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

K12 Standards

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NC K-12 Science Standard Course of Study

9-12

Chemistry

Energy

PS.Chm.7.3

kinetic-molecular-theory-molecular-velocities-temperature-kinetic

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

所有气体粒子都有动能，它是粒子质量 和速度，或是速率的大小，的函数。随着每次碰撞，各个气体粒子的速率改变。因此，气体粒子的集合 其实有速度的分布或范围 和动能。意思是在任何瞬间，有些分子 移动的比其他慢，然而，平均动能维持一样。平均动能与速度平方的 平均有关，或均方速度 对于给定气体，两者在给定温度下 维持固定不变。现在，一莫耳气体的平均动能 透过引入亚佛加厥常数NA来表示。每粒子质量 和每莫耳亚佛加厥常数的乘积 等于气体的莫耳质量，以公斤/莫耳为单位 回想一下动力分子理论中 一莫耳气体的平均动能 正比于温度。透过复杂的推导，等比常数 是3/2 R。结合两个方程式，重新排列 各项，并在两边取平方根 可得出均方速度的平方根 也被称为均方根速度，或RMS，速度 也就是莫耳质量，和气体的绝对温度。RMS速度反比 于莫耳质量，并正比于温度。假设两个气体 氦气和氩气 在相同温度下。氦气有较低的莫耳质量，方程式指出氦气必有高于氩气的 RMS速度。在相同温度下，三种气体—氦气，氩气和氯气的分子速度的分布图中，也得到类似的观察。注意虽然所有气体有 相同的平均动能，最轻的气体，氢气，同时有最高的RMS速度和最广的速度 分布，对应分子速 率的最广范围。任何气体的速度分布图，例如氩气，在不同温度呈现RMS速度的增加 以及在较高温度下速度分 布的扩大。简言之，气体在较高温度下移动较快。例如，热的食物中产生香气的气体颗粒 比冷的食物中的粒子移动更快。因此，热的食物测到的比冷的食物快。

分子速度和动能

动力学分子理论定性地解释了各种气体定律所描述的行为。可以更定量地应用该理论的假设，以得出这些个体定律。
 
 总体地，气体样品中的分子具有平均动能和平均速度；但它们各自以不同的速度运动。分子经常发生弹性碰撞，从而保持了动量。由于碰撞分子以不同的速度偏转，各个分子的速度变化很大。但是，由于涉及大量的分子和碰撞，因此分子速度分布和平均速度是恒定的。这种分子速度分布称为麦克斯韦-玻尔兹曼分布，它描述了具有给定速度的大量气体样品中分子的相对数目。
 
 粒子的质量（ m ）和速度（ u ）的动能（KE）由下式给出：
 
 <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />
 
 以千克 (kg) 为单位表示质量，以米每秒 (m/s) 为单位表示速度将产生以焦耳为单位的能量值（J = kg·m 2 / s 2 ）。为了处理大量的气体分子，我们使用速度和动能的平均值。在KMT中，粒子的均方根速度 u rms 被定义为 n的速度平方的均方根 =粒子数：
 
 <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />
 
 一摩尔粒子的平均动能KE avg 等于：
 
 <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />
 
 其中 M 是摩尔质量，单位为kg / mol。一摩尔气体分子的KE avg 也与气体的温度成正比，可以用以下等式描述：
 
 <img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />
 
 其中 R 是气体常数，而 T 是开尔文温度。当在该方程式中使用时，气体常数的适当形式为8.314J / mol·K（8.314kg·m 2 / s 2 ·mol·K。可以将KE avg 的两个单独的方程组合并重新排列以产生分子速度和温度之间的关系：
 
 <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;" />
 
 如果气体的温度升高，则其KE avg 升高，更多的分子具有更高的速度，而更少的分子具有更低的速度，并且分布总体上朝着更高的速度移动，即向右移动。如果温度降低，则KE avg 降低，更多的分子具有较低的速度，较少的分子具有较高的速度，并且分布总体上朝着较低的速度移动，即向左移动。
 
 在给定温度下，所有气体的分子均具有相同的KE avg 。气体的分子速度与分子质量直接相关。由较轻分子组成的气体具有更高的高速粒子和更高的 u rms ，其速度分布在相对较高的速度下达到峰值。由较重分子组成的气体具有较低的低速粒子，较低的 u rms ，以及在相对较低的速度达到峰值的速度分布。
 
 本文改编自<a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory"> Openstax，化学2e， 9.5节：动力学-分子理论。</a>

动力学分子理论定性地解释了各种气体定律所描述的行为。该理论的假设可应用于……

Education

教育

JoVE Core

化学

Gases

气体

KEY TERMS AND CONCEPTS

关键术语与概念

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 | JoVE K12

chemistry

JoVE Core 化学通过简单明了且通俗易懂的动画视频课程，将普通化学概念带入到现实生活当中。此外，在科学家行动视频中，我们演示了在实验室中进行的经典和原始研究实验。

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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Gas laws

Tennessee Academic Standards

High School

Matter and Its Interactions

CHEM1.PS1.5

CHEM1.PS3.1

Virginia  Standards of Learning

HIgh School

CH.6

CH.6.b

Physical Science

PS.2

PS.2.c

Arizona Science Standards

HS+C.P1

HS+C.P1U1.3

Texas Essential Knowledge and Skills

CHEM.10

CHEM.10.A

Alabama Course of Study Science

9-12.C.1.4.e

9-12.C.4.7

Florida Department of Education

SC.912.P.10

SC.912.P.10.5

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New York State Science Learning Standards

HS. Structure and Properties of Matter

HS-PS1-9.

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States of Matter and Phase Changes

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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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Phase Transitions: Melting and Freezing

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PS.Chm.7.1

Energy Basics

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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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Thermochemical Equations

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Constant Pressure Calorimetry

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Constant Volume Calorimetry

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Hess's Law

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Standard Enthalpy of Formation

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PS.Chm.7.2

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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

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Ideal Gas Law

Source: Laboratory of Dr. Andreas Z&#252;ttel - Swiss Federal Laboratories for Materials Science and Technology
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Gas Particle Speed Distributions and Temperature

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