sp³ hybridized orbitals and sigma bonds

Let's remind ourselves a little bit of what we already know about orbitals and I've gone over this early on in the regular chemistry playlist. Let's say that this is the nucleus of our atom, super small, and around that we have our first orbital, the 1s orbital. The 1s orbital, you can kind of just view it as a cloud around the nucleus. So you have your 1s orbital and it can fit two electrons, so the first electron will go into the 1s orbital and then the second electron will also go into the 1s orbital. For example, hydrogen has only one electron, so it would go into 1s. Helium has one more, so that will also go into the 1s orbital. After that is filled, then you move onto the 2s orbital. The 2s orbital, you can view it as a shell around the 1s orbital, and all of these, you can't really view it in our conventional way of thinking. You can kind of view it as a probability cloud of where you might find the electrons. But for visualization purposes, just imagine it's kind of a shell cloud around the 1s orbital. So imagine that it's kind of a fuzzy shell around the 1s orbital, so it's around the 1s orbital, and your next electron will go there. Then the fourth electron will also go there, and I drew these arrows upward and downward because the first electron that goes into the 1s orbital has one spin and then the next electron to go into 1s orbital will have the opposite spin, and so they keep pairing up in that way. They have opposite spins. Now, if we keep adding electrons, now we move to the 2p orbitals. Actually, you can view it as there are three 2p orbitals and each of them can hold two electrons, so it can hold a total of six electrons in the 2p orbitals. Let me draw them for you just so you can visualize it. So if we were to label our axis here, so think in three dimensions. So imagine that that right there is the x-axis. Let me do this in different colors. Let's say that this right here is our y-axis and then we have a z-axis. I'll do that in blue. Let's say we have a z-axis just like that. You actually have a p orbital that goes along each of those axes. So you could have your two-- let me do it in the same color. So you have your 2p sub x orbital, and so what that'll look like is a dumbbell shape that's going in the x-direction. So let me try my best attempt at drawing this. It's a dumbbell shape that goes in the x-direction, in kind of both directions, and it's actually symmetric. I'm drawing this end bigger than that end so it looks like it's coming out at you a little bit, but let me draw it a little bit better than that. I can do a better job. And maybe it comes out like that. Remember, these are really just probability clouds, but it's helpful to kind of visualize them as maybe a little bit more things that we would see in our world, but I think probability cloud is the best way to think about it. So that is the 2px orbital, and then I haven't talked about how they get filled yet, but then you also have your 2py orbital, which'll go in this axis, but same idea, kind of a dumbbell shape in the y-direction, going in both along the y-axis, going in that direction and in that direction. Then, of course, so let me do this 2py, and then you also have your 2pz, and that goes in the z-direction up like that and then downwards like that. So when you keep adding electrons, the first-- so far, we've added four electrons. If you add a fifth electron, you would expect it to go into the 2px orbital right there. So even though this 2px orbital can fit two electrons, the first one goes there. The very next one won't go into that one. It actually wants to separate itself within the p orbital, so the very next electron that you add won't go into 2px, it'll go into 2py. And then the one after that won't go into 2py or 2px, it'll go into 2pz. They try to separate themselves. Then if you add another electron, if you add-- let's see, we've added one, two, three, four, five, six, seven. If you add an eighth electron, that will then go into the 2px orbital, so the eighth electron would go there, but it would have the opposite spin. So this is just a little bit of review with a little bit of visualization. Now, given what we just reviewed, let's think about what's happening with carbon. Carbon has six electrons. Its electron configuration, it is 1s2, two electrons in the 1s orbital. Then 2s2, then 2p2, right? It only has two left, because it has a total of six electrons. Two go here, then there, then two are left to fill the p orbitals. If you go based on what we just drew and what we just talked about here, what you would expect for carbon-- let me just draw it out the way I did this. So you have your 1s orbital, your 2s orbital, and then you have your 2px orbital, your 2py orbital, and then you have your 2pz orbital. If you just go straight from the electron configuration, you would expect carbon, so the 1s orbital fills first, so that's our first electron, our second electron, our third electron. Then we go to our 2s orbital, That fills next, third electron, then fourth electron. Then you would expect maybe your fifth electron to go in the 2px. We could have said 2py or 2z. It just depends on how you label the axis. But you would have your fifth electron go into one of the p orbitals, and then you would expect your sixth to go into another. So you would expect that to be kind of the configuration for carbon. And if we were to draw it-- let me draw our axes. That is our y-axis and then this is our x-axis. Let me draw it a little bit better than that. So that is the x-axis and, of course, you have your z-axis. You have to think in three dimensions a little bit. Then you have your z-axis, just like that. So first we fill the 1s orbital, so if our nucleus is sitting here, our 1s orbital gets filled with two electrons. You can imagine that as a little cloud around the nucleus. Then we fill the 2s orbital and that would be a cloud around that, kind of a shell around that. Then we would put one electron in the 2px orbital, so one electron would start kind of jumping around or moving around, depending how you want to think about it, in that orbital over there, 2px. Then you'd have the next electron jumping around or moving around in the 2py orbital, so it would be moving around like this. If you went just off of this, you would say, you know what? These guys, this guy over here and that guy over there is lonely. He's looking for a opposite spin partner. This would be the only places that bonds would form. You would expect some type of bonding to form with the x-orbitals or the y-orbitals. Now, that's what you would expect if you just straight-up kind of stayed with this model of how things fill and how orbitals look. The reality of carbon, and I guess the simplest reality of carbon, is if you look at a methane molecule, is very different than what you would expect here. First of all, what you would expect here is that carbon would probably-- maybe it would form two bonds. But we know carbon forms four bonds and it wants to