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

Alle Gasteilchen haben kinetische Energie, was eine Funktion der Masse des Teilchens ist, in Kilogramm und Geschwindigkeit oder die Höhe seiner Geschwindigkeit, in Metern pro Sekunde. Bei jeder Kollision verändern sich die Geschwindigkeiten der einzelnen Gasteilchen. Daher hat eine Sammlung von Gasteilchen eine bestimmte Verteilung oder Reichweite an Geschwindigkeiten und kinetischen Energien.Das bedeutet jedoch, dass zu jedem Zeitpunkt einige Moleküle sich langsamer bewegen als andere, die mittlere kinetische Energie bleibt jedoch gleich. Die mittlere kinetische Energie bezieht sich auf die durchschnittlichen Quadrate der Geschwindigkeiten oder die quadratisch gemittelte Geschwindigkeit wobei beide bei einer gegebenen Temperatur für ein gegebenes Gas konstant bleiben. Nun wird die durchschnittliche kinetische Energie eines Gasmoles durch die Einführung der Avogadro-Konstante NA ausgedrückt.Das Produkt der Masse pro Teilchen und die Avogadro-Konstante von Teilchen pro Mol entspricht der molaren Masse des Gases in Kilogramm/Mol. Erinnern wir uns an die kinetische Gastheorie:die durchschnittliche kinetische Energie eines Gasmoles ist direkt proportional zur Temperatur. Durch komplexe Ableitungen wird die Boltzmann-Konstante als 3/2*R festgestellt.Wenn wir die beiden Gleichungen zusammenführen und umstellen sowie die Quadratwurzel auf beiden Seiten ziehen, ergibt das die Quadratwurzel der mittleren quadratischen Geschwindigkeit auch RMS genannt, Geschwindigkeit die molare Masse und die absolute Temperatur eines Gases. Die mittlere quadratische Geschwindigkeit ist umgekehrt proportional zur molaren Masse und direkt proportional zur Temperatur. Angenommen, zwei Gase Helium und Argon haben die gleiche Temperatur.Da Helium die geringere Molmasse hat, gibt die Gleichung an, dass Helium eine höhere mittlere quadratische Geschwindigkeit als Argon haben muss. Eine ähnliche Beobachtung wird in einem Diagramm der Verteilung der Teilchengeschwindigkeiten für drei Gase Helium, Argon, und Chlor bei gleicher Temperatur gemacht. Beachten Sie, dass obwohl alle Gase die gleiche durchschnittliche kinetische Energie haben, das leichteste Gas, Helium, sowohl die höchste mittlere quadratische Geschwindigkeit als auch die breiteste Geschwindigkeitsverteilung hat, die dem breitesten Spektrum der Teilchengeschwindigkeiten entspricht.Ein Diagramm der Geschwindigkeitsverteilung für jedes Gas sagen wir Argon zeigt bei verschiedenen Temperaturen einen Anstieg der mittleren quadratischen Geschwindigkeit und eine Erweiterung der Geschwindigkeitsverteilung bei höheren Temperaturen. Kurz gesagt:Gase bewegen sich bei höheren Temperaturen schneller. Wie zum Beispiel die aromaverursachenden Gasteilchen von heißen Lebensmitteln bewegen sich schneller als Teilchen aus kalten Lebensmitteln.So werden warme Speisen schneller gerochen als kalte.

kinetische molekültheorie: molekülgeschwindigkeiten, temperatur und kinetische energie

