋅ --></mo> <mn>3</mn> <mo>⋅<!-- ⋅ --></mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>⋅<!-- ⋅ --></mo> <mo stretchy="false">(</mo> <mn>1</mn> <mo>−<!-- − --></mo> <mi>s</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (1-s)!\,=\,1\cdot 2\cdot 3\cdot ...\cdot (1-s)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4ccc5c4e83287d3ab485b6ab402cc83185aa941c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:29.566ex; height:2.843ex;" alt="{\displaystyle (1-s)!\,=\,1\cdot 2\cdot 3\cdot ...\cdot (1-s)}"></span>. Hinshelwoodin määritelmä nopeusvakio <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 k_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/376315fd4983f01dada5ec2f7bebc48455b14a66" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.265ex; height:2.509ex;" alt="{\displaystyle k_{1}}"></span>:n riippuvuudesta vapausasteesta on johdettu siitä, miten <a href="/wiki/Ideaalikaasu" title="Ideaalikaasu">ihannekaasun</a> kineettinen energia jakaantuu molekyylissä. Molekyylin keskimääräinen kineettinen energia yhtä ulottuvuutta kohden on <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\langle E\right\rangle ={\frac {1}{2}}k_{B}T=sk_{B}T}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow> <mo>⟨</mo> <mi>E</mi> <mo>⟩</mo> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> <mo>=</mo> <mi>s</mi> <msub> <mi>k</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>B</mi> </mrow> </msub> <mi>T</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \left\langle E\right\rangle ={\frac {1}{2}}k_{B}T=sk_{B}T}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dfc8bf55890a04a8d8a1b40583022cf0b214c21f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:21.525ex; height:5.176ex;" alt="{\displaystyle \left\langle E\right\rangle ={\frac {1}{2}}k_{B}T=sk_{B}T}"></span>.</span> </li> <li id="cite_note-7"><span class="mw-cite-backlink"><a href="#cite_ref-7">↑</a></span> <span class="reference-text">Cyril Norman Hinshelwood jakoi vuoden 1956 kemian Nobelin tästä teoriasta yhdessä Nikolay Semenov'in kanssa.</span> </li> <li id="cite_note-10"><span class="mw-cite-backlink"><a href="#cite_ref-10">↑</a></span> <span class="reference-text"><a href="/wiki/Tilastollinen_termodynamiikka" title="Tilastollinen termodynamiikka">Tilastollisessa termodynamiikassa</a> mikrokanoninen yhdelmä tarkoittaa energiatilajoukkoa, jolla on tarkka kokonaisenergia. Tämä joukko on eristetty eikä se vaihda energiaa ympäristönsä kanssa ajan funktiona.</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><a href="#cite_ref-12">↑</a></span> <span class="reference-text">Esimerkiksi kun virittyneessä etaanimolekyyylissä (<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 {\ce {C2H6}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msubsup> <mtext>C</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> <msubsup> <mtext>H</mtext> <mrow class="MJX-TeXAtom-ORD"> <mn>6</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mspace width="0pt" height="0pt" depth=".2em" /> </mrow> </msubsup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\ce {C2H6}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a797fa211068b1b0c64f6239f0fdab0b53ce386a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:5.53ex; height:2.843ex;" alt="{\displaystyle {\ce {C2H6}}}"></span>) riittävä määrä energia kasaantuu C-C -sidoksen vibraatiomoodiin ja lopputuloksena sidos katkeaa homolyyttisesti muodostaen kaksi metyyliradikaalia.</span> </li> <li id="cite_note-13"><span class="mw-cite-backlink"><a href="#cite_ref-13">↑</a></span> <span class="reference-text">Esim. kun on 2 värähtelijää, niin 2 vibraatiokvanttilukua voidaan jakaa kolmella tapaa: (2,0), (1,1), (0,2)</span> </li> <li id="cite_note-15"><span class="mw-cite-backlink"><a href="#cite_ref-15">↑</a></span> <span class="reference-text">Unimolekulaarisen reaktion lähtöainemolekyylit virittyvät energialla, jolloin suuri määrä vibraatiotiloja välillä <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 dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f662874afa890ebdf23cceecf7d48210ef2bf2c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.991ex; height:2.176ex;" alt="{\displaystyle dE}"></span> on saatavilla. Tämä lukumäärä on <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 