Name: gas particle speed distributions and temperature
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 7 s
Channel: JoVE

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NC K-12 Science Standard Course of Study

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PS.Chm.7.3

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Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

Tutte le particelle di gas hanno un'energia cinetica, che è una funzione della massa della particella, definita in chilogrammi, e della velocità, o l'entità della sua velocità, in metri al secondo. Con ogni collisione, le velocità delle singole particelle di gas cambiano. Pertanto, una raccolta di particelle di gas ha effettivamente una distribuzione, o intervallo di velocità ed energie cinetiche diverse.

Ciò significa che in qualsiasi istante alcune molecole si muovono più lentamente di altre;tuttavia, l'energia cinetica media rimane la stessa. L'energia cinetica media è correlata alla media dei quadrati delle velocità, o velocità quadratica media:entrambe rimangono costanti ad una data temperatura per una data tipologia di gas. Ora, l'energia cinetica media di un mole di un gas viene espressa introducendo la costante di Avogadro, NA.Il prodotto della massa per particella e della costante di particelle per mole di Avogadro è uguale alla massa molare del gas in chilogrammi per mole.

Ricordiamo dalla teoria molecolare cinetica che l'energia cinetica media di una mole di gas è direttamente proporzionale alla temperatura. Attraverso derivazioni complesse, la costante di proporzionalità risulta essere 3/2 R.Combinando le due equazioni, riorganizzando i termini e prendendo la radice quadrata su entrambi i lati, si mette in relazione la radice quadrata della velocità quadratica media, chiamata anche velocità quadratica media, o RMS, la massa molare e la temperatura assoluta di un gas. La velocità RMS è inversamente proporzionale alla massa molare e direttamente proporzionale alla temperatura.

Supponiamo che due gas, elio e argon, siano alla stessa temperatura. Poiché l'elio ha la massa molare inferiore, l'equazione indica che l'elio deve avere una velocità RMS maggiore dell'argon. Un'osservazione simile viene fatta in un grafico della distribuzione delle velocità molecolari per tre gas.

Elio, argon e cloro. alla stessa temperatura. Notate che anche se tutti i gas hanno la stessa energia cinetica media, il gas più leggero, l'elio, ha sia la velocità RMS più alta che la distribuzione di velocità più ampia, corrispondente alla più ampia gamma di velocità molecolari.

Un grafico della distribuzione della velocità per qualsiasi gas, per esempio l'argon, a diverse temperature mostra un aumento della velocità RMS e un ampliamento della distribuzione della velocità a temperature più elevate. In breve, i gas si muovono più velocemente a temperature più elevate. Per esempio, le particelle di gas che causano aroma dal cibo caldo si muovono più velocemente di quelle dal cibo freddo.

Pertanto, il cibo caldo viene rilevato più velocemente di quello freddo.

teoria molecolare cinetica: velocità molecolari, temperatura ed energia cinetica

La teoria cinetica molecolare spiega qualitativamente i comportamenti descritti dalle varie leggi dei gas. I postulati di questa teoria possono essere applicati in modo più quantitativo per ricavare queste leggi individuali.

Collettivamente, le molecole in un campione di gas hanno energia cinetica media e velocità media; ma individualmente si muovono a velocità diverse. Le molecole subiscono spesso urti elastici in cui la quantità di moto è conservata. Poiché le molecole in collisione vengono deviate a velocità diverse, le singole molecole hanno velocità molto variabili. Tuttavia, a causa del vasto numero di molecole e di collisioni coinvolte, la distribuzione della velocità molecolare e la velocità media sono costanti. Questa distribuzione della velocità molecolare è nota come distribuzione di Maxwell-Boltzmann e descrive il numero relativo di molecole in un campione globale di gas che possiede una determinata velocità.

