Dissoziationsgrad – Wikipedia

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Base in einer wässrigen <a href="/wiki/L%C3%B6sung_(Chemie)" title="Lösung (Chemie)">Lösung</a> an. Der Dissoziationsgrad einer Säure bzw. Base hängt von ihrer <a href="/wiki/S%C3%A4urekonstante" title="Säurekonstante">Säurekonstante</a> (bzw. <a href="/wiki/Basenkonstante" title="Basenkonstante">Basenkonstante</a>), ihrer <a href="/wiki/Konzentration_(Chemie)" title="Konzentration (Chemie)">Konzentration</a> und dem vorliegenden <a href="/wiki/PH-Wert" title="PH-Wert">pH-Wert</a> einer Lösung ab. Liegt in einer Lösung nur eine Säure oder Base vor, lässt sich der Dissoziationsgrad aus der <a href="/wiki/Elektrolytische_Leitf%C3%A4higkeit" title="Elektrolytische Leitfähigkeit">elektrolytischen Leitfähigkeit</a> der Lösung experimentell bestimmen. Ist der pH-Wert einer Lösung bekannt, lässt sich der Dissoziationsgrad rechnerisch <a href="/wiki/Absch%C3%A4tzen" class="mw-redirect" title="Abschätzen">abschätzen</a>. </p><p>Der Dissoziationsgrad kann Werte zwischen 0 und 1 annehmen. </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="de" dir="ltr"><h2 id="mw-toc-heading">Inhaltsverzeichnis</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div> <ul> <li class="toclevel-1 tocsection-1"><a href="#Einprotonige_Säuren_HA"><span class="tocnumber">1</span> <span class="toctext">Einprotonige Säuren HA</span></a></li> <li class="toclevel-1 tocsection-2"><a href="#Zweiprotonige_Säuren_H2A"><span class="tocnumber">2</span> <span class="toctext">Zweiprotonige Säuren H<sub>2</sub>A</span></a></li> <li class="toclevel-1 tocsection-3"><a href="#Mehrprotonige_Säuren_HnA"><span class="tocnumber">3</span> <span class="toctext">Mehrprotonige Säuren H<sub>n</sub>A</span></a></li> <li class="toclevel-1 tocsection-4"><a href="#Konduktometrische_Bestimmung"><span class="tocnumber">4</span> <span class="toctext">Konduktometrische Bestimmung</span></a></li> <li class="toclevel-1 tocsection-5"><a href="#Siehe_auch"><span class="tocnumber">5</span> <span class="toctext">Siehe auch</span></a></li> <li class="toclevel-1 tocsection-6"><a href="#Weblinks"><span class="tocnumber">6</span> <span class="toctext">Weblinks</span></a></li> <li class="toclevel-1 tocsection-7"><a href="#Einzelnachweise"><span class="tocnumber">7</span> <span class="toctext">Einzelnachweise</span></a></li> </ul> </div> <div class="mw-heading mw-heading2"><h2 id="Einprotonige_Säuren_HA"><span id="Einprotonige_S.C3.A4uren_HA"></span>Einprotonige Säuren HA</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=1" title="Abschnitt bearbeiten: Einprotonige Säuren HA" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=1" title="Quellcode des Abschnitts bearbeiten: Einprotonige Säuren HA"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="sieheauch" role="navigation" style="font-style:italic;"><span class="sieheauch-text">Siehe auch</span>: <a href="/wiki/Henderson-Hasselbalch-Gleichung" title="Henderson-Hasselbalch-Gleichung">Henderson-Hasselbalch-Gleichung</a></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Datei:Protolysegrad-Konzentration.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Protolysegrad-Konzentration.svg/300px-Protolysegrad-Konzentration.svg.png" decoding="async" width="300" height="300" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/83/Protolysegrad-Konzentration.svg/450px-Protolysegrad-Konzentration.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/83/Protolysegrad-Konzentration.svg/600px-Protolysegrad-Konzentration.svg.png 2x" data-file-width="700" data-file-height="700" /></a><figcaption>Dissoziationsgrad α<br />in Abhängigkeit von der Konzentration (<a href="/wiki/Logarithmische_Skala" class="mw-redirect" title="Logarithmische Skala">logarithmische Skala</a>)<br />von a) <a href="/wiki/Chlorwasserstoff" title="Chlorwasserstoff">HCl</a>, b) <a href="/wiki/Salpeters%C3%A4ure" title="Salpetersäure">HNO<sub>3</sub></a>, c) <a href="/wiki/Chlorige_S%C3%A4ure" title="Chlorige Säure">HClO<sub>2</sub></a>, d) <a href="/wiki/Fluorwasserstoff" title="Fluorwasserstoff">HF</a>, e) <a href="/wiki/Essigs%C3%A4ure" title="Essigsäure">HOAc</a>, f) <a href="/wiki/Hypochlorige_S%C3%A4ure" title="Hypochlorige Säure">HClO</a>, g) <a href="/wiki/Cyanwasserstoff" title="Cyanwasserstoff">HCN</a> </figcaption></figure> <p>Für eine ein<a href="/wiki/Proton_(Chemie)" title="Proton (Chemie)">protonige</a> Säure <i>HA</i> mit der formalen Ausgangskonzentration c<sub>0</sub>, die dissoziiert gemäß der Gleichung </p> <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 \mathrm {HA+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{-}} ,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">A</mi> <mo>+</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> <mo class="MJX-variant" stretchy="false">⇌</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>+</mo> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {HA+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{-}} ,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2513a4bf90cd7549c1b6f09584f9cf4d11c3dd60" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:27.404ex; height:2.843ex;" alt="{\displaystyle \mathrm {HA+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{-}} ,}"></span></dd></dl></dd></dl> <p>gilt: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {[\mathrm {A^{-}} ]}{c_{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {[\mathrm {A^{-}} ]}{c_{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/dbb4e8958da641b50a99c8c8a84e6a6d8fb97d3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" style="vertical-align: -2.171ex; width:9.97ex; height:6.009ex;" aria-hidden="true" alt="{\displaystyle \alpha ={\frac {[\mathrm {A^{-}} ]}{c_{0}}}}"></span></dd></dl> <p><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> gibt also den relativen Anteil an dissoziierter Säure an, c<sub>0</sub> die Anfangskonzentration der undissoziierten Säure. </p><p>Die Definition eines Dissoziationsgrades für Basen ist nicht eigens erforderlich, da er bereits in <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> enthalten ist. </p><p>Der <b>Assoziationsgrad</b> („<span lang="en">degree of formation</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 \alpha ',}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ',}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3c2d7a9cd2198caf5939cff60aeefcf3218ebffd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.819ex; height:2.843ex;" alt="{\displaystyle \alpha ',}"></span> der relative Anteil an <i>nicht</i> dissoziierter Säure, ergibt sich aus: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha '={\frac {[\mathrm {HA} ]}{c_{0}}}=1-\alpha .}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>α</mi> <mo>′</mo> </msup> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mn>1</mn> <mo>−</mo> <mi>α</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha '={\frac {[\mathrm {HA} ]}{c_{0}}}=1-\alpha .}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bd39dbe90cc4423c7bb54544c8b0f4ce7f98df6d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:20.123ex; height:6.009ex;" alt="{\displaystyle \alpha '={\frac {[\mathrm {HA} ]}{c_{0}}}=1-\alpha .}"></span></dd></dl> <p>Die Kombination des <a href="/wiki/Massenwirkungsgesetz" title="Massenwirkungsgesetz">Massenwirkungsgesetzes</a> für das Protolysegleichgewicht </p> <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 K_{\mathrm {s} }={\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">s</mi> </mrow> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>c</mi> <mo stretchy="false">(</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">O</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">)</mo> <mo>⋅</mo> <mi>c</mi> <mo stretchy="false">(</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">A</mi> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>c</mi> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{\mathrm {s} }={\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/08ef97912634f7f07a78fb448884b16ddf02ff9f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:23.469ex; height:6.676ex;" alt="{\displaystyle K_{\mathrm {s} }={\frac {c(\mathrm {H} _{3}\mathrm {O} ^{+})\cdot c(\mathrm {A} ^{-})}{c(\mathrm {HA} )}}}"></span></dd></dl></dd></dl> <p>(K<sub>S</sub> ist die <a href="/wiki/S%C3%A4urekonstante" title="Säurekonstante">Säurekonstante</a>, die als Maß für die <a href="/wiki/S%C3%A4urekonstante#Säurestärke" title="Säurekonstante">Säurestärke</a> gilt)<br /> mit der <a href="/wiki/Massenerhaltung" class="mw-redirect" title="Massenerhaltung">Massenerhaltung</a> der Säure in der Lösung </p> <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 {\begin{aligned}\![\mathrm {A^{-}} ]+[\mathrm {HA} ]&=c_{0}\\\Leftrightarrow \alpha \!\ +\alpha '&=1\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mspace width="negativethinmathspace" /> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">H</mi> <mi mathvariant="normal">A</mi> </mrow> <mo stretchy="false">]</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">⇔</mo> <mi>α</mi> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mo>+</mo> <msup> <mi>α</mi> <mo>′</mo> </msup> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\![\mathrm {A^{-}} ]+[\mathrm {HA} ]&=c_{0}\\\Leftrightarrow \alpha \!