Name: gas pressure and molecular motion
Uploaded: 2023-04-30T12:30:41.000Z
Duration: 1 min 21 s
Channel: JoVE

K12 Standards

Louisiana Student Standards for Science

High School

Chemistry

Matter And Its Interactions

HS-PS1-4

Molecular Kinetic Energy

容器内の気体を考えてみましょう。分子のランダムな動きにより、壁と数回の衝突が発生します。
衝突時には、各分子が容器の壁に力を及ぼし、これがガスによって圧力がかかる原因となります。
すべての気体分子の速度の大きさが同じである場合、短い時間間隔で壁とx方向の相互作用により、速度と運動量のx成分が変化します。
単位体積あたりの分子数が均一なままであれば、ある領域での衝突回数と、短い間隔での総運動量の変化を求めることができます。
ニュートンの第二法則を適用すると、ガスによって加えられる圧力は、分子の質量、速度、および体積あたりの分子の数に依存します。
等方性条件を考慮すると、気体分子の平均速度は速度成分に関連し、成分の速度の3倍に等しくなります。
理想気体方程式を代入して比較することにより、nモルの気体の平均並進運動エネルギーが決定されます。

このテキストは、<a href="https://openstax.org/books/university-physics-volume-2/pages/2-1-molecular-model-of-an-ideal-gas">Openstax, University Physics Volume 2, Section 2.2: Pressure, Temperature, and RMS Speed から引用しています。</a>

分子の運動エネルギー

「ガス」という言葉は、「カオス」を意味するフランドル語に由来しています。 化学者 J. B. ヴァン ヘルモントによって蒸気を説明するために初めて使用されました。 分子が連続的かつランダムに運動する、ガスで満たされた容器を考えてみましょう。 衝突中、壁に平行な速度成分は変化せず、壁に垂直な成分は方向が反転しますが、大きさは変わりません。 分子の速度がx方向に変化すると、その運動量も変化します。 衝突の短時間の間に、各分子は容器の壁に力を及ぼし、これがガスによって加えられる圧力の源となります。 加えられる力は速度で表現できます。総速度の二乗は、その成分 (x-、y-、) の二乗の合計です。 z方向）。 さらに、これらの値を代入して理想気体方程式と比較することにより、n モルの理想気体の平均並進運動エネルギーを求めることができます。 得られた結果は、平均並進運動エネルギーが絶対温度に正比例することを示しています。

気体中の粒子の二乗平均平方根速度は、気体中の分子の平均速度の二乗の平方根として定義され、平均移動距離と衝突間の時間は平均自由行程と呼ばれます。 はそれぞれ自由時間を意味します。 平均自由行程は単位体積あたりの分子の数に反比例し、分子の断面積にも反比例します。 分子が大きいほど、または分子の数が多いほど、衝突間の平均距離は短くなります。

「ガス」という言葉は、化学者J.B.ファンヘルモントによって蒸気を表すために最初に使用された「カオス」を意味するフランドル語に由来します。考える。。。

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

The Kinetic Theory of Gases

気体分子運動論

KEY TERMS AND CONCEPTS

主要用語と概念

gas pressure and molecular motion

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way.

When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its momentum changes. During the short collision, the molecule exerts a force on the wall. That force is the source of gas pressure.

The force from many collisions can be written in terms of velocity. The total speed squared equals the sum of the squares of the x-, y-, and z-direction components. By substituting these values and comparing the result with the ideal gas equation, the average translational kinetic energy of n moles of an ideal gas can be found. This average translational kinetic energy is directly proportional to absolute temperature.

The root-mean-square speed is the square root of the average of the velocity squared for gas molecules. Gas motion also includes mean free path and mean free time. Mean free path is the average distance a molecule travels between collisions, and mean free time is the average time between collisions. The mean free path becomes shorter when there are more molecules per unit volume or when molecule cross-sectional area is larger.

