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- Balancing chemical equations is one of those concepts in chemistry that often confuses people. But I think we'll see that if we work through this carefully and methodically, and we also appreciate the art of balancing chemical equations, that it's actually not too bad. So first of all, what is a chemical equation? Well this is a chemical equation right over here. It's describing a reaction. So if I take an atom of aluminum and I add it to a dioxygen molecule, so a molecule that has two oxygens with it, under the appropriate conditions they will react to form aluminum oxide. And the aluminum oxide molecule has two aluminum atoms and three oxygen atoms. And so you might say, "Okay, well what's "the balancing business all about? "I have a chemical reaction. "What do I have to balance?" Well if you look carefully, you might notice that you don't have the same number of each atom on both sides. For example, right over here on the left-hand side, how many aluminums do we have? Well on the left-hand side, we have one aluminum. How many do we have on the right-hand side? Well on the right-hand side, we have two aluminums. And so aluminum just can't appear out of thin air by virtue of some magical reaction. You have to have the same amount of aluminums on both sides, and the same thing is true for the oxygens. Over here on the left-hand side, we have two oxygens. They form one dioxygen molecule that has two oxygen atoms. And then over here in the aluminum oxide molecule, we have three. We have three oxygen atoms. So once again, we can't just have miraculously an oxygen atom appear out of nowhere. So we have to balance the number of aluminums on both sides, this number and this number should be the same, and we have to balance the number of oxygens, this number and that number should be the same. So how do we do that? Well one thing might be to say, "Okay, if I've got "two aluminums here and I have one aluminum here, "well why don't I just double the number "of aluminums right over here?" I could just write a two in front of it, so now this has two aluminums, so I no longer have one aluminum here. I now have two aluminums, and so it looks like the aluminums are balanced, and they are indeed balanced. But still we have an issue with the oxygens. Over here I have two oxygens. Over here I have three oxygens. So one thing that you might say is, "Okay, well how do I go from two to three? "I could multiply by 1.5." So I could multiply by 1.5, and if I multiply 1.5 times two, that's going to be three. So now I have three oxygen atoms on this side and three oxygen atoms on this side. But the convention is that we don't like writing "1.5 molecules." We don't like having this notion of a half molecule, which is kind of this bizarre notion. We want whole number molecules. So what can we do? Well, you can imagine that this makes it very similar to what you did in algebra, an algebraic equation. We just can multiply both sides by the same number that gets rid of having this fraction or this decimal here. So if we multiplied both sides by two, we're going to do that. This is going to be a four, this is going to be a three, this is going to be a two right over here. So let me do that. Let me multiply both sides by two. So instead of two aluminum atoms, let me have four aluminum... Actually, let me just write the chemical equation first in the form that it was before. So I had aluminum plus dioxygen, a molecule of two oxygens, yielding in the reaction -- these are the reactants, this is the product -- aluminum, aluminum, aluminum oxide. So what I'm saying here is to get rid of this 1.5, to turn it into a whole number, let's multiply all of these, all of the number of molecules by two. And here, there's implicitly a one... Let me do this in a different color. There is implicitly a one right over here. So let's multiply all of these by two. So two times two is... Let me do that same color. Two times two is four... That's not the same color. Two times two is four. 1.5 times two is three. And then one times two, one times two is two. And now you can verify how many aluminums do we have on each side? Well I have four aluminum atoms on the left-hand side, and how many do I have on the right-hand side? I have four aluminum atoms. How many oxygens do I have on the left-hand side? I have three molecules of dioxygen. Each molecule has two oxygen atoms, so I have six oxygens on the left, and I have two times three oxygens on the right, or I have six oxygens. So my chemical equation is now balanced.