Balancing Chemical Equations

[00:00:00]All right, welcome to another module.

[00:00:03]Uh, this module is on chemical reactions. Uh, we're going to first talk about how to balance chemical reactions and then delve into the different kinds of chemical reactions and how to categorize them and how to identify the different kinds or types. So, the first thing we're going to talk about, of course, in this video is balancing chemical reactions. Now the reason uh we balance chemical equations is because we would like to follow the law of the conservation of matter. We talked about in the very first chapter that the law of the conservation of matter means that if you go into a reaction or a chemical reaction with let's say four hydrogens when you come out of the reaction at the end even though the atoms may be rearranged they need to also have four hydrogens total in the products. So let's look at how we might uh describe or or or um make sure that the reaction itself is balanced and that the law of the conservation of matter is conserved.

[00:01:05]So the first bullet point says that the chemical equation describes uh chemical reactions and how atoms move around and rearrange to form new substances. Think of it like a recipe with ingredients called reactants on the left separated by an arrow and the products are on the right. So they do want to make a point that uh you want to make a note that all of these are the reactants here and all of these are the products right the ones before the arrow are the reactants uh and the ones at the end are the products. There's also a thing that says that uh we like to represent the states of matter and remember the states of matter are solid, liquid and gas. And so we would like to represent them uh in terms of the substances that we either add as reactants or form as products. So here you've got the states. You've got solid for S, L for liquid, G for gas. And aquous means that that substance is dissolved in water. So for example, if I have NAC aquous, that means that my NaCCl or table salt is dissolved in water. So that just basically means I've taken some salt and I've dissolved it in water. And water is a solvent that that basically allows me to do the reaction in a liquid form.

[00:02:31]So what are the whole numbers uh shown in red? Uh let me just erase my highlight so you can see the red the numbers in red and these are very important. These ones here okay must balance the equation to maintain the number of atoms on both sides. So if you look at it if I wrote the equation like this H2 gas is reacting with O2 gas and it's forming H2O. This would be an unbalanced version of the reaction. H2 the little subscript two means that H and H are connected together. O2 means that O and O are connected together. And from from Lewis dot structures chapter, we know O2 is a double bond. And then it forms H2O. Now, if you look at what we've drawn so far, you'll see that the reaction is not balanced, right? because you've got two oxygen's on the left and an oxygen on the right. So, it can't I mean this is not possible. It breaks the law of the conservation of matter.

[00:03:35]That's why you need the two in front because the 2 H means that now there are two molecules two molecules of H. And then two H2O means that there are two molecules of H2O being formed. Right? So that's what that two means. Two means that there are two separate substances or molecules and then these things are reacting together and forming two of the waters. So that now if you count everything is balanced. You have your four hydrogens. Yes, they're rearranged and connected differently. Now that's the hallmark of a chemical reaction. And you've got your oxygens, two oxygens again. and they are rearranged and no longer connected to one another. They're connected to the hydrogens's now in water. But again, the number of oxygens and the number of hydrogens are the same. So when we balance, what we're doing is we're we're just taking a number putting it in front and making it balanced so that the law of the conservation of matter is uh observed.

[00:04:42]I'm sorry, not observed is um applied.

[00:04:45]Okay.

[00:04:47]So this video basically will help us to write the correct numbers in front. So these numbers in front, how do we know what numbers to write in front? That's what this video is all about. All right.

[00:05:02]So now that we understand uh in terms of why we are trying to balance equations, let's actually balance some equations.

[00:05:10]Now, if you've done balancing equations before and you feel like you have a good handle on it, you can actually pause the video and write down these equations on a clean sheet of paper and try and balance them and see what you how you do. Okay? If you've never balanced equations before, uh it might be good to watch me do it first, then go back, rewrite this on a clean sheet of paper, and do it again, and then check your answers. Really, with chemistry, practice makes perfect. So again, you don't want to just watch me do it. You want to also do it yourself. All right.

[00:05:44]So underbalancing chemical equations, we want one, same number of atoms to appear on both sides of the equation. Same number of atoms. That's that's what we discussed in the previous slide. The chemical formulas cannot be altered.

[00:05:58]I.e. don't change the subscripts. Okay?

[00:06:02]Again, if you're thinking about, you know, H2 plus O2, this was your unbalanced equation, right? it forms water, right? Some students will say, "Well, Dr. Chang, why don't I just put a two here and now it's balanced, right?"