W(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c22e7d910286376b2f4ee66a401fde88e3950f6e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:6.02ex; height:2.843ex;" alt="{\displaystyle W(E)}"></span> ja se on suhteutettu tilojen summaan <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(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fab049a54174eb1496f65c7cd21a515e5021cf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.412ex; height:2.843ex;" alt="{\displaystyle G(E)}"></span>, ja tiheyteen <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 N(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fbe797df2434f2e14ced1b8d3440dbd580799b63" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.649ex; height:2.843ex;" alt="{\displaystyle N(E)}"></span>. <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(E)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>G</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle G(E)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fab049a54174eb1496f65c7cd21a515e5021cf6" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.412ex; height:2.843ex;" alt="{\displaystyle G(E)}"></span> on määritelty vibraatioenergiatilojen lukumääräksi energiavälillä <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 0\rightarrow E}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mo stretchy="false">→<!-- → --></mo> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0\rightarrow E}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0e2d1dff9f2eac2d0f2efa03ad4f03ae6bf77942" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.552ex; height:2.176ex;" alt="{\displaystyle 0\rightarrow E}"></span>. Energiatilojen luk]umäärä välillä <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 E\rightarrow E+dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo stretchy="false">→<!-- → --></mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E\rightarrow E+dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/56133f4c45588809998758c3f556a92657e07fd2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.997ex; height:2.343ex;" alt="{\displaystyle E\rightarrow E+dE}"></span> on <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 W(E)=N(E)dE}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mi>d</mi> <mi>E</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)=N(E)dE}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c292bd55848893ae77484f6d15e4e7f28c12cd00" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:17.759ex; height:2.843ex;" alt="{\displaystyle W(E)=N(E)dE}"></span>. Energiatilojen tiheys on <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 N(E)={\frac {G(E+dE)-G(E)}{dE}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>G</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo>+</mo> <mi>d</mi> <mi>E</mi> <mo stretchy="false">)</mo> <mo>−<!-- − --></mo> <mi>G</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>d</mi> <mi>E</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N(E)={\frac {G(E+dE)-G(E)}{dE}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4f19ec277a1697ff348455053c624c741d038b5c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:29.079ex; height:5.843ex;" alt="{\displaystyle N(E)={\frac {G(E+dE)-G(E)}{dE}}}"></span>. Molekyylille, jolla on <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span> värähtelijää, kaikki molekyylin värähdystaajuudet <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 \nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ν<!-- ν --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c15bbbb971240cf328aba572178f091684585468" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.232ex; height:1.676ex;" alt="{\displaystyle \nu }"></span> ovat yhtäsuuria ja molekyylin kokonaisenergia on <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 E=jh\nu }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>E</mi> <mo>=</mo> <mi>j</mi> <mi>h</mi> <mi>ν<!