\ +\alpha '&=1\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/90d46cc182aaaada3a43a9d9f9bcce05c823afaa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; margin-left: -0.024ex; width:17.715ex; height:6.176ex;" alt="{\displaystyle {\begin{aligned}\![\mathrm {A^{-}} ]+[\mathrm {HA} ]&=c_{0}\\\Leftrightarrow \alpha \!\ +\alpha '&=1\end{aligned}}}"></span></dd></dl></dd></dl> <p>führt zu folgendem Ausdruck für den Dissoziationsgrad: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Rightarrow \alpha =\!\ {\frac {K_{\mathrm {S} }}{[\mathrm {H_{3}O^{+}} ]+K_{\mathrm {S} }}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">⇒</mo> <mi>α</mi> <mo>=</mo> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> <mrow> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Rightarrow \alpha =\!\ {\frac {K_{\mathrm {S} }}{[\mathrm {H_{3}O^{+}} ]+K_{\mathrm {S} }}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a892a48b441853275310fae84dd41d1c4af6b888" class="mwe-math-fallback-image-inline mw-invert skin-invert" style="vertical-align: -2.671ex; width:22.601ex; height:6.176ex;" aria-hidden="true" alt="{\displaystyle \Rightarrow \alpha =\!\ {\frac {K_{\mathrm {S} }}{[\mathrm {H_{3}O^{+}} ]+K_{\mathrm {S} }}}.}"></span></dd></dl> <p>Die Gleichung zeigt, dass der Dissoziationsgrad einer bestimmten Säure mit bekanntem p<i>K</i><sub>s</sub>-Wert nur vom <a href="/wiki/PH-Wert" title="PH-Wert">pH-Wert</a> der Lösung abhängt. Sie lässt sich umformen zu: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\Leftrightarrow [\mathrm {H_{3}O^{+}} ]&=\!\ K_{\mathrm {S} }\cdot {\frac {1-\alpha }{\alpha }}\\\Leftrightarrow \mathrm {pH} &=\!\ \mathrm {p} K_{\mathrm {S} }+\lg {\frac {\alpha }{1-\alpha }}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mo stretchy="false">⇔</mo> <mo stretchy="false">[</mo> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> </mrow> <mo stretchy="false">]</mo> </mtd> <mtd> <mi></mi> <mo>=</mo> <mspace width="negativethinmathspace" /> <mtext> </mtext> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mrow> <mi>α</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mo stretchy="false">⇔</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> <mi mathvariant="normal">H</mi> </mrow> </mtd> <mtd> <mi></mi> <mo>=</mo> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">p</mi> </mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">S</mi> </mrow> </mrow> </msub> <mo>+</mo> <mi>lg</mi> <mo>⁡</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>α</mi> <mrow> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\Leftrightarrow [\mathrm {H_{3}O^{+}} ]&=\!\ K_{\mathrm {S} }\cdot {\frac {1-\alpha }{\alpha }}\\\Leftrightarrow \mathrm {pH} &=\!\ \mathrm {p} K_{\mathrm {S} }+\lg {\frac {\alpha }{1-\alpha }}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/15da05673ad0150704145a47d52d402012215abd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -4.332ex; margin-bottom: -0.173ex; width:30.198ex; height:10.176ex;" alt="{\displaystyle {\begin{aligned}\Leftrightarrow [\mathrm {H_{3}O^{+}} ]&=\!\ K_{\mathrm {S} }\cdot {\frac {1-\alpha }{\alpha }}\\\Leftrightarrow \mathrm {pH} &=\!\ \mathrm {p} K_{\mathrm {S} }+\lg {\frac {\alpha }{1-\alpha }}\end{aligned}}}"></span></dd></dl> <p>d. h. der pH-Wert einer solchen Lösung ist selbst eine Funktion der Gesamtkonzentration <i>c</i><sub>0</sub> der Säure. </p> <div class="mw-heading mw-heading2"><h2 id="Zweiprotonige_Säuren_H2A"><span id="Zweiprotonige_S.C3.A4uren_H2A"></span>Zweiprotonige Säuren H<sub>2</sub>A</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=2" title="Abschnitt bearbeiten: Zweiprotonige Säuren H2A" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=2" title="Quellcode des Abschnitts bearbeiten: Zweiprotonige Säuren H2A"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bei zwei oder mehrprotonigen Säuren ist es zweckmäßig, auf die Unterscheidung zwischen Dissoziationsgrad <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> und Assoziationsgrad <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-\alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>1</mn> <mo>−</mo> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 1-\alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9afa7876fb8b4fb8c4d8039ebed6cd1cbc4781cd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.49ex; height:2.343ex;" alt="{\displaystyle 1-\alpha }"></span> zu verzichten. Stattdessen definiert man allgemein den Anteil <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 \alpha }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b79333175c8b3f0840bfb4ec41b8072c83ea88d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.488ex; height:1.676ex;" alt="{\displaystyle \alpha }"></span> an der formalen Ausgangskonzentration c<sub>0</sub> der Säure, der auf eine der in Lösung vorliegenden <a href="/wiki/Spezies_(Chemie)" title="Spezies (Chemie)">Spezies</a> entfällt. Die Verteilung auf die verschiedenen Formen hängt dabei vom pH-Wert der Lösung ab. </p><p>Eine zweiprotonige Säure dissoziiert in wässriger Lösung in zwei <a href="/wiki/Gleichgewichtsreaktion" class="mw-redirect" title="Gleichgewichtsreaktion">Gleichgewichtsreaktionen</a>: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \mathrm {H_{2}A+H_{2}O\rightleftharpoons H_{3}O^{+}+HA^{-}\qquad HA^{-}+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{2-}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">A</mi> <mo>+</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> <mo class="MJX-variant" stretchy="false">⇌</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>+</mo> <mi mathvariant="normal">H</mi> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mspace width="2em" /> <mi mathvariant="normal">H</mi> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo>+</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">O</mi> <mo class="MJX-variant" stretchy="false">⇌</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo>+</mo> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> </mrow> </msup> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \mathrm {H_{2}A+H_{2}O\rightleftharpoons H_{3}O^{+}+HA^{-}\qquad HA^{-}+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{2-}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/617e428cf04600f7234c9460aaf653fdaff5be14" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:63.289ex; height:3.009ex;" alt="{\displaystyle \mathrm {H_{2}A+H_{2}O\rightleftharpoons H_{3}O^{+}+HA^{-}\qquad HA^{-}+H_{2}O\rightleftharpoons H_{3}O^{+}+A^{2-}} }"></span></dd></dl> <p>Die Gleichgewichte werden durch die zwei <a href="/wiki/S%C3%A4urekonstante" title="Säurekonstante">Säuredissoziationskonstanten</a> beschrieben: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle K_{S1}=\mathrm {\frac {[H_{3}O^{+}]\cdot [HA^{-}]}{[H_{2}A]}} \qquad K_{S2}=\mathrm {\frac {[H_{3}O^{+}]\cdot [A^{2-}]}{[HA^{-}]}} }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> <mo>⋅</mo> <mo stretchy="false">[</mo> <mi mathvariant="normal">H</mi> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">A</mi> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> <mspace width="2em" /> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>2</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> <mo>⋅</mo> <mo stretchy="false">[</mo> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow> <mo stretchy="false">[</mo> <mi mathvariant="normal">H</mi> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{S1}=\mathrm {\frac {[H_{3}O^{+}]\cdot [HA^{-}]}{[H_{2}A]}} \qquad K_{S2}=\mathrm {\frac {[H_{3}O^{+}]\cdot [A^{2-}]}{[HA^{-}]}} }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e7040001a0355468067db89c119bc4fbf317210" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:50.528ex; height:6.676ex;" alt="{\displaystyle K_{S1}=\mathrm {\frac {[H_{3}O^{+}]\cdot [HA^{-}]}{[H_{2}A]}} \qquad K_{S2}=\mathrm {\frac {[H_{3}O^{+}]\cdot [A^{2-}]}{[HA^{-}]}} }"></span></dd></dl> <p>Die bei gegebenem pH-Wert auf die verschiedenen Säurespezies entfallenden Anteile berechnen sich dann gemäß: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\begin{aligned}\alpha _{0}&={\frac {\mathrm {[H_{2}A]} }{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]^{2}} }{D}}\\\alpha _{1}&={\frac {\mathrm {[HA^{-}]} }{c_{0}}}={\frac {K_{S1}\cdot \mathrm {[H_{3}O^{+}]} }{D}}\\\alpha _{2}&={\frac {\mathrm {[A^{2-}]} }{c_{0}}}={\frac {K_{S1}\cdot K_{S2}}{D}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="3pt" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mi mathvariant="normal">A</mi> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mi>D</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <mi mathvariant="normal">H</mi> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> </mrow> <mi>D</mi> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msup> <mi mathvariant="normal">A</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>1</mn> </mrow> </msub> <mo>⋅</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>2</mn> </mrow> </msub> </mrow> <mi>D</mi> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}\alpha _{0}&={\frac {\mathrm {[H_{2}A]} }{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]^{2}} }{D}}\\\alpha _{1}&={\frac {\mathrm {[HA^{-}]} }{c_{0}}}={\frac {K_{S1}\cdot \mathrm {[H_{3}O^{+}]} }{D}}\\\alpha _{2}&={\frac {\mathrm {[A^{2-}]} }{c_{0}}}={\frac {K_{S1}\cdot K_{S2}}{D}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ff23ba353ce79909bfaf4c695c7d63442aecb679" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -8.608ex; margin-bottom: -0.23ex; width:30.63ex; height:18.843ex;" alt="{\displaystyle {\begin{aligned}\alpha _{0}&={\frac {\mathrm {[H_{2}A]} }{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]^{2}} }{D}}\\\alpha _{1}&={\frac {\mathrm {[HA^{-}]} }{c_{0}}}={\frac {K_{S1}\cdot \mathrm {[H_{3}O^{+}]} }{D}}\\\alpha _{2}&={\frac {\mathrm {[A^{2-}]} }{c_{0}}}={\frac {K_{S1}\cdot K_{S2}}{D}}\end{aligned}}}"></span></dd></dl> <p>mit der Hilfsvariablen <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 D=\mathrm {[H_{3}O^{+}]^{2}} +K_{S1}\mathrm {[H_{3}O^{+}]} \!\ +K_{S1}K_{S2}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>D</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <msup> <mo stretchy="false">]</mo> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mrow> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>1</mn> </mrow> </msub> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mspace width="negativethinmathspace" /> <mtext> </mtext> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>1</mn> </mrow> </msub> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>S</mi> <mn>2</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D=\mathrm {[H_{3}O^{+}]^{2}} +K_{S1}\mathrm {[H_{3}O^{+}]} \!\ +K_{S1}K_{S2}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2475543247717846c2b856131673dec9a9a44ca3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:39.68ex; height:3.176ex;" alt="{\displaystyle D=\mathrm {[H_{3}O^{+}]^{2}} +K_{S1}\mathrm {[H_{3}O^{+}]} \!\ +K_{S1}K_{S2}.}"></span> </p><p>Titrationskurven lassen sich erhalten, indem man den (verallgemeinerten) Assoziationsgrad <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {n}}=2\alpha _{0}+1\alpha _{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mn>2</mn> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>+</mo> <mn>1</mn> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {n}}=2\alpha _{0}+1\alpha _{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf20ea6d1da15e12b51ba3d59720f196d005cbc5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:14.742ex; height:2.509ex;" alt="{\displaystyle {\bar {n}}=2\alpha _{0}+1\alpha _{1}}"></span> als Funktion des pH-Wertes aufträgt. Der analoge Dissoziationsgrad ist dann gegeben durch <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 2-{\bar {n}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>2</mn> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 2-{\bar {n}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5e6c616766edfbfe584bfc9581e188cbe870a8e7" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:5.398ex; height:2.343ex;" alt="{\displaystyle 2-{\bar {n}}}"></span>. Analog geht man im Fall einer mehrprotonigen Säure vor.<sup id="cite_ref-Butler1998_1-0" class="reference"><a href="#cite_note-Butler1998-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Mehrprotonige_Säuren_HnA"><span id="Mehrprotonige_S.C3.A4uren_HnA"></span>Mehrprotonige Säuren H<sub>n</sub>A</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=3" title="Abschnitt bearbeiten: Mehrprotonige Säuren HnA" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=3" title="Quellcode des Abschnitts bearbeiten: Mehrprotonige Säuren HnA"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Eine mehrprotonige Säure H<sub>n</sub>A unterliegt in Lösung n gekoppelten Protolysegleichgewichten, beschrieben durch die Säuredissoziationskonstanten <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},K_{2},\ldots ,K_{n}}"> <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> <mo>,</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <mo>…</mo> <mo>,</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle K_{1},K_{2},\ldots ,K_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f61535b73ea7d40a7c77ae36652ca79b6475d1d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.458ex; height:2.509ex;" alt="{\displaystyle K_{1},K_{2},\ldots ,K_{n}}"></span>. Bei gegebenem pH-Wert berechnet sich der auf die Spezies <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_{n-m}A^{m-}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>H</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>m</mi> </mrow> </msub> <msup> <mi>A</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle H_{n-m}A^{m-}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7404252ad9e2d4390b17302bb7747129843ec884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.568ex; height:2.843ex;" alt="{\displaystyle H_{n-m}A^{m-}}"></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 (m\in \{0,1,2,\ldots ,n\})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>m</mi> <mo>∈</mo> <mo fence="false" stretchy="false">{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo fence="false" stretchy="false">}</mo> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (m\in \{0,1,2,\ldots ,n\})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/02b5352a7bd81742032d60197288c02b67e8adb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:21.143ex; height:2.843ex;" alt="{\displaystyle (m\in \{0,1,2,\ldots ,n\})}"></span> entfallende Anteil <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 \alpha _{m}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{m}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/251a293d0e46862cdeba1f4a095eb3c6415fa69b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.163ex; height:2.009ex;" alt="{\displaystyle \alpha _{m}}"></span> gemäß: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha _{m}={\frac {[{\text{H}}_{n-m}{\text{A}}^{m-}]}{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]} ^{n-m}}{D_{n}}}\cdot \prod _{i=0}^{m}K_{i}\qquad (K_{0}=1)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">[</mo> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>H</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>m</mi> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mtext>A</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> <mo>−</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <msub> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mi>m</mi> </mrow> </msup> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mfrac> </mrow> <mo>⋅</mo> <munderover> <mo>∏</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>m</mi> </mrow> </munderover> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mspace width="2em" /> <mo stretchy="false">(</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha _{m}={\frac {[{\text{H}}_{n-m}{\text{A}}^{m-}]}{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]} ^{n-m}}{D_{n}}}\cdot \prod _{i=0}^{m}K_{i}\qquad (K_{0}=1)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/153dfb4699d4333aeefb0a8941290cb2db566a85" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:55.606ex; height:7.176ex;" alt="{\displaystyle \alpha _{m}={\frac {[{\text{H}}_{n-m}{\text{A}}^{m-}]}{c_{0}}}={\frac {\mathrm {[H_{3}O^{+}]} ^{n-m}}{D_{n}}}\cdot \prod _{i=0}^{m}K_{i}\qquad (K_{0}=1)}"></span></dd></dl> <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 D_{n}=\mathrm {[H_{3}O^{+}]} ^{n}+K_{1}\mathrm {[H_{3}O^{+}]} ^{n-1}+K_{1}K_{2}\mathrm {[H_{3}O^{+}]} ^{n-2}+\ldots +K_{1}K_{2}\cdot \ldots \cdot K_{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>D</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> <mo>=</mo> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>+</mo> <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> <msup> <mrow class="MJX-TeXAtom-ORD"> <mo stretchy="false">[</mo> <msub> <mi mathvariant="normal">H</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msub> <msup> <mi mathvariant="normal">O</mi> <mrow class="MJX-TeXAtom-ORD"> <mo>+</mo> </mrow> </msup> <mo stretchy="false">]</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mo>…</mo> <mo>+</mo> <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>⋅</mo> <mo>…</mo> <mo>⋅</mo> <msub> <mi>K</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle D_{n}=\mathrm {[H_{3}O^{+}]} ^{n}+K_{1}\mathrm {[H_{3}O^{+}]} ^{n-1}+K_{1}K_{2}\mathrm {[H_{3}O^{+}]} ^{n-2}+\ldots +K_{1}K_{2}\cdot \ldots \cdot K_{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/449e53de08f5682eb4c1fa542ecc12a166d7a302" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:74.822ex; height:3.509ex;" alt="{\displaystyle D_{n}=\mathrm {[H_{3}O^{+}]} ^{n}+K_{1}\mathrm {[H_{3}O^{+}]} ^{n-1}+K_{1}K_{2}\mathrm {[H_{3}O^{+}]} ^{n-2}+\ldots +K_{1}K_{2}\cdot \ldots \cdot K_{n}}"></span></dd></dl> <p>In allen Fällen gilt stets: <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 \sum \alpha _{i}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>∑</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sum \alpha _{i}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b56b5118e16cd8464874a2eead053d9cdb55f1ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.338ex; width:10.29ex; height:3.843ex;" alt="{\displaystyle \sum \alpha _{i}=1}"></span>. </p><p>Analog zum Fall der zweiprotonigen Säure ist der Assoziationsgrad