Gas Pressure and Molecular Motion

equation of state

Gas Behavior in the Equation of State

The equation of state describes how a gas’s pressure, volume, temperature, and number of moles are related. These macroscopic properties help define the condition, or state, of the matter in a thermodynamics system. The relationship between these quantities can be written as a simple mathematical expression. In some cases, it is too complex to express in a formula. Even then, the link between the quantities still exists. When an equation of state cannot be written mathematically, scientists...

ideal gas equation

Gas Laws Behind the Ideal Equation

The ideal gas equation links pressure, volume, temperature, and amount of gas. It describes a hypothetical gas and is built from four empirical gas laws: Boyle’s law, Charles’s law, Avogadro’s law, and Gay-Lussac’s law. When these proportionalities are combined, they give one constant called the universal gas constant. This gas constant has the same value for all real gases under certain conditions. In chemical calculations, that constant is used in the ideal gas equation. The equation works...

van der waals equation

How Real Gases Deviate from Ideal Behavior

Real gases often deviate from the ideal gas law, especially at low temperatures and high pressures. The van der Waals equation improves the ideal gas model by adding two corrections that account for these real-world effects. One correction accounts for attractive forces between molecules. These forces become stronger at higher densities and lower the measured pressure, so the equation adds a pressure term based on the square of the molar density and a positive constant a. The second...

pv-diagrams

Liquid-Gas Changes on pV Curves

pV curves show how gas pressure changes with volume. A pV diagram is a graph of pressure versus volume for the gas being studied. It helps describe how the substance behaves. When the gas acts like an ideal gas, the ideal gas equation gives the link between pressure and volume. A common pV curve is an isotherm, which is a line drawn at fixed temperature and fixed number of molecules. For an ideal gas, pressure times volume stays constant. That means volume goes down as pressure goes up. The...

kinetic theory of an ideal gas

Avogadro's Number and Gas Particle Motion

Avogadro's number and gas particle motion help explain how gases behave at the particle level. A mole is the amount of a substance that contains as many molecules as there are atoms in exactly 12 grams of carbon-12. This idea came from Amedeo Avogadro, who proposed that equal volumes of gas at the same pressure and temperature contain equal numbers of molecules, no matter what the gas is. Avogadro's number is the number of molecules in one mole. Its value is 6.02 × 10^23 mol−1. This number...

molecular kinetic energy

Gas pressure comes from the motion of molecules in a container. The word gas came from a Flemish word meaning “chaos,” and J. B. van Helmont first used it to describe vapors. In a gas, molecules move in a continuous and random way. When a molecule hits a container wall, its velocity changes. The part of the velocity parallel to the wall stays the same. The part perpendicular to the wall reverses direction, but its size does not change. If the molecule’s velocity changes in the x-direction, its...

distribution of molecular speeds

Molecular Speed Curves and Vapor Pressure

Molecular speed curves show how the speeds of gas particles are spread out at a given temperature. For a gas with many molecules, this spread is predictable even though each molecule moves randomly in direction and speed. The pattern is called the Maxwell-Boltzmann distribution. Liquids have a similar speed distribution, but it is not exactly the same as in gases. This difference helps explain boiling and vapor pressure. A molecule must reach at least a certain speed, v a, to escape from the...

maxwell-boltzmann distribution: problem solving

maxwell-boltzmann-distribution-problem-solving

Maxwell-Boltzmann Gas Speed Ratio

The Maxwell-Boltzmann distribution describes how molecular speeds are spread in a gas. Even though individual molecules move in random directions, the whole gas has a predictable speed pattern. This distribution is written as f(v), where v is molecular speed. The distribution function is used to find the expected number of particles with speeds between v1 and v2. Because N is dimensionless, f(v) has units of seconds per meter. The relationship can also be written in differential form for speed...

phase diagram

Water Phase Changes on a Pressure Chart

Water phase changes can be mapped on a pressure and temperature chart called a phase diagram. These plots show which phase a substance is in at different conditions. They also reveal where phase transitions happen, because the boundary lines mark the temperatures and pressures where two phases coexist. The water phase diagram shows how pressure affects boiling. As pressure rises, the boiling temperature increases gradually until it reaches 374 °C at 218 atm. A pressure cooker works this way.

