Name: gas laws behind the ideal equation
Uploaded: 2023-04-30T12:30:10.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Chemistry

Matter and Its Interactions

CHEM1.PS1.6

Ideal Gas Equation

Die Zustandsvariablen für das untersuchte Gas sind Druck, Volumen, Temperatur und die Anzahl der Mol.
Das Avogadrosche Gesetz besagt, dass das Gasvolumen proportional zu seiner Molzahl bei konstanter Temperatur und konstantem Druck ist.
In ähnlicher Weise drückt das Boylesche Gesetz aus, dass der Druck für eine gegebene Anzahl von Mol und bei konstanter Temperatur umgekehrt proportional zum Volumen des Gases ist.
Darüber hinaus gibt das Charles-Gesetz die Beziehung zwischen dem Volumen und der Temperatur des Gases bei konstantem Druck und einer gegebenen Molzahl an.
In ähnlicher Weise besagt das Gay-Lussac-Gesetz, dass der Druck eines Gases proportional zu seiner Temperatur für eine gegebene Anzahl von Mol und bei konstantem Volumen ist.
Diese vier Gesetze zusammen ergeben die ideale Gasgleichung. Die Proportionalitätskonstante ist die universelle Gaskonstante mit einem Wert von 8,314 Joule pro Molkelvin in den SI-Einheiten. Sie ist unabhängig von der Art des untersuchten Gases.
Die ideale Gasgleichung beschreibt jedes Gas bei höheren Temperaturen und niedrigen Drücken.

<ol>
	<li>Young, H.D. und Freedman, R.A. (2012). Universitätsphysik mit moderner Physik. San Francisco, Kalifornien: Pearson; Abschnitt 18.1; Seite 591–593.</li>
	<li>OpenStax. (2019). Universitätsphysik Vol. 2. [Webversion]. Abgerufen von <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; Abschnitt 2.1; Seite 68–73.</li>
</ol>

ideale gasgleichung

Die ideale Gasgleichung ist eine Zustandsgleichung, die die Zustandsvariablen Druck, Volumen, Temperatur und die Stoffmenge eines hypothetischen Gases in Beziehung setzt. Diese Gleichung ist eine Kombination aus vier empirischen Gesetzen, nämlich dem Boyle'schen Gesetz, dem Charles'schen Gesetz, dem Avogadro'schen Gesetz und dem Gay-Lussac'schen Gesetz. Wenn die Proportionalitäten der oben genannten vier empirischen Gesetze kombiniert werden, resultiert dies in einer einzigen Proportionalitätskonstante, die als universelle Gaskonstante bekannt ist.

<img alt="Equation1" src="/files/ftp_upload/13667/13667_Equation_1.svg" style="text-align: center; height: 12px;" />

Diese Gaskonstante ist für alle realen Gase unter bestimmten Bedingungen gleich. Der Wert der universalen Gaskonstante ist

<img alt="Equation2" src="/files/ftp_upload/13667/13667_Equation_2.svg" style="text-align: center; height: 10px;" />

Aber, wenn die ideale Gasgleichung in chemischen Berechnungen verwendet wird, beträgt der Wert der universellen Gaskonstante

<img alt="Equation3" src="/files/ftp_upload/13667/13667_Equation_3.svg" style="text-align: center; height: 12px;" />

Die ideale Gasgleichung beschreibt die Natur eines realen Gases, wenn seine Dichte ausreichend niedrig ist oder seine Temperatur ausreichend hoch ist, dass es weit von der Verflüssigung entfernt ist.

In realen Situationen wird das ideale Gasgesetz auf eine Gasprobe mit einer konstanten Anzahl von Molekülen angewendet. Zum Beispiel kann sich das Gas in einem versiegelten Behälter befinden. Wenn die Stoffmenge konstant ist, dann ist das Verhältnis von Druck mal Volumen zur Temperatur eines Gases konstant. In solchen Fällen kann das Verhältnis von Druck mal Volumen zu den Temperaturen in zwei verschiedenen Zuständen des Gases gleichgesetzt werden. Hierbei muss die Temperatur in Kelvin ausgedrückt werden und der Druck muss absoluter Druck sein, der die Summe aus dem Überdruck und dem atmosphärischen Druck ist.

Die ideale Gasgleichung kann auch in Bezug auf die Boltzmann-Konstante ausgedrückt werden als

<img alt="Equation4" src="/files/ftp_upload/13667/13667_Equation_4.svg" style="text-align: center; height: 12px;" />

Hierbei ist kb Boltzmanns Konstante und NA Avogadros Zahl. Die ideale Gasgleichung kann mit Hilfe der kinetischen Gastheorie hergeleitet werden. Die ideale Gasgleichung steht in enger Beziehung zur Energie. Die Einheiten auf beiden Seiten der Gleichung sind Joule.

Ideale Gasgleichung

Die ideale Gasgleichung ist eine Zustandsgleichung, die die Zustandsvariablen Druck, Volumen, Temperatur und die Molzahl eines hypothetischen ...

Education

Lehre

JoVE Core

Physics

Physik

Unit 1

Einheit 1

The Kinetic Theory of Gases

Die kinetische Gastheorie

KEY TERMS AND CONCEPTS

KERNBEGRIFFE UND KONZEPTE

gas laws behind the ideal equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law.

When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation.

The equation works best when a gas has low density or a high temperature, so it is far from liquefaction. In many real-world cases, the gas sample has a constant number of molecules. A sealed container is one example. If the number of moles stays constant, then the ratio of pressure multiplied by volume to temperature stays constant as well.

That means the ratio can be set equal for two different states of the same gas. The temperature must be written in kelvin. The pressure must be absolute pressure, which is gauge pressure plus atmospheric pressure.

The ideal gas equation can also be written with Boltzmann’s constant, kB, and Avogadro’s number, NA. It can be derived from the kinetic theory of gases. The equation is also closely related to energy, and the units on both sides are joules.

Gas Laws Behind the Ideal Equation

equation of state

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

van der waals equation

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Water Phase Changes on a Pressure Chart

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Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

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key terms and concepts

Learn how Boyle’s, Charles’s, Avogadro’s, and Gay-Lussac’s laws combine into the ideal gas equation, and why kelvin and absolute pressure matter.

Gas Laws Behind the Ideal Equation | JoVE K12

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CHEM1.PS1.5

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CHEM1.PS1.7

Gas Laws Behind the Ideal Equation

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