Die kinetische Molekulartheorie erklärt qualitativ das durch die verschiedenen Gasgesetze beschriebene Verhalten. Die Postulate dieser Theorie können auf quantitativere Weise angewendet werden, um diese einzelnen Gesetze abzuleiten. Zusammengenommen haben die Moleküle in einer Gasprobe eine durchschnittliche kinetische Energie und eine durchschnittliche Geschwindigkeit; aber einzeln bewegen sie sich mit unterschiedlichen Geschwindigkeiten. Moleküle unterliegen häufig elastischen Stößen, bei denen der Impuls erhalten bleibt. Da die kollidierenden Moleküle unterschiedlich schnell abgelenkt werden, weisen die einzelnen Moleküle stark unterschiedliche Geschwindigkeiten auf. Aufgrund der großen Anzahl beteiligter Moleküle und Kollisionen sind die molekulare Geschwindigkeitsverteilung und die Durchschnittsgeschwindigkeit jedoch konstant. Diese molekulare Geschwindigkeitsverteilung ist als Maxwell-Boltzmann-Verteilung bekannt und stellt die relative Anzahl von Molekülen in einer Gasprobe dar, die eine bestimmte Geschwindigkeit besitzt. Die kinetische Energie (KE) eines Teilchens mit Masse (m) und Geschwindigkeit (u) ist gegeben durch: <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;"> Wenn man die Masse in Kilogramm und die Geschwindigkeit in Metern pro Sekunde ausdrückt, erhält man Energiewerte in der Einheit Joule (J = kg·m2/s2). Um mit einer großen Anzahl von Gasmolekülen umzugehen, verwenden wir Durchschnittswerte sowohl für die Geschwindigkeit als auch für die kinetische Energie. In der KMT wird der quadratische Mittelwert der Geschwindigkeit eines Teilchens, urms, als Quadratwurzel des Durchschnitts der Quadrate der Geschwindigkeiten definiert, wobei n = die Anzahl der Teilchen ist: <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;"> Die durchschnittliche kinetische Energie für ein Mol Teilchen, KEavg, ist dann gleich: <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;"> Dabei ist M die Molmasse, ausgedrückt in der Einheit kg/mol. Der KEavg eines Mols Gasmoleküle ist ebenfalls direkt proportional zur Temperatur des Gases und kann durch die Gleichung beschrieben werden: <img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;"> Dabei ist R die Gaskonstante und T die Kelvin-Temperatur. Bei Verwendung in dieser Gleichung beträgt die geeignete Form der Gaskonstante 8,314 J/mol⋅K (8,314 kg·m2/s2·mol·K). Diese beiden separaten Gleichungen für KEavg können kombiniert und neu angeordnet werden, um eine Beziehung zwischen molekularer Geschwindigkeit und Temperatur zu erhalten: <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;"> Wenn die Temperatur eines Gases steigt, erhöht sich sein KEavg, mehr Moleküle haben höhere Geschwindigkeiten und weniger Moleküle haben niedrigere Geschwindigkeiten und die Verteilung verschiebt sich insgesamt zu höheren Geschwindigkeiten, also nach rechts. Wenn die Temperatur sinkt, nimmt KEavg ab, mehr Moleküle haben niedrigere Geschwindigkeiten und weniger Moleküle haben höhere Geschwindigkeiten, und die Verteilung verschiebt sich insgesamt zu niedrigeren Geschwindigkeiten, also nach links. Bei einer bestimmten Temperatur haben alle Gase den gleichen KEavg für ihre Moleküle. Die Molekülgeschwindigkeit eines Gases steht in direktem Zusammenhang mit der Molekülmasse. Gase, die aus leichteren Molekülen bestehen, haben mehr Teilchen mit hoher Geschwindigkeit und eine höhere urms, mit einer Geschwindigkeitsverteilung, die bei relativ höheren Geschwindigkeiten ihren Höhepunkt erreicht. Gase, die aus schwereren Molekülen bestehen, haben mehr Partikel mit niedriger Geschwindigkeit, eine niedrigere urms und eine Geschwindigkeitsverteilung, die bei relativ niedrigeren Geschwindigkeiten ihren Höhepunkt erreicht. Dieser Text wurde angepasst von <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>

Kinetische Molekültheorie: Molekülgeschwindigkeiten, Temperatur und kinetische Energie

Die kinetische Molekültheorie erklärt qualitativ die Verhaltensweisen, die durch die verschiedenen Gasgesetze beschrieben werden. Die Postulate dieser Theorie können in einer ...