mean free path and mean free time

Gas collisions: path length and time

Gas collisions in a cylinder help explain the mean free path and mean free time. Gas molecules move in random motion. They collide with each other and change speed and direction. The mean free path is the average path length between collisions. The mean free path depends on how many molecules are packed into a volume. It varies inversely with density. When more molecules are present, collisions happen more often, so the mean free path becomes shorter. It also depends on molecule size. Larger...

heat capacity: problem-solving

Heat Capacity of Gases by Degrees of Freedom

Heat capacity of gases depends on the gas type and the motion of its molecules. It is the amount of heat energy needed to raise the temperature of a unit mass of gas by one degree Celsius. This thermodynamic property is important in science and industry. To solve heat capacity problems, first identify the gas. A gas's molecular structure affects its heat capacity because the molecules have different degrees of freedom. These values can be found from tables or from empirical equations. Next,...

dalton's law of partial pressure

Gas Mixtures and Their Partial Pressures

Gas mixtures have a total pressure that comes from the partial pressures of each gas. A partial pressure is the pressure one gas would make if it filled the whole container by itself. This idea helps explain how gases behave when they are mixed together. When two or more gases share a container, their molecules move randomly and collide with one another. If the gases are at the same temperature, they reach thermal equilibrium. Their molecules then have the same average kinetic energy. In that...

escape velocities of gases

Why Lighter Gases Escape Earth First

Earth’s escape velocity is the speed an object needs to leave gravity behind. Near the top of the atmosphere, about 100 km above Earth, that speed is 11.1 km/s. Gas molecules can escape only if their speeds become high enough to reach that limit. The chance of escape depends on gas temperature and molecular speed. According to kinetic theory, the average kinetic energy of gas molecules is proportional to temperature. As temperature rises, the rms speed, or root-mean-square speed, also rises.

key terms and concepts

Explore how gas pressure comes from molecular collisions, how ideal gas temperature links to kinetic energy, and what mean free path and rms speed mean.

Gas Pressure and Molecular Motion | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

HS-PS1-5

Arizona Science Standards

Physical Science

HS+C.P1

HS+C.P1U1.3

Next Generation Science Standards

Energy

HS-PS3-1

HS-PS3-2

Florida Department of Education

SC.912.P.10

SC.912.P.10.5

SC.912.P.12

SC.912.P.12.10

SC.912.P.12.11

The Periodic Table

As early chemists discovered more elements, they realized that various elements could be grouped by their similar chemical behaviors. One such grouping ...

Periodic Classification of the Elements

The periodic table arranges atoms based on increasing atomic number so that elements with the same chemical properties recur periodically. When their ...

the-periodic-table-and-organismal-elements

The Periodic Table And Organismal Elements

Atomic Structure

The Greek philosopher Democritus proposed that everything on Earth is made up of tiny particles called atomos, Greek for &#34;indivisible,&#34; from which ...

Electron Configurations

Electron configurations and orbital diagrams can be determined by applying the Aufbau principle (each added electron occupies the subshell of lowest ...

Electronic Structure of Atoms


An atom comprises protons and neutrons, which are contained inside the dense, central&#160;core called the nucleus, with electrons present around the ...

electron-configuration-of-multielectron-atoms

Electron Configuration of Multielectron Atoms

The alkali metal sodium (atomic number 11) has one more electron than the neon atom. This electron must go into the lowest-energy subshell available, the ...

atomic-radii-and-effective-nuclear-charge

Atomic Radii and Effective Nuclear Charge

The elements in groups of the periodic table exhibit similar chemical behavior. This similarity occurs because the members of a group have the same number ...

The Aufbau Principle and Hund's Rule

To determine the electron configuration for any particular atom, we can build the structures in the order of atomic numbers. Beginning with hydrogen, and ...

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude ...

Electric Charges

From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the ...

sources-and-properties-of-electric-charge

Sources and Properties of Electric Charge

All objects we see around us consist of atoms, which combine to form molecules. The lightest element in the universe is hydrogen, and a hydrogen atom ...