-- ν --></mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle E=jh\nu }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e820052df998924ea94753f8008ce95855c87b55" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.403ex; height:2.509ex;" alt="{\displaystyle E=jh\nu }"></span>. Tällöin <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 j}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>j</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle j}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2f461e54f5c093e92a55547b9764291390f0b5d0" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.027ex; width:0.985ex; height:2.509ex;" alt="{\displaystyle j}"></span> kvanttia voidaan jakaa <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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>-värähtelijälle seuraavasti:<sup id="cite_ref-Steinfeld1998_14-0" class="reference"><a href="#cite_note-Steinfeld1998-14"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> <dl><dd><dl><dd><dl><dd><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 W(E)\,=\,{\frac {(j+s-1)!}{j!(s-1)!}}\qquad \qquad }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>W</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>j</mi> <mo>+</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> <mrow> <mi>j</mi> <mo>!</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo>−<!-- − --></mo> <mn>1</mn> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> <mspace width="2em" /> <mspace width="2em" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle W(E)\,=\,{\frac {(j+s-1)!}{j!(s-1)!}}\qquad \qquad }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1a642f4886d39346edd8e6baa509549503f93ae4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:31.367ex; height:6.509ex;" alt="{\displaystyle W(E)\,=\,{\frac {(j+s-1)!}{j!(s-1)!}}\qquad \qquad }"></span>ja<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 \qquad \qquad G(E)\,=\,{\frac {(j+s)!}{j!(s)!}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mspace width="2em" /> <mspace width="2em" /> <mi>G</mi> <mo stretchy="false">(</mo> <mi>E</mi> <mo stretchy="false">)</mo> <mspace width="thinmathspace" /> <mo>=</mo> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mi>j</mi> <mo>+</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> <mrow> <mi>j</mi> <mo>!</mo> <mo stretchy="false">(</mo> <mi>s</mi> <mo stretchy="false">)</mo> <mo>!</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \qquad \qquad G(E)\,=\,{\frac {(j+s)!}{j!(s)!}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/eef596387635fd0f2c72cdc17e7760ecd3d2716f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:26.756ex; height:6.509ex;" alt="{\displaystyle \qquad \qquad G(E)\,=\,{\frac {(j+s)!}{j!(s)!}}}"></span></dd></dl></dd></dl></dd></dl></dd></dl> </span></li> <li id="cite_note-16"><span class="mw-cite-backlink"><a href="#cite_ref-16">↑</a></span> <span class="reference-text">Tässä oletetaan, että jokaisella värähtelijällä (<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 s}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>s</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/01d131dfd7673938b947072a13a9744fe997e632" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.09ex; height:1.676ex;" alt="{\displaystyle s}"></span>-kappaletta) on sama värähdystaajuus, joten kaikki vibraatiokvantit ovat samansuuruisia.</span> </li> </ol> </div> <div class="mw-heading mw-heading2"><h2 id="Katso_myös"><span id="Katso_my.C3.B6s"></span>Katso myös</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=7" title="Muokkaa osiota Katso myös" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=7" title="Muokkaa osion lähdekoodia: Katso myös"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="div-col columns column-count column-count-2" style="-moz-column-count: 2; -webkit-column-count: 2; column-count: 2;"> <ul><li><a href="/wiki/Reaktiokinetiikka" title="Reaktiokinetiikka">Reaktiokinetiikka</a></li> <li><a href="/wiki/Arrheniuksen_yht%C3%A4l%C3%B6" title="Arrheniuksen yhtälö">Arrheniuksen yhtälö</a></li> <li><a href="/wiki/T%C3%B6rm%C3%A4ysteoria" title="Törmäysteoria">Törmäysteoria</a></li> <li><a href="/wiki/Siirtym%C3%A4tilateoria" title="Siirtymätilateoria">Siirtymätilateoria</a></li> <li><a href="/wiki/RRKM-teoria" title="RRKM-teoria">RRKM-teoria</a></li> <li><a href="/wiki/Molekulaarinen_jakaumafunktio" title="Molekulaarinen jakaumafunktio">Molekulaarinen jakaumafunktio</a></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="Lähteet"><span