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

Alle gasdeeltjes hebben kinetische energie, die een functie is van de massa van het deeltje, in kilogram, en snelheid, of de grootte van zijn snelheid, in meter per seconde. Bij elke botsing veranderen de snelheden van individuele gasdeeltjes. Daarom heeft een verzameling gasdeeltjes in feite een verdeling of bereik van snelheden en kinetische energieën.Dit betekent dat sommige moleculen op elk moment langzamer bewegen dan andere;de gemiddelde kinetische energie blijft echter hetzelfde. De gemiddelde kinetische energie is gerelateerd aan het gemiddelde van de kwadraten van de snelheden, of de gemiddelde kwadraatsnelheid die beide constant blijven bij een bepaalde temperatuur voor een bepaald gas. Nu wordt de gemiddelde kinetische energie van één mol gas uitgedrukt door de constante van Avogadro, NA, in te voeren.Het product van de massa per deeltje en Avogadro's constante van deeltjes per mol is gelijk aan de molaire massa van het gas in kilogram per mol. Bedenk uit de kinetische moleculaire theorie dat de gemiddelde kinetische energie van een mol gas recht evenredig is met de temperatuur. Door middel van complexe afleidingen blijkt de evenredigheidsconstante 3/2 R te zijn.Door de twee vergelijkingen te combineren, de termen opnieuw te rangschikken en de wortel aan beide zijden te nemen, wordt de wortel van de gemiddelde-kwadraatsnelheid ook wel kwadratisch gemiddelde, of RMS, snelheid genoemd de molaire massa en de absolute temperatuur van een gas. De RMS snelheid is omgekeerd evenredig met de molaire massa en recht evenredig met de temperatuur. Stel dat twee gassen helium en argon dezelfde temperatuur hebben.Omdat helium een lagere molaire massa heeft, geeft de vergelijking aan dat helium een hogere RMS snelheid moet hebben dan argon. Een soortgelijke waarneming wordt gedaan in een grafiek van de verdeling van moleculaire snelheden voor drie gassen helium, argon en chloor bij dezelfde temperatuur. Merk op dat, hoewel alle gassen dezelfde gemiddelde kinetische energie hebben, het lichtste gas, helium, zowel de hoogste RMS snelheid als de breedste snelheidsverdeling heeft, wat overeenkomt met het grootste bereik van moleculaire snelheden.Een grafiek van de snelheidsverdeling voor elk gas bijvoorbeeld argon bij verschillende temperaturen toont een toename van de RMS snelheid en een verbreding van de snelheidsverdeling bij hogere temperaturen. Kortom, gassen bewegen sneller bij hogere temperaturen. Zo bewegen de geurveroorzakende gasdeeltjes van warm voedsel sneller dan deeltjes van koud voedsel.Zo worden warme gerechten sneller opgemerkt dan koude gerechten.

kinetische moleculaire theorie: moleculaire snelheden, temperatuur en kinetische energie

De kinetische moleculaire theorie verklaart kwalitatief het gedrag dat wordt beschreven door de verschillende gaswetten. De postulaten van deze theorie kunnen op een meer kwantitatieve manier worden toegepast om deze individuele wetten af te leiden. Gezamenlijk hebben de moleculen in een gasmonster gemiddelde kinetische energie en gemiddelde snelheid; maar individueel bewegen ze met verschillende snelheden. Moleculen ondergaan vaak elastische botsingen waarbij het momentum behouden blijft. Omdat de botsende moleculen met verschillende snelheden worden afgebogen, hebben individuele moleculen sterk variërende snelheden. Vanwege het grote aantal betrokken moleculen en botsingen zijn de moleculaire snelheidsverdeling en de gemiddelde snelheid echter constant. Deze moleculaire snelheidsverdeling staat bekend als een Maxwell-Boltzmann-verdeling en geeft de relatieve aantallen moleculen weer in een bulkmonster gas dat een bepaalde snelheid bezit. De kinetische energie (KE) van een deeltje met massa (m) en snelheid (u) wordt gegeven door: <img alt="Eq1" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;"> Het uitdrukken van massa in kilogram en snelheid in meter per seconde levert energiewaarden op in eenheden van joule (J = kg·m2/s2). Om met een groot aantal gasmoleculen om te gaan, gebruiken we gemiddelden voor zowel snelheid als kinetische energie. In de KMT wordt de wortel van de gemiddelde kwadratische snelheid van een deeltje, urms, gedefinieerd als de vierkantswortel van het gemiddelde van de kwadraten van de snelheden met n = het aantal deeltjes: <img alt="Eq2" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;"> De gemiddelde kinetische energie voor een mol deeltjes, KEavg, is dan gelijk aan: <img alt="Eq3" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;"> waarbij M de molaire massa is, uitgedrukt in eenheden kg/mol. De KEavg van een mol gasmoleculen is ook recht evenredig met de temperatuur van het gas en kan worden beschreven door de vergelijking: <img alt="Eq4" src="https://www.jove.com/files/core/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;"> waarbij R de gasconstante is en T de Kelvin-temperatuur. Bij gebruik in deze vergelijking is de juiste vorm van de gasconstante 8,314 J/mol⋅K (8,314 kg·m2/s2·mol·K). Deze twee afzonderlijke vergelijkingen voor KEavg kunnen worden gecombineerd en herschikt om een verband tussen moleculaire snelheid en temperatuur te verkrijgen: <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;"> Als de temperatuur van een gas stijgt, neemt de KEavg toe, hebben meer moleculen hogere snelheden en minder moleculen lagere snelheden, en verschuift de verdeling over het geheel genomen naar hogere snelheden, dat wil zeggen naar rechts. Als de temperatuur daalt, neemt KEavg af, hebben meer moleculen lagere snelheden en minder moleculen hogere snelheden, en verschuift de verdeling over het geheel genomen naar lagere snelheden, dat wil zeggen naar links. Bij een bepaalde temperatuur hebben alle gassen dezelfde KEavg voor hun moleculen. De moleculaire snelheid van een gas houdt rechtstreeks verband met de moleculaire massa. Gassen die uit lichtere moleculen zijn samengesteld, hebben meer snelle deeltjes en een hogere urms, met een snelheidsverdeling die piekt bij relatief hogere snelheden. Gassen die uit zwaardere moleculen bestaan, hebben meer deeltjes met lage snelheid, een lagere urms en een snelheidsverdeling die piekt bij relatief lagere snelheden.

Kinetische moleculaire theorie: moleculaire snelheden, temperatuur en kinetische energie

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

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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...

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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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New York State Science Learning Standards

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Classifying Matter by State

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States of Matter and Phase Changes

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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

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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

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Heating and Cooling Curves

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Phase Diagrams

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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

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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

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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

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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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Using Differential Scanning Calorimetry to Measure Changes in Enthalpy

Source: Laboratory of Dr. Terry Tritt &#8212; Clemson University
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Hess's Law

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Standard Enthalpy of Formation

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

PS.Chm.7.2

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

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Kinetic Molecular Theory and Gas Laws Explain Properties of Gas Molecules

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

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

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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

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

	Determining the Mass of the Unknown LiquidExpand
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Understand the relationship among pressure, temperature, volume, and phase.

Gas Particle Speed Distributions and Temperature

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