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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

definition and measurement of pressure: atmospheric pressure, barometer, and manometer

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Pressure Units and Tools for Gas Measurement

Pressure is the force applied to a given area, and gas pressure comes from gas molecules colliding with surfaces. Each collision is tiny, but many collisions over a small area can create high pressure. Pressure increases when force increases or when the area gets smaller. It decreases when force drops or when the area gets larger. Pressure is measured in pascals, or Pa, in the SI system. One pascal equals 1 newton per square meter, and a newton is a unit of force equal to 1 kg·m/s2. A pascal...

gas laws: boyle's, gay-lussac, charles', avogadro's, and ideal gas law

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How Gas Pressure, Volume, and Temperature Change

Gas pressure, volume, temperature, and amount are linked by several gas laws. Scientists found these relationships by studying how a confined gas changes when one variable is held constant and another changes. These patterns apply to an ideal gas, which is a useful model for gases under low pressure and high temperature. Gay-Lussac’s law, also called Amontons’s law, connects pressure and temperature. If gas is trapped in a rigid container, the volume and number of moles stay constant. When the...

applications of the ideal gas law: molar mass, density, and volume

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Ideal Gas Law at STP and Gas Density

The ideal gas law links pressure, volume, number of moles, and temperature. It helps explain how gas volume changes when pressure or temperature changes. At standard temperature and pressure, or STP, the values are 273.15 K and 1 atm. At STP, one mole of an ideal gas occupies about 22.4 L. This is called the standard molar volume. The gas can be hydrogen, oxygen, argon, or carbon dioxide, and the volume is still about 22.4 liters. Half a mole occupies 11.2 L, and 2 moles occupy 44.8 L. The...

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...

chemical stoichiometry and gases: using ideal gas law to determine moles

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Stoichiometry of Gases with the Ideal Gas Law

Chemical stoichiometry links the amounts of reactants and products in a chemical reaction. For gases, those amounts can also be measured by volume. If a gas’s volume, pressure, and temperature are known, the ideal gas equation can be used to find the number of moles present. The same idea works in reverse. If the moles of a gas are known, its volume can be found at any temperature and pressure. The transcript gives an example using 8.88 g of gallium reacting with excess hydrochloric acid.

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...

kinetic molecular theory and gas laws explain properties of gas molecules

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Gas Pressure Patterns in Kinetic Molecular Theory

Kinetic molecular theory explains gas pressure by linking it to the motion of gas molecules. Gas pressure comes from rapidly moving molecules hitting the walls of a container. It depends on how many molecules strike a unit area in a given time. The theory also helps explain the main gas laws. In Gay-Lussac’s law, also called Amontons’s law, raising temperature increases the average speed and kinetic energy of gas molecules. If volume stays constant, the molecules collide with the walls more...

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...

behavior of gas molecules: molecular diffusion, mean free path, and effusion

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Gas Particle Motion, Diffusion, and Effusion

Gas particle motion, diffusion, and effusion explain how gases spread and escape in everyday settings. Gas molecules move at very high speeds, but they collide with other gas molecules and change direction many times before reaching a target. At room temperature, a gas molecule can experience billions of collisions each second. The mean free path is the average distance a molecule travels between collisions. This distance becomes larger when pressure decreases. In general, the mean free path...

real gases: effects of intermolecular forces and molecular volume deriving van der waals equation

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Real Gases: When the Ideal Gas Law Breaks Down

Real gases are gases that do not always follow the ideal gas law, PV = nRT, especially when pressure is high or temperature is low. The ideal gas model assumes gas particles have no attractive or repulsive forces and take up negligible space compared with the container. At room temperature and 1 atm or less, many gases behave close to ideally. When conditions change, the measured relationships between pressure, volume, and temperature can drift away from the ideal prediction. One way to see...

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.

Gas Particle Speed Distributions and Temperature | JoVE K12

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Classifying Matter by State

Chemistry is the study of matter and the changes it undergoes. Matter is anything that has mass and occupies space. Matter is all around us; the air, ...

Classifying Matter by Composition

Matter: Pure Substances and Mixtures
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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 ...

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Molecular Comparison of Gases, Liquids, and Solids

Particles in a solid are tightly packed together (fixed shape) and often arranged in a regular pattern; in a liquid, they are close together with no ...

Intermolecular vs Intramolecular Forces

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

Intermolecular Forces

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Comparing Intermolecular Forces: Melting Point, Boiling Point, and Miscibility

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Surface Tension, Capillary Action, and Viscosity

Surface Tension
The various IMFs between identical molecules of a substance are examples of cohesive forces. The molecules within a liquid are surrounded ...

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 ...

Phase Transitions

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Phase Transitions: Vaporization and Condensation

The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize ...

Vapor Pressure

When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase molecules move randomly about, they will occasionally ...

