So, gases. So we're going to kind of go through a lot of things in this one. We're going to start sort of conceptually and then walk into the calculations. But by the end of this quarter, the thing that we need to be able to do is we need

to know very both conceptually, you guys have figured out I like those questions, along with calculating how volume, pressure, and temperature are all related to each other. You're going to know a lot of this already, especially once I point it out to you, which I realize is a little bit of an oxymoron. But you'll realize that you know a lot of it already, at least conceptually.

And we'll actually put that into equation form probably today, if not today, next class. So we're going to learn about how the ideal gas law, that you kind of have an idea about how things work in real life, how that's going to be related to if you have one ideal gas or if you have a bunch of different mixtures of ideal gases, and how

you can kind of calculate really complicated problems with lots of different gases altogether just by breaking them down into a whole bunch of simple problems. Then what we're going to do is after we're starting with sort of bulk properties, we're starting with these big liters, two liters of gases, and we're just talking

about them in terms of pressure, volume, temperature, moles, things of that sort. Once we learn that, we're going to go a little bit deeper and we're going to actually look at the kinetics of it and see really qualitatively, kinetics really isn't until 1C, but we'll get an idea of how the actual way that the atoms are moving around

is giving you those bulk properties, the pressure and the volume, and why things that the atoms are doing are making those properties be like they are. And that's called kinetic molecular theory. So we'll get into that near the end. And then as standard in chemistry, we're going to tell you a bunch of things that almost work, and then we're going to tell you why we lied to you a little bit.

You're getting the pattern there, I think. So we're pretty much going to spend 95% of the chapter on what we call ideal gases that we'll get into. But real gases aren't going to be ideal. And so we'll show you one of the ways that you can sort of make up for this and fix issues with not being quite ideal. And then there's lots of actual ways to do this, but we're just going to pick the

one that's used the most and we're going to walk through that. So that'll be sort of the last 5% of the chapter. Okay. First, what is a gas? So, you know, kind of going back, we talk about solids, we talk about liquids, we talk about gases, right? Those are sort of our three main phases that we talk about. The idea with gases that's different from all the rest is that they're moving

freely, right? They aren't necessarily near each other. Depending on the pressure, they may be farther or closer to each other. But in general, they're just moving freely. It's not like a liquid where they're all sitting on top of each other just rotating around, or like a solid which you can think of as like a tight lattice. Like we filled up all the chairs in here and, you know, you guys would be sort of

a solid lattice. Yeah. So it'll be, yeah, actually I meant to say that. So she asked the final for the sake of studying so you know, it'll be 25% midterm 1, 25% midterm 2, and 50% chapter 4.

Okay. Sounded like you guys were surprised. I'm not sure why, but I guess it was a good thing to talk about. Okay. So unlike liquids and solids, they aren't going to be touching each other most of the time. When they are, it's going to be sort of a quick thing, right? They're going to bounce off each other and move their own way. They're not really going to be interacting with each other at all.

Or at least not much. Now this gives gases some properties that liquids and solids don't have. If you try to take a solid, like a real solid that doesn't have a bunch of air pockets in it, and you try to compress it, you're not really going to be able to do that. Take like a solid piece of metal and try to compress it. You're not going to be able to do it.

You can say, well, I can compress something like wood, but what are you really compressing? Air pockets and cell pockets and, you know, things like that. You're not actually compressing the solid. So anything that's a solid, you're not going to actually be able to compress. Same thing with liquids. If you try to take water and you try to compress it down, you might be able to get a little tiny bit if you have really good measurements, but nothing perceptible.

Now can you take a gas and compress it? Sure. That's what all these sorts of containers always are, right? They just take a ton and ton of gas and they put it all into a little container so that then you can, you know, fill up balloons all day at a party with just one little container.

Now, they also don't have a defined shape, which of course both liquids and liquids and gases and, if you believe, the internet cats all have. So, some of you have seen that meme. Okay, so they, you know, they fill the shape of whatever you put them in. If I put them in some odd-shaped container, they're just going to fill it up, whatever it is.

