 Okay, the next couple of videos, a lot of students typically find these to be among the most difficult in the course, so if you find this difficult, you know, you're not alone. What we're going to talk about is using balanced equations. So again, the analogy, and this is a pretty good analogy to recipes is probably most appropriate. If things aren't making sense, maybe try to fall back on the idea of equations being very much like recipes that have to have the correct amount of ingredients and the correct amount of servings that you can make. So before we get started, I want to talk about maybe not how to read an equation out loud, but how to think about an equation. So this is a balanced equation. There's a two here. There's a one implied to be here, but we don't have to write it. There's a two there. I think this is the first equation that we actually just balanced. A lot of times students will look at this and they'll say, well, this means two H2 molecules needs to be mixed with one O2 molecule molecule, and that makes two H2O molecules. And I think that's even how I described it in the previous videos. That's perfectly fine, but it doesn't have to be two molecules, one molecule, two molecules. This could mean two dozen H2 molecules, then this would mean one dozen, and this would mean two dozen again. This could mean two million. This would mean one million, two million. You can kind of see where I'm going with this. For the types of problems that we're going to do in the next couple of videos, it's best to actually think of these numbers as meaning moles. So I want you to sort of get accustomed to looking at these types of equations and thinking two moles, one mole, two moles, or whatever the numbers happen to be in the equation. So if we were going to be really fancy and formal about this, if we were going to sort of say this out loud or think about it, we would say two moles of molecular hydrogen, that's H2, react with one mole of molecular oxygen, the one mole corresponds to that one, to produce two moles of water. So that's kind of how I want you to think of these numbers that are in front of the formulas in our balanced equation. Think of them as moles. So you can pause and think about this, but you know, tell me how you would think about this one in your head or say it out loud. And un-pausing, again, there are a lot of different variations of answers to this, so don't take what I say as the absolute perfect way to say this, but there's a one implied here. So what I would say is one mole of solid carbon, because that S means solid, mixes with two moles of H2 and produces one mole of CH4 gas. And again, remember, if there's no number in front of the formula, the number one is implied, which is where this one and that one, they're the same thing. So again, I'm just trying to sort of get you in the right frame of mind and get you accustomed to looking at these numbers and thinking moles. So let's keep going. Here's a question. I think it's from an old version of your textbook. Here's the relevant equation. However, the relevant equation is not balanced, so I would at least, before we go rampaging off to dealing with this question. I want you to balance this equation, so it's more practice. You can pause the video and then I'll go through practicing it. And then when we're done with that, we will tackle the actual problem. Okay, so let's balance this equation. We're going to make our traditional table with three columns. We're going to start with carbon. How many carbons do we have? Let's actually, let's write the ones in just for clarity at the beginning. They're all ones. How many carbons on the left? Well, we do one times three. That's three. How many carbons on the right? Well, there's no number, there's no subscript to the right of the carbon here, so the number one is implied, one times one is one. Not balanced. So, before we go, try to fix anything else, or before we go looking for any more problems, we need to fix this. We need to turn this one into a three. We're only allowed to change the numbers in front of the formulas. This is the only one that we can change that's going to adjust the number of carbons, so this is the one we need to change. We should triple it, because if we triple it, then the number of carbons on the right side is also three. So, we have balanced our equation by putting a three there. Next atom is hydrogen. Hydrogen, how many hydrogens on the left? Well, it's one times eight, so eight hydrogens. How many on the right? It's one times two. Only two hydrogens. Again, we've got a slight problem. The easiest way to fix this is to mess with this number, because if we mess with that number, we can boost the number of H's on the right side, so if we change this to a four, four times two is also going to equal eight, so we have eight H's on the left, we have eight hydrogens on the right as well. So, moving right along, right, this is maybe a tiny bit more complicated than previous ones that we have practiced. The only other element we have left is O for oxygen. How many on the left? One times two is two. Now here it's a little more complicated. On the right side, there are, oxygens are in two different molecules. So how many oxygens in this guy over here? Well, three times two. Six oxygens. How many oxygens here? There's a one implied to the right of that oxygen, so it's four times one is four. So a total of six oxygens here, four oxygens there, that makes a total of ten oxygens on the right side. But we only have two oxygens on the left side, so not balanced again. And the only way that we can boost the side that doesn't have enough is to start messing with this number. If we change it, if we quintuple it, if we change it to a five from a one, then five times two is also going to be ten oxygens. So now we're balanced. It took a little while, maybe slightly more problematic than the other ones that we've done in previous videos, but we are sort of good to go to address the question, which we haven't even talked about yet. This is the balanced equation, so let's get rid of all the noise so that we have some room to deal with. Here's our equation. Think