Name: how real gases deviate from ideal behavior
Uploaded: 2025-05-22T09:05:49.000Z
Duration: 1 min 10 s
Channel: JoVE

Równanie gazu doskonałego ma dwie istotne wady: po pierwsze, nie uwzględnia objętości cząsteczek gazu, a po drugie, nie uwzględnia przyciągających sił międzycząsteczkowych między cząsteczkami gazu. 
Jeśli gaz zawiera n moli i każdy z nich zajmuje objętość b, to całkowita objętość zajmowana przez cząsteczki gazu wynosi nb. Zatem objętość dostępna dla cząsteczek gazu do poruszania się będzie równa objętości całkowitej minus nb.
Przyciągające siły międzycząsteczkowe zmniejszają ciśnienie proporcjonalnie do kwadratu gęstości molowej. W przypadku braku przyciągających sił międzycząsteczkowych, do osiągnięcia tego samego nRT wymagane jest wyższe ciśnienie.
Jest to równanie stanu van der Waalsa, które próbuje rozwiązać problemy z wadami równania gazu doskonałego. Tutaj a i b są stałymi empirycznymi, które są zależne od rodzaju badanego gazu.
Równanie van der Waalsa odpowiednio przewiduje zachowanie rzeczywistego gazu, takie jak przejście cieczy w parę i efekt Joule'a-Thomsona.

<ol>
	<li>Young, H.D. i Freedman, R.A. (2012). Fizyka uniwersytecka z fizyką współczesną. San Francisco, Kalifornia: Pearson; sekcja 18.1; strony 595 i 617.</li>
	<li>Protokół OpenStax. (2019). Fizyka uniwersytecka Vol. 2. [Wersja internetowa]. Źródło: <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sekcja 2.1; Strona 75.</li>
</ol>

równanie van der waalsa

Van der Waals Equation

Prawo gazu doskonałego to przybliżenie, które sprawdza się dobrze w wysokich temperaturach i niskich ciśnieniach. Równanie stanu van der Waalsa (nazwane na cześć holenderskiego fizyka Johannesa van der Waalsa, 1837–1923) poprawia je poprzez uwzględnienie dwóch czynników.

Najpierw rozważa się siły przyciągania między cząsteczkami, które są silniejsze przy wyższych gęstościach i zmniejszają ciśnienie, dodając do ciśnienia składnik równy kwadratowi gęstości molowej pomnożonej przez dodatni współczynnik a. Po drugie, objętość cząsteczek jest reprezentowana przez dodatnią stałą b, którą można traktować jako objętość mola cząsteczek. Jest ona odejmowana od całkowitej objętości, aby otrzymać pozostałą objętość, w której mogą się poruszać cząsteczki. Stałe a i b są wyznaczane eksperymentalnie dla każdego gazu. Wynikowe równanie to

<img alt="Równanie1" src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" />

Dla gazowego dwutlenku węgla z równaniem van der Waalsa stała a wynosi 0,364 J·m3/mol2 i stała b wynosi 4,27 x 10−5 m3/mol. Jeżeli 1 mol tego gazu jest zamknięty w objętości 300 cm3 w temperaturze 300 K, wówczas ciśnienie gazu można obliczyć za pomocą równania van der Waalsa. Przekształcenie równania van der Waalsa na ciśnienie,

<img alt="Równanie2" src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" />

i podstawiając w nim znane ilości

<img alt="Równanie3" src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" />

podaje ciśnienie dwutlenku węgla

<img alt="Równanie4" src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" />

W granicy niskiej gęstości (małe n) składniki a i b są pomijalne, a równanie van der Waalsa zmniejsza do prawa gazu doskonałego. Z drugiej strony, jeśli drugi składnik równania van der Waalsa jest mały, co oznacza, że ​​cząsteczki są bardzo blisko siebie, wówczas ciśnienie musi być wyższe, aby uzyskać ten sam nRT, jak oczekiwano w sytuacji silnie sprężonego gazu. Jednakże wzrost ciśnienia jest mniejszy, niż sugerowałby ten argument, ponieważ przy dużych gęstościach składnik korekcji ciśnienia z równania van der Waalsa jest znaczący. Ponieważ składnik korekcji ciśnienia jest dodatni, wymagane jest niższe ciśnienie, aby uzyskać ten sam nRT. Równanie stanu van der Waalsa działa dobrze dla większości gazów w różnych warunkach, na przykład do przewidywania przejść fazowych ciecz-gaz.

Równanie Van der Waalsa

Prawo gazu doskonałego to przybliżenie, które działa dobrze w wysokich temperaturach i niskich ciśnieniach. Równanie stanu van der Waalsa (nazwane na cześć holenderskiego ...

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The Kinetic Theory of Gases

Kinetyczna teoria gazów

KEY TERMS AND CONCEPTS

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how real gases deviate from ideal behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects.

One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a.

The second correction accounts for the space occupied by the molecules themselves. A positive constant b represents the volume of the molecules, or the volume of a mole of molecules, and this amount is subtracted from the total volume to leave the space the gas can actually move in. The values of a and b are found experimentally for each gas.

For carbon dioxide, the van der Waals constants are a = 0.364 J·m3/mol2 and b = 4.27 x 10−5 m3/mol. If 1 mole of carbon dioxide is confined to 300 cm3 at 300 K, the pressure can be calculated by rearranging the van der Waals equation for pressure and substituting the known values.

At low density, the a and b terms are small, so the van der Waals equation reduces to the ideal gas law. At very high density, the molecules are close together, so a higher pressure is needed to reach the same nRT. Even then, the pressure increase is smaller than a simple compression argument suggests because the pressure correction term becomes significant. This makes the van der Waals equation useful for many gases, including cases that involve liquid-gas phase transitions.

How Real Gases Deviate from Ideal Behavior

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key terms and concepts

See how the van der Waals equation corrects the ideal gas law for molecular attraction and finite molecular volume, with a carbon dioxide example.

How Real Gases Deviate from Ideal Behavior | JoVE K12

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How Real Gases Deviate from Ideal Behavior

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