[00:06:17]But the problem here is that H2O2 is not what we think it is. H2O2 is this. This is hydrogen peroxide.

[00:06:31]Uh and if we've used any kind of hydrogen peroxide before, we know that that is not something that is drinkable.

[00:06:38]It is not the same as water. It has very different chemical properties than water. And so you cannot just write a two right here and just say, "Oh, it's balanced." Because the moment you change the subscript, you change the formula.

[00:06:52]And the moment you change the formula, you change the identity of the substance. So if you change the formula because you change the subscript, the substance is no longer the same.

[00:07:25]And the problem with that is now now it's no longer the same expression of a chemical uh chemical reaction. So whatever you do, don't do not do not do not do not change the subscript numbers.

[00:07:38]When you're balancing, you can only change the numbers in front. We will talk in the uh in in one of the next videos about when it is okay to alter the subscript numbers. Uh but for now, when you're balancing, you cannot alter the subscript numbers. other reactants or products cannot be added. So you can't just add another O2 right at the end. Uh and balanced with the smallest whole number of coefficients. So the numbers uh the numbers in front uh they have to be the lowest uh whole number of coefficients or the smallest whole number coefficients. And we'll talk about that in a little bit as to what we mean by that. All right. So I I went ahead and copied the first equation onto a clean sheet of paper. And so I'm going to describe what I'm I'm doing as I do it.

[00:08:27]So the first step is I'm going to tally the atoms or ions. Okay. Under the arrow. So underneath the arrow where clearly is the differentiating mark between the products and the reactants.

[00:08:48]I'm gonna write K, Cl, and O. I I've basically tallied or or listed, sorry, listed all of the atoms in the reactants and products.

[00:09:01]Okay. Now, I'm going to count. I've got one potassium, one chlorine, and three oxygens. Three because of that subscript three. On the other side of the equation, I have one potassium, one chlorine, and two oxygens. Okay, so given that this is the case, we can see that the oxygens are not balanced. And remember, I can't change the subscript. So really, I have to write numbers in front of the oxygen and the KO3 to be able to balance it. So the between three and two, the lowest common multiple is six. So what I want to do is I want to write a two in front so that this two times the three becomes a six.

[00:09:52]So now I've got six oxygens, right? I also want to write a three in front because the 3 * the two makes this a six. Okay? Don't forget though that writing a two in front of the KO3 also changes the amount of K and the amount of Cl. You remember the K is really one.

[00:10:13]Cl is also really one. We just don't write it. Right? So K the 2 * 1 makes this K a two and makes the chlorine a two as well. Right? So really it is important to recognize that when you write a number in front like this. This affects this one the potassium the chlorine and the oxygen count across the board. Okay.

[00:10:37]Now, because I've balanced my oxygens, my K and my Cl are not balanced. So, I'm going to put a two in front of the KCl so that my potassium is two on the right side and my Cl is also two on the right side. Now, the reaction is balanced 2 and six. So, this is the balanced reaction. So, one, I've put a tally of the atoms underneath. Then, two, I balance using the numbers in front.

[00:11:13]Okay, I often will start with the most complex compound. That's why I started with the KO3 because that is the most complex. It is turnary, right? Another way of saying this is turnary. Okay. And then the last step is uh if you have O2, right, or H2 or anything diatomic, right? Remember diatomic is like H2, O2, Br2, etc. You can write any number in front to get the number you need. And we'll talk a little bit more about rule number three in in a later problem to just show you how that works.

[00:12:27]Okay. Uh but but really we're going to just again do the rule one and two and then I'll show you how to do three when it when it pops up.

[00:12:37]You don't always need to do that. Uh but sometimes you will need to apply that rule. All right. So again, I'm going to copy and paste my rules.

[00:12:53]Okay. Paste it right here.

[00:12:57]So the first thing I should do is tally, right? So underneath the arrow, I'm going to write H. Okay, I'm going to write. Now, now notice I'm going to write NOO3 because that is my polyatomic ion. And I can do that because NOO3 is also here. You see? So if I what?