L'energia cinetica (KE) di una particella di massa (m) e velocità (u) è data da:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />

Esprimendo la massa in chilogrammi e la velocità in metri al secondo si otterranno valori di energia in unità di joule (J = kg·m^2/s^2). Per gestire un gran numero di molecole di gas, utilizziamo le medie sia della velocità che dell'energia cinetica. Nel KMT, la radice quadrata della velocità media di una particella, u_rms, è definita come la radice quadrata della media dei quadrati delle velocità con n = il numero di particelle:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />

L’energia cinetica media per una mole di particelle, KE_avg, è quindi pari a:

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />

dove M è la massa molare espressa in unità di kg/mol. Anche il KE_avg di una mole di molecole di gas è direttamente proporzionale alla temperatura del gas e può essere descritto dall'equazione:

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />

dove R è la costante dei gas e T è la temperatura Kelvin. Quando utilizzata in questa equazione, la forma appropriata della costante dei gas è 8,314 J/mol⋅K (8,314 kg·m^2/s^2·mol·K). Queste due equazioni separate per KE_avg possono essere combinate e riorganizzate per produrre una relazione tra velocità molecolare e temperatura:

<img alt="Eq5" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-05.png" style="height: 40px;" />

<img alt="Eq6" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-06.png" style="height: 40px;" />

Se la temperatura di un gas aumenta, il suo KE_avg aumenta, più molecole hanno velocità più elevate e meno molecole hanno velocità più basse e la distribuzione si sposta complessivamente verso velocità più elevate, cioè verso destra. Se la temperatura diminuisce, KE_avg diminuisce, più molecole hanno velocità inferiori e meno molecole hanno velocità più elevate e la distribuzione si sposta complessivamente verso velocità inferiori, cioè verso sinistra.

Ad una data temperatura, tutti i gas hanno lo stesso KE_avg per le loro molecole. La velocità molecolare di un gas è direttamente correlata alla massa molecolare. I gas composti da molecole più leggere hanno più particelle ad alta velocità e un u_rms più elevato, con una distribuzione della velocità che raggiunge il picco a velocità relativamente più elevate. I gas costituiti da molecole più pesanti hanno più particelle a bassa velocità, un u_rms più basso e una distribuzione della velocità che raggiunge il picco a velocità relativamente più basse.

Questo testo è adattato da <a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory">Openstax, Chemistry 2e, Section 9.5: Kinetic-Molecular Theory. </a>

Teoria molecolare cinetica: velocità molecolari, temperatura ed energia cinetica

La teoria cinetica molecolare spiega qualitativamente i comportamenti descritti dalle varie leggi dei gas. I postulati di questa teoria possono essere applicati in un ...

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gas particle speed distributions and temperature

Gas particle speed distributions and temperature are key ideas in the kinetic molecular theory. This theory explains the gas laws by describing how gas molecules move, collide, and share energy.

Gas molecules do not all move at the same speed. A gas sample has an average speed and an average kinetic energy, but individual molecules move at different speeds. Their collisions are elastic, which means momentum is conserved. Because so many molecules collide, the overall speed distribution stays constant.

That distribution is called the Maxwell-Boltzmann distribution. It shows the relative number of molecules in a gas sample at each speed. Kinetic energy depends on both mass and speed, and it is measured in joules when mass is in kilograms and speed is in meters per second. For large numbers of molecules, chemists use averages for speed and kinetic energy.

The root mean square velocity, or u rms, is one way to describe average molecular speed. It is the square root of the average of the squared velocities. The average kinetic energy for one mole of gas also depends on molar mass, and it can be written in terms of the gas constant and the kelvin temperature. In this equation, the correct gas constant is 8.314 J/mol·K.

These relationships show how speed changes with temperature. When temperature increases, average kinetic energy increases. More molecules move at higher speeds, fewer move at lower speeds, and the distribution shifts to the right. When temperature decreases, average kinetic energy decreases, more molecules move slowly, and the distribution shifts to the left.

At the same temperature, gases have the same average kinetic energy, even if their molecules have different masses. Molecular mass still affects speed. Lighter gases have more high-speed particles and a higher u rms, while heavier gases have more low-speed particles and a lower u rms. Their speed distributions peak at different velocities, with lighter gases peaking at higher speeds and heavier gases peaking at lower speeds.

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Gas Particle Speed Distributions and Temperature

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