So balance the following equation. We have calcium, oxygen, and phosphorous involved in this equation. And so, whenever I want to balance a equation, the first thing I'm actually going to do is make a list of all the elements present. So that I can then tally how many I have on the reactant side and the product side to aid me in the balancing process. So I see on the left side I have 1 calcium, I have 11 oxygens, because I have 1 oxygen here and 10 there for a total of 11. And I have 4 phosphorous atoms. On the right side of the equation I have 3 calciums, I have 2 phosphorus, because I have 2 times 1 for 2. And for oxygen I have 8 because I have 2 phosphates, and each phosphate has 4 oxygens for a total of 8. Now, in order to balance this, I have to make sure that everything has the same number of atoms on the, both sides of the equation. One thing I notice is that oxygen is present in two of my reactants. And so I'm actually going to save that one for last in hopes that balancing the calcium and the phosphorus will actually balance out the oxygen. So the first thing I'm going to do is add in my coefficient for calcium because I want to balance that. So I need a three in front of the calcium oxide, when I do that changes the calcium from one on the left to three on the left. It also changes my oxygens. Now I have 3 oxygens and 10 oxygens, for a total of 13 oxygens. So now my calcium is balanced, my oxygen is still not balanced, and my phosphorus is not balanced. But I see that I have 4 phosphorus on the left and 2 phosphorous on the right so I'm going to have to add in the coefficient. I'm going to add in a 2 on the right side. Now, I have 6 calciums, because I have 2 times 3. Then I look and say, I've got, well, 2 phosphorous in 1 unit of calcium phosphate, but I have 2 units so that's going to give me 4 phosphorus atoms. And it's also going to give 16 oxygen atoms because I have 2 times 4 is 8 times 2 is 16. So, in balancing the phosphorus, I actually got the calcium out of balance. So now I need to go back and change that coefficient to a 6. And when I do, now I have 6 calcium, and I can recount my oxygens. I have 6 oxygens of the calcium oxide, and 10 oxygens in the P4O10, which gives me a total of 16. So it appears that everything is balanced, but I'm going to go back and check everything just to make sure. So on the left, I have 6 calciums, on the right I have 2 times 3 so 6 calciums. On the left I have 6 plus 10 oxygens, and on the right I have 2 times 4 is 8 times 2 is 16 oxygens. And then I have 4 phosphorous and 2 times 1 times 2 is 4 phosphorous on the right. So it appears that, with these coefficients, I have a balanced chemical equation. These are the lowest set of coefficients I can have because my coefficients all can't be divided by any number and still get whole integers for the coefficients.
