Name: gas particle motion, diffusion, and effusion
Uploaded: 2020-09-03T13:38:27.000Z
Duration: 3 min 48 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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Behavior of Gas Molecules: Molecular Diffusion, Mean Free Path, and Effusion

A closed bottle of perfume contains a high concentration of gaseous aromatic molecules that are constantly moving and randomly colliding. Meanwhile, the air outside of the bottle contains essentially none of these molecules.

On opening the bottle, a concentration gradient is established between these high- and low-concentration regions. The molecules continue moving randomly, with overall movement from the high-concentration region to the low-concentration region. 

The spontaneous mixing and spreading of liquids or gases in response to a concentration gradient is called molecular diffusion.

Diffusion is a slow process. Even though gas particles travel at high speeds, the numerous collisions cause frequent changes in speed and direction. 

The average distance a particle travels between collisions is known as its mean free path. For a gas particle, its mean free path is influenced by the particle density, which also affects the pressure. 

As the particle density increases, so does the collision frequency. Thus, their mean free path is shorter. Likewise, as the particle density decreases, so does the collision frequency, leading to a longer mean free path. 

Different gases diffuse at different rates, depending on the speed of the gas particles. Since the root-mean-square, or RMS, speed and the molar mass of a gas are inversely related, lighter gases diffuse faster than heavier gases.

Consider a glass tube between reservoirs of equal amounts of ammonia and hydrogen chloride gas. 

When the diffusing gases meet, they react to form a ring of ammonium chloride. The ring is closer to the hydrogen chloride end of the tube because the lighter ammonia molecules traveled farther down the tube than the heavier hydrogen chloride molecules in the same amount of time. 

Effusion is another process that involves the movement of gas molecules. It is the ability of gas molecules to travel through a hole whose diameter is much smaller than the mean free path of the gas itself in response to a pressure difference. 

This is why helium balloons eventually deflate &#8212; the helium gradually effuses through tiny pores in the balloon material.

Like diffusion, the rate of effusion is dependent on the RMS speed and molar mass of the gas. Specifically, the rate of effusion is inversely proportional to the square root of the molar mass of the gas. Therefore, heavier gases effuse more slowly than lighter ones.

For any two gases, the ratio of their effusion rates is the square root of the inverse ratio of their molar masses. This is called Graham&#8217;s law of effusion. 

Consider two balloons inflated to the same pressure &#8212; one filled with helium and the other with oxygen. Helium has a lower molar mass than oxygen, as shown by the helium balloon&#8217;s buoyancy in air.

Applying Graham&#8217;s law to helium and oxygen suggests that helium effuses 2.8 times faster than oxygen. Thus, the helium balloon deflates faster than the oxygen balloon.

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 different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be hundreds of times the diameter of the molecule

In general, when a sample of gas is introduced to one part of a closed container, its molecules very quickly disperse throughout the container; this process by which molecules disperse in space in response to differences in concentration is called diffusion. The gaseous atoms or molecules are, of course, unaware of any concentration gradient; they simply move randomly &#8212; regions of higher concentration have more particles than regions of lower concentrations, and so a net movement of species from high to low concentration areas takes place. In a closed environment, diffusion will ultimately result in equal concentrations of gas throughout. The gaseous atoms and molecules continue to move, but since their concentrations are the same in both bulbs, the rates of transfer between the bulbs are equal (no net transfer of molecules occurs). The amount of gas passing through some area per unit time is the rate of diffusion.

<img alt="Rate of diffusion formula; diagram of gas diffusion through an area per unit time." src="/files/core/CDNSource/lessons/1044/1044_Equations-01.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq1" />

The diffusion rate depends on several factors: the concentration gradient (the increase or decrease in concentration from one point to another), the amount of surface area available for diffusion, and the distance the gas particles must travel.

A process involving the movement of gaseous species similar to diffusion is effusion, the escape of gas molecules through a tiny hole, such as a pinhole in a balloon into a vacuum. Although diffusion and effusion rates both depend on the molar mass of the gas involved, their rates are not equal; however, the ratios of their rates are the same.

