The kinetic molecular theory of gases | AP Chemistry | Khan Academy

In this video, we're going to talk about something called kinetic molecular theory, which sounds very fancy. But as we'll see in the next few seconds or the next few minutes, it actually helps build our intuition for what is going on with a gas, or at least an approximation of what's going on with a gas.

So first, let's think about the types of things that we know we can measure about a gas at a macro level. Now, what do I mean at a macro? I'm saying at a large scale, at a scale that's much larger than the scale of atoms or molecules. We know the types of things that we can measure. We can measure pressure. How do we do that?

Well, pressure is just force per unit area. So you can do this; there're various contraptions you can use to measure pressure depending on what you're using it for. Force you can measure with springs, and you can apply certain forces to certain square areas, but these are all ways that you can measure pressure.

We can measure the pressure of a gas in a container. You can measure the volume of a container. That's actually pretty straightforward. You can imagine a container that looks something like this; its volume. We know how to find the volume of a rectangular prism like this, or even if it was a sphere or some other type of figure. There're many ways of measuring the volume without even being able to observe or even know that things like molecules exist.

We know how to measure temperature, and we can do that on different scales. Kelvin is what we use because it's more of an absolute scale, but you can use literally thermometers to measure temperature. Once again, you can measure temperature without knowing anything about atoms or molecules or whether they even exist.

And you can also measure an amount of a substance. In particular, we could say you can measure the number of moles. Now, you might say, "Don't moles involve a certain number of a molecule or an atom?" Well, they do, but the notion of a mole actually existed even before we knew exactly how many molecules, how many particles made up a mole. It was just viewed as an amount where people knew it must be some number of particles, but they didn't know exactly.

So all of these things we can measure at a macro level, and we know that we can connect them all with the ideal gas equation that tells us that pressure times volume is equal to the amount of the gas we're dealing with. Of course, we're talking about an ideal gas, and in future videos, we'll talk about how some gases approach being an ideal gas while some are less than ideal.

But the amount we have measures the number of moles. You have your ideal gas constant that just helps us make all the units work out depending on our units for everything else. Then you have your temperature measured in kelvin. Scientists, long before we were actually able to know about things like atoms or even observe atoms or molecules directly or even indirectly, were able to establish this relationship using these macro measurements.

But how do these macro measurements in this relationship actually make sense at a molecular level? That's what kinetic molecular theory provides us. It says imagine the gas as being made up of a bunch of really, really small particles. Those are really the gas molecules, and their collective volume is very small compared to the volume of the container. So it's mostly empty space between those particles.

Now, the pressure is caused by these particles bouncing into the sides of the container because, at any given moment, you have enough particles bouncing off the side of any unit area that it's providing a force per unit area; it's providing a pressure. It assumes that those collisions are what's known as elastic, which you'll study in much more detail in a physics course, but it really says that your kinetic energy is preserved.

You might already be familiar with the notion that kinetic energy is equal to one-half times mass times velocity squared. So the kinetic energy of these particles, when they bounce off, their mass doesn't change; the mass of the particle's still there, and we're saying that the velocity is going to be preserved.

So you have all these really small particles. Even their collective volume is small compared to the volume of the container. They're providing the pressure by having these elastic collisions with the side of the container. Temperature is related to the average kinetic energy of these particles. It would be proportional; the higher the temperature, the higher the average kinetic energy.

Now, average kinetic energy is really important because some of these particles might be moving faster than others. And, of course, the number of moles tells us how many particles we're dealing with. We know that each mole has Avogadro's number of particles. So if you just multiply the moles times Avogadro's number, you have the number of particles.

What's cool about kinetic molecular theory—I know it's billed as a theory—but this is fundamentally what chemists and physicists visualize when they imagine a gas in a container of some kind. Just to make it a little bit more clear, the axioms, you could say, of kinetic molecular theory, the assumptions of it, I'll give them here.

It's important to realize that these are assumptions, and in the real world, we have slight variations from it. But these assumptions get us a long way to explaining the behaviors of gases. So we've already talked about a gas consists of particles in constant random motion. We've already talked about that they're bouncing off the side of the container.

The combined volume of the particles is negligible compared to the total volume in which the gas is contained, and that also matters when you talk about things like ideal gases. Because if it stops becoming negligible, then you have to start thinking about the repulsive and attractive interactions a little bit more.

The particles exert no attractive or repulsive forces on each other, and that kind of builds into the last point I just made, which is if they did, then we're getting closer to being a less than ideal gas, and we'll talk about that in other videos. The collisions between the particles are completely elastic, so they preserve kinetic energy, and they would also preserve momentum.

The average kinetic energy of the particles is proportional to the Kelvin temperature, and we already talked about that—the macro variable, the macro measurement of temperature is giving us an indication. It's proportional to the average kinetic energy of the particles.