Inscribed Polygon Method
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have you ever wondered why the Hucles rule number of pi electrons 26, 10, 14 make molecules so stable. Okay. Maybe you weren't wondering that maybe it wasn't keeping you up at night. But in this video, I'm going to finally explain why these numbers are so important. Why are they so special? And we're gonna learn a visualization technique that will help us to understand molecular orbital theory better when it comes to aromatic molecules. Okay, so this is called the inscribed polygon method. It also goes by a lot of other names. It's also called the polygon and circle method or a frost circle. Okay, if you see any of those terms, it's all referring to the same exact thing. It's a method that helps us to visualize the identities of pi electrons. Okay, and this is going to explain to us. It's going to be a visual representation of why our Hucles rule numbers are so special, why they're so important. Okay, so we're gonna do is we're gonna do a worked example of three different molecules and then we'll go ahead and and uh, you know, do some practice problems. Okay, so here we have three different molecules. It says use the polygon a circle method to predict the stability of the following molecules. I'm gonna go ahead and add some stuff here. So, for example, with this nitrogen, um, let's go ahead and make this a hydrogen. Okay, so let's go ahead and make it a nitrogen with one lone pair and a hydrogen the cyclops to dying or keeping just as is the triangle? It's got a longer name that I don't want to complicate you with, but um the three member ring has a negative charge. That's fine. Okay, so what we're gonna do is we're just gonna do kind of steps and I'm going to do all the steps with all three molecules, so you can see how they work. The very first step of this method, whether you call it a frost circle or polygon and circle. Your first method is your first step is always gonna be to draw the polygon whatever shape it is with one corner facing down. So, as you can see, I've already done that step, I've already drawn it every single shape with one of these corners facing down. Now, if you were given the shape like this, then it would simply be your responsibility to redraw it in a way that one corner is at the bottom. Think of it like it's standing on its very tip. Okay, now we're going to do in the next step is you have to draw molecular orbital's on all corners of the ring, guys, that sounds a lot harder than it is. It just means draw a line next to every adam of the ring. Okay, so a five member ring gets five molecular orbital's Foreman, Bergrin gets four, three member ring gets three. It's that easy. Okay, now we're going to draw a line that splits the polygon down the middle in a basically a horizontal line, that's going to split it into two different halves. Okay, so now, for the square, that happens to be easy because the halfway line would just go right through the middle of both of those corners. Now for a triangle, that's also easy because you're just gonna put the dotted line somewhere in the middle. But now, for a five member ring or sometimes bigger rings, sometimes it can get confusing where to put the line. Obviously when it's drawn like this, the line is gonna go above three molecular orbital's and below two molecular orbital's but some students, because they're really bad at drawing, they just suck at drawing. I don't blame you. I used to be one of you. I had to get good because this is like my job now, um some students make the mistake of doing this. They like go below that molecular orbital. And you'd be surprised if you draw, let's say you draw your five member ring like this. Um not like this. Okay, no, I'm messing up, but there's a way to draw it. There you go. So let's say you draw your five membrane like this. Well then when you draw the halfway point you're gonna think that it's actually below four orbital's and above only one, but that's not the way it should be. You should if you're splitting with an uneven number of orbital's, you should make it so that they're as close together as possible. So instead of being four orbital's on top and one orbital on the bottom, it should be two on the top and three on the bottom like we have here. Okay, so hopefully that kind of helps if you ever see a completely unequal number of orbital's that means you probably drew it wrong. You should have a relatively even number of orbital's on both sides. Okay, excellent. So we drew the line. Now you're going to insert the number of pi electrons that you have into. Your orbital's starting from your lowest energy orbital and working your way up guys. This is called the half bow principle right after the principal was the building of principle. It just means that you have to always fill your lowest energy orbital's first. And we're saying the energy goes up so energy increases the higher you go. So let's just look at the first molecule. The first molecule is one that we already learned how to solve it's a hetero cycle. How many pi electrons does that molecule have? You have to think will the nitrogen donate? Does it want to donate its lone pair? Yes, it does. Okay, because we've got 24 electrons. Four pi electrons. That lone pair is going to make it six. It's sp three. So that works out. So that means I have six electrons to add how do we add them one and here then? My third electron goes here, my fourth electron goes here. Okay, that's a whole other rule. Okay, that was actually hun's rule, huns rule says that you can't if you have orbital of the same energy level, you have to fill them evenly. Okay, so your third and your fourth electrons go one apiece, but we have six total. So then my fifth goes here and my sixth goes there. That's it. So I'm done with that step. Let's move on to cyclops to dying. How many pi electrons do I have for that one? Quattro. Okay, so it's gonna be according to a principle. And then according to Hahn's rule that I have those too, even energy orbital's so I have to fill them evenly. Okay, now, just so you guys know there's a more technical term for orbital's that have the same energy level. Do you guys remember that name? That term? It's actually from chapter one of organic chemistry, They're called degenerate orbital's. Okay, so if you have degenerate