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor ...

Phase Transitions: Melting and Freezing

Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy ...

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Phase Transitions: Sublimation and Deposition

Some solids can transition directly into the gaseous state, bypassing the liquid state, via a process known as sublimation. At room temperature and ...

Heating and Cooling Curves

When a substance&#8212;isolated from its environment&#8212;is subjected to heat changes, corresponding changes in temperature and phase of the substance ...

Phase Diagrams

A phase diagram combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. ...

Use models to explain how changes in energy affect the arrangement and movement of the particles in solids, liquids, and gases, as well as the relative strengths of their intermolecular forces.

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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

Energy can be converted from one form into another, but all of the energy present before a change occurs always exists in some form ...

Internal Energy

The total of all possible kinds of energy present in a substance is called the internal energy (U), sometimes symbolized as E. Suppose a system with ...

Quantifying Heat

Thermal Energy&#160;

Microscopically, thermal energy is the kinetic energy associated with the random motion of atoms and molecules. Temperature is a ...

Quantifying Work

As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the ...

Enthalpy

Chemists ordinarily use a property known as enthalpy (H) to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum ...

Thermochemical Equations

For a chemical reaction (the system) carried out at constant pressure &ndash; with the only work done caused by expansion or contraction &ndash; the ...

Constant Pressure Calorimetry

Calorimetry is a technique used to measure the amount of heat involved in a chemical or physical process or to measure the heat transferred to or from a ...

Constant Volume Calorimetry

Calorimeters are useful to determine the heat released or absorbed by a chemical reaction. Coffee cup calorimeters are designed to operate at constant ...

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Using Differential Scanning Calorimetry to Measure Changes in Enthalpy

Source: Laboratory of Dr. Terry Tritt &#8212; Clemson University
Differential Scanning Calorimetry (DSC) is a method of thermodynamic analysis based on ...

Hess's Law

There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally ...

Standard Enthalpy of Formation

Enthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions. A standard state is a commonly ...

Enthalpies of Reaction

Hess&rsquo;s law can be used to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products ...

Use mathematics and computational thinking to execute simple calorimetric calculations based on the Law of Conservation of Energy.

PS.Chm.7.2

Definition and Measurement of Pressure: Atmospheric Pressure, Barometer, and Manometer

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Gas Laws: Boyle's, Gay-Lussac, Charles', Avogadro's, and Ideal Gas Law

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Applications of the Ideal Gas Law: Molar Mass, Density, and Volume

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Mixtures of Gases: Dalton's Law of Partial Pressures and Mole Fractions

Unless individual gases chemically react with each other, the individual gases in a mixture of gases do not affect each other&rsquo;s pressure. Each gas ...

Chemical Stoichiometry and Gases: Using Ideal Gas Law to Determine Moles

Chemical stoichiometry describes the quantitative relationships between reactants and products in chemical reactions.

In addition to measuring quantities ...

Basic Postulates of Kinetic Molecular Theory: Particle Size, Energy, and Collision

The ideal-gas equation, which is empirical, describes the behavior of gases by establishing relationships between their macroscopic properties. For ...

Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

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The kinetic molecular theory qualitatively explains the behaviors described by the various gas laws. The postulates of this theory may be applied in a ...

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

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many ...

Real Gases: Effects of Intermolecular Forces and Molecular Volume Deriving Van der Waals Equation

Thus far, the ideal gas law, PV = nRT, has been applied to a variety of different types of problems, ranging from reaction stoichiometry and empirical and ...

Ideal Gas Law

Source: Laboratory of Dr. Andreas Z&#252;ttel - Swiss Federal Laboratories for Materials Science and Technology
The ideal gas law describes the behavior ...

Derivation of the Ideal Gas Law
Gases are a fundamental state of matter. A gas is a collection of molecules that have a significant distance between their ...

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

	Preparation of the LaboratoryExpand
	Here, we show the laboratory preparation for 10 students ...

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

	Determining the Mass of the Unknown LiquidExpand
	According to the ideal gas law for a given ...

Use mathematics and computational thinking to explain the relationships among pressure, temperature, volume, and quantity of gas, both qualitatively and quantitatively.

Understand the relationship among pressure, temperature, volume, and phase.

Gas Particle Speed Distributions and Temperature

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