It doesn't matter. A solid doesn't do that, of course, right? You put a solid into, you know, a container, it's just going to sit there in the same shape it always was. They also are going to expand. Now this is different than a liquid, right? If you put a liquid in a container this, you know, this big, and then you give it a container this big, the only thing it's going to do is flatten itself out.

It's not going to get bigger where a gas is. A gas is going to expand to fill whatever space you give it, it's going to fill. They're going to mix evenly amongst each other. So, sometimes liquids will do this, sometimes they won't. It depends. You'll learn about that in, I think, 1B.

But, in this case, gases are going to mix. They're lower density, so that sort of makes sense, right? Like, they weigh less for a given volume because they're not as closely packed. They're not all on top of each other. So, those are sort of your general guidelines for what a gas are. That's how we define a gas.

I'll give you a few more minutes to write down. All of these are things that I think on some level you probably know, but now they're sort of written out and defined so I could ask you, you know, how do you know if something is a gas? And you could say, well, I can compress it, it takes the shape of its surroundings, it'll mix evenly with each other, things of that sort.

Okay, so now a little bit of a word on units because it's one of those, you know, things of life. I'm not going to go through unit conversion with you. I don't think you would have made it past the first midterm if you didn't know how to do unit conversion, but I do want to talk about the units. So, we have something called a Pascal, which is a Newton meter.

So, you're going to, the gases really, really don't have a unit that pretty much is always used. Like, it's really sort of scattered is how people report it. So, make sure you do know the other units. Of course, you'll have the same equation sheet for your final that you had for your midterm and midterm two. So, you'll know that you have these given to you.

You'll also see kilopascal written a lot just because kilopascal gets you closer to an ATM. What is approximate atmospheric pressure? About one, right? So, that's where this comes in. But a lot of times you see it measured in millimeters of mercury. Why millimeters of mercury?

I'll show you in a minute. Actually, I'll show you right now. Barometers. Okay, I hear lots of people whispering, go back. So, I'll go back in a sec. So, just know how to convert back and forth between these. You're going to do it a lot, and you want to be able to do it really quickly just because it's given you, when we do the ideal gas law

there's going to be a lot of times that you have to do it in atmospheres. There's going to be a lot of times that you don't. And you want to watch out for those because you don't want to waste a lot of time converting units when you don't have to. But you want to be careful to make sure you always convert them when you do. And when we get to those sorts of problems, I'll go over it in more detail.

Okay, so now why the millimeters of mercury thing came about? Something called a barometer. Which you've probably seen somewhere in an antique store or something. But, the idea behind barometers is they give you a measure of atmospheric pressure. So, you can't really see what's happening in something like this.

This is like an old, you know, something that you can make in a lab style barometer. So, what you can do with this is you take and you put an empty tube in a thing of mercury. And then you put a little bit of room around the mercury so that the atmosphere can push down on it. So, the atmosphere is going to be pushing down on this liquid vat of mercury.

When it does that, what happens if you push on a liquid and you have an empty tube in there? It goes up, right? So, if it pushes on this, it's going to push the mercury up into the tube. That's how a barometer actually works.

So, you have a vacuum tube, you have a disk of mercury. And then, depending on how much atmospheric pressure we have, because it changes day to day, right? It changes with storms, it changes with a variety of different things. So, this will give you a measure of that. Now, because this was how atmospheric pressure was originally measured, it ended up being measured in millimeters of mercury.

Because you could just measure, you could just measure how much mercury was going up into the tube. And then you could sit with your ruler and say, okay, well the atmospheric pressure today is about 764 millimeters of mercury. Okay? So, that's how the millimeters of mercury unit came about.

Now, maybe a good question at this point becomes, okay, mercury. Why did we use mercury? What's special about mercury? It's a liquid, right? And why maybe not water? What else is special about mercury? It's really heavy.

Or so I guess we should say dense, right? A small amount of mercury is going to weigh a lot more than a small amount of water. So, this height is going to be dependent on how heavy it is, right? Because all of this right here, that's being pulled down too, right? It's being pushed up by the atmospheric pressure pushing into the tube.