of this as the correct recipe. If you want to think of these numbers as moles, this is one mole of CH3, has to be mixed with five moles of O2, and that can make three moles of CO2, and it can also make four moles of water. So let's now look at the question. Propane gas, don't worry about this word, they're telling you that's C3H8. So this thing reacts with O2, here's our O2, to produce carbon dioxide, that's the carbon dioxide that's produced because there's an arrow here, produce carbon dioxide, water, there's our water. And don't worry so much about the energy, I just think I was trying to copy the question faithfully. Don't worry about the energy, it's not going to come up in this problem. So propane gas mixes with oxygen to produce carbon dioxide and water. And the question is, how many moles of carbon dioxide can be made with 2.25 moles of C3H8? So if this seems confusing to you, again maybe the best way to think about it is as a recipe. So we're going to sort of abandon this equation for a minute, for a couple of minutes. We're going to talk about a more realistic recipe. Making pancakes. Let's see, this is just pretend I have no idea if this is really true. Let's say 1 cup pancake mix plus 2 eggs makes 5 pancakes, I don't know if that's really true but let's pretend. If that's true, 2 cups pancake mix plus 4 eggs makes how many pancakes? You can pause and think about this or maybe you can do it in your head. Unpausing, if our original recipe is correct then our second recipe can make 10 pancakes. The reasoning is that we doubled the amount of pancake mix. We also doubled the amount of eggs, so it stands to reason that we can make twice as many pancakes. So the idea is if the ingredients go up by a certain proportion then the products, the stuff that you make also goes up by the same proportion. So that principle is going to apply in this equation as well. So what we are saying is 1 mole of C3H8 can make 3 moles of CO2. That 1 is coming from here and this 3 is coming from here. It's basically coming from the balanced equation. The only way you can know this is if the amounts of everything are balanced. I say can here because we're omitting some information. I'm basically saying 1 mole of C3H8 can make 3 moles of CO2 but that's only true if we have enough oxygen but I'm saying can so we're assuming that we have enough oxygen. So if I have 1 mole of C3H8 I can, under the right conditions, make 3 moles of CO2. The question says how many moles of CO2, so question mark moles of CO2, can we make not with 1 mole of C3H8, which is in our equation, but 2.25 moles. So 2.25 moles of C3H8 can make, I don't know, how many moles of CO2. But the idea to solving this is very similar to the pancake question except it's not quite as nice of a number. In the pancake question I just doubled the amount of the ingredients and so we had twice as many pancakes. Here the amount of C3H8 goes up by 2.25 fold. So whatever the question mark is it also has to go up by 2.25 fold. So in other words the answer to the question mark is going to be 3 times 2.25 because this number has to get 2.25 times bigger just because this number got 2.25 times bigger. And if you do that out it's going to be 6.75 moles of CO2 can be made from 2.25 moles of C3H8. Now if you like that type of reasoning and sort of writing these things out as sentences and you can see that this to figure out the question mark we have to multiply 3 times 2.25 you are welcome to do it that way. There's a slightly different way that I tend to do this. I don't know. There are other ways too. So if you have an alternate way of solving this question you're more than welcome to do it any way you want that is not cheating and that works. So here's the other way that I would do it. I would write these things, oops not that one, not the four, I would write this one and this one as a ratio. I would say one mole C3H8, I think I need to talk to Microsoft about fixing their pen. One mole of C3H8 can make 3 moles CO2. All I'm doing is writing this as a ratio and but then I say in my question I don't have one mole of C3H8, I have 2.25 moles. So I make an equal fraction over here except I stuff 2.25 moles of C3H8 in the place where the one mole would have gone and then I call this X moles of CO2. And then to figure out what X is we cross multiply. So let's do it all out in all its ugly glory. And doing this times this, so one mole C3H8 times X moles CO2 equals the other two things multiplied together three moles CO2 times 2.25 moles C3H8. And we want to get this X all by itself which means we want to get rid of this one mole C3H8. To do that we have to divide this side by one mole C3H8 which means all of those things will reduce down to one. But if we do that to the left side we also have to do it to the right to keep everything equal. So we're going to divide this side by one mole C3H8. And what you will see is moles of C3H8 cancel. The only unit we're left with is moles of CO2 on the left. Only unit we're left with on the right is moles of CO2. And what is the question asking, how many moles of CO2? So we have the correct units and we're going to do three times 2.25 divided by one. And we already did that, three times 2.25 divided by one is 6.75 moles of CO2. This type of problem that we just did is sometimes called a mole-to-mole problem because we're taking number of moles in one part of an equation and relating it to number of moles in a different part of the equation. So that's why it's called a mole-to-mole problem. There are about six trillion different types of these problems. You can practice them in your book, you can practice them online, and you're going to have to be able to do at least one type of these problems on an upcoming exam and probably one on the final. This is for the chemistry 101 students, this is probably one of the more difficult problems in the course. There are two more that are coming up that are even more difficult but we're sort of nearing the peak. So that is it for introduction of mole-to-mole problems. The next video is going to deal with a slightly more complicated type of problem called a mole-to-gram problem.