Types of Forces

In most situations, forces can be grouped into two categories: contact forces and field forces.&#160; Contact forces occur as a result of direct physical ...

Electric Fields

Source: Yong P. Chen, PhD, Department of Physics &#38; Astronomy, College of Science, Purdue University, West Lafayette, IN
An electric field is generated ...

Intermolecular Forces

Atoms and molecules interact through bonds (or forces): intramolecular and intermolecular. The forces are electrostatic as they arise from interactions ...

Van der Waals Interactions

Atoms and molecules interact with each other through intermolecular forces. These electrostatic forces arise from attractive or repulsive interactions ...

Chemical Bonds


Atoms participate in a chemical bond formation&#160;to acquire a completed valence-shell electron configuration similar to that of the noble gas nearest ...

Electron Behavior

Electrons are negatively charged subatomic particles attracted to and orbit around the positively-charged nucleus of an atom. They reside in spaces ...

Subatomic Particles

Dalton was only partially correct about the particles that make up matter. All matter is composed of atoms, and atoms are composed of three smaller ...

Ions and Ionic Charges

In ordinary chemical reactions, the nucleus &mdash; which contains the protons and neutrons of each atom and thus identifies the element &mdash; remains ...

Use the periodic table as a model to predict the relative properties of elements based on the patterns of electrons in the outermost energy level and the composition of the nucleus of atoms.  Clarification Statement: Chemistry: Examples of properties that could be predicted from patterns could include reactivity of metals, types of bonds formed, numbers of bonds formed, atomic radius, atomic mass, or reactions with oxygen. Emphasis is on main group elements and qualitative understanding of the relative trends of ionization energy and electronegativity.

HS-PS1-1

Properties of Transition Metals

Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3&#8211;12 are ...

The Atomic Theory of Matter

The earliest recorded discussion of the basic structure of matter comes from ancient Greek philosophers. Leucippus and Democritus argued that all matter ...

Chemical Reactions

A chemical reaction is a process by which the bonds in the atoms of substances are rearranged to generate new substances. Matter cannot be created or ...

Chemical Equations

Chemical equations represent the identities and relative quantities of substances involved in a chemical reaction. The substances undergoing reaction are ...

Introduction to Chemical Reactions

All chemical reactions begin with a reactant, the general term for one or more substances entering the reaction. Sodium and chloride ions, for example, ...

Temperature Dependence on Reaction Rate

The Collision Theory
Atoms, molecules, or ions must collide before they can react with each other. Atoms must be close together to form chemical bonds. ...

stoichiometry-product-yield-and-limiting-reactants

Stoichiometry, Product Yield, and Limiting Reactants

Source: Smaa Koraym at Johns Hopkins University, MD, USA

	Preparation of 25% v/v Ethylenediamine in Deionized WaterExpand
	Here, we show the laboratory ...

physical-and-chemical-properties-of-matter

Physical and Chemical Properties of Matter

The characteristics that enable us to distinguish one substance from another are called properties.

Physical Properties of Matter

A physical property is ...

Dynamic Equilibrium

A reversible chemical reaction represents a chemical process that proceeds in both forward (left to right) and reverse (right to left) directions. When ...

Construct and revise an explanation for the outcome of a simple chemical reaction based on the outermost electron states of atoms, trends in the periodic table, and knowledge of the patterns of chemical properties.  Clarification Statement: Chemistry: Examples of chemical reactions could include the reaction of sodium and chlorine, carbon and oxygen, or carbon and hydrogen. Reaction classification aids in the prediction of products (e.g. synthesis, decomposition, single displacement, double displacement, and acid-base).