What is it being pulled down by? I guess maybe pulled is the better term here. Gravity. So, the heavier it is, the more dense that it is. The more dense that this liquid is, the smaller it's going to be. Now, why would we want something to be small? Well, let's talk about it. Let's do an example. Okay, so suppose we were marooned on a tropical island

and we wanted to know the atmospheric pressure. Because it's really important information to know when you're marooned on a tropical island. It could be. Storms, right? You need to know if a storm is coming. Okay, so how do we do this? Well, you have to know first that the density and the height are going to be proportional to each other.

So, we can set up this. Now, this looks pretty similar to like an M1V1 equals M2V2 problem, right? It's the same sort of idea. It's a ratio. We have the density of seawater because that's theoretically what you have around.

We have the height that it would reach in a mercury-thrown islander. So, let's try to figure this out. Well, let's set this up to be seawater. And this up to be what a mercury barometer would be.

And fill in all our numbers and see what happens. So, our density of water, seawater here, is 1.10. And we don't know what our height of seawater is, so we'll just leave that as H.

Our height of seawater. And then we know what our density of mercury is. So, we'll fill that in. And we know our mercury barometer reach.

We don't have to worry too much about our units here for the same reason we don't have to worry about it in M1V1 equals M2V2. Or, if you haven't seen that recently, sometimes they do C1V1 equals C2V2. Because it's a ratio. The units will all cancel out.

So, we're left with the height of the seawater. Just cancel.

And we end up with 908 centimeters. So, it's pretty big, right? So, why wouldn't we want to use a water barometer in our houses? Because if you, you know, likely if you've, I'll go back in a sec.

Likely if you've seen these anywhere, it was probably at like maybe your grandma's house or something. Where they used to, you know, it would be next to a thermometer, things like that. You want to know the thermometer, the atmospheric pressure. So, why not a water?

Why wouldn't we want to use water for it? Yeah, who wants to have a thermometer that's like that big sitting around, right? So, it's a density height thing. We can use mercury because it's so dense that it doesn't take up a lot of height. And so that was why it was picked. Why don't we tend to have them sitting around our house now?

Turns out mercury is kind of toxic. So, same reason that we don't really have mercury thermometers anymore.

Alright, so now I'll start moving on to a little bit of definition things that we'll need to know for the chapter. What is an ideal gas? So, we talked about what a gas is. But what is an ideal gas? This is sort of a definition that we've made up in order to be able to do a bunch of calculations.

And is a relatively good approximation for some of the gases. Sometimes it breaks down and we'll talk about those examples. But for a lot of the gases, the ideal gas, or calling it an ideal gas or approximating it using the ideal gas is pretty close. So, if you have an ideal gas or something that acts like an ideal gas, the molecules are going to move completely randomly.

So, that means they don't interact. So, if you have two molecules and they come close to each other, if they're ideal gases or they're acting like ideal gases, they're not going to have much interaction with each other. They're just going to kind of whip by each other and keep going. They have no volume. So, now if you think about an atom, we can agree that the atom has volume, right?

Well, for the sake of ideal gases, we're going to pretend that's not a thing, that they don't have volume. And of course, this is sometimes more true than others, right? Something like helium is going to be a lot smaller than something like nitrogen. So, you would expect helium to be a bit more ideal than nitrogen. But, it's a good approximation.

All collisions are elastic. What does elastic collision mean? It means they don't lose any energy. So, the sort of technical term here is that they don't, there's a complete conservation of energy. So, if two things bounce into each other with a certain amount of energy, they're going to fly off with the exact same amount of energy.

Now, maybe one that was going slower is now going to move faster, or one that was moving faster is now going to move slower. You can kind of think of it like billiard balls, only of course with pool balls, it eventually stops because of friction and it's not completely elastic. But it's a good kind of visual, if it helps.

So, a lot of your gases are going to be able to be treated as ideal, and then a lot of the gases are only going to be able to be treated as ideal in certain situations. So, it's going to work really well at low pressures. And it's going to work really well at high temperatures. So, let's think about why that is, because this is hard to remember if you don't think about why it is.

And I'd rather you understand it than memorize it. Low pressures. So, at low pressures, is the space between two molecules going to be high or really small? It's going to be really at low pressure.