pretend like it has eight electrons. Frankly, almost every atom wants to pretend like it has eight electrons. So in order for that to happen, you have to think about a different reality. This isn't really what's happening when carbon bonds, so not what happens when carbon bonds. What's really happening when carbon bonds, and this will kind of go into the discussion of sp3 hybridization, but what you're going to see is it's not that complicated of a topic. It sounds very daunting, but it's actually pretty straightforward. What really happens when carbon bonds, because it wants to form four bonds with things, is its configuration, you could imagine, looks more like this. So you have 1s. We have two electrons there. Then you have your 2s, 2px, 2py and 2pz. Now what you can imagine is it wants to form four bonds. It has four electrons that are willing to pair up with electrons from other molecules. In the case of methane, that other molecule is a hydrogen. So what you could imagine is that the electrons actually-- maybe the hydrogen brings this electron right here into a higher energy state and puts it into 2z. That's one way to visualize it. So this other guy here maybe ends up over there, and then these two guys are over there and over there. Now, all of a sudden, it looks like you have four lonely guys and they are ready to bond, and that's actually more accurate of how carbon bonds. It likes to bond with four other people. Now, it's a little bit arbitrary which electron ends up in each of these things, and even if you had this type of bonding, you would expect things to bond along the x, y, and z axis. The reality is, the reality of carbon, is that these four electrons in its second shell don't look like they're in just-- the first one doesn't look like it's just in the s orbital and then the p and y and z for the other three. They all look like they're a little bit in the s and a little bit in the p orbitals. Let me make that clear. So instead of this being a 2s, what it really looks like for carbon is that this looks like a 2sp3 orbital. This looks like a 2sp3 orbital, that looks like a 2sp3 orbital, that looks like a 2sp3 orbital. They all look like they're kind of in the same orbital. This special type of-- it sounds very fancy. This sp3 hybridized orbital, what it actually looks like is something that's in between an s and a p orbital. It has a 25% s nature and a 75% p nature. You can imagine it as being a mixture of these four things. That's the behavior that carbon has. So when you mix them all, instead of having an s orbital, so if this is a nucleus and we do a cross-section, an s orbital looks like that and the p orbital looks something like that in cross-section. So this is a an s and that is a p. When they get mixed up, the orbital looks like this. An sp3 orbital looks something like this. This is a hybridized sp3 orbital. Hybrid just means a combination of two things. A hybrid car is a combination of gas and electric. A hybridized orbital is a combination of s and p. Hybridized sp3 orbitals are the orbitals when carbon bonds with things like hydrogen or really when it bonds with anything. So if you looked at a molecule of methane, and people talk about sp3 hybridized orbitals, all they're saying is that you have a carbon in the center. Let's say that's the carbon nucleus right there. And instead of having one s and three p orbitals, it has four sp3 orbitals. So let me try my best at drawing the four sp3 orbitals. Let's say this is the big lobe that is kind of pointing near us, and then it has a small lobe in the back. Then you have another one that has a big lobe like that and a small lobe in the back. Then you have one that's going back behind the page, so let me draw that. You can kind of imagine a three-legged stool, and then its small lobe will come out like that. And then you have one where the big lobe is pointing straight up, and it has a small lobe going down. You can imagine it as kind of a three-legged stool. One of them is behind like that and it's pointing straight up, So a three-legged stool with something-- it's kind of like a tripod, I guess is the best way to think about it. So that's the carbon nucleus in the center and then you have the hydrogens, so that's our carbon right there. Then you have your hydrogens. You have a hydrogen here. A hydrogen just has one electron in the 1s orbital, so the hydrogen has a 1s orbital. You have a hydrogen here that just has a 1s orbital. It has a hydrogen here, 1s orbital, hydrogen here, 1s orbital. So this is how the hydrogen orbital and the carbon orbitals get mixed. The hydrogens 1s orbital bonds with-- well, each of the hydrogen's 1s orbital bonds with each of the carbon's sp3 orbitals. Just so you get a little bit more notation, so when people talk about hybridized sp3 orbitals, all they're saying is, look, carbon doesn't bond. Once carbon-- this right here is a molecule of methane, right? This is CH4, or methane, and it doesn't bond like you would expect if you just want with straight vanilla s and p orbitals. If you just went with straight vanilla s and p orbitals, the bonds would form. Maybe the hydrogen might be there and there, and if it had four hydrogens, maybe there and there, depending on how you want to think about it. But the reality is it doesn't look like that. It looks more like a tripod. It has a tetrahedral shape. The best way that that can be explained, I guess the shape of the structure, is if you have four equally-- four of the same types of orbital shapes, and those four types of orbital shapes are hybrids between s's and p's. One other piece of notation to know, sometimes people think it's a very fancy term, but when you have a bond between two molecules, where the orbitals are kind of pointing at each other, so you can imagine right here, this hydrogen orbital is pointing in that direction. This sp3 orbital is pointing that direction, and they're overlapping right around here. This is called a sigma bond, where the overlap is along the same axis as if you connected the two molecules. Over here, you connect the two molecules, the overlap is on that same axis. This is the strongest form of covalent bonds, and this'll be a good basis for discussion maybe in the next video when we talk a little bit about pi bonds. The big takeaway of this video is to just understand what does it mean? What is an sp3 hybridized orbital? Nothing fancy, just a combination of s and p orbitals. It has 25% s character, 75% p character, which makes sense. It's what exists when carbon forms bonds, especially in the case of methane. That's what describes it's tetrahedral structure. That's why we have an angle between the various branches of a 109.5 degrees, which some teachers might want you know, so it's useful to know. If you take this angle right here, 109.5, that's the same thing as that angle, or if you were to go behind it, that angle right there, 109.5 degrees, explained by sp3 hybridization. The bonds themselves are sigma bonds. The overlap is along the axis connecting the hydrogen.