%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% ANFANG des Dokumentenkopfs %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \documentclass[9pt,a5paper,smallheadings,listof=totoc]{scrartcl} %% benötigte Pakete laden %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % KOMA-Script-Grundklassen \usepackage{scrbase} % Farben \usepackage{color} \usepackage[utf8]{inputenc} \usepackage[ngerman]{babel} % AMS-Mathematik-Pakete \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} % schmälere Seitenränder \usepackage[margin=20pt,head=20pt,headsep=20pt,foot=20pt]{geometry} \usepackage{url} %Inhaltsverzeichnis verlinken \usepackage[linktocpage=false]{hyperref} %% Metadaten und weitere Einstellungen und Festlegungen %%%%%%%%%%%%%%%%%%%%%%% %\titlehead{} \title{Formelsammlung Chemie} \author{Joachim Jakob, Kronberg-Gymnasium Aschaffenburg} \date{\href{http://chemie-lernprogramme.de/daten/programme/js/formelsammlung/}{chemie-lernprogramme.de/daten/programme/js/formelsammlung/}} % eigene Farbe definieren \definecolor{meinblau}{rgb}{0.2,0.4,0.6} % Schriftart: Adobe Helvetica \renewcommand*{\familydefault}{phv} % Überschriften Farbig in der eigenen Farbe, hier für den Ausdruck deaktiviert %\addtokomafont{sectioning}{\color{meinblau}} % Kleinere Seitennummerierung \setkomafont{pagenumber}{\normalfont\small} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% ENDE des Dokumentenkopfs %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% ANFANG des Dokumenteninhalts %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% Titelseite mit Dokumententitel, Autor, Datum (oben angepasst) %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Titel, Metadatenanzeige \maketitle % Inhaltsverzeichnis \tableofcontents % erzwungener Seitenumbruch \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 1. Avogadro-Konstante N_{A} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Avogadro Konstante $N_{A}$} \begin{minipage}[t]{0.4\textwidth} Die Avogadro-Konstante $N_{A}$ ist der Quotient aus der Teilchenzahl $N$ der Teilchen X und der Stoffmenge $n$ der Teilchen X. Ihre Einheit ist $mol^{-1}$. Sie gibt an, wie viele Teilchen in der Stoffmenge von einem MOL Teilchen enthalten sind. Sie ist unabhängig von der Art der Teilchen. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} N_{A} & = & \dfrac{ N(X) }{ n(X) } \\ N_{A} & = & 6,022 \cdot 10^{23} \dfrac{ 1 }{ mol } \\ \Rightarrow n(X) & = & \dfrac{ N(X) }{ N_{A} } \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 2. Molare Masse M %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Molare Masse $M$} \begin{minipage}[t]{0.4\textwidth} Die Molare Masse $M$ der Teilchen X ist der Quotient aus der Masse $m$ der Teilchen X und der Stoffmenge $n$ der Teilchen X. Ihre Einheit ist $g/mol$. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} M(X) & = & \dfrac{ m(X) }{ n(X) } \\ \Rightarrow n(X) & = & \dfrac{ m(X) }{ M(X) } \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 3. Molares Volumen V_{M} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Molares Volumen $V_m$} \begin{minipage}[t]{0.4\textwidth} Das Molare Volumen $V_{m}$ eines (idealen) Gases ist der Quotient aus dem Volumen $V$ der Gasteilchen X und der Stoffmenge $n$ der Gasteilchen X. Seine Einheit ist $l/mol$. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} V_{m} & = & \dfrac{ V(X) }{ n(X) } \\ V_{m} & = & 22,41 \dfrac{l}{mol} \\ \Rightarrow n(X) & = & \dfrac{ V(X) }{ V_{m} } \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 4. Stoffmengenkonzentration c %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Stoffmengenkonzentration $c$} \begin{minipage}[t]{0.4\textwidth} Die Stoffmengenkonzentration $c$ ist der Quotient aus der Stoffmenge $n$ der gelösten Teilchen X und dem Volumen der Lösung $V_{Lösung}$. Ihre Einheit ist $mol/l$. