 In this video I'm going to show you how to balance a chemical equation on the example of a combustion reaction. On a combustion reaction you have some type of fuel, in this case a hydrocarbon, that is reacting with oxygen to form carbon dioxide and water. Now when we observe the reaction we can often tell what are the compounds involved. C5H12, O2, CO2 and H2O. But we cannot tell how many molecules of C5H2 will react with how many oxygen to create how many carbon dioxide to create how many water molecules. So one job that you will often have to do is to try to balance the equation so it works out. Remember in a chemical reaction the number of atoms on the left of each element have to be equal to the number of atoms of each element on the right. So how do we find these numbers here? There are several ways. I'm going to present you two approaches. The first one, if it's very simple, you can simply try out different combinations. So what I like to do is the following. I like to write down how many atoms of carbon I have on the left and on the right. How much hydrogen I have on the left and on the right. And how much oxygen I have on the left and have on the right. I'm going to start with my numbers. Here I had 1 times C5. That means I have 1 times 5 equals 5 carbon on the left. Meaning I need to have 5 carbon on the right. So I know this one has to be 5. So I know that there's no other molecule with carbon inside. So here we have C1. So I know that this one must be 5. I'm going to go to the next one. Hydrogen I have 1 H12. So I have 1 times 12 equals 12. Hydrogen on the left. Meaning I need 12 hydrogen on the right. So I need 12. Here I have H2. So 2 in each molecule. So basically 2 times how much is 12. 2 times 6 is 12. So I know there's a 6. Next step is oxygen. I don't know how many are on the left. But now I only have to count here on the right. How many oxygen I have on total? I have 5 times 2. 5 times 2 plus 6 times 1. 6 times 1. So 5 times 2 is 10. Plus 6 times 1 is 16. So I have 16 oxygen on the right. Meaning I must have been 16 oxygen on the left. I have O2 molecules here. Oxygen molecules with 2 atoms per molecule. So the question is 2 times how much is 16. And the answer is 2 times 8 is 16. So here I have my balanced equation. Option number 2 is using math. So what I do in this case, I simply give names for unknowns here. So this is my first unknown x. This is my second unknown y. This is my third unknown set. And I'm going to write equations. I actually have 3 unknowns. So a math teacher will tell you if you have 3 unknowns, you need to have 3 independent equations to solve for it. So let's see if we can find 3 equations. Let's look first. The first equation I'm going to get from my carbon. I know that 1 times 5 carbons must be equal to y times 1 carbon. Then I have the same on both sides. Second equation I can get from oxygen. So let's go for oxygen. Where I have x times 2 oxygen equal to y times 2 oxygen plus set times 1 oxygen. Last equation is from my third element that's involved here. Hydrogen. So how many hydrogen I have on the left? I have 1 times 12. And on the right I have unknown set times 2. So I have a system of equations with 3 equations and 3 unknowns. There are several ways of solving this. There is also a whole branch of linear algebra that you can use to solve this. If you're lucky and you're only having 3 equations, 3 unknowns, quite many calculators have actually the options to solve this for you. If you know how to type it in your calculator. Here it looks actually fairly simple. So I have 1 times 5 equals y times 1. So I have 5 is y. Well, that's already solved. So now this one is going to be 5. Here I have this one too complicated. Let's skip it. And then here I have 1 times 12. 12 is 2 times set. So I know immediately that 12 divided by 2 is set equals 6. So I have this 6 here. And now for my equation here, this one I'm going to take it down here. It's a bit more complicated. So I have 2 times x equals 2 times y plus 1 times set. I already know that y is 5. So the right side I can write 5, 2 times 5 plus. And I know the set already. So plus 1 times 6 is 2 times my x. So I know that x is 10 plus 6 divided by 2, which is 8. Gave me the same answer as before. Again, how we get from the system of equations to the answer depends a bit on how your problem is. You can solve for one unknown, substitute in the other. You can use the Gauss algorithm or you can use the calculator. If your calculator has the setting to solve a linear equation with 3 unknowns.