[00:13:19]Because the polyatomic appears on the left and the right. I can count the entire polyatomic rather than breaking it up into nitrogen and oxygen. All right, Ca and C and O. Now, you might be like, well, why don't you write CO3 cuz CO3 is carbonate and also a polyatomic. It is because CO3, the polyatomic, does not appear on the right hand side. So, you've got to separate them since they don't appear on the right hand side. All right. So, now that I've listed everything out underneath both as atoms and ions, I'm going to tally and count. So, I've got one hydrogen, one NO3 polyatomic, one Ca, one carbon, and three oxygens. Then I have one carbon. I have two hydrogens. I have one Ca and I have two NO3s.

[00:14:16]Now with the oxygen, be careful. I'm not going to count this oxygen because this oxygen is already accounted for in the NO3. But I am going to count these oxygens here and instead of writing oxygen is three, it is three. I'm going to write 2 + 1. The reason for that is if I put a number here three in front for example, it does not change the entire number. And if I wrote three, often times students will say 3 * 3 and write 9. And that would be incorrect because three only affects this two. So it really is 6 + 1. So it ends up being 7, not 9. So really, you don't want to write the number together if the number is separated. Okay? All right. So now let's go ahead and again, we want to start with balancing the most complex molecule. So in my mind, it's the calcium nitrate. Okay. So really I have two NO3s and I'm going to write a two here to make it I want two on this side as well. Right? So I'm going to make that a red. So this makes it two NO3s and makes the hydrogen two as well.

[00:15:26]Okay? Now if you look at it everything else seems balanced right the calcium is balanced carbon is balanced. 2+ 1 is three. So everything else is balanced.

[00:15:36]So in this particular case just by writing that two in front of the HNO3 this reaction is balanced. Uh hopefully you know it would be nice if every reaction was this easily balanced. You'll see that it is not the case. Uh but often times reactions are very straightforward to balance. All right looking at the next one again we're going to tally underneath and we're going to go carbon. Oops. Do it in same color.

[00:16:03]carbon, hydrogen, and oxygen. It's very straightforward to tally this one. Okay, I've got eight carbons, 18 hydrogens, and two oxygens. One carbon, be careful, two hydrogens, and two and one. So, 2 + one.

[00:16:24]Okay, so now that we have that all listed out, step number two is to balance with the numbers in front.

[00:16:31]Again, we want to try and go with the most complex. In my mind, this is the most complex because that has eight and 18. It's a lot of atoms, right? So, I'm going to go ahead and write eight in front of the CO2. And the reason for that is because if I write eight in front of the CO2, that fixes the carbon count. I get eight. Now, this 8 affects this oxygen count. So, 8 * 2 is 16. It does not affect the other oxygen count.

[00:17:00]Now, we're going to go ahead and look at hydrogen. Hydrogen is 18. I obviously need to multiply this by 9 because 9 * 2 is 18. So, this gets me 18 hydrogens's.

[00:17:12]But it also affects this oxygen which is now nine. Okay. So, uh, if you are counting along with me, uh, 2 + sorry, 16 + 9 is 25. So, my carbon count and my hydrogen count look good, but my oxygen count is not quite right. So, really, if I have a 25 here, this would fix the issue altogether, right? So, really, you might say, okay, well, what number can I write in front of oxygen to make it 25?

[00:17:48]uh if I write uh there is really no whole number that I can write. Okay. But here if you look at rule number three if you have O2 or H2 anything diatomic any X in front to get the number you need. Right? So I can write here I'm going to write O2 here.

[00:18:07]Okay. I can write 25 over two. Okay. So X over two. Right? So basically, if I want 25, I just put it over two because if you think about it, 25 / 2 * 2 is 25, right? So if I put a 25 over two here, now I have 25 underneath. Okay, that looks pretty good. Now everything is balanced. And this is the case for all diatomic molecules. Like for example, if you have H2 and you need, let's pretend you need, you know, 35 H2s, then you can write 35 over two in front. And again, 35 / 2 * 2 gets you 35. Then you have 35 hydrogens.

[00:19:03]So whatever number you need, put it over two. Remember, you can write any number you want in front of the diatomic as long as it gets you the number you need.

[00:19:13]In this case, what number you need over two gets you what you need. All right?

[00:19:18]Now, you can't leave it as um 25 over two because one of the rules says that uh you need to have whole number coefficients, right? Whole number means 1 2 3 4 5 6 7 8 because uh atoms really don't exist as half atoms, right? But you can fix that really easily. All you need to do now once you've used the 25 over2 as you get out of jail free card is multiply by two. Right? That will get rid of the denominator al together. So then you end up with 2 C8 H18. 25 / 2 * 2 is just 25 O2. Now you've gotten rid of that uh fraction. 8 * 2 is 16 CO2 and 9 * 2 is 18 H2O. Okay. And again, if you want to check underneath and make sure your tally is still correct, you can. Okay. So, you just think 2 * 8 is 16. 2 * 18, that's a harder one. You might need to pull out a calculator for that. It is 36.