If a mixture of gases is placed in a container with porous walls, the gases effuse through the small openings in the walls. The lighter gases pass through the small openings more rapidly (at a higher rate) than the heavier one. In 1832, Thomas Graham studied the rates of effusion of different gases and formulated Graham&#8217;s law of effusion: The rate of effusion of a gas is inversely proportional to the square root of the mass of its particles:

<img alt="Rate of effusion formula: rate &#8733; 1/&#8730;M, illustrating molecular velocity and mass relationship." src="/files/core/CDNSource/lessons/1044/1044_Equations-02.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq2" />

This means that if two gases, A and B, are at the same temperature and pressure, the ratio of their effusion rates is inversely proportional to the ratio of the square roots of the masses of their particles:

<img alt="Effusion rate equation, Graham's law formula, gas diffusion concept, chemistry calculation." src="/files/core/CDNSource/lessons/1044/1044_Equations-03.png" style="height: 40px;" data-altupdatedat="1761830439000" data-alt="Eq3" />

The relationship indicates that the lighter gas has a higher effusion rate.

For example, a helium-filled rubber balloon deflates faster than an air-filled one because the rate of effusion through the pores of the rubber is faster for the lighter helium atoms than for the air molecules.

This text is adapted from <a href="https://openstax.org/books/chemistry-2e/pages/9-4-effusion-and-diffusion-of-gases">Openstax, Chemistry 2e, Section 9.4: Effusion and Diffusion of Gases.</a>

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

Education

JoVE Core

Gases

KEY TERMS AND CONCEPTS

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 of a gas molecule is hundreds of times greater than the molecule’s diameter.

Diffusion is the spread of gas particles through space because of differences in concentration. When a gas is added to one part of a closed container, its molecules quickly disperse throughout the container. The molecules move randomly, but the net movement is from higher concentration to lower concentration. In a closed environment, diffusion eventually leads to equal concentrations throughout. The gas particles still move, but there is no net transfer between regions when the concentrations are the same.

The rate of diffusion is the amount of gas that passes through an area in a given time. It depends on the concentration gradient, the available surface area, and the distance the particles must travel. A related process is effusion, which is the escape of gas molecules through a tiny opening, such as a pinhole in a balloon into a vacuum. Diffusion and effusion rates both depend on molar mass, but the rates are not the same.

If a mixture of gases is placed in a container with porous walls, the gases effuse through the small openings. The lighter gases pass through more quickly than the heavier gases. Thomas Graham studied these rates in 1832 and formed Graham’s law of effusion. This law states that the rate of effusion is inversely proportional to the square root of the mass of the particles. For two gases at the same temperature and pressure, the ratio of their effusion rates follows the same relationship. A helium-filled rubber balloon, for example, deflates faster than an air-filled balloon because helium atoms effuse faster through the rubber pores than air molecules.

Gas Particle Motion, Diffusion, and Effusion

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

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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...

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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...

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 molecules move, diffuse, and effuse, plus why lighter gases pass through tiny openings faster than heavier gases.

Gas Particle Motion, Diffusion, and Effusion | JoVE K12

chemistry

JoVE Core Chemistry brings general chemistry concepts to life using concise and easy-to-understand animated video lessons. Plus, in the scientist-in-action videos, we demonstrate classical and original research experiments performed in today's laboratories worldwide.

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Ohio’s Learning Standards and Model Curriculum

Interactions Of Matter

Gas laws

Virginia  Standards of Learning

HIgh School

CH.6

CH.6.b

Texas Essential Knowledge and Skills

High School

CHEM.10

CHEM.10.A

Alabama Course of Study Science

Matter and Its Interactions

9-12.C.1.4.e

9-12.C.4.7

9-12.C.4.7.a

Florida Department of Education

Physical Science

SC.912.P.10

SC.912.P.10.5

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Structure and Properties of Matter

HS-PS1-9.

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Phase Transitions

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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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PS.Chm.7.1

Energy Basics

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First Law of Thermodynamics

Energy Conservation

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PS.Chm.7.2

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Gas Particle Motion, Diffusion, and Effusion

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