Name: gas pressure in mixtures: partial pressures
Uploaded: 2020-09-03T13:38:26.000Z
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Chemistry

Energy

PS.Chm.7.3

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Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

La pressione di un gas puro è la somma delle collisioni molecolari tra le sue particelle e le superfici circostanti. Un campione di gas con meno particelle in un dato volume esercita una pressione inferiore rispetto ad un campione con più particelle nello stesso volume. Ma qual è la pressione di una miscela di gas diversi?

Per una miscela di gas multicomponente, la pressione è la somma delle collisioni di tutte le molecole di gas. Si presume che ogni componente della miscela eserciti una propria pressione, indipendente dagli altri gas presenti. La pressione di ogni singolo componente è detta pressione parziale.

La pressione totale della miscela di gas ideali è uguale alla somma delle pressioni parziali dei suoi componenti. Questa osservazione è la legge di Dalton delle pressioni parziali. Applicando la legge dei gas ideali, le pressioni parziali delle singole componenti del gas vengono sostituite con variabili misurabili.

Poiché i gas nella miscela occupano lo stesso volume e sono alla stessa temperatura, l'equazione può essere semplificata. La somma delle moli dei singoli componenti è uguale al numero totale di moli di tutti i componenti del gas, n-totale. Pertanto, la pressione totale della miscela di gas è uguale a n-totale moltiplicato per la costante R-T su V.Il numero di moli di un componente diviso per le moli totali nella miscela è la frazione molare.

Riorganizzando la frazione molare per le moli totali e sostituendo n-totale nella legge di Dalton delle pressioni parziali si ottengono equazioni per la pressione totale. Riorganizzando ancora, la pressione parziale di un gas in una miscela è il prodotto della sua frazione molare e la pressione totale della miscela. Dunque, in una miscela di gas, la pressione parziale di qualsiasi componente, i, è uguale alla frazione molare di i moltiplicata per la pressione totale.

Come calcolo di esempio, supponiamo che un contenitore riempito con due gas, elio e argon, contenga il 40 percento in volume di argon. Questo implica che la frazione molare di argon sia 0, 4. Se la pressione totale è di 4 atm, qual è la pressione parziale dell'elio?

Usando l'equazione per la pressione parziale di un gas, la pressione parziale dell'argon è uguale alla sua frazione molare moltiplicata per la pressione totale. Pertanto, 0, 4 volte 4 atm danno la pressione parziale dell'argon a 1, 6 atm. Poiché la somma delle pressioni parziali è uguale alla pressione totale, l'equazione può essere riorganizzata in modo che la pressione parziale dell'argon possa essere sottratta dalla pressione totale.

Pertanto, la pressione parziale dell'elio è di 2, 4 atm.

miscele di gas: legge delle pressioni parziali di dalton e frazioni molari

A meno che i singoli gas non reagiscano chimicamente tra loro, i singoli gas in una miscela di gas non influenzano la pressione reciproca. Ogni gas presente in una miscela esercita la stessa pressione che eserciterebbe se fosse presente da solo nel contenitore. La pressione esercitata da ogni singolo gas in una miscela è chiamata pressione parziale.

Ciò significa che in una miscela contenente tre gas diversi A, B e C, se P_A è la pressione parziale del gas A; P_B è la pressione parziale del gas B; P_C è la pressione parziale del gas C; quindi la pressione totale è data dall'equazione 1:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-01.png" style="height: 40px;" />

Questa è la legge delle pressioni parziali di Dalton: la pressione totale di una miscela di gas ideali è uguale alla somma delle pressioni parziali dei gas che la compongono.

Siano n_A, n_B e n_C il numero di moli di ciascuno dei gas nella miscela. Se ciascun gas rispetta l’equazione dei gas ideali, la pressione parziale può essere scritta come:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-02.png" style="height: 40px;" />

Poiché tutti i gas sono alla stessa temperatura e occupano lo stesso volume, sostituendo nell'equazione 1 si ottiene:

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-03.png" style="height: 40px;" />

L'equazione indica che a temperatura e volume costanti, la pressione totale di un campione di gas è determinata dal numero totale di moli di gas presenti.

Per le miscele di gas è conveniente introdurre una quantità chiamata frazione molare, χ, che è definita come il numero di moli di una particolare sostanza in una miscela diviso per il numero totale di moli di tutte le sostanze presenti. Matematicamente, la frazione molare di una sostanza A in una miscela con B e C è espressa come:

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-04.png" style="height: 40px;" />

Allo stesso modo, la frazione molare di B e C è:

<img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-05.png" style="height: 40px;" />

<img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-06.png" style="height: 40px;" />

Combinando l'equazione per la frazione molare di A e l'equazione per la pressione parziale si ottiene:

<img alt="Eq7" src="https://www.jove.com/files/core/CDNSource/lessons/1038/1038_Equations-07.png" style="height: 40px;" />

La pressione parziale del gas A è correlata alla pressione totale della miscela di gas tramite la sua frazione molare.

In altre parole, la pressione di un gas in una miscela di gas è il prodotto della sua frazione molare e della pressione totale della miscela.

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/9-3-stoichiometry-of-gaseous-substances-mixtures-and-reactions">Openstax, Chemistry 2e, Section 9.3: Stoichiometry of Gaseous Substances, Mixtures, and Reactions.</a>

Miscele di gas: legge delle pressioni parziali di Dalton e frazioni molari

A meno che i singoli gas non reagiscano chimicamente tra loro, i singoli gas in una miscela di gas non influenzano la pressione reciproca. Ogni gas ...

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gas pressure in mixtures: partial pressures

Gas pressure in mixtures is described by partial pressure and mole fraction. When gases do not chemically react, each gas in the mixture acts as if it were alone in the container. The pressure from one gas is called its partial pressure.

For a mixture of three gases, A, B, and C, the total pressure equals the sum of their partial pressures: PA, PB, and PC. This is Dalton's law of partial pressures. It states that the total pressure of a mixture of ideal gases is the sum of the pressures from each gas.

If each gas follows the ideal-gas equation, its partial pressure can be written in terms of moles, temperature, and volume. Because every gas in the mixture has the same temperature and takes up the same volume, these terms can be combined. At constant temperature and constant volume, the total pressure depends on the total number of moles of gas present.

For gas mixtures, chemists also use mole fraction, x. Mole fraction is the number of moles of one substance divided by the total number of moles in the mixture. For gas A in a mixture with B and C, the mole fractions of A, B, and C are found in this way.

Mole fraction also links directly to partial pressure. The partial pressure of gas A equals its mole fraction times the total pressure of the mixture. In other words, a gas's pressure in a mixture is its share of the total pressure.

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mixtures of gases: dalton's law of partial pressures and mole fractions

Gas pressure in mixtures is described by partial pressure and mole fraction. When gases do not chemically react, each gas in the mixture acts as if it were alone in the container. The pressure from one gas is called its partial pressure. For a mixture of three gases, A, B, and C, the total pressure equals the sum of their partial pressures: PA, PB, and PC. This is Dalton's law of partial pressures. It states that the total pressure of a mixture of ideal gases is the sum of the pressures from...

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Gas Pressure in Mixtures: Partial Pressures

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