Gas mixtures and partial pressures | AP Chemistry | Khan Academy

In this video, we're going to introduce ourselves to the idea of partial pressure due to ideal gases. The way to think about it is to imagine some type of a container, and you don't just have one type of gas in that container; you have more than one type of gas.

So, let's say you have gas one that is in this white color. Obviously, I'm not drawing it to scale, and I'm just drawing those gas molecules moving around. You have gas 2 in this yellow color. You have gas 3 in this blue color.

It turns out that people have been able to observe that the total pressure in this system, and you could imagine that's being exerted on the inside of the wall, or if you put anything in this container, the pressure, the force per area that would be exerted on that thing, is equal to the sum of the pressures contributed from each of these gases, or the pressure that each gas would exert on its own.

So, this is going to be equal to the partial pressure due to gas 1 plus the partial pressure due to gas 2 plus the partial pressure due to gas 3. This makes sense mathematically from the ideal gas law that we have seen before. Remember, the ideal gas law tells us that pressure times volume is equal to the number of moles times the ideal gas constant times the temperature.

If you were to solve for pressure here, just divide both sides by volume. You get pressure is equal to nRT over volume. We can express both sides of this equation that way. Our total pressure, that would be our total number of moles, so let me write it this way: n total times the ideal gas constant times our temperature in Kelvin divided by the volume of our container.

That's going to be equal to, so the pressure due to gas 1, that's going to be the number of moles of gas 1 times the ideal gas constant times the temperature. The temperature is not going to be different for each gas; we're assuming they're all in the same environment, divided by the volume.

Once again, the volume is going to be the same; they're all in the same container in this situation. And then we would add that to the number of moles of gas 2 times the ideal gas constant, which once again is going to be the same for all the gases, times the temperature divided by the volume.

Then, to that, we could add the number of moles of gas 3 times the ideal gas constant times the temperature divided by the volume. Now, I just happen to have three gases here, but you could clearly keep going and keep adding more gases into this container.

When you look at it mathematically like this, you can see that the right-hand side, we can factor out the RT over V. If you do that, you are going to get (n1 + n2 + n3) times RT over V. This is the exact same thing as our total number of moles. If you say the number of moles of gas 1 plus the number of moles of gas 2 plus the number of moles of gas 3, that's going to give you the total number of moles of gas that you have in the container.

So, this makes sense mathematically and logically, and we can use these mathematical ideas to answer other questions or to come up with other ways of thinking about it. For example, let's say that we knew that the total pressure in our container due to all of the gases is four atmospheres.

Let's say we know that the total number of moles in the container is equal to 8 moles, and let's say we know that the number of moles of gas 3 is equal to 2 moles. Can we use this information to figure out what is going to be the partial pressure due to gas 3? Pause this video and try to think about that.

Well, one way you could think about it is the partial pressure due to gas 3 over the total pressure. The total pressure is going to be equal to, if we just look at this piece right over here, it's going to be the number of moles of gas 3 times the ideal gas constant times the temperature divided by the volume, and then the total pressure, well, that's just going to be this expression.

So, the total number of moles times the ideal gas constant times that same temperature because they're all in the same environment, divided by that same volume. They're in the same container. You can see very clearly that the RT over V is in the numerator and the denominator, so they're going to cancel out.

We get this idea that the partial pressure due to gas 3 over the total pressure is equal to the number of moles of gas 3 divided by the total number of moles. This quantity right over here is known as the mole fraction. Let me just write that down.

It's a useful concept, and you can see the mole fraction can help you figure out what the partial pressure is going to be. So, for this example, if we just substitute the numbers we know, the total pressure is four, we know that the total number of moles is eight, we know that the moles of gas 3 is two.

Then we can just solve. Let me just do it right over here; I'll write it in one color. The partial pressure due to gas 3 over 4 is equal to 2 over 8, which is equal to 1/4.

You can just pattern match this or multiply both sides by 4 to figure out that the partial pressure due to gas 3 is going to be 1. Since we were dealing with units of atmosphere for the total pressure, this is going to be 1 atmosphere, and we would be done.