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balancing chemical equations is one of those concepts in chemistry that often confuses people but I think if we will see if we work 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 and with 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 so for example right over here on the left-hand side how many aluminum's do we have well on the left-hand side we have one aluminum how many do we have on the right-hand side on the right-hand side we have two aluminum's 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 aluminum's 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 but 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 some we can't just have a miraculously an oxygen atom appear for out of out of nowhere so we have to balance the number of aluminum's 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 say okay if I've got two aluminum's here and I have one aluminum here well why don't I just double the number of aluminum's right over here so I could just write a to it in front of it so now this says two aluminum's so I no longer have one aluminum here I now have two aluminum's and so it looks like the aluminum's 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 one and a half so I could multiply by one point five and if I multiply one point five times two well 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 is that we don't like writing one-and-a-half 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 this makes it very similar to what you did in algebra an algebraic equation is we just can multiply both sides by the same number that gets rid of having this fraction or this decimal here so if we multiply 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 set of two aluminum atoms let me have for 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 one point five 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 there's implicitly a one let me just 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 do that same color two times two is four that's not the same color two times two is four 1.5 times 2 is 3 and then one times two 1 times 2 is 2 and now you can verify how many aluminum's do we have on each side well I have 4 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

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