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

L'equazione del gas ideale ha due svantaggi significativi: in primo luogo, non considera il volume delle molecole di gas e, in secondo luogo, non tiene conto delle forze intermolecolari attrattive tra le molecole di gas. 
Se il gas contiene n numero di moli e ognuna di esse occupa il volume b, allora il volume totale occupato dalle molecole di gas è nb. Pertanto, il volume disponibile per il movimento delle molecole di gas sarà il volume totale meno nb.
Le forze intermolecolari attrattive riducono la pressione proporzionale al quadrato della densità molare. In assenza di forze intermolecolari attrattive, è necessaria una pressione più elevata per raggiungere lo stesso nRT.
Questa è l'equazione di stato di van der Waals che cerca di affrontare gli svantaggi dell'equazione dei gas ideali. Qui, a e b sono costanti empiriche che dipendono dal tipo di gas in studio.
L'equazione di van der Waals prevede adeguatamente il comportamento del gas reale, come la transizione da liquido a vapore e l'effetto Joule-Thomson.

<ol>
	<li>Young, H.D. e Freedman, R.A. (2012). Fisica universitaria con fisica moderna. San Francisco, CA: Pearson; sezione 18.1; pagine 595 e 617.</li>
	<li>OpenStax. (2019). Fisica universitaria Vol. 2. [Versione web]. Estratto da <a href="https://openstax.org/details/books/university-physics-volume-2">https://openstax.org/details/books/university-physics-volume-2</a>; sezione 2.1; pagina 75.</li>
</ol>

equazione di van der waals

Van der Waals Equation

La legge dei gas ideali è un'approssimazione che funziona bene ad alte temperature e a bassa pressione. L'equazione di van der Waals (chiamata così dal fisico olandese Johannes van der Waals, 1837 – 1923) la migliora considerando due fattori.

In primo luogo, le forze attrattive tra le molecole, che sono più forti ad alte densità e riducono la pressione, sono considerate dall'aggiungere alla pressione un termine uguale al quadrato della densità molare moltiplicato per una coefficiente positivo a. In secondo luogo, il volume delle molecole è rappresentato da una costante positiva b, che può essere pensata come il volume di una mole di molecole. Questo viene sottratto dal volume totale per ottenere il volume rimanente in cui le molecole possono muoversi. Le costanti a e b sono determinate sperimentalmente per ogni gas. L'equazione risultante è:

<img alt="Equation1" src="/files/ftp_upload/13668/13668_Equation_1.svg" style="text-align: center; height: 30px;" />

Per il gas di diossido di carbonio con l'equazione di van der Waals, la costante a è 0.364 J·m3/mol2 e la costante b è 4.27x10-5 m3/mol. Se 1 mole di questo gas è confinata in un volume di 300cm3 a 300K, allora la pressione del gas può essere calcolata usando l'equazione di van der Waals. Riorganizzando l'equazione di van der Waals per la pressione:

<img alt="Equation2" src="/files/ftp_upload/13668/13668_Equation_2.svg" style="text-align: center; height: 30px;" />

e sostituendo le quantità in essa conosciute

<img alt="Equation3" src="/files/ftp_upload/13668/13668_Equation_3.svg" style="text-align: center; height: 32px;" />

otteniamo la pressione del gas di diossido di carbonio

<img alt="Equation4" src="/files/ftp_upload/13668/13668_Equation_4.svg" style="text-align: center; height: 16px;" />

Nel limite di bassa densità (n piccola), i termini a e b sono irrilevanti, e l'equazione di van der Waals si riduce alla legge dei gas ideali. D'altro canto, se il secondo termine dell'equazione di van der Waals è piccolo, significa che le molecole sono molto vicine tra loro, allora la pressione dev'essere più alta per ottenere lo stesso nRT, come previsto in queste situazioni di gas altamente compressi. Tuttavia, l'aumento di pressione è minore di quanto suggerirebbe questo ragionamento, perché ad alte densità, il termine di correzione di pressione dall'equazione di van der Waals è significativo. Visto che il termine di correzione della pressione è positivo, richiede una pressione più bassa per ottenere lo stesso nRT. L'equazione di stato di van der Waals funziona bene per la maggior parte dei gas in varie condizioni, come nel predire le transizioni di fase da liquido a gassoso.

Equazione di van der Waals

La legge dei gas ideali è un'approssimazione che funziona bene ad alte temperature e basse pressioni. L'equazione di stato di van der Waals (dal nome dell'olandese ...

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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.

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How Real Gases Deviate from Ideal Behavior | JoVE K12

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How Real Gases Deviate from Ideal Behavior

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