id="L.C3.A4hteet"></span>Lähteet</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&veaction=edit&section=8" title="Muokkaa osiota Lähteet" class="mw-editsection-visualeditor"><span>muokkaa</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Unimolekulaarinen_reaktio&action=edit&section=8" title="Muokkaa osion lähdekoodia: Lähteet"><span>muokkaa wikitekstiä</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="viitteet-malline" class="viitteet-malline" style="list-style-type:decimal;"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><a href="#cite_ref-1">↑</a></span> <span class="reference-text">F. A. Lindemann, Trans. Faraday Soc., vol 17, (1922), 598.; Lindemannin suullinen esitys tästä aiheesta oli Faraday Societyn-symposiumissa 28.9. 1921</span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><a href="#cite_ref-2">↑</a></span> <span class="reference-text">J. A. Cristiansen, Ph.D. thesis (väitöskirja), Kööpenhaminan yliopisto, (1921), lokakuu</span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><a href="#cite_ref-6">↑</a></span> <span class="reference-text">C. N. Hinshelwood, Proc. Roy. Soc. (A), vol. 113, (1927), s. 230</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><a href="#cite_ref-8">↑</a></span> <span class="reference-text">O. K. Rice ja H. C. Ramsperger, J. Am. Chem. Soc., vol 49, (1927), s. 1616 ja vol 50, (1928), s. 617</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><a href="#cite_ref-9">↑</a></span> <span class="reference-text">L. S. Kassel, J. Phys. Chem., vol 32, (1928), s. 225</span> </li> <li id="cite_note-Laidler1987-11"><span class="mw-cite-backlink"><a href="#cite_ref-Laidler1987_11-0">↑</a></span> <span class="reference-text">Keith J. Laidler, <i>Chemical Kinetics</i>, 3. painos, (1987), sivu 157, HarperCollinsPublisher, <a href="/wiki/Toiminnot:Kirjal%C3%A4hteet/0060438622" class="internal mw-magiclink-isbn">ISBN 0-06-043862-2</a></span> </li> <li id="cite_note-Steinfeld1998-14"><span class="mw-cite-backlink">↑ <a href="#cite_ref-Steinfeld1998_14-0"><sup><i>a</i></sup></a> <a href="#cite_ref-Steinfeld1998_14-1"><sup><i>b</i></sup></a> <a href="#cite_ref-Steinfeld1998_14-2"><sup><i>c</i></sup></a> <a href="#cite_ref-Steinfeld1998_14-3"><sup><i>d</i></sup></a></span> <span class="reference-text">Jeffrey I. Steinfeld, Joseph S. Francisco, ja William L. Hase, <i>Chemical Kinetics and Dynamics</i>, 2. painos, (1998), Prentice Hall, <a href="/wiki/Toiminnot:Kirjal%C3%A4hteet/0137371232" class="internal mw-magiclink-isbn">ISBN 0-13-737123-2</a></span> </li> </ol> </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="">Noudettu kohteesta ”<a dir="ltr" href="https://fi.wikipedia.org/w/index.php?title=Unimolekulaarinen_reaktio&oldid=22700687">https://fi.wikipedia.org/w/index.php?title=Unimolekulaarinen_reaktio&oldid=22700687</a>”</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Toiminnot:Luokat" title="Toiminnot:Luokat">Luokka</a>: <ul><li><a href="/wiki/Luokka:Kemialliset_reaktiot" title="Luokka:Kemialliset reaktiot">Kemialliset reaktiot</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Piilotettu luokka: <ul><li><a href="/wiki/Luokka:Sivut,_jotka_k%C3%A4ytt%C3%A4v%C3%A4t_ISBN-taikalinkkej%C3%A4" title="Luokka:Sivut, jotka käyttävät ISBN-taikalinkkejä">Sivut, jotka käyttävät ISBN-taikalinkkejä</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigointivalikko</h2> <div id="mw-head"> <nav id="p-personal" class="mw-portlet mw-portlet-personal vector-user-menu-legacy vector-menu" aria-labelledby="p-personal-label" > <h3 id="p-personal-label" class="vector-menu-heading " > <span class="vector-menu-heading-label">Henkilökohtaiset työkalut</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="IP-osoitteesi käyttäjäsivu">Et ole kirjautunut</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Toiminnot:Oma_keskustelu" title="Keskustelu tämän IP-osoitteen muokkauksista [n]" accesskey="n"><span>Keskustelu</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Toiminnot:Omat_muokkaukset" title="Luettelo tästä IP-osoitteesta tehdyistä muokkauksista [y]" accesskey="y"><span>Muokkaukset</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Toiminnot:Luo_tunnus&returnto=Unimolekulaarinen+reaktio" title="On suositeltavaa luoda käyttäjätunnus ja kirjautua sisään. 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