Gases: Critical to Our Lives

Gas: A Unique State of Matter Some key questions to begin with... Why do gases behave so similarly? Why are the physical properties of gases different from those of liquids and solids?

The Kinetic-Molecular Theory Around 1860, Ludwig Boltzman and James Maxwell developed a model to explain the properties of gases. It came to be known as the kinetic-molecular theory. Kinetic molecular theory: explains the properties of gases in terms of energy, size, and motion of their particles.

1st Aspect of the Theory: Particle Size Gases consist of small particles that are separated from one another by empty space. The volume of the particles is small compared with the volume of the empty space. Because gas particles are far apart, there are no significant attractive or repulsive forces among them. This accounts for the low density of gases and their compressibility.

2nd Aspect of the Theory: Particle Motion Gas particles are in constant, random motion. Particles move in a straight line until they collide with other particles or with the walls of the container. Collisions between particles are elastic. elastic collision: Describes a collision in which kinetic energy may be transferred between colliding particles but the total kinetic energy of the two particles remains the same. There is no net loss of energy.

An Illustration of Gas Particles You can think of gas molecules as behaving like small billiard balls. When they collide, they do not stick together but immediately bounce apart.

3rd Aspect of the Theory: Particle Energy Two factors determine the kinetic energy of a particle: mass and velocity. KE = ½mv2 in which KE is kinetic energy, m is the mass of the particle, and v is its velocity. Therefore, all particles do not have the same kinetic energy. Because all the particles of a specific gas have the same mass, their kinetic energies depend only on their speeds.

Kinetic Energy and Temperature Temperature: a measure of the average kinetic energy of the particles in a sample of matter. At a given temperature, all gases have the same average kinetic energy. Therefore, at the same temperature, lighter gas particles, such as hydrogen molecules, have higher average speeds than do heavier gas particles, such as oxygen molecules.

Explaining the Behavior of Gases The kinetic-molecular theory can help explain the behavior of gases in at least three areas: Low density Compression and expansion Diffusion and effusion

Low Density of Gases The density of a substance in the gaseous state is about 1/1000 the density of the same substance in the liquid or solid state. That is because the particles are so much farther apart in the gaseous state. As the kinetic-molecular theory states, a great deal of space exists between gas particles.

Compression & Expansion During compression, the gas particles, which are initially very far apart (according to the kinetic- molecular theory), are crowded closer together. The volume of a given sample of gas can be greatly decreased. During expansion, gases completely fill any container in which they are enclosed, and they take its shape. According to the kinetic-molecular theory, gas particles move rapidly in all directions without significant attraction or repulsion between them. Compression & Expansion

Compression and Expansion

Diffusion (Linked to the Theory) According to kinetic-molecular theory, there are no significant forces of attraction between gas particles. Thus, gas particles can easily flow past each other. Also, the random and continuous motion of gas particles carry them throughout all the available space. For this reason, gases may mix easily. We call this process diffusion.

Diffusion Defined Diffusion: the movement of one material through another from an area of higher concentration to an area of lower concentration. Alternatively, the spontaneous mixing of the particles of two substances caused by their random motion. Examples: Perfume or ammonia or a sulfur- containing gas moving through the room to mix with the air and attract your attention.

The Rate of Diffusion The rate of diffusion depends mainly on the mass of the particles involved. Lighter particles diffuse more rapidly than heavier particles. For example, at a uniform temperature, hydrogen's molecules will diffuse quickly into other gases' molecules because they are smaller and faster.

Effusion: a Related Process Effusion is a process by which gas particles pass through a tiny opening. Think about a tightly- sealed plastic bag of onions. When the bag is punctured with a small hole, what would you soon smell? In 1846, Thomas Graham did experiments to measure the rates of effusion for different gases at the same temperature such that they effused into a vacuum, a space containing no matter. The result of his experiments was Graham's law of effusion.

Illustrations of Effusion of Gases

Graham's Law of Effusion Graham's law of effusion: states that the rate of effusion for a gas is inversely proportional to the square root of its molar mass. Rate of effusion ------------------------

Comparing Rates of Effusion of Helium and Argon Gases

Graham's Law Applied to Diffusion Building upon this idea, if we compare two gases at the same temperature, the one with heavier particles will diffuse more slowly into the one with lighter particles. So using Graham's law, we can set up the following proportion to compare diffusion rates for two gases: RateA RateB

Example of Gases Diffusing

Practice Problems with Graham's Law What is the ratio of the diffusion rates of hydrogen and oxygen gases? Calculate the molar mass of butane. Butane's rate of diffusion is 3.8 times slower than that of helium.