It's going to be really high, right? At low pressure, you're giving them lots and lots of room to move around. So, you know, let's say we take out all the seats here. We don't want you guys to be a solid anymore. We take out all the seats, and I have all of you in here. That's pretty high pressure, right? Well, we'll pretend some of you guys are in, like, competing sororities and fraternities, too.

There's a lot of pressure. Now, I take three-quarters of you and I say, okay, go away. We've lowered the pressure now, right? So, is there going to be more room between those people or less room? More room. So, are they going to interact as much? No, they're not going to interact as much. It's because they're going to be more spaced out. We'll give them blindfolds and tell them to wander aimlessly.

So, they're not going to interact. And so, because of that, they're going to be more ideal. They're going to be more like an ideal gas. Now, if instead we just put tons and tons and tons of people in here, and our pressure goes up, that's like mimicking our pressure going up, now they're going to interact a lot. Well, that means that they're not acting like an ideal gas, okay?

So, this one has to do with how much you're going to be interacting with each other. High temperatures? We may have to leave that one a little bit toward the end, but I'm going to go ahead and explain it here anyways. So, at high temperatures, does anyone remember, know, what do molecules do at high temperatures? Are they faster or slower?

You do all remember, yay. Okay, faster. So, if now they're really, really fast, and they're bumping into things, their collisions are, let's actually reverse that, at low temperatures. So, at low temperatures, they're going to be doing what? Going really, really slow. Now, let's say that, you know, some of these people are friends,

and they're talking to each other. If I tell them they all have to run around really, really fast, or they have to run around really, really slow, where are they going to be able to talk to their friends more? They're going slow, right? If two people are just kind of walking by each other, okay, well they can talk, they can talk, they can talk. If they're racing by each other, they're not going to be talking much. So, this has to do with how much you can interact to.

If they're going slower, if there's an attraction between two molecules, they're going to be able to interact a little bit more. So, all of this is, how do we minimize interactions? So, let's do some talking about what's going to happen

if we change different components of a system. So, there's, I think I've shown you one of these before. There's a great website, and there's a lot of these on here. If you're someone who really likes learning by, like, playing around with things, go visit this website and just, you know, play. It's fun. So, I've shown you this, I think with the photoelectric effect,

I think it was the last time I showed this to you. So, let's say we have a container, and we have lots of different things we can change. We can change temperature, we can change the amount of gas we have, we can change volume, we can change all sorts of things. We can change even the size of the species. So, let's say we put some gas in here.

That was maybe a little more than I wanted. Luckily, we can let it go, too. Okay. So, we have some gas in here. Now, let's kind of base this all on what's going to happen to the pressure

if we change different things. So, let's say we make the volume smaller. What do you think is going to happen to the pressure? It's going to get bigger. And we can see this here. Definitely gets bigger, right? Now, what do you think, let's move this back out. What do you think would happen based on what we just talked about on the last slide?

If we increase temperature, what happens to the speed of molecules? It's faster. And so, what do you think that's going to do to the pressure? It's going to go up, right? They're going to all have a little bit more energy. So, we can do this. We can raise the temperature. Watch the thermometer climb.

We can watch the pressure climb. I'll stop it now or it'll burst. Put some ice on it. Okay, so if we decrease volume, what happened to our pressure? It went up, right? Because we were squishing the molecules together.

We increased our temperature, what happened to our pressure? It went up because now they're moving around faster. Now, what happens if we just add more molecules? What's going to happen to our pressure? It's going to go up, too. And it may burst.

So, those are sort of the things we're going to go through and talk about in a little bit more detail now. But most of you were able to pretty much guess what was going to happen before it happened, right? So, that's good. You already know some of this stuff. So, when we put it into equation form, that's really all we're doing. We're just taking what you already kind of know and we're putting it into equation form.

Go and play around with this a little bit, though. It is kind of fun. Okay, now these that I'm going to be talking about have names associated with them. Perhaps I should care more that you can associate the name with the equation, but I don't.

I want you to know the equation. I want you to be able to use it. I want you to be able to make graphs of them and I want you to be able to explain them. And four years from now, if I see you walking down the street and I say, Hey, Boyle's Law, go. I want you to be able to say, it has something to do with gases.

