Kinetic Molecular Theory

You have learned in CH 104 about the three phases of matter: solid, liquid, and gas. In this lesson we are focusing on gases, and our learning will be structured by Kinetic Molecular Theory. This theory provides a framework for understanding the properties and behavior of gases, based on some fairly simple assumptions.

In solids and liquids, of course, the molecules (or atoms) touch one another. For this reason, solids and liquids are hard to compress into smaller volumes, but gases are easily compressible – the particles are so far apart that the only resistance to compression that they offer is due to their pressure, the origin of which is the high speed collisions that occur with the walls of the container. We will discuss the factors that cause the pressure to increase when gases are compressed shortly.

The particles are moving so fast that when they collide they bounce off of each other, even though they are attracted to one another by intermolecular forces. The KMT also assumes that the energy of these collisions is so great that the gas particles do not “feel” the effects of their attraction at all and so lose no energy in their collisions.

Such collisions are called “elastic collisions.” All collisions of ordinary objects are inelastic, that is, some of the energy of the objects is lost as a result. That is why a rubber ball, when dropped to a hard surface, bounces lower and lower with each succeeding bounce – it is losing energy from friction with the ground, the air, and internally as well. A superball has a more elastic collision – it loses height less rapidly and continues to bounce longer, but will eventually slow down.

In the world of atoms, collisions can be truly elastic. If you could do the experiment, an atom would bounce on a hard surface forever. This is because the forces of friction that dissipate energy at the human scale do not exist for individual atoms and molecules.

To review, there are two important assumptions of Kinetic Molecular Theory:

• Particle volumes are negligible compared to gas volumes

• Particles experience no intermolecular forces, so their collisions are fully elastic and their paths are not altered by one another except in collisions

These two assumptions form the basis of the concept of Ideal Gases. The idea behind Ideal Gases is this: the major physical differences between any two molecules are 1) their size and 2) the strengths of their intermolecular forces. Because under KMT we are assuming neither of these factors matter in gases, we can draw a somewhat shocking conclusion: all gases, no matter what their molecular structure, have the same physical behavior.

This prediction has been tested on hundreds of different gases and shown to be mostly true. Using mathematics, scientists have created a set of equations that any ideal gas (a gas with zero particle volume and no IMFs) should theoretically obey. Measurements have shown that for almost all gases (or mixtures of gases) these equations hold up. We will learn many of these equations in the following sections.

Ideal and Non-Ideal Gases

Gases that fit the description of the KMT are referred to as ideal gases. Of course, no gas is truly “ideal,” but many real gases come close enough under ordinary conditions to behave as if they were ideal gases. All gases behave somewhat like ideal gases and we will make the assumption that we can treat all gases as though they behaved ideally. The errors this assumption causes vary from gas to gas and also depend on the temperature and pressure of the gas, but for ordinary gases at room temperature and pressure, they are relatively small, ranging from 5-10% to much less than 1%.

We will now discuss a few factors that can cause a gas to be more or less ideal.

IMF Strength

Gases that tend to behave as ideal gases have weak intermolecular attractions. The weaker the attraction, the more “ideally” a gas will behave.

In a gas, not all the particles are traveling at high speeds and some collisions will be relatively “soft.” A collision between atoms or molecules is inelastic only if the two particles stick together. Since any two gas particles have at least a weak attraction for one another, the softest collisions will always result in inelastic collisions. The stronger the attraction, the greater the fraction of collisions that will be soft enough to be inelastic and the less like an ideal gas the real gas will be. In an ideal gas, all of the collisions are elastic.

Particle Size

Gases whose particles are small will also behave more like ideal gases than gases consisting of large molecules, because one assumption of ideality is that particles have no volume at all. For this reason, small molecules like He and CO tend to behave more ideally than large ones like SF_6.

Gas Pressure

It is important to understand the distinction between the volume occupied by a gas and the volume occupied by the gas molecules. Picture a 2,000 square foot ballroom with only 10 people in it who are wandering all over the room. In a sense, the people fill the room because, in the course of a few minutes, they visit every part of it, so the “volume occupied” by the people is 2,000 square feet. But each person may physically occupy only two square feet or so, so the individuals themselves only occupy about 20 square feet.

In the same sense, the volume occupied by gas molecules themselves is very small compared to the volume of the container that they spread out into. The smaller the less their actual volume is compared to the volume of their container.

Because the KMT assumes that the volume of the gas particles is small compared to the total volume occupied by the gas, a gas can also satisfy this assumption if it occupies a large enough total volume. Since increasing the volume lowers the pressure, gases tend to behave more ideally at lower pressures.

Let’s return to the analogy of the people in the ballroom. In the 2,000 square foot room, the 10 people themselves occupied 20 square feet, or about 1% of the available space. That’s not zero, but it’s close.

If we take the same 10 people and put them in a 10,000 square foot room, they now occupy only 0.2% of the space. Our assumption that they occupy no space at all is, comparatively speaking, closer to the truth.

In the same way, the larger the volume occupied by a given amount of gas, the closer to ideal the gas will become. Since increasing the volume occupied by a gas reduces its pressure, we also say that the lower the pressure, the closer to ideal the properties of the gas become.

Temperature

And because the KMT assumes that the forces of attraction are small compared to the force of the collisions, a gas can also satisfy this assumption if its collisions are violent enough. Increasing the temperature increases the force of the collisions, therefore, gases tend to behave more ideally at higher temperatures.

The higher the temperature, the more forceful the collisions will tend to be and the fewer the collisions that are soft enough to result in the gas particles sticking together.

You might guess that even substances with very strong intermolecular forces can be made to behave like ideal gases if the temperature is raised high enough. You would be right for pure elements, but for molecules, when the temperature gets too high, collisions can also cause chemical reactions to occur.

Gas Mixtures

Because ideal gases are not affected by the forces of attraction between particles, it does not matter what those particles are. A mixture of several gases behaves exactly the same as if it consisted of only a single kind of gas. This is consistent with the idea that gases are a collection of particles flying around at high speed crashing into each other and the walls of their container. Since all they do is bounce off of things, it does not matter what their internal structure is.

It is also consistent with the observation that, unlike liquids, any two gases can be freely mixed in any proportion. Oil and water don’t mix, but oil vapor and water vapor do.

In both these cases, an important caveat is that the gases being mixed must not undergo a reaction with each other.

The answer is that temperature measures the energy of a molecule, which depends on both its speed and its mass. If two gases are at the same temperature, the heavier of the two will, on the average, be traveling more slowly, so that the two gases will, on the average, collide with the walls of their containers with exactly the same force. Neither V, T, nor n depend on what kind of gas molecules are present, so the pressure of the gas, P, doesn't either.

Of course, there are some properties that do depend on the identity of an ideal gas: its density, for example, is influenced by the mass of the gas particles; and its chemical properties are determined by the chemical nature of the gas particles.

In general, we will be concerned with the pressure, volume, and temperature of gases, so their identities will not matter. However, we will occasionally be interested in such things as their molecular weights. To determine such properties, we will need more information than pressure, volume, and temperature. We can’t determine a property that depends on what a gas is using variables that don’t. In such cases, we will need to know the values of properties such as density that do depend on the identity of the gas.

For now, we will confine ourselves to the properties of gases that do not depend on what the gas is. It will be important, however, for you to recognize which properties are which. P, V, n, and T do not depend on the nature of the gas. All others do.

In the next section, we will deal specifically with these properties of ideal gases: temperature, pressure, volume, and number of moles, what they are, how they are measure, and the relationships between them.