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} c(X) & = & \dfrac{ n(X) }{ V_{Lösung} } \\ \Rightarrow n(X) & = & c(X) \cdot V_{Lösung} \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 5. Mittlere Reaktionsgeschwindigkeit v %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Mittlere Reaktionsgeschwindigkeit $\overline{v}$} \begin{minipage}[t]{0.4\textwidth} Die Mittlere Reaktionsgeschwindigkeit $\overline{v}$ ist der Quotient aus der Konzentrationsänderung der Produkte $\Delta c(Prod)$ und der Zeitänderung $\Delta t$. Sie beschreibt sowohl die Bildungsgeschwindigkeit der Produkte als auch die Zerfallsgeschwindigkeit der Edukte (mit umgekehrtem Vorzeichen). \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \lefteqn{ Ed \rightleftharpoons Prod } \\ \\ \overline{v} & = & + \dfrac{ \Delta c(Prod) }{ \Delta t } \\ & = & - \dfrac{ \Delta c(Ed) }{ \Delta t } \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 6. Massenwirkungsgesetzt (MWG) %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Massenwirkungsgesetz ($MWG$)} \begin{minipage}[t]{0.4\textwidth} Die Gleichgewichtskonstante $K_{C}$ für Reaktionen in Lösungen ist der Quotient aus dem Produkt der Konzentration $c$ der Produkte und dem der Edukte. Die Gleichgewichtskonstante $K_{P}$ für Gasreaktionen wird entsprechend aus den Partialdrücken $p$ der Produkte und Edukte ermittelt. \\ \\ Feststoffe werden in beiden Fällen gleich 1 (ohne Einheit) gesetzt. Die Koeffizienten gehen als Exponenten ein. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \lefteqn{a \, A + b\, B \rightleftharpoons c\, C + d\, D} \\ \\ K_{C} & = & \dfrac{ c(C)^{c} \cdot c(D)^{d} }{ c(A)^{a} \cdot c(B)^{b} } \\ & = & \dfrac{ k_{hin} }{ k_{rück}} \\ K_{P} & = & \dfrac{ p(C)^{c} \cdot p(D)^{d} }{ p(A)^{a} \cdot p(B)^{b} } \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 7. Gibbs-Helmholtz-Gleichung %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Gibbs-Helmholtz-Gleichung} \begin{minipage}[t]{0.4\textwidth} Die Änderung der freien Enthalpie $\Delta G$ ist die Differenz aus der Enthalpieänderung $\Delta H$ und dem Produkt aus der absoluten Temperatur $T$ (in der Einheit Kelvin $K$) und der Entropieänderung $\Delta S$. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \Delta G & = & \Delta H - T \cdot \Delta S \end{eqnarray*} \end{minipage} \hline % erzwungener Seitenumbruch \newpage %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 8. Ionenprodukt des Wasser K_{W} %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Ionenprodukt des Wassers $K_{W}$} \begin{minipage}[t]{0.4\textwidth} Das Ionenprodukt des Wassers $K_{W}$ ist das Produkt der Konzentrationen der Oxoniumionen und der Hydroxidionen in der Einheit $mol^{2}/l^{2}$. Der $pK_{W}$-Wert ist der negative dekadische Logarithmus des Ionenprodukts $K_{W}$. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} K_{W} & = & c(H_{3}O^{+}) \cdot c(OH^{-}) = 10^{-14} mol^{2}/l^{2} \\ pK_{W} & = & -lg \{K_{W}\} = 14 \\ K_{W} & = & K_{S} \cdot K_{B} \\ pK_{W} & = & pK_{S} + pK_{B} \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 9. Säurekonstante K_{S} und pK_{S}-Wert %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Säurekonstante $K_{S}$ und $pK_{S}$-Wert} \begin{minipage}[t]{0.4\textwidth} Je größer die Säurekonstante $K_{S}$, desto stärker ist die Säure. Der $pK_{S}$-Wert ist der negative dekadische Logarithmus der Säurekonstante $K_{S}$ in der Einheit $mol \cdot l^{-1}$. Je kleiner die Säurekonstante $pK_{S}$, desto stärker ist die Säure. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \lefteqn{H_{2}O + HA \rightleftharpoons H_{3}O^{+} + A^{-}} \\ \\ K_{S} & = & \dfrac{c(H_{3}O^{+}) \cdot c(A^{-})} {c(HA) } \\ pK_{S} & = & -lg \{K_{S}\} \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 10. Basenkonstante K_{B} und pK_{B}-Wert %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Basenkonstante $K_{B}$ und $pK_{B}$-Wert} \begin{minipage}[t]{0.4\textwidth} Je größer die Basenkonstante $K_{B}$, desto stärker ist die Base. Der $pK_{B}$-Wert ist der negative dekadische Logarithmus der Basenkonstante $K_{B}$ in der Einheit $mol \cdot l^{-1}$. Je kleiner die Basenkonstante $pK_{B}$, desto stärker ist die Base. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \lefteqn{B + H_{2}O \rightleftharpoons BH^{+} + OH-} \\ \\ K_{S} & = & \dfrac{c(BH^{+}) \cdot c(OH^{-})} {c(B) } \\ pK_{B} & = & -lg \{K_{B}\} \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 11. pH-Wert %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pH$-Wert} \begin{minipage}[t]{0.4\textwidth} Der $pH$-Wert ist der negative dekadische Logarithmus des Zahlenwerts der Oxoniumionenkonzentration. Je kleiner der $pH$-Wert, desto saurer ist die Lösung. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} pH & = & -lg \{c(H_{3}O^{+})\} \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 12. pOH-Wert %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pOH$-Wert} \begin{minipage}[t]{0.4\textwidth} Der $pOH$-Wert ist der negative dekadische Logarithmus des Zahlenwerts der Hydroxidionenkonzentration. Je niedriger der $pOH$-Wert, desto alkalischer ist die Lösung. \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} pOH & = & -lg \{c(OH^{-})\} \\ pK_{W} & = & pH + pOH = 14 \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 13. pH-Wert für starke Säuren %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pH$-Wert für starke Säuren} \begin{minipage}[t]{0.4\textwidth} Die Näherungsformel für starke Säuren ergibt sich aufgrund der vollständigen Dissoziation wie folgt aus der Ausgangskonzentration dieser Säure $c_{0(HA)}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} c(H_{3}O^{+}) & = & c_{0}(HA) \\ pH & = & -lg\{c_{0}(HA) \} \\ \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 14. pH-Wert für schwache Säuren %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pH$-Wert für schwache Säuren} \begin{minipage}[t]{0.4\textwidth} Die Näherungsformel für schwache Säuren ergibt sich wie folgt aus der Ausgangskonzentration dieser Säure $c_{0(HA)}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} pH & = & \dfrac{1}{2} \cdot (pK_{S} -lg\{c_{0}(HA) \}) \\ \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 15. pH-Wert für starke Basen %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pH$-Wert für starke Basen} \begin{minipage}[t]{0.4\textwidth} Die Näherungsformel für starke Basen ergibt sich aufgrund der vollständigen Dissoziation wie folgt aus der Ausgangskonzentration dieser Base $c_{0(B)}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} c(OH^{-}) & = & c_{0}(B) \\ c(H_{3}O^{+}) & = & pK_{W} - pOH \\ pH & = & 14 -(-lg\{ c_{0}(B) \}) \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 16. pH-Wert für schwache Basen %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{$pH$-Wert für schwache Basen} \begin{minipage}[t]{0.4\textwidth} Die Näherungsformel für schwache Basen ergibt sich wie folgt aus der Ausgangskonzentration dieser Base $c_{0(B)}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} c(H_{3}O^{+}) & = & pK_{W} - pOH \\ pH & = & 14 - \left( \dfrac{1}{2} \cdot (pK_{B} -lg\{c_{0}(B) \}) \right) \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 17. Henderson-Hasselbalch-Gleichung %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Henderson-Hasselbalch-Gleichung} \begin{minipage}[t]{0.4\textwidth} Der pH-Wert für Pufferlösungen einer schwachen Säure HA und ihrer korrespondierenden Base $A^{-}$ ergibt sich wie folgt aus den Ausgangskonzentrationen $c_{0}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} pH & = & pK_{S} + lg \left\lbrace \dfrac{ c_{0}(A⁻) }{ c_{0}(HA) } \right\rbrace \\ %\mbox{ist gleichbedeutend mit:} \\ pH & = & pK_{S} - lg \left\lbrace \dfrac{ c_{0}(HA) }{ c_{0}(A⁻) } \right\rbrace \end{eqnarray*} \end{minipage} \hline %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% 18. Nernstsche Gleichung %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \section{Nernstsche Gleichung} \begin{minipage}[t]{0.4\textwidth} Das Redoxpotenzial Normalpotenzial $E$ für ein korrespondierendes Redoxpaar (Halbzelle/galvanisches Element: Redm/Oxm) lautet bei 25$^{\circ}C$ ausgehend vom Normalpotenzial $E^{0}$: \\ \end{minipage} \hfill \vspace{3mm}\vline \hfill \begin{minipage}[t]{0.5\textwidth} \begin{eqnarray*} \lefteqn{Ox.: a \, Redm \rightleftharpoons b \, Oxm^{n+} + n \, e^{-}} \\ \\ E & = & E^{0} + \dfrac{0,059 V}{n} \cdot lg \left\lbrace \dfrac{ c(Oxm)^{b} }{ c(Redm)^{a} } \right\rbrace \end{eqnarray*} \end{minipage} \hline \end{document} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% ENDE des Dokumenteninhalts %% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%