The ideal gas law (PV = nRT) | Intermolecular forces and properties | AP Chemistry | Khan Academy

In this video, we're going to talk about ideal gases and how we can describe what's going on with them. So the first question you might be wondering is, what is an ideal gas? It really is a bit of a theoretical construct that helps us describe a lot of what's going on in the gas world, or at least close to what's going on in the gas world.

So, in an ideal gas, we imagine that the individual particles of the gas don't interact. Particles don't interact, and obviously, we know that's not generally true. There's generally some light intermolecular forces as they get close to each other, as they pass by each other, or if they collide into each other. But for the sake of what we're going to study in this video, we'll assume that they don't interact, and we'll also assume that the particles don't take up any volume.

Now we know that that isn't exactly true; individual molecules, of course, do take up volume. But this is a reasonable assumption because, generally speaking, it might be a very, very infinitesimally small fraction of the total volume of the space that they are bouncing around in. So, these are the two assumptions we make when we talk about ideal gases. That's why we're using the word "ideal."

In future videos, we'll talk about non-ideal behavior, but these assumptions allow us to make some simplifications that approximate a lot of the world. So, let's think about how we can describe ideal gases.

We can think about the volume of the container that they are in. We can imagine the pressure that they would exert on, say, the inside of the container. That's how I visualize it, although that pressure would be the same at any point inside of the container. We can think about the temperature, and we want to do it on an absolute scale. So, we generally measure temperature in Kelvin.

Then, we can also think about just how much of that gas we have, and we can measure that in terms of the number of moles, and so that's what this lowercase n is. So, let's think about how these four things can relate to each other.

Let's just always put volume on the left-hand side. How does volume relate to pressure? Well, what I imagine is if I have a balloon like this, and I have some gas in the balloon. If I try to decrease the volume by making it a smaller balloon, without letting out any other air or without changing the temperature—so I'm not changing t and n—what's going to happen to the pressure?

Well, that gas is going to, per square inch or per square area, exert more and more force. It gets harder and harder for me to squeeze that balloon. So, as volume goes down, pressure goes up. Or likewise, if I were to make the container bigger, not changing—once again—the temperature or the number of moles I have inside of the container, it's going to lower the pressure.

So, it looks like volume and pressure move inversely with each other. What we could say is that volume is proportional to 1 over pressure, the inverse of pressure. Or you could say that pressure is proportional to the inverse of volume. This just means proportional to, which means that volume would be equal to some constant divided by pressure in this case.

Now, how does volume relate to temperature? Well, if I start with my balloon example—and you could run this example if you don't believe me—if you take a balloon and you were to blow it up at room temperature, and then if you were to put it into the fridge, you should see what happens. It's going to shrink.

You might say, "Why is it shrinking?" Well, you could imagine that the particles inside the balloon are a little less vigorous at that point. They have lower individual kinetic energies. So, in order for them to exert the same pressure to offset atmospheric pressure on the outside, you are going to have a lower volume. So, volume—you could say—is proportional to temperature.

Now how does volume compare to number of moles? Well, think about it: if you blow air into a balloon, you're putting more moles into that balloon, and holding pressure and temperature constant, you are going to increase the volume. So, volume is proportional to the number of moles. If you were to take air out, you're also going to decrease the volume, keeping pressure and temperature constant.

So, we can use these three relationships, and these are actually known as: this first one is known as Boyle's law, this is Charles's law, this is Avogadro's law. But you can combine them to realize that volume is going to be proportional to the number of moles times the temperature divided by the pressure.

Another way to say it is, you could say that volume is going to be equal to some constant—that's what proportionality is just talking about. It's going to be equal to some constant; let's call it r—times all of this business, r n t over p. Or another way to think about it is we can multiply both sides by p, and what will you get?

We will get p times v, and this might be looking somewhat familiar to some of you, is equal to—and I'll just change the order right over here—n, which is the number of moles, times some constant times t, our temperature measured in Kelvin.

This relationship right over here, pv is equal to nrt, is one of the most useful things in chemistry, and it's known as the ideal gas law. In future videos, we're going to apply it over and over again to see how useful it is.

Now, one question you might be wondering is: what is this constant? It's known as the ideal gas constant, and you can look it up, but it's going to be dependent on what units you use for pressure, volume, and temperature, and we will see that in future videos.