And then give me a lecture on gases. Okay, maybe the last one is a little optimistic, but hey. I want you to know that I have something to do with gases. I should be able to ask you to list the different gas laws and you can list the names. But if you can't associate them, I don't necessarily care too much.

Okay, so the first one we're going to talk about, though, is Boyle's Law. Now, you're also going to notice, you know, normally I intersperse examples. I'm going to wait to do examples until the end because you can do all of these using the very end combined law. And so I think that's almost a little bit better to teach you than using individual laws. So I'm going to hold all examples until the end of this section.

Okay, so Boyle's Law. We have pressure and volume. So this was, you know, equivalent to me squishing the box a little bit. If you increase the volume, pressure decreases. So we sort of did this in the opposite manner, right? We had this box with all the molecules floating around and then we took and we made the box smaller.

And when we made the box smaller, what happened to the pressure? It increased because you were squishing all the molecules together, right? It's like now I put everybody, you know, free wandering around with blindfolds and earplugs in their, you know, ears. And you're wandering around in the room and now I start bringing the walls in. Right? That's going to increase the pressure. Everyone's going to be a little bit more squished.

They're going to be running into the walls more. And that's increasing pressure. So this just states the reverse. If you increase the volume, now the walls would be expanding out and everyone can move around a little bit more. Everyone's hitting the walls a little less. That's decreasing the pressure. This is true when you have gaps in temperature held constant.

For all of these laws, in order to sort of define, like say, when you do this, this happens. We have to hold everything else constant. Otherwise, whatever's changing there could change some things. So in this case, this is true if you hold moles of gas in temperature constant.

So, now with all of these, we want to see what the graphs look like. And we want to see sort of if what would happen as we decrease temp- or excuse me, as we decrease volume, what would happen to pressure. So we'll look at that in a minute. So here we have pressure versus volume and pressure versus 1 over volume.

So you have this sort of decay here, this 1 over x shape, if you remember back to your Algebra 2 days where you had to recognize shapes of graphs. And this is because as your volume increases, your pressure decreases. Now, it's a little bit easier to see if we actually graph this in a linear fashion.

We say, okay, well, we have pressure here, we have volume here, or 1 over volume here, and we can make a linear graph this way. From an experimental standpoint, a lab standpoint, this is a much easier graph to work with. Why? Well, we can come up with the equation for this line, and then we can say, well, for this system at any given volume, what's the pressure?

And you can just find it. So, these are the sorts of graphs I want you to know how to recognize, see, sketch, things of that sort. So, our next one now that we're going to talk about is relating volume and temperature.

So, this comes into play in lots of different places where you have cold weather, actually. So, occasionally you'll see this also called Gay-Lussac's Law. You can kind of interchange the two. So, this one says as volume increases, temperature increases. And as volume decreases, temperature decreases.

So, you can see this one fairly easily in real life. Has anyone ever stuck a balloon in the freezer? Okay, maybe that's not the most normal thing to do as a kid, but you know, I liked chemistry. We don't have time to deal with freezers here today, though.

So, we're just going to use liquid nitrogen. So, I don't think I've ever brought liquid nitrogen into this class. So, what liquid nitrogen is is exactly what it says. But liquid nitrogen is very, very cold. And so, you have to get it very, very cold in order to make it liquid.

So, now we've made our balloon cold, and it's shrunk. And now it's warming up, so it's getting bigger. It's also very, very cold still. And maybe overdone- oh no, there it goes. I thought I might have overdone the coldness, but- And if we let it sit for long enough, it'll go back to its original shape, assuming the rubber didn't do anything bad, but it's fine.

And you can just do it over and over again, right? It's not like we lost molecules. This is my- you know, you saw me stick it in, you saw me pull it back out. I didn't, you know, magically switch balloons or anything like that. I can have someone come up and check to make sure, you know, I'm not doing a magic trick here.

Mostly, I have no motivation to lie to you, so. So, this is how you can remember this one, right? You stick a balloon in the freezer, or you're impatient like I am, and you stick it in liquid nitrogen. It shrinks. And it can only make it so small because this isn't a perfect system, and so the balloon- I'm worried about it breaking.

