 Start recording. The first thing we'll do today is, well, I guess, the application of Avogadro's law. But like I said, I'm going to break it down with this pv equals nrt thing. So pv equals nrt is the ideal gas law. So this p stands for pressure, as you might imagine. b stands for volume, n stands for number of moles, and t stands for temperature. r is what's called the universal gas constant, and it's a constant. So it stays the same, no matter what problem it is. It's, in fact, 0.0821 liters atm over moles kelp. But it's something that'll be given to you so you don't have to memorize it. But anyways, whenever you're doing one of these gas law problems, I want you to write down pv equals nrt and then write little ones. Or if you like initial, you can write little i's below them. And then I want you to divide both sides by pv equals nrt and put little 2's below those, or f's, if you prefer that. Notice I didn't put anything below the r. Why is that? It's a constant. It doesn't change, right? So what am I going to do with it? I'm going to cancel it out, right? It's just like 2 divided by 2 equals what? 1, right? So anything divided by itself equals what? 1, right? So r divided by r equals 1. Yeah, very good. Everybody else can answer 2, you know? I know you guys know that stuff. So we just divide those out, OK? So those are all wrong. OK, so our equation now essentially is p1v1 over p2v2 equals n1t1 over n2t2. Is everybody cool with that? OK, so the next thing we're going to do now is look at our problem, OK? Our problem says if 5.5 moles of carbon monoxide occupy 20.6 liters, how many liters will 16.5 moles of carbon monoxide occupy at the same temperature and pressure, OK? So that problem is giving us a lot of information, right? Let's write down in numerical or mathematical terms what the problem is giving us. So can anybody tell me one of the things that the problem is giving us? So the initial number of moles it's saying, right? So it says if 5.5 moles of carbon monoxide occupy 20.6 liters, then 16.5 will occupy a common, right? So it's saying the initial moles is 5.5, right? So do you guys remember moles is n, OK? So let's just write that. And again, a lot of people like i. I like 1, so you know, I don't know why. But anyways, n equals n1 equals 5.50 moles. And you got to remember that 0 because it's significant. What else did it give us? Volume. Initial, right? It gave us the volume initial, right? 20.6. And it's kind of scoot over there, especially when you're tall and there's a little TV in the way. What else does it give us? Yeah, another mole. So what happens if I change the number of moles, right? That's what it's saying. So it's n2, like that, OK? And what was that? 16.5 moles. Does it give us anything else? No, but it asks us something, right? It says, how many liters, right? So it's asking us for what? V2, V2, that's what it's asking us for. But it also tells us something else, right? So yeah, it says that the pressure and temperature are the same, right? So that means they've stayed the same, right? So the pressure is, I don't know, two before. And two after, it's going to cancel out. So what does it mean? P1 equals P2, right? So we can cancel those out. Is that cool? Why don't it say temperature, too, right? We're doing all the gauges. Temperature remains the same, too, right? So T1 equals T2, right? So we can cancel those out, too. Is everybody cool with that? So now our equation breaks down to this, right? V1, V2 equals N1 over N2, right there. And we've got all that information, right? Except for V2. So all we gotta do is isolate that variable. You guys remember algebra, how to isolate the variable? We'll do it, okay? Let's do it together, okay? So the first thing I'm going to do, I like, if I zoom the denominator, I like to just flip the whole thing over, okay? So if I flip this side over, I gotta flip that side over, right? So my new equation is V2, V1 equals N2, N1. Is everybody okay with that? It's okay? Yeah, you can do that, right? Or you can do all of that if you want to, which we're about to do with V1, right? So is V2 isolated? Isolated being by itself? No, it's not. We gotta get V1 out of there, right? So how do we get V1 out of there? Multiply by V1, right? Both sides, because of course if you do the one side, you gotta do the other side, right? Cancel, cancel. And our new equation is V2 equals N2, V1 over N1. And do you have all this? Yep, plug each other, right? So, N2, V1, 20.6 liters divided by N1, 5.5. Cool thing about it, doing it this way, right? Is you can cancel out your units and you're gonna get units of liters, of course, right? And is liters good units per volume? Yes, it's great volume units. Okay, so all we gotta do is plug into our calculator now. So 16.5, okay. 20.6 divided by 5.5, yeah, and so what'd you guys get? 61.8. 61.8, and of course that's what the calculator gives you, but even if it gave you more digits than that, you would have to cut it to that because all of these have three signatures. Is everybody cool with that? Cool, so, and box your answer just so you can say, that's it, okay? So are there any questions on this? So the thing is, is actually what you find is this is Avogadro's law, here. And you can do all of these, Charles law, all of these, from just by canceling out the things that are the same, okay, so all you gotta remember is this Pv equals Nrt. We'll do a lot of these today and I'll prove to you that's the case, okay? Really cool.