orbital's that means that you have to fill them evenly. Okay, that's it. You can't just put two on one side and zero on the other. That doesn't make a lot of sense. Finally, what we get for the triangle. Okay, the cyclo pro penal an ion. Um so what we would get is 123, four. Right, because again, we've got four pi electrons and so we've got to have that uneven of that. Even distribution at the top. Perfect. So what did we just do? You know, I've been wondering, Okay, johnny we drew all these arrows But where is this going? Well, it turns out that we can use this diagram to understand why molecules are more stable or less stable and we can understand the identities of the electrons and the identities of the orbital's because it turns out that that halfway point actually represented what we call the non bonding line in the molecular orbital theory where everything below that line represents a bonding molecular orbital. Okay, so bonding molecular orbital's are the first ones to get filled. They're the ones that contribute to bonding. They're ones that contribute to things wanting to stay together and then our anti bonding molecular orbital's are the ones that get filled up after all the bonding ones are full. Okay, you would never put something on the top orbital until all of your bottom ones are full. Okay, well, it turns out that when you have filled molecular orbital, remember, molecular orbital would just be one of these. Right. If all of your molecular orbital are filled, that's going to contribute to unique stability because Remember that we learned a long time ago from Chapter one of organic chemistry and from gen cam that orbital's love to have two electrons. If if an orbital has two electrons, two electrons, it's happy. Okay, now, what if all of the bonding orbital's have two electrons that's going to make it uniquely stable because that means that basically all of your bonding orbital's are perfectly filled. Okay, now, what if you have partially filled molecular orbital? What if you have a weird number of electrons and you have some molecular orbital just hanging out with one electronic piece that's going to contribute to unique instability guys. That's gonna make it unstable because now you have these unfilled orbital's that are trying to get filled with something no orbital likes to only carry one electron. They always want to carry two. Okay, so what does this mean back to our diagrams? Well, look what's going on normally we would predict that what would be the authenticity of these molecules? Well, the first one would be aromatic. The 2nd 1 is supposed to be anti aromatic. And the last one is also supposed to be anti aromatic. Now, are you seeing a pattern here notice look what's going on? The aromatic molecule. The one with six pi electrons Hucles rule number happens to have all of its bonding orbital's perfectly filled. Right. That's gonna make it stable. That's gonna make it really stable. Right. Whereas the ones that are anti aromatic, the ones that have a non Hucles rule number or what we call breast slows rule number. Notice that they have this, what is that? They have these partially filled orbital's partially filled. Do you think that's gonna make it stable? That's gonna make it uniquely unstable? Look at these numbers, the electrons here are four electrons, the electrons over there for the first one is six. So guys, the reason that the Hucles rule numbers of 26, 10, 14 are so stable is because those are the combinations of electrons that are always going to be required to perfectly fill your bonding orbital's any number off of that? An odd number. Right. Or instead of an odd number um four end number, these are going to kick electrons up to the anti bonding orbital's and make unfilled partially filled orbital's that are gonna contribute to instability. Okay, so hopefully this helps you guys get a better grip on. Wow, this wasn't just like a memory game. This actually made sense. These numbers are important. There's a reason that Benzene is so stable and it's because this is this example. Here is Benzene. It's because Benzene has six pi electrons, so all of its bonding orbital are perfectly filled. All right, so you guys are gonna do some practice. You guys can get a better idea of this. But hopefully that makes sense. Let me know if you have any questions, let's move on to the next topic.
Inscribed Polygon Method
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Hey, guys, let's take a look at the following question. So here apply the Polygon Circle method, which we also call frost circles to the following compound Doesn't show any special stability. If yes, why? So basically we have to determine. Is this molecule aromatic, Non aromatic or anti aromatic? Aromatic shows very high stability. Non aromatic just means your normal compound anti rheumatic means you're super unstable. So if we take a look at the name we have trope ilium cat ion Now, another name for trope ilium just means that we have cyclo. Heh PTA trying. Okay, so the trope ilium just means cyclo Hector trying cyclo means ring have to mean seven carbons, so we have seven carbons and trying means three double bonds. Now I say the word cat ion, which means this carbon up here, which is not double bond like the others, is positive. So that will be our molecule. Now here, we're gonna draw the frost circle. Now we're gonna draw apex down the molecule, so pointing part down. So the larger these rings get, the harder it becomes to draw them. So it takes practice guys to make sure you draw correctly so not the straightest, but good enough. Now we're gonna cut this in half. So here this is your non bonding region. Down here is your bonding up. Here is your anti bonding everywhere. Ah, carbon touches becomes a molecular orbital. Now we're gonna say how maney pie electrons do. We have. We have to four six pi electrons. So one up, one down, up, up, down, down. We're going to say this molecule show special stability because all the molecular orbital's in the Bonny region are completely filled in, which would indicate that we have an aromatic compound. So Trump Ilium can Ion is aromatic here. We know it from the old rules that we talked about. But we also know because we just did a frost circle and improves it. The molecular orbital's and the bonding region are all completely filled. It