target="_blank" rel="nofollow" href="#fb3_img_img_7bc56d36-cacf-58d8-834c-0b6b938fe0fa.png" alt="p dot upper V equals n dot upper R overTilde dot upper T"/>
mit
n: Stoffmenge in mol,
allgemeine oder universelle Gaskonstante in J · mol–1 · K–1.
Die allgemeine Gaskonstante hat den Wert
(2.7)
Abbildung 2.8 zeigt anhand eines einfachen Beispiels, wie das ideale Gasgesetz angewendet werden kann. In ein mit Wasser gefülltes Gefäß werden 5 mol Luft mit 20 °C (Temperatur des gesamten Systems aus Wasser und Luft) bei einem Druck 1,013 · 10
5 Pa geleitet. Gesucht ist das Volumen, das die Luft einnimmt.
Bei den gegebenen Bedingungen kann das ideale Gasgesetz verwendet werden. Formel 2.6 wird nach dem Volumen V aufgelöst:
Die Luft nimmt bei diesen Bedingungen ein Volumen von 0,12 m3 oder 120 l ein.
Abbildung 2.8 Beispiel für das ideale Gasgesetz
Was ist jetzt eigentlich ein Mol?
Lassen Sie uns kurz über das Mol diskutieren, das Nichtchemikern immer irgendwie suspekt erscheint. Eine Masse lässt sich wiegen, da haben Sie etwas in der Hand. Sie kennen vielleicht noch die Standardfrage aus Kindestagen: »Was ist schwerer, 1 kg Blei oder 1 kg Federn?« Die Antwort war häufig: 1 kg Blei natürlich. Heute wissen Sie, dass diese Antwort nicht wirklich richtig ist. Dennoch, die Masse ist uns geläufig, wir wiegen uns (manchmal lassen wir das auch lieber), wir kaufen Waren in Masseeinheiten und schauen hier auf den spezifischen Preis, der in €/kg angegeben ist, um Warenpreise miteinander vergleichen zu können. Nirgendwo finden Sie €/mol!
Schauen Sie sich zuerst die Definition des Mols an.
1 mol ist die Stoffmenge eines Systems, das aus ebenso vielen Einzelteilchen besteht, wie Atome in 0,012 kg des Kohlenstoffisotops
12C enthalten sind.
Auch wenn Ihnen diese Definition immer noch nicht so ganz behagt, hat sie doch eine ganz wichtige Bedeutung: 1 mol eines Stoffs enthält immer die gleiche Anzahl von Einzelteilchen. Diese Einzelteilchen können zum Beispiel Atome oder Moleküle sein.
Die Teilchenzahl in der Stoffmenge 1 mol ist die Avogadro-Konstante
N A. Diese besagt, dass ein Mol immer aus
N A = 6,022 · 10
23 Teilchen besteht.
Avogadro bezieht die Teilchenzahl also nicht auf das Volumen, sondern auf ein Mol. Das ist rechentechnisch bei großen Teilchenzahlen auch irgendwie einfacher. Oder wollen Sie mit der kaum nachvollziehbar großen Summe von 6,022 · 1023 Teilchen rechnen? Da ist es doch besser, Sie haben ein Mol.
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Stellen Sie sich vor, Sie wollen Reis und Weizen kaufen. Sie kaufen jeweils 1 kg. Es würde Ihnen nicht einfallen, in den Laden zu gehen und von der Verkäuferin 33.333 Reiskörner zu verlangen. So viele Reiskörner sind nämlich bei einem Gewicht von circa 0,03 g pro Korn in einem Kilo enthalten. Der Einfachheit halber verlangen Sie sicherlich größere Gebinde. Wenn Sie Weizen kaufen, müssten Sie 20.000 Weizenkörner verlangen, da 1 Weizenkorn mit 0,05 g etwas schwerer ist als ein Reiskorn. Auch hier verlangen Sie ein Kilo. Sie verlangen ja auch keine 1000 Tropfen Bier! Der Wirt erschlägt Sie. Wir sind noch nicht beim Mol, ich weiß, aber Sie sehen, es ist sinnvoll, in größeren Einheiten zu rechnen. Beim Kilogramm haben Sie das Problem, dass die Anzahl der Reiskörner und die Anzahl der Weizenkörner in so einem Kilogramm unterschiedlich ist. Das stört Sie nicht, aber den Chemiker. Daher will er kein Kilogramm mit einer unbestimmten Teilchenzahl, sondern ein Mol mit immer exakt der gleichen Teilchenzahl.
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Jetzt aber wieder zum Mol. Ich will Ihnen zeigen, welche Vorteile diese Einheit gegenüber dem Kilogramm hat, speziell natürlich, wenn es um chemische Reaktionen geht. In
Abbildung 2.9 sind die drei Gase Wasserstoff (H
2), Stickstoff (N
2) und Methan (CH
4) gezeigt. Alle drei Gase nehmen mit
das gleiche Volumen ein. Der Druck und die Temperatur sind bei allen drei Gasen ebenfalls identisch
. Nun müssen Sie etwas in Ihren chemischen Grundlagen wühlen oder sich in
Abbildung 2.10 das Periodensystem der Elemente anschauen. Dann sehen Sie, dass 1 Mol Wasserstoff als Molekül (H
2) 2 g wiegt, Stickstoff als Molekül (N
2) 28 g und dementsprechend Methan
16 g. Da Sie alles auf ein Mol beziehen, müssen laut Avogadro alle drei Gase die gleiche Anzahl an Gasmolekülen enthalten, nämlich 6,022 · 10
23 Teilchen pro Mol. Da die Masse von Wasserstoff am kleinsten ist, die Anzahl der Teilchen aber genauso groß ist wie bei den zwei anderen Gasen, können Sie daraus schließen, dass die Wasserstoffatome am kleinsten sein müssen. Sie können bei allen drei Gasen mit 1 Mol arbeiten, obwohl die Gase unterschiedliche Massen aufweisen. Aus
Abbildung 2.9 können Sie ebenfalls herauslesen, dass 1 Mol eines Gases bei einer Temperatur von 273,15 K und einem Druck von 1,013 · 10
5 Pa ein Volumen von 22,42 m
3 einnimmt.
Abbildung 2.9 Gesetz von Avogadro
Wenn Ihnen dieses Beispiel immer noch nicht so recht weiterhelfen sollte, hilft Ihnen vielleicht das folgende praktische Beispiel: Jedes Element hat ein Atomgewicht, das Sie im Periodensystem der Elemente ablesen können. Aluminium (Al) zum Beispiel hat ein Atomgewicht von 26,98 kg/kmol, siehe
Abbildung 2.10. Achtung: die Einheit ist im Periodensystem der Elemente nicht angegeben. Wenn Sie Altaluminium sammeln, das Aluminium wiegen und feststellen, dass Sie genau 26,98 kg gesammelt haben, so wird der Chemiker Ihnen mitteilen, dass sie genau 1 kmol