Name: gas particle speed distributions and temperature
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 7 s
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K12 Standards

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NC K-12 Science Standard Course of Study

9-12

Chemistry

Energy

PS.Chm.7.3

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

Todas as partículas de gás têm energia cinética, que é uma função da massa das partículas, em quilogramas, e velocidade, ou a magnitude da sua velocidade, em metros por segundo. Em cada colisão, as velocidades das partículas individuais do gás mudam. Portanto, um conjunto de partículas de gás tem realmente uma distribuição, ou alcance, de velocidades e energias cinéticas.Isto significa que num dado, algumas moléculas estão a mover-se mais lentamente do que outras;no entanto, a energia cinética média permanece igual. A energia cinética média está relacionada com a média dos quadrados das velocidades, ou velocidade quadrada-média ambas permanecem constantes a uma dada temperatura para um dado gás. Agora, a energia cinética média de um mol de um gás é expressa pela introdução da constante de Avogadro, NA.O produto da massa por partícula e a constante de partículas por mol de Avogadro é igual à massa molar do gás em quilogramas por mol.Lembremo-nos da teoria molcular cinética onde a energia cinética média de um mol de gás é diretamente proporcional à temperatura. Através de derivações complexas, a constante de proporcionalidade é de 3/2 R.Combinando as duas equações, reorganizando os termos e tomando a raiz quadrada em ambos os lados se relaciona a raiz quadrada da velocidade quadrada-média também denominada de raiz-quadrada-média ou RMS, velocidade a massa molar e a temperatura absoluta de um gás. A velocidade RMS é inversamente proporcional à massa molar e diretamente proporcional à temperatura.Suponhamos que dois gases hélio e argônio estão à mesma temperatura. Como o hélio tem a massa molar inferior, a equação indica que o hélio deve ter uma velocidade RMS mais elevada do que o argônio. Uma observação semelhante é feita numa parcela da distribuição de velocidades molculares para três gases hélio, argônio e cloro à mesma temperatura.Note-se que, apesar de todos os gases terem a mesma energia cinética média, o gás mais leve, o hélio, tem tanto a maior velocidade RMS como a distribuição da velocidade mais ampla, correspondente à mais vasta gama de velocidades molculares. Um gráfico da distribuição de velocidade para qualquer gás digamos, argônio a diferentes temperaturas apresenta um aumento da velocidade RMS e um alargamento da distribuição da velocidade a temperaturas superiores. Em resumo, os gases movem-se mais rapidamente a temperaturas mais elevadas.Por exemplo, as partículas de gás que provocam o aroma dos alimentos quentes movem-se mais rapidamente do que as partículas dos alimentos frios. Assim, os alimentos quentes são detectados mais rapidamente do que os alimentos frios.

velocidades moleculares e energia cinética

A teoria cinética molecular explica qualitativamente os comportamentos descritos pelas várias leis de gases. Os postulados desta teoria podem ser aplicados de forma mais quantitativa para derivar essas leis individuais.

Colectivamente, as moléculas de uma amostra de gás têm energia cinética média e velocidade média; mas individualmente, movem-se a velocidades diferentes. As moléculas sofrem frequentemente colisões elásticas nas quais o momentum é conservado. Uma vez que as moléculas que colidem são desviadas a diferentes velocidades, as moléculas individuais têm velocidades muito variáveis. No entanto, devido ao grande número de moléculas e colisões envolvidas, a distribuição da velocidade molecular e a velocidade média são constantes. Esta distribuição de velocidade molecular é conhecida como uma distribuição de Maxwell-Boltzmann, e descreve os números relativos de moléculas em uma amostra geral de gás que possui uma determinada velocidade. 

A energia cinética (KE) de uma partícula de massa (m) e velocidade (u) é dada por:

<img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />

A expressão da massa em quilogramas e da velocidade em metros por segundo produz valores de energia em unidades de joules (J = kg·m2/s2). Para lidar com um grande número de moléculas de gás, usam-se médias tanto para a velocidade como para a energia cinética. Na KMT, a raiz do valor quadrático médio da velocidade de uma partícula, urms, é definida como a raiz quadrada da média dos quadrados das velocidades com n = o número de partículas:

<img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />

A energia cinética média para um mole de partículas, KEavg, é então igual a:

<img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />

onde M é a massa molar expressa em unidades de kg/mol. A KEavg de um mole de moléculas de gás também é diretamente proporcional à temperatura do gás e pode ser descrita pela equação:

<img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />

onde R é a constante de gás e T é a temperatura em kelvin. Quando utilizada nesta equação, a forma apropriada da constante de gás é 8,314 J/mol⋅K (8,314 kg·m2/s2·mol·K). Estas duas equações separadas para a KEavg podem ser combinadas e reorganizadas para estabelecer uma relação entre a velocidade molecular e a 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 a temperatura de um gás aumentar, a sua KEavg aumenta, mais moléculas têm velocidades mais elevadas e menos moléculas têm velocidades mais baixas, e a distribuição muda para velocidades mais elevadas em geral, ou seja, para a direita. Se a temperatura diminuir, a KEavg diminui, mais moléculas têm velocidades mais baixas e menos moléculas têm velocidades mais elevadas, e a distribuição muda para velocidades mais baixas em geral, ou seja, para a esquerda. 

A uma determinada temperatura, todos os gases têm a mesma KEavg para as suas moléculas. A velocidade molecular de um gás está diretamente relacionada com a massa molecular. Os gases compostos por moléculas mais leves têm partículas de alta velocidade e urms mais elevados, com uma distribuição de velocidade que atinge velocidades relativamente mais elevadas. Os gases compostos por moléculas mais pesadas têm partículas de velocidade mais baixa, urms mais baixos, e uma distribuição de velocidade que atinge velocidades relativamente mais baixas. 

Este texto é adaptado de <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>

Velocidades Moleculares e Energia Cinética

A teoria cinética molecular explica qualitativamente os comportamentos descritos pelas várias leis dos gases. Os postulados desta teoria podem ser aplicados de forma ...

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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

gas-particle-speed-distributions-and-temperature

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

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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...

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basic postulates of kinetic molecular theory: particle size, energy, and collision

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Kinetic Molecular Theory and Gas Behavior

Kinetic molecular theory explains gas behavior at the particle level. It gives a microscopic model for what happens when pressure or temperature changes. Gas laws describe how macroscopic properties change, but they do not explain why those changes happen. The theory was put into a complete form by Rudolf Clausius in 1857. It was built from hundreds of experimental observations about gases. Those observations helped explain the different gas laws through a few basic postulates. One key idea...

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Gas Pressure Patterns in Kinetic Molecular Theory

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kinetic molecular theory: molecular velocities, temperature, and kinetic energy

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...

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key terms and concepts

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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New York State Science Learning Standards

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Phase Transitions

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Phase Transitions: Vaporization and Condensation

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Vapor Pressure

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Clausius-Clapeyron Equation

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Energy Basics

Chemical reactions, such as those that occur when you light a match, involve changes in energy as well as matter.

Chemical changes and their accompanying ...

First Law of Thermodynamics

Energy Conservation

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Internal Energy

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Quantifying Heat

Thermal Energy&#160;

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Quantifying Work

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Enthalpy

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Standard Enthalpy of Formation

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PS.Chm.7.2

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Gas Particle Speed Distributions and Temperature

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