 Just touch it like that, and then it goes. We only have 21 minutes, right? Well, we can only do it. We have to do it in less than 15 minutes. So we'll just go through these problems one by one. This one seems good enough for me. So this one is Boyle's Law. So if you want to memorize a bunch of formulas, like I say, this is a good one to memorize. Boyle's Law is Vi, let's do this one. Vi or V1, I and 1 are the same. I is the initial 1. 1 and 2 I use, but I think the book uses I and F. But V1, P1 equals V2, P2. And remember, I taught you guys that you can use that ideal gas law to get any of these laws. And I'll show you how to do that. So let's just do that really quick. So remember, PV equals nRT, and divide that by PV equals nRT. But this top one's going to be 1, 1, 1, R is constant T. 1, 1, 1, 1, R is constant. So since R is constant, we can already cancel that out. And then we're going to look at the problem. So the problem says gas occupies 10 liters at 1 atm of pressure. So V1 is 10 liters. Is everybody cool with that? 10.0. And P1 is 1.008. It asks, if you double the pressure to 2 atm, so P2 is going to be 2.0 atm. Let's give it 2.00. Let's do 3.0 atm like that. What is the new volume? So that's all you've got to do. So now we want to go look over here again. And we have to ask ourselves, did P change in this problem? Guys? Yeah. So we've got to leave that one there. Oh, sorry. It used to be 2 down here. You guys can tell me. So P changed, right? Did V change with V1 to V2? We're looking for V2, right? So did it change? Yeah, it changed, right? Because if it didn't change, then the problem would be easy, right? You just put 10 liters on it. That would be an easy chemistry class. We should do that one instead, right? So let's ask this question again. Did V change? Yeah. So we can't cancel that out, right? Because they're not the same number. Did the number of moles change? Did we add gas or take gas away from this problem? No, right? So the number of moles stayed the same. So if the number of moles was 2, right, we take 2 divided by 2, what does that do? It cancels that out, right? So N1 equals N2, effectively, so they cancel out. Did the temperature change in this problem? So T1 equals T2. Is everybody cool with that? So since T1 equals T2, we can cancel that out, right? So what does this equation break down to? It actually is P1 V1 divided by P2 V2 equals 1. Everybody cool with that? And then, if we want to, we can make it look like this, right? But we don't even have to do that, because all we want to do is look for V2, right? So this is the way I like to do problems, because I only have to memorize one thing, right? This one, PV equals NRT. But there's a lot of chemistry students that insist they have to memorize so many things, OK? So if you'd like to memorize things, you can memorize Boyle's Law, some guy who's long since dead. So maybe he'll be proud of you. I don't know if you memorized it or whatever. But I think it's easy to just break it down like this, OK? So what are we looking for? We're looking for V2, right? So where is that? It's down here, right? So let's just take that equation that we got, P1V1 over P2V2 equals 1, right? So we could do a couple of things. I think the easiest thing to do is just flip both of the sides over, OK? If I flip this over, what do I get? I get P2V2, right? Is everybody cool with that? And what's on the bottom? P1V1, right? What if I flip the other side over? What do I get? Just 1, because this is really 1 over 1, right? And then what I can do is multiply like that, right? So multiply both sides by P1V1. I'm going to erase this one. P1V1, right? And that's going to cancel that out with that. And what's my new equation? P2V2 equals P1V1. And then divide both sides by P2. I get this equation, right? P2 equals P1V1 over P2. Is that cool? No, no, I'm not done yet. We've got to solve the problem. So what's P1? Guys, 1 ATM or 1.00, I guess. You all saw that, though. What's V1? 10.0 liters, right? Divided by P2, what's that? 2.00 ATM. Are there any units that we can cancel out here? ATM will cancel. So that will leave us units of what? Letters, is that a volume unit? So that's cool, right? So that's what we're looking for. So all we've got to do is if you can't do this calculation in your head, take your calculator. And if you can, it's all right. You've all got a calculator, OK? So let's do it with our calculator. 1 times 10 divided by 2. So what do you get? What's 5? Is that it? 5.00, right? So we can do 6. Is everybody cool with that one? Are there any questions on that one? So this is going to be exactly like the problems on your test, OK? So again, for me, it's easy to do it this way, OK? Again, if you want to memorize all these formulas, we'll go through a bunch of them, OK? But you only really have to memorize one thing. Can I kill it? Any question? OK. Because I wanted to do getV2 on the top. So what I before, V2 was on the bottom. We'll do another one, OK? You can isolate it. Well, I mean, you've got to isolate the variable, right? So if I was using this one, I'd have to divide both sides by P2, right? To isolate that variable, V2. We'll do another one, OK? Let's do another one, so we kill it.