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

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

Todas las partículas de gas tienen energía cinética, la cual es una función de la masa, en kilogramos, y la velocidad de la partícula, o la magnitud de su velocidad, en metros por segundo. Con cada colisión, las velocidades de las partículas individuales de gas cambian. Por lo tanto, una agrupación de partículas de gas en realidad tiene una distribución, o rango, de velocidades y energías cinéticas.Esto significa que, en cualquier momento, algunas moléculas se mueven más lento que otras;sin embargo, la energía cinética promedio permanece igual. La energía cinética promedio está relacionada con el promedio de los cuadrados de las velocidades, o la media cuadrática de la velocidad, los cuales permanecen constantes a una temperatura dada para un gas determinado. Ahora, la energía cinética promedio de un mol de un gas se expresa mediante la introducción de la constante de Avogadro, NA.El producto de la masa por partícula y la constante de Avogadro de partículas por mol es igual a la masa molar del gas en kilogramos por mol.Recordemos que la teoría cinética molecular dice que la energía cinética promedio de un mol de gas es directamente proporcional a la temperatura. A través de derivaciones complejas, se determina que la constante de proporcionalidad es 3/2 R.Al combinar las dos ecuaciones, reorganizar los términos y sacar la raíz cuadrada en cada lado, se crea una relación entre la raíz cuadrada de la media cuadrática de la velocidad también llamada media cuadrática o velocidad RMS, la masa molar y la temperatura absoluta de un gas. La velocidad media cuadrática es inversamente proporcional a la masa molar y directamente proporcional a la temperatura.Supongamos que dos gases, helio y argón, están a la misma temperatura. Como el helio tiene la masa molar más baja, la ecuación indica que el helio debería tener una mayor velocidad media cuadrática que el argón. Se hace una observación similar en un gráfico de la distribución de velocidades moleculares para tres gases, helio, argón y cloro, a la misma temperatura.Es de notar que, aunque todos los gases tienen el mismo promedio de energía cinética, el gas más ligero, el helio, tiene la velocidad media cuadrática más alta y la más amplia distribución de velocidad, lo que corresponde al rango más amplio de velocidades moleculares. Un gráfico de la distribución de velocidad para cualquier gas, como el argón, a diferentes temperaturas muestra un aumento en la velocidad media cuadrática y una ampliación de la distribución de la velocidad a temperaturas más altas. En resumen, los gases se mueven más rápido a más altas temperaturas.Por ejemplo, las partículas de gas que producen el aroma de la comida caliente se mueven más rápido que las partículas en la comida fría. Así, la comida caliente se percibe más rápido que la comida fría.

velocidades moleculares y energía cinética

La teoría cinético molecular explica cualitativamente los comportamientos descritos por las diversas leyes de los gases. Los postulados de esta teoría pueden ser aplicados de una manera más cuantitativa para deducir estas leyes individuales.
 
 Colectivamente, las moléculas en una muestra de gas tienen una energía cinética promedio y una velocidad promedio; pero individualmente, se mueven a diferentes velocidades. Las moléculas suelen sufrir colisiones elásticas en las que se conserva el impulso. Dado que las moléculas en colisión se desvían a diferentes velocidades, las moléculas individuales tienen velocidades muy variables. Sin embargo, debido al gran número de moléculas y colisiones involucradas, la distribución de la velocidad molecular y la velocidad media son constantes. Esta distribución de la velocidad molecular se conoce como distribución Maxwell-Boltzmann y representa el número relativo de moléculas en una muestra de gas a granel que posee una velocidad dada. 
 
 La energía cinética (Ec) de una partícula de masa (m) y velocidad (v) viene dada por:
 
 <img alt="Eq1" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-01.png" style="height: 40px;" />
 
 Expresar la masa en kilogramos y la velocidad en metros por segundo producirá valores de energía en unidades joules (J = kg·m2/s2). Para trabajar con un gran número de moléculas de gas, utilizamos promedios tanto para la velocidad como para la energía cinética. En la TCM, la raíz cuadrada de la velocidad de una partícula, vrms, se define como la raíz cuadrada del promedio de los cuadrados de las velocidades con n = el número de partículas:
 
 <img alt="Eq2" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-02.png" style="height: 40px;" />
 
 La energía cinética promedio para un mol de partículas, Ecpr, es entonces igual a:
 
 <img alt="Eq3" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-03.png" style="height: 40px;" />
 
 donde M es la masa molar expresada en unidades de kg/mol. La Ecpr de un mol de moléculas de gas también es directamente proporcional a la temperatura del gas y puede ser descrito por la ecuación:
 
 <img alt="Eq4" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-04.png" style="height: 40px;" />
 
 Donde R es la constante de gas y T es la temperatura kelvin. Cuando se utiliza en esta ecuación, la forma apropiada de la constante de gas es 8,314 J/mol·K (8,314 kg·m2/s2·mol·K). Estas dos ecuaciones separadas para Ecpr pueden combinarse y reorganizarse para producir una relación entre velocidad molecular y temperatura:
 
 <img alt="Eq5" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-05.png" style="height: 40px;" />
 
 <img alt="Eq6" src="https://www.jovecore.com/CDNSource/lessons/1043/1043_Equations-06.png" style="height: 40px;" />
 
 Si la temperatura de un gas aumenta, su Ecpr aumenta, más moléculas tienen velocidades más altas y menos moléculas tienen velocidades más bajas, y la distribución se desplaza hacia velocidades más altas en general, es decir, a la derecha. Si la temperatura disminuye, la Ecpr disminuye, más moléculas tienen velocidades más bajas y menos moléculas tienen velocidades más altas, y la distribución se desplaza hacia velocidades más bajas en general, es decir, hacia la izquierda. 
 
 A una temperatura dada, todos los gases tienen la misma Ecpr para sus moléculas. La velocidad molecular de un gas está directamente relacionada con la masa molecular. Los gases compuestos por moléculas más ligeras tienen partículas de mayor velocidad y una mayor vrms, con una distribución de velocidad que alcanza un máximo de velocidades relativamente más altas. Los gases que consisten en moléculas más pesadas tienen más partículas de baja velocidad, una vrms más baja y una distribución de velocidad que alcanza su máximo a velocidades relativamente más bajas. 
 
 Este texto ha sido adaptado de <a href="https://openstax.org/books/chemistry-2e/pages/9-5-the-kinetic-molecular-theory">Openstax, Química 2e, Sección 9.5: Teoría cinético-molecular.</a>

Velocidades Moleculares y Energía Cinética

La teoría cinética molecular explica cualitativamente los comportamientos descritos por las diversas leyes de los gases. Los postulados de esta teoría pueden ser aplicados de manera ...

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KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Gas laws

Tennessee Academic Standards

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Virginia  Standards of Learning

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CH.6

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9-12.C.4.7

Florida Department of Education

SC.912.P.10

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New York State Science Learning Standards

HS. Structure and Properties of Matter

HS-PS1-9.

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

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Physical Properties of Matter

A physical property is ...

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Molecular Comparison of Gases, Liquids, and Solids

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Intermolecular vs Intramolecular Forces

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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

Whether solid, liquid, or gas, a substance&#39;s state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the ...

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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

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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.

PS.Chm.7.1

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

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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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