And as it heats up, it gets bigger. And again, why is this? What's happening to the molecules as we heat them up? Yeah, the temperature, or the speed is increasing. So, as you increase the temperature, you increase the speed, and it makes more pressure, or more volume. Excuse me. So, we're assuming that this is a model to say it's basically constant pressure, because remember, we have to keep the other things constant, right?

So, what is about the general pressure of this? Atmospheric pressure, right? So, a balloon works good for a constant pressure situation, because you can say, well, okay, it's basically atmospheric pressure.

Sure, the rubber is going to make a little bit of a difference, but for the most part, it's just kind of atmospheric. So, places that this comes into play in sort of real life. It's not quite as big of an issue here, because you don't have a lot of weather.

But, if you live someplace like Alaska, and you fill your tires in the middle of winter when it's like negative 20 degrees, and then summertime comes, what happens to your tires? Yeah, the pressure, or the volume is going to try to expand. And, again, this isn't, real life doesn't tend to be a great model for these things individually, because it's hard to hold this constant.

But, eventually, you'll increase your pressure so much that your volume can't increase, and it'll blow. This is the little bit better way of modeling it. Has anyone ever gone camping and slept on an air mattress? Yeah. Well, either the rest of you are hardcore campers, or you should try it sometime. It's fun.

I like air mattresses when I camp, because, you know, the ground's hard. So, what happens is if you fill it in the middle of the day, especially in the summer, you know, you fill it up, you're ready to go to bed, you go to bed, and then you wake up at 2 a.m. on the ground. And, while this has happened because there's a hole in the air mattress, a lot of times it's really just because it got cold.

So, now you're cold and sleeping on the ground. That's when camping becomes not quite as much fun. So, the lesson to be learned here is you set up your tent first, and then you don't set up the air mattress until it's already started dropping in temperature. Okay. Also, the, you know, actual important lesson, that volume and tent temperature are proportional, that's good to learn, too.

Okay. So, this is that same picture that was up for the other one. You guys have a similar picture in your book. This one comes from the Chang book that we used in previous years. So, this just kind of goes through and shows you the exact same idea.

That if you're holding moles, R, which we haven't really talked about yet, and we'll just call that a constant, and then pressure constant, what's going to happen as you change the temperatures? And then, the reverse of that, too, which is pressure, which we sort of talked about with the tires, right? If you increase temperature, what do you think is going to happen to pressure if the volume isn't changing much?

That's going to increase, too. So, the pressure and volume are kind of closely related in this one in the sense that it's, in real life examples, it's hard to actually hold them both, or one of them completely constant. So, keep this in mind when you're looking at things. If you increase the temperature, you're going to either increase the pressure or the volume, assuming everything else is held constant.

So, let's look at a graph of this. I heard it go back, so we'll look at this one more time. So, as you raise temperature, you can increase your volume.

Or, if you're holding your volume constant, if you're refusing to let this move, you can increase your pressure. If you lower your temperature, you're decreasing your volume. Or, if you're holding your volume constant and instead allowing the pressure to change, your pressure is going to decrease. Okay? So, very similar.

Okay, so now let's look at a graph of this one. Now, this would be the same if we put volume over here. Or, excuse me, pressure over here. Whether we hold volume constant or whether we hold pressure constant, it turns out to be the same graph. And these are linear. So, if you know how much for an ideal gas, you know how much you're increasing the temperature by, you know how much you're increasing the volume by.

And, you know, vice versa. Okay. Now, let's look at this one. This one's a little bit more complicated, right? So, now we have four different lines. And what's the big difference here? Yeah, your pressures, right? So, this is an ideal gas graph of Charles' law, but at different pressures.

Because we know pressure affects this, right? What does pressure do to volume? If you increase the pressure, it increases the volume, too. So, what happens here is that if you take this, it changes what's happening here. So, this just shows you, for all different pressures, what's happening to your volume.

Okay? So, if you had four atmospheres, you would have it here, two here, one here, .5 here. Alright? So, that's all that graph is going through. Okay. Next one.