für die n-protonigen Säure durch <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {n}}=\sum _{i=0}^{n}(n-i)\cdot \alpha _{i}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>n</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </munderover> <mo stretchy="false">(</mo> <mi>n</mi> <mo>−</mo> <mi>i</mi> <mo stretchy="false">)</mo> <mo>⋅</mo> <msub> <mi>α</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>i</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {n}}=\sum _{i=0}^{n}(n-i)\cdot \alpha _{i}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b57f9d6950b4842eb29331bf73377edcbcab91e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -3.005ex; width:18.661ex; height:6.843ex;" alt="{\displaystyle {\bar {n}}=\sum _{i=0}^{n}(n-i)\cdot \alpha _{i}}"></span> gegeben. </p> <div class="mw-heading mw-heading2"><h2 id="Konduktometrische_Bestimmung">Konduktometrische Bestimmung</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=4" title="Abschnitt bearbeiten: Konduktometrische Bestimmung" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=4" title="Quellcode des Abschnitts bearbeiten: Konduktometrische Bestimmung"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Bei Säuren mit einem Wasserstoffatom lässt sich der Dissoziationsgrad über <a href="/wiki/Konduktometrie" title="Konduktometrie">konduktometrische</a> Messungen bestimmen nach der Formel: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \alpha ={\frac {\Lambda _{\mathrm {m} }}{\Lambda _{0}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>α</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \alpha ={\frac {\Lambda _{\mathrm {m} }}{\Lambda _{0}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/23d3934f94dada8361e1c36e1a706ce3fe94044b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.636ex; height:5.843ex;" alt="{\displaystyle \alpha ={\frac {\Lambda _{\mathrm {m} }}{\Lambda _{0}}}}"></span></dd></dl> <p>mit </p> <ul><li>der <a href="/wiki/Molare_Leitf%C3%A4higkeit" title="Molare Leitfähigkeit">molaren Leitfähigkeit</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 \Lambda _{\mathrm {m} }}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">m</mi> </mrow> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda _{\mathrm {m} }}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5f9cffed212c6fb358591580386c169fb4e6f5de" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.214ex; height:2.509ex;" alt="{\displaystyle \Lambda _{\mathrm {m} }}"></span></li> <li>der <a href="/wiki/Molare_Leitf%C3%A4higkeit#Molare_Grenzleitfähigkeit" title="Molare Leitfähigkeit">molaren Grenzleitfähigkeit</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 \Lambda _{0}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi mathvariant="normal">Λ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Lambda _{0}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f311b6fa89a959c139b2b85986ac03577903ec9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.314ex; height:2.509ex;" alt="{\displaystyle \Lambda _{0}.}"></span></li></ul> <p>Eine ähnliche Bestimmung ist auch für Säuren mit mehreren Wasserstoffatomen oder auch mit Salzen möglich (<a href="/wiki/Aktivit%C3%A4t_(Chemie)" title="Aktivität (Chemie)">Aktivität (Chemie)</a>). </p> <div class="mw-heading mw-heading2"><h2 id="Siehe_auch">Siehe auch</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=5" title="Abschnitt bearbeiten: Siehe auch" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=5" title="Quellcode des Abschnitts bearbeiten: Siehe auch"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Ostwaldsches_Verd%C3%BCnnungsgesetz" title="Ostwaldsches Verdünnungsgesetz">Ostwaldsches Verdünnungsgesetz</a></li> <li><a href="/wiki/Dissoziationskonstante" title="Dissoziationskonstante">Dissoziationskonstante</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Weblinks">Weblinks</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=6" title="Abschnitt bearbeiten: Weblinks" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=6" title="Quellcode des Abschnitts bearbeiten: Weblinks"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="http://www.chem.uoa.gr/applets/AppletAcid/Appl_Distr2.html">Verteilungsdiagramme polyprotischer Systeme</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Einzelnachweise">Einzelnachweise</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Dissoziationsgrad&veaction=edit&section=7" title="Abschnitt bearbeiten: Einzelnachweise" class="mw-editsection-visualeditor"><span>Bearbeiten</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Dissoziationsgrad&action=edit&section=7" title="Quellcode des Abschnitts bearbeiten: Einzelnachweise"><span>Quelltext bearbeiten</span></a><span class="mw-editsection-bracket">]</span></span></div> <ol class="references"> <li id="cite_note-Butler1998-1"><span class="mw-cite-backlink"><a href="#cite_ref-Butler1998_1-0">↑</a></span> <span class="reference-text"><span class="book">James Newton Butler: <cite style="font-style:italic">Ionic Equilibrium: Solubility and PH Calculations</cite>. John Wiley & Sons, 1998, <a href="/wiki/Spezial:ISBN-Suche/9780471585268" class="internal mw-magiclink-isbn">ISBN 978-0-471-58526-8</a>, <span style="white-space:nowrap">S.