 Today, we'd like to talk about balancing equations. Balancing equations is a fundamental task that chemists and students have to do. The balanced equation is an equation that has the same numbers of each atom on both sides of the equation. And there are a few rules that we need to obey when we're balancing equations. The first rule is that you want to count the number of atoms on each side of the equation before you begin balancing. The reason is that sometimes an equation is already balanced and needs no further work. The second thing that you need to know about a balanced equation is that equations may be balanced using coefficients. The coefficients that are used have to be whole numbers. They cannot be fractions. A balanced equation cannot be balanced by changing a subscript. When you change a subscript, you change the identity of the compound and that is not allowed. When you are balancing equations, the best way to begin is to start with the more complicated molecule and work your way back to the less complicated molecule or to a single atom. Once you've made your manipulations to the equation, what you want to do is to recheck, recount to make sure that the equation is in fact balanced. The equation that I have on the board is the reaction of titanium plus chlorine to give titanium tetrachloride. To balance this equation, let's begin by counting the atoms. I typically write the atom in the center on the left-hand side, we have one titanium. The subscript two in chlorine tells us that there's two chlorines. In the titanium tetrachloride molecule, there's one titanium, there are four chlorines. This equation, in starting from titanium tetrachloride, since we have our titanium's balance, we shouldn't have to worry about titanium, but our chlorines are not balanced. So if you look at the relationship between two and four, you know that in order to get four chlorines on this side, you're gonna need to multiply by two. We have to multiply the entire molecule by two. So if we put a coefficient two in front of chlorine, that means that now we have four chlorines here. We have one titanium, and remember that on this side, we have one and four, so we balanced our equation. I mentioned to you earlier that you can balance an equation using coefficients. You cannot balance an equation using subscripts. Let me share with you why that's the case. If we have hydrogen plus oxygen giving us water, let's balance this equation. We have two hydrogens on the left-hand side. We have two oxygens on the left-hand side. On the right-hand side, we have two hydrogens. On the right-hand side, we have one oxygen. Many times I have students who want to do this. They want to change the subscript beside of the oxygen in order to balance the equation. Now, let me share with you that the molecule H2O is water. The molecule H2O2 is hydrogen peroxide. If you have dark hair like mine, and you use hydrogen peroxide instead of water, you will most likely not have dark hair like mine anymore. Peroxide is a bleach, water is not. So, again, you're changing the identity here, so we can't balance it that way, so we can remove this. And we ask ourselves, how should we do this properly? Well, since you have your hydrogens balanced, let's focus on the oxygens, two versus one. What do you multiply one by to get two? Well, the answer is two. Notice that in a molecule, you have to multiply everything in the molecule by the same coefficient. So we're gonna put a two here. So, we do have oxygen now at two, but we've also doubled our hydrogens. So that means that now, on this side, we have four hydrogens. We don't worry about that because we start it with this complicated molecule, and we look at our numbers, and we see that, yes, we have four hydrogens, but we have a two here, so that means that if we multiply the two by two, we can balance our equation. So by putting a two here, our hydrogens are now balanced, and by counting, recounting, we see that we have four hydrogens on each side, we have two oxygens on each side. So we need to make sure that we use coefficients to balance the equations, that we never use subscripts to balance equations. There's some other helpful hints that may benefit you when balancing equations. Suppose we have aluminum plus oxygen giving us aluminum oxide. When we balance this equation, we find that we have one aluminum and two oxygens. On the left-hand side, we have two aluminum and three oxygens on the right-hand side. Now, notice here that it's no longer a possibility to simply multiply one value by two to double it. Here we have a difference between two and three, which can create a little bit of a problem. Always remind my students that back when we were in four, fifth, and sixth grades, we learned how to find what was called a common denominator for addition of fractions. How did you do that? You multiplied the denominators together to come up with a value. If we multiply two and three together, that will give us six, meaning that our initial goal should be to have six oxygens on each side of the equation. To do that, we're gonna put a two here and a three here. When we change the three in the right-hand side, I'm sorry, on the left-hand side, we have six oxygens. We still have one aluminum. On this side of the equation, we have six oxygens, but we now have four aluminum. So the question becomes, how do we complete the balancing? We do that by changing the coefficient in front of the aluminum. When we do that, we balance the equation. Another thing that sometimes complicates situations has to do with reactions in which we have combustion taking place. This reaction is C3H8, which is propane. It's the gas that you use in gas grills, reacting with oxygen to give carbon dioxide and water. When we balance this equation and any other equation, we have to remember that sometimes you will have an area where you will have two sources for one atom. You need to make sure and count all of the atoms on both sides. Some people overlook this. Let's count our atoms. We have three carbons, eight hydrogens and two oxygens. We have one carbon, two hydrogens, and two plus one or three oxygens. When we look at this equation, propane, C3H8, is our most complicated molecule. So if we have three carbons here, in order to have three carbons on the right-hand side, we're gonna put a three here. And that's gonna change our carbon count to three. If we have eight hydrogens on the left-hand side, it's eight versus two. If we multiply two by four, that will give us eight hydrogens. We have carbon and hydrogen balance. Now let's count the oxygens. We have four water molecules. So we have four oxygens here. We have three carbon dioxide molecules. So we have six oxygens here for a total of 10. So there's 10 oxygens over here. If you have 10 oxygens here and two oxygens here, you simply have to multiply two by five to get 10. When you recheck the equation, you can see that it's balanced. Balance in equations is not difficult. And if you follow the rules and the guidelines that I've given you, you should be able to do it. What you do need to do is to practice lots of different problems so that you can acquire the skills that you need.