Avogadro's law. So, what is Avogadro sort of known for? Avogadro's number, which has to do with what? Number of atoms, right? Number of atoms in a mole. So, what do we think this one's going to have to do with? Moles. So, let's say we have a balloon. Maybe.

Alright, we have a balloon. So, we can make it bigger a couple different ways. We already talked about one, right? Changing the temperature, so I could put this in someplace warmer. What's an easier way for our setup at the moment? Okay, it's bigger now. So, what does that mean?

What did I do to make it larger? Awesome. I increased the number of moles. I made it bigger by putting more molecules in it, right? So, this one says that volume and temperature and, you know, similarly volume and pressure are going to be related to each other and that they're going to be proportional, right? The more moles I put in, the larger the balloon gets.

And again, this kind of, you can kind of model this as a constant volume system. So, this one relates moles and volume. As your number of moles increases, so does your volume. So, if I want to make this smaller, what do I do?

Now it's really small, but I could have just let it go a little bit. I kind of slipped. Alright, so this is true when your pressure and your temperature is held constant, right? Because if I had changed my temperature a bit, then all sorts of other things are happening that we have to calculate in.

So, for all of these, we're talking about a couple of different, we're only relating two variables at once. If you bring in a third or a fourth variable, you can't necessarily say this. Sure, if you increase the number of moles, that's going to add to making it larger, but what if I then make it really cold? What's going to happen? Well, it depends on the ratio, right?

It depends on how much extra I put in versus how the cold is making it happen. Okay. So, all of these then involve graphs, right? We have to be able to graph all of these in sort of a similar fashion to each other. Where this one would, I didn't graph this one, this one would just be linear again.

It would look the same as the Charles Law graph. So, we have two people talking, and, you know, I don't know if you've ever read XKCD. If you're in the sciences and math, you really probably should as just part of life. So, we have two of them. You can, this guy and girl, I think we should give it another shot.

She says, we should break up and I can prove it. She graphs this, our relationship, and it's obviously been going downhill. And he says, huh, maybe you're right. She says, I knew data would convince you. No, I just think I can do better than this one who doesn't label our axes. I mean, it's kind of classic XKCD humor.

Don't forget to label your axes, right? If I tell you to graph something, if I tell you to graph pressure versus volume, and you don't put pressure and volume, maybe I thought you had it flip-flopped. Maybe I thought temperature was down here and pressure was up here. So, make sure when, if I ask you to draw these graphs, you label your axes properly, okay?

You need to make sure that you put temperature and pressure, temperature and volume, or whatever it is that I'm asking for. Otherwise, I won't know that you actually knew to put one of them on the bottom and one of them on the top or whichever. Okay, now if we come back here a minute,

oh, we could actually go through and calculate all this if we wanted. We could actually go through and say, change the temperature by a set amount and calculate the new pressure. We could say, okay, well, we want this to be exactly 600

and see what would happen. And we could say, okay, well, we know how many molecules are in here and we could put exactly double in and we could calculate the difference. We could do all three, right? We haven't really talked about how to do that in detail, but we could. We could say that, okay, well, I'm going to increase the pressure

by adding more gases, but then let's say I want to offset that. How would I offset that using temperature? Make it colder. Make it colder. So I could remove heat by doing this. And you could get it to go back to the exact same pressure. And we kind of guessed all this ahead of time.

You guys were really good about guessing it all ahead of time, so I won't walk through it in too much detail again. But, you know, you can walk through there if you didn't quite guess it ahead of time and play around with it a bit. Okay. Now, though, we're going to take, in the last few minutes, and we're going to take all of what we just learned and we're going to combine it together. And then we're going to do a bunch of examples.

I just, it's, to me, you can do all of the examples from the ideal gas law and something we're going to derive off the ideal gas law, so I think it's a little bit better to teach it after we've learned everything. Okay. So this is going to be a combination of all of the things that we've learned. So up until now, we've said you can relate two of them at a time, and as one increases, the other one decreases,

and it's proportional or inversely proportional, right? But we haven't really talked about what happens if we want to change lots of things. What happens if I want to add more moles, but then I want to cool it down? Or I want to, you know, increase the pressure, but also increase the volume.

