21. Kinetic Theory of Ideal Gases

The Ideal Gas Law

# Ideal Gases and the Ideal Gas Law

Patrick Ford

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Hey guys. So throughout our discussion on thermodynamics, we'll often be talking about gasses and specifically, we're talking about these things called ideal gasses. So in this video, I want to introduce you what an ideal gas is and the equation that we use for them, which is called the ideal gas law. So let's get started here. What is an ideal gas? Well, the definition I like to use is it's kind of like a simplified perfect gas. The analogy is that when we talk about forces and drew free body diagrams, it didn't matter whether it was a plane or a train or a car or whatever. We do everything as boxes because it was the simplest model for an object and similarly, the simplest model for a gas is called an ideal gas. Now, it's basically just satisfies a couple of conditions here and I want to go over them really quickly because you may need to know for a conceptual question on a homework or test. So let's get started. The first one is the gas has a low density. So what happens is that the particles in a container are going to be kind of spread out doing their own thing. They're not going to be super, super tightly crammed in together. So generally what this means is that the pressure is pretty low, but the temperature is pretty high. You won't see many extreme values or anything like that. The second condition is that there are no forces between the gas particles. So in real life and real gasses, you have particles that exist that exert some forces on each other, that you usually like electromagnetic forces. And for an ideal gas, we just consider that they don't exist. The third condition is that the particles have zero physical size. And what this means is that we're going to just treat ideal gas particles like points. So you basically just treat them as tiny little balls that are moving, they're very, very tiny, can treat them as point particles, whereas real gas molecules actually do take up space. But for an ideal gas we just assume that it's zero. The last one is that the particles are moving in straight lines and they collide elastically. This is the most important part here. So basically these tiny little balls, like these tiny little points are moving around. They move in perfectly straight lines until they collide with either the walls of the container or even each other, they can bounce off of each other. However, when they do collide, they collide elastically. And what that means is the energy in the container is conserved. There's no energy loss because these things are bumping around into each other. All right. So the night, the what you really need to know about everyday conditions and ideal gasses is that, you know, even under everyday conditions like in our atmosphere and things like that, most real gasses already behave very much like ideal gasses. So, you know, we can still use this model for an ideal gas, even when we talk about real gasses, like oxygen and nitrogen in our atmosphere. Alright, so let's get to the equation. Then the equation that governs ideal gasses is called the ideal gas law and it relates for related variables. We have pressure, volume, temperature and moles which is the amount of substance for an ideal gas. And it actually works for any ideal gas, doesn't matter what it is. Now, there's two different versions of this and you may see both of them. So I want to go over them. So the first one is PV equals N R. T. If you've ever taken an introductory chemistry course or something like that, you may be pretty familiar with this one, The other one is PV equals N K b T. Where the end is a big end. And the difference between them, they both work for ideal gasses is that you use this equation whenever you have the number of moles of substance and you use this one whenever you're when you're you're asked to find or you're given the number of particles in a gas and these things actually have a pretty simple relationship between them and the number of moles big. And this number of particles And they're related by this equation over here where moles is particles divided by avocados number around. That's 6.2 times 10 to the 23. Alright, so let's move on here. There's two constants that you need to know in both of these equations. The first one is big R and it's called the universal gas constant. It's sometimes called the ideal gas constant. And it's just this number here. 8.314 joules per mole kelvin. The other one is KB. This KB is called bolts means constant And it has a value 1.38 times 10 to the -23. Now, the last thing here is that we're working with absolute temperatures not changes in temperature. So the temperature actually must be in kelvin. That's really, really important. You have to plug in all your temperatures in kelvin. And the very last thing I want to mention here is that this is something you might see in your problems. So something called S. T. P. It's an acronym that stands for standard temperature and pressure. Basically, it's just a common set of conditions. That's very much like what we experience here at Earth's surface, which is that the temperature is zero degrees Celsius or 2 73 kelvin and the pressure is one atmosphere or 1.1 times 10 to the fifth. This is basically just whenever you see STP these are your numbers for temperature and pressure. Alright, so let's get to our example here, Which is we're going to calculate the volume of exactly one Mole of an ideal gas that is at STP So we're going to use those conditions here. So we have S. T. P, which means the temperature is zero Celsius or 2 73 kelvin and we also have that the pressure is 1.1 times 10 to the fifth pascal's. Now if we have one mole of substance that's N. Equals one, we want to figure out what is the volume. So we have these four variables. Remember they're all related using the ideal gas law. So which version are we going to use? Well remember we're given the number of moles of a substance. So that means we're gonna use N. R. T. So we're gonna use PV equals N. R. T. So what happens here is that there are five variables. There's five letters in this equation, but one of them is a constant. So there's really only four variables. You need to know if you ever have three, you can always figure out the other one. So we know what the pressure is, we know what the number of moles is and we have the temperature. Remember this is just a constant. So we can figure out what this volume is by just rearranging the equation. So what happens is this P. Goes to the other side like this and your V. Is going to be N. R. T. Divided by P. So I'm just gonna start plugging in one mole. We have 8.314, that's the gas constant to 73. That's the temperature. And then 1.1 times 10 to the fifth pascal's. So when you work this out or you're gonna get is 0.0224 and this is gonna be meters cubed. Now there's also a couple of other volume conversions that you may need to know for these types of problems. One of them is that one centimeter cubed is one mil leader and then sort of, if you work this out and you play around with the zeros, you'll figure out that one m cubed is 1000 liters. So one thing, when you might see this number represented 0.0224 is when they multiply it by this conversion factor, you're gonna multiply by 1000 liters divided by one meter cubed meters cubed cancels. And you're gonna get 22.4 liters and that's the answer. Either one of these will work. So either one of these uh, these numbers will be the answer and that's actually a really sort of special number here. So the idea is that one mole of any ideal gas at STP sort of at these special conditions has a molar volume of exactly 22.4 leaders notice how we didn't talk about what type of gas it is, all we had was these conditions. So what this means here is that any gas at STP, whether you might have one mole occupies this amount of space and this is sometimes called the molder volume of a gas at STP. Alright, so guys, so that's it for this one, let me know if you have any questions.

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