HS-PS1-2

Intermolecular vs Intramolecular Forces

Intermolecular forces (IMF) are electrostatic attractions arising from charge-charge interactions between molecules. The strength of the intermolecular ...

comparison-between-electrical-and-gravitational-forces

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To ...

intermolecular-forces-and-physical-properties

Intermolecular Forces and Physical Properties



Intermolecular forces are attractive forces that exist between molecules. They dictate several bulk properties, such as melting points, boiling points, ...

electric-field-of-two-equal-and-opposite-charges

Electric Field of Two Equal and Opposite Charges

Atoms generally contain the same number of positively and negatively charged particles, protons, and electrons. Hence, they are electrically neutral. ...

Electric Field

Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by ...

Ionic Bonding and Electron Transfer

Ions are atoms or molecules bearing an electrical charge. A cation (a positive ion) forms when a neutral atom loses one or more electrons from its valence ...

Electric Dipoles and Dipole Moment

Consider two charges of equal magnitude but opposite signs. If they cannot be separated by an external electric field, the system is called a permanent ...

Plan and conduct an investigation to gather evidence to compare the structure of substances at the macroscale to infer the strength of electrical forces between particles.  Clarification Statement: Emphasis is on understanding the strengths of forces between particles, not on naming specific intermolecular forces (such as dipole-dipole). Examples of particles could include ions, atoms, molecules, and network solids (such as graphite). Examples of macro-properties of substances could include the melting point and boiling point, vapor pressure, and surface tension.

HS-PS1-3

bond-dissociation-energy-and-activation-energy

Bond Dissociation Energy and Activation Energy

Bond energy is the energy required to break a bond homolytically. These values are usually expressed in units of kcal/mol or kJ/mol and are referred to as ...

Bond Energies and Bond Lengths

Stable molecules exist because covalent bonds hold the atoms together. The strength of a covalent bond is measured by the energy required to break it, ...

Coupled Reactions

Cellular processes such as building and breaking down complex molecules occur through stepwise chemical reactions. Some of these chemical reactions are ...

energy-diagrams-transition-states-and-intermediates

Energy Diagrams, Transition States, and Intermediates

Free-energy diagrams, or reaction coordinate diagrams, are graphs showing the energy changes that occur during a chemical reaction. The reaction ...

What is Metabolism?

Overview

Metabolism represents all of the chemical activity in a cell, including reactions that build molecules (anabolism) and those that break ...

types-of-chemical-reactions-anabolic-and-catabolic

Types of Chemical Reactions: Anabolic and Catabolic

The first law of thermodynamics holds that energy can neither be created nor destroyed&#8212;it can only change form. An organism&#39;s essential function ...

Non-equilibrium in the Cell

An important concept in studying metabolism and energy is that of chemical equilibrium. Most chemical reactions are reversible. They can proceed in both ...

Activation Energy

Activation energy is the minimum amount of energy necessary for a chemical reaction to move forward. The higher the activation energy, the slower the rate ...

Energy Transfer in Chemical Reactions

Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ...

factors-influencing-the-rate-of-chemical-reactions

Factors Influencing the Rate of Chemical Reactions

A variety of factors influence the rate of chemical reactions. For a chemical reaction to happen, atoms must collide with enough energy to overcome the ...

Predicting Reaction Outcomes

Kinetics describes the rate and path by which a reaction occurs. In contrast, thermodynamics deals with state functions and describes the properties, ...

States of Matter and Phase Changes

The internal energy of a substance&#8212;the total kinetic energy of all its molecules and the potential energy of their associated forces&#8212;depends ...

Reaction Mechanisms

Chemical reactions often occur in a stepwise fashion, involving two or more distinct reactions taking place in a sequence. A balanced equation indicates ...

Temperature Dependence

Chemical Kinetics 
The reaction rate is the speed at which a chemical reaction occurs. The reaction rate is defined as the change in concentration of a ...

Develop a model to illustrate that the release or absorption of energy from a chemical reaction system depends upon the changes in total bond energy.  Clarification Statement: Emphasis is on the idea that a chemical reaction is a system that affects the energy change.  Examples of models could include molecular-level drawings and diagrams of reactions, graphs showing the relative energies of reactants and products, and representations showing energy is conserved.

Gas Pressure and Molecular Motion

Description

Transcript

Tags

More videos by Standards