And the ideal gas law will allow us to do this. So what this is basically doing is putting all of the things together into one form of the equation. Now there's this r that we've sort of shown up in some of our figures that we've been talking about and we haven't really talked about. This is called the ideal gas constant, and it's just a constant that relates all of these together.

So if you take all of the equations and you combine them, you get this. And if you go through and, you know, cancel everything out, you can go through and say, well, now I can see that pressure is equal to one over volume if all of these are held constant.

Or volume is proportional to temperature if pressure moles, and of course r is always a constant, are held constant. This incorporates everything that we've just talked about into one equation, which is really nice. This is what r is equal to. You may have r memorized slightly differently.

Anyone else have it memorized as something different? 8.31, does that sound familiar? That one has joules in it. So that's also r. But that one has to do with energy. So as far as which one to use, because you'll have both of them on the exam, how do you know in this one to pick this? Do you memorize it?

No. Yeah, no is usually a good answer to that when it comes to me. How do you know? Let's look at this a second. Well, what is pressure in? Atmospheres. What is volume in? It's an SI unit for volume. Liters. What about temperature? Kelvin. So are you going to want to use something that looks like this for units?

Or are you going to want to use something that has an energy unit in it? Yeah, this doesn't have any sort of energy going on. So we're going to use this one. Later on in the chapter when we get into kinetic molecular theory, then we'll start using the energy. We kind of already did that. And this is actually kind of what comes off this.

Now, as we go on to problems, there's going to be ones where you have to really worry about units and there's going to be ones where you don't really have to worry about units. If you need to worry about them, use the ideal gas constant. And I have the units written on the exam to help you remember what to use. It's got to be liters, it's got to be atmospheres, and it's got to be Kelvin.

Always, always, always, even on the ones where I tell you you don't have to worry about switching units around too much, temperature has to be in Kelvin. If you see a temperature written down in Celsius, just put plus 273 next to it. Like you're reading through a problem and you see, ok, 62.4 written down, write a little plus 273 there so that when you fill it into equation you don't forget to do it.

When these get kind of long, I'll start listing out what we know and what we're trying to figure out. Just put plus 273 next to every single temperature that's listed in Celsius so you don't forget. It's one of the most commonly missed things on an exam and on a short answer question, that's all your points, right? So don't, just be really careful about that.

Ok, let's do one of these. So, we have a general idea of what happens when we change things, but now we can also calculate the results of one thing based on all the other things that we measure.

So, if we have this, sulfur hexafluoride is a colorless, odorless, very unreactive gas. Calculate the pressure exerted by 1.82 moles in a steel vessel of volume 5.43 at 69.5 degrees C. Ok, so if we look at our PV equals and RT, let's just write in a plus 273 here so that we don't forget,

and what do we want to solve for? Well, we're looking for pressure. So we're not changing anything here, we're not going from one set to another set,

so we can just solve for pressure. Now, we can just fill everything in, making sure all of our units are ok, so we have 1.82 moles. We fill in R, making sure to fill in the right one, and we can fill in temperature.

I'll admit, I normally fill it into my calculator just like this.

If you do that, you have to watch out for parentheses though. It may not be a bad idea to fill in the, you know, added number here. And do it in one step, or two steps. And then we solve, and we get this.

Ok, so that's how you do an ideal gas law that doesn't change around, where you're not changing things, you're not going back and forth. Ok, so let's see. We have two minutes.

So see if you can do this in two minutes, and I'll give you the answer. You guys see if you can beat me to it. You're going to do it exactly the same, only you're solving for what now? Volume.

I would suggest rearranging the equation first. Usually for these, that's your best bet, especially when they get harder.

Down to one minute, so I'll get you started on the equation.

Looks like you're on the calculator point, so I'll fill some things in for you.

Alright, do we have answers? What do we think? Do it price is right style. What's the first digit? We get 9.28 liters. Ok, so that's how you go about doing those.

Next time what we'll do is we'll show you ways to calculate when things are changing. So when we're going from one thing, and then one set of conditions, we change the set of conditions and what we get for that.