Name: gas particle speed distributions and temperature
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 7 s
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Kinetic Molecular Theory: Molecular Velocities, Temperature, and Kinetic Energy

Toutes les particules de gaz ont une énergie cinétique, qui est fonction de la masse de la particule, en kilogrammes, et de la vitesse, ou de l'amplitude de sa vitesse, en mètres par seconde. À chaque collision, les vitesses des particules de gaz individuelles changent. Par conséquent, une collection de particules de gaz a en fait une distribution, ou gamme, des vitesses et des énergies cinétiques.Cela signifie qu'à tout moment, certaines molécules se déplacent plus lentement que d'autres;cependant, l'énergie cinétique moyenne reste la même. L'énergie cinétique moyenne est liée à la moyenne des carrés des vitesses, ou vitesse moyenne-carrée-qui restent toutes deux constantes à une température donnée pour un gaz donné. Maintenant, l'énergie cinétique moyenne d'une mole d'un gaz est exprimée en introduisant la constante d'Avogadro, NA.Le produit de la masse par particule et de la constante d'Avogadro de particules par mole est égal à la masse molaire du gaz en kilogrammes par mole.Rappelons de la théorie moléculaire cinétique que l'énergie cinétique moyenne d'une mole de gaz est directement proportionnelle à la température. Grâce à des dérivations complexes, on trouve que la constante de proportionnalité est de 3/2 R.En combinant les deux équations, en réarrangeant les termes et en prenant la racine carrée des deux côtés, on rapporte la racine carrée de la vitesse moyenne-carrée aussi appelée vitesse moyenne-carrée, ou RMS la masse molaire et la température absolue d'un gaz. La vitesse RMS est inversement proportionnelle à la masse molaire et directement proportionnelle à la température.Supposons que deux gaz-hélium et argon-soient à la même température. Comme l'hélium a la masse molaire inférieure, l'équation indique que l'hélium doit avoir une vitesse RMS plus élevée que l'argon. Une observation similaire est faite dans un graphique de la distribution des vitesses moléculaires pour trois gaz hélium, argon et chlore à la même température.Notez que même si tous les gaz ont la même énergie cinétique moyenne, le gaz le plus léger, l'hélium, a à la fois la vitesse RMS la plus élevée et la distribution de vitesse la plus large, correspondant à la plus large gamme de vitesses moléculaires. Un graphique de la distribution de la vitesse pour n'importe quel gaz disons, argon à différentes températures montre une augmentation de la vitesse RMS et un élargissement de la distribution de la vitesse à des températures plus élevées. En bref, les gaz se déplacent plus rapidement à des températures plus élevées.Par exemple, les particules de gaz provoquant l'arôme des aliments chauds se déplacent plus rapidement que les particules des aliments froids. Ainsi, les aliments chauds sont détectés plus rapidement que les aliments froids.

vitesses moléculaires et énergie cinétique

La théorie cinétique des gaz explique de façon qualitative les comportements décrits par les différentes lois sur les gaz. Les postulats de cette théorie peuvent être appliqués d'une façon plus quantitative pour déduire ces lois individuelles. 
 
 Collectivement, les molécules d'un échantillon de gaz ont une énergie cinétique moyenne et une vitesse moyenne ; mais individuellement, elles se déplacent à des vitesses différentes. Les molécules subissent fréquemment des chocs élastiques dans lesquels la quantité de mouvement est conservée. Comme les molécules entrant en collision sont déviées à des vitesses différentes, les molécules individuelles ont des vitesses très variables. Cependant, en raison du grand nombre de molécules et de chocs impliqués, la distribution de la vitesse moléculaire et la vitesse moyenne sont constantes. Cette distribution de la vitesse moléculaire est connue sous le nom de distribution de Maxwell-Boltzmann, et elle représente le nombre relatif de molécules dans un large échantillon de gaz qui possède une vitesse donnée.  
 
 L'énergie cinétique (Éc) d'une particule de masse (m) et de vitesse (u) est donnée par : 
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />
 
 L'expression de la masse en kilogrammes et de la vitesse en mètres par seconde donne des valeurs d'énergie en joules (J = kg·m2/s2). Pour traiter un grand nombre de molécules de gaz, nous utilisons des moyennes à la fois pour la vitesse et pour l'énergie cinétique. Dans la TCG, la vitesse quadratique moyenne d'une particule, uqm, est définie comme la racine carrée de la moyenne des carrés des vitesses avec n = le nombre de particules : 
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />
 
 L'énergie cinétique moyenne pour une mole de particules, Écmoy, est alors égale à : 
 
 <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />
 
 où M est la masse molaire exprimée en kg/mol. L'Écmoy d'une mole de molécules de gaz est également directement proportionnelle à la température du gaz et peut être décrite par l'équation : 
 
 <img alt="Eq4" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />
 
 où R est la constante des gaz et T la température en Kelvin. Lorsqu'elle est utilisée dans cette équation, la forme appropriée de la constante des gaz est 8,314 J/mol⋅K (8,314 kg·m2/s2·mol·K). Ces deux équations distinctes pour Écmoy peuvent être combinées et réorganisées pour générer une relation entre la vitesse moléculaire et la température : 
 
 <img alt="Eq5" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-05.png" style="height: 40px;" />
 
 <img alt="Eq6" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-06.png" style="height: 40px;" />
 
 Si la température d'un gaz augmente, son Écmoy augmente ; il y a plus de molécules qui ont des vitesses plus élevées et moins de molécules qui ont des vitesses plus faibles, et la distribution se déplace vers des vitesses plus élevées globalement, c'est-à-dire, vers la droite. Si la température diminue, Écmoy diminue ; il y a plus de molécules qui ont des vitesses plus faibles et moins de molécules qui ont des vitesses plus élevées, et la distribution se déplace vers des vitesses plus faibles globalement, c'est-à-dire vers la gauche.  
 
 À une température donnée, tous les gaz ont, pour leurs molécules, la même Écmoy. La vitesse moléculaire d'un gaz est directement liée à la masse moléculaire. Les gaz composés de molécules plus légères ont plus de particules à grande vitesse et une uqm plus élevée, avec une distribution de la vitesse dont le pic se trouve à des vitesses relativement plus élevées. Les gaz constitués de molécules plus lourdes ont plus de particules à faible vitesse, une uqm plus faible et une distribution de la vitesse qui culmine à des vitesses relativement faibles.  
 
 Ce texte est adapté de <a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory">Openstax, Chimie 2e, Section 9.5 : Théorie cinétique-moléculaire.</a>

Vitesses moléculaires et énergie cinétique

La théorie moléculaire cinétique explique qualitativement les comportements décrits par les différentes lois des gaz. Les postulats de cette théorie peuvent être appliqués dans 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.

Gas Particle Speed Distributions and Temperature

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Explore how gas particle speeds, Maxwell-Boltzmann distributions, temperature, and kinetic energy are linked in kinetic molecular theory for high school chemistry.

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Gas Particle Speed Distributions and Temperature

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