[00:20:30]25 * 2 is 50 oxygens.

[00:20:36]16 carbons. I'm going to count the oxygen last. Uh 18 * 2 is again 36 hydrogens. Now for the oxygen count, 16 * 2 is 32 and 18 * 1 is just 18 and 32 + 18 is 50. So again we have balanced the equation. So some of the equations are a little bit more tedious to balance.

[00:21:06]That's okay. Uh it I I really like this problem because it actually allows us to use this rule number three which I think is very useful. All right let's look at the next one. The last problem we have carbon, hydrogen, nitrogen and oxygen. Carbon is three, hydrogen is five, nitrogen is three and oxygen is 9.

[00:21:36]Nitrogen is 2, hydrogen is 2, oxygen is, be careful, this is one, this is two, and this is two. So 1 + 2 + 2 and my carbon count is of course 1. All right.

[00:21:55]Again, you want to start with the most complex. To me, this is the most complex. So let's go ahead and fix the carbon, hydrogen, and nitrogen count. We have this diatomic oxygen as our get out of jail free card because we can put whatever number we want in front and it'll fix the situation. However, I would like to say this. We already know that this n3 is difficult to fix, right? Because then I'm going to end up with a three over two in front of this number. I think the easiest thing to do is if you see an odd number like that, you can actually just know you need to multiply by two, at least two to make it even, right? So, I'm going to go ahead and do that first.

[00:22:34]I'm going to go ahead and multiply by two and get 6 10 6 and 18. That will make balancing the nitrogen a lot easier. All right, so now that we're here, let's go ahead and balance the carbon first. The carbon, we need six. So, we need to put a six here. This affects this oxygen count. 6 * 2 is 12. Okay. Then, let's fix the hydrogen count. We need 10. So, we're going to put a five here. This affects this oxygen count, which now is a five. Okay. And let's fix the nitrogen. We put a three in front.

[00:23:15]That makes it a six. Okay. Easy enough to do. So really now the oxygen is the only thing that's problematic. We have 5 + 12, which is 17 + 2, which is 19. If only this was a 1. If this was a 1, then I would have 18, right? So really, I just want this to be a one. So, we know how to do that, right? Because the rule number three says I just put whatever number I need over two, right? If I had need 35, I put 35 over two. If I need 25, I put 25 over two. If I need one, I just put one over two, right? Because 12 * 2 is 1. Okay, so now I'm good because 15 + sorry 5 + 12 is 17 + 1 is 18. So now everything is balanced. We know that we cannot leave the two as the denominator here because we know that you can't have a fraction. You've got to have a whole number. We can easily fix that. All we got to do is what we did before. We need to multiply by 2. All right? So, it becomes I'm just going to cross out the number rather than rewriting the whole thing. 2 * 2 is 4. This becomes 6. This becomes 10. This becomes 12. And 1/2 * 2, we just did it below, is 1. You don't really need to put the one there. You can if you want, but um usually when you write a chemical equation, you don't put the one there. Uh if you again recheck the tally and you can definitely do that uh you will see that and and uh we can recheck that real quickly. I I don't I don't want to list it totally underneath but I'll list it here. H and O. You'll see that 4 * 3 is 12. So you have 12 carbons. 4 * 5 is 20 hydrogens. 4 * 3 is 12. and 4 * 9 is 36. Then you've got 6 * 2 is 12 nitrogens. 10 * 2 is 20 hydrogens. 10 * 1 is just 10. Okay. Then 12 carbons. 12 * 2 is 24. And then you've got your O2 which is just two, right? So 10 + 24 is 34 + 2 is 36. So yes, uh by putting those numbers in front, you have a balanced equation and more importantly, everything is whole numbers. Uh again, this is a little bit more of a difficult problem, a challenging problem. Uh again, what I would suggest you do now at this point is pause the video or stop the video. Uh and I'm going to go ahead and stop the video. I would go back, do these problems again on a clean sheet of paper, and check your answers. Uh hopefully this has been a good walk through the park on how to do balancing equations.