<span style="display:inline-block;width:.2em"> </span>185<span style="display:inline-block;width:.2em"> </span>ff</span>. (<a rel="nofollow" class="external text" href="http://books.google.com/books?id=mQuTkVNkrIUC&pg=PA185&dq=titration">google.com</a>).<span class="Z3988" title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rfr_id=info:sid/de.wikipedia.org:Dissoziationsgrad&rft.au=James+Newton+Butler&rft.btitle=Ionic+Equilibrium%3A+Solubility+and+PH+Calculations&rft.date=1998&rft.genre=book&rft.isbn=9780471585268&rft.pages=185+ff.&rft.pub=John+Wiley+%26+Sons" style="display:none"> </span></span></span> </li> </ol></div><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="">Abgerufen von „<a dir="ltr" href="https://de.wikipedia.org/w/index.php?title=Dissoziationsgrad&oldid=238766442">https://de.wikipedia.org/w/index.php?title=Dissoziationsgrad&oldid=238766442</a>“</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Wikipedia:Kategorien" title="Wikipedia:Kategorien">Kategorien</a>: <ul><li><a href="/wiki/Kategorie:Acidit%C3%A4t_und_Basizit%C3%A4t" title="Kategorie:Acidität und Basizität">Acidität und Basizität</a></li><li><a href="/wiki/Kategorie:Chemische_Gr%C3%B6%C3%9Fe" title="Kategorie:Chemische Größe">Chemische Größe</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Versteckte Kategorie: <ul><li><a href="/wiki/Kategorie:Wikipedia:Vorlagenfehler/Vorlage:Cite_book/tempor%C3%A4r" title="Kategorie:Wikipedia:Vorlagenfehler/Vorlage:Cite book/temporär">Wikipedia:Vorlagenfehler/Vorlage:Cite book/temporär</a></li></ul></div></div> </div> </div> <div id="mw-navigation"> <h2>Navigationsmenü</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">Meine Werkzeuge</span> </h3> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anonuserpage" class="mw-list-item"><span title="Benutzerseite der IP-Adresse, von der aus du Änderungen durchführst">Nicht angemeldet</span></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Spezial:Meine_Diskussionsseite" title="Diskussion über Änderungen von dieser IP-Adresse [n]" accesskey="n"><span>Diskussionsseite</span></a></li><li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Spezial:Meine_Beitr%C3%A4ge" title="Eine Liste der Bearbeitungen, die von dieser IP-Adresse gemacht wurden [y]" accesskey="y"><span>Beiträge</span></a></li><li id="pt-createaccount" class="mw-list-item"><a href="/w/index.php?title=Spezial:Benutzerkonto_anlegen&returnto=Dissoziationsgrad" title="Wir ermutigen dich dazu, ein Benutzerkonto zu erstellen und dich anzumelden. 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class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD%D1%8C_%D0%B4%D0%B8%D1%81%D1%81%D0%BE%D1%86%D0%B8%D0%B0%D1%86%D0%B8%D0%B8" title="Степень диссоциации – Russisch" lang="ru" hreflang="ru" data-title="Степень диссоциации" data-language-autonym="Русский" data-language-local-name="Russisch" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A1%D1%82%D0%B5%D0%BF%D0%B5%D0%BD_%D0%B4%D0%B8%D1%81%D0%BE%D1%86%D0%B8%D1%98%D0%B0%D1%86%D0%B8%D1%98%D0%B5" title="Степен дисоцијације – Serbisch" lang="sr" hreflang="sr" data-title="Степен дисоцијације" data-language-autonym="Српски / srpski" data-language-local-name="Serbisch" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A1%D1%82%D1%83%D0%BF%D1%96%D0%BD%D1%8C_%D0%B4%D0%B8%D1%81%D0%BE%D1%86%D1%96%D0%B0%D1%86%D1%96%D1%97" title="Ступінь дисоціації – Ukrainisch" lang="uk" hreflang="uk" data-title="Ступінь дисоціації" data-language-autonym="Українська" data-language-local-name="Ukrainisch" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E7%94%B5%E7%A6%BB%E5%BA%A6" title="电离度 – Chinesisch" lang="zh" hreflang="zh" data-title="电离度" data-language-autonym="中文" data-language-local-name="Chinesisch" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q907334#sitelinks-wikipedia" title="Links auf Artikel in anderen Sprachen bearbeiten" class="wbc-editpage">Links bearbeiten</a></span></div> </div> 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Dissoziationsgrad – Wikipedia