Hybridization is going to be the topic of this lesson. And we'll actually introduce valence bond theory to start, which kind of talks about atomic orbitals overlapping during bond creation. And then we're going to talk about the different hybrid orbitals, sp, sp2, sp3 hybrid orbitals, and even some of the more complex ones for expanded octets. And we'll talk about how you look at a Lewis structure and know the hybridization of an atom, as well as look at a bond and know what atomic orbitals or hybrid orbitals are overlapping in the creation of that bond. My name is Chad, and welcome to Chad's Prep, where my goal is to take the stress out of learning science. Now, in addition to high school and college science prep, we also do MCAT, DAT, and OAT prep as well. You'll find those courses at chadsprep.com. Now, this lesson's part of my new General Chemistry playlist. It covers an entire year of General Chemistry. I'm releasing several lessons a week throughout the school year, so if you want to be notified every time I post a new one, subscribe to the channel, click the bell notification. All right, so we're going to start with talking about valence bond theory, and valence bond theory says that... Atoms use their unpaired electrons to form bonds, that's the first part, and so, you know, each of two atoms are going to chip in an unpaired electron, and that pair of electrons is now going to be shared to create a bond, but it says a little more than that as well. It says that there's orbitals, the atomic orbitals from both of those atoms overlapping in the process of bond creation. So if we take a look at, say, a molecule of H2, and these are the three molecules to take a look at here. With H2, we can see that each of these hydrogens... only have a single electron, 1s1, and so it has to be that unpaired electron in the 1s orbital that is involved in bond creation. And so if we look at an s orbital, an s orbital is spherical in shape, and so for both hydrons, their s orbitals are going to overlap, and they're going to have the two shared electrons in these overlapping orbitals, and that's kind of what valence bond theory looks at as the creation of a bond. And so we've got a nucleus there, and a nucleus there, and then overlapping orbitals sharing those electrons. Now, In the case of HF, it's a little more complicated because even though, again, hydrogen is 1s1, well, fluorine, 1s2, 2s2, 2p5. And if we draw out the valence electrons in the 2s and the 2p, we see the unpaired electron is in one of the p orbitals. And so hydrogen's still got that 1s orbital that's going to be involved in bond creation. But the fluorine... is going to have a p orbital overlapping with that, the one with the unpaired electron in it. And again, overlapping orbitals is going to lead to the creation of a bond, according to valence bond theory here, with the sharing of two electrons in those overlapping orbitals. And so in this case, it's a 1s orbital from hydrin overlapping with a 2p orbital from fluorine. And finally, we'll go to a fluorine molecule, an F2 molecule. And in this case, both fluorines have that unpaired electron in that 2p orbital. And so it'll be overlapping. p orbitals in both cases. So, and in this case, that's the overlapping orbitals leading to the creation of the bond in a molecule of F2, once again, according to valence bond theory. Now, we'll talk about molecular orbital theory in the very last lesson in this chapter, which will kind of build on valence bond theory and then take it to a whole new level. And it turns out it's actually a better depiction of reality. But valence bond theory, we'll suffice it to say, will fit for most of our purposes in this chapter. And many of you actually... won't even probably be on the hook for molecular orbital theory in your general chemistry course. So I'd say it's probably 50-50 for most students. Cool, so this is Valens Bond Theory and we wanted to introduce this because we'll find out that when you've got an atom that's making more than one bond, the original atomic orbitals like just an s orbital or just a p orbital, so those are not actually going to be sufficient to get the bond angles we now recognize in the molecular geometries we've learned about like again linear, trigonal planar, tetrahedral, so on and so forth. And so it turns out if it's not using the original atomic orbitals to make bonds to, you know, get these overlapping orbitals, then what is it using? Well, it turns out it's going to be using these hybrid orbitals, which are going to be combinations of the different S and P and expanded octets, the d orbitals even get involved as well. So let's take a look at that. All right, so we're going to take a look at methane here, CH4, and use it to kind of describe why this need for hybrid orbitals even comes about. We'll find out the atomic orbitals carbon has available here are just not going to be sufficient to form a molecule of CH4. So first of all, we've got a couple of problems we're going to encounter, and the first one we're going to encounter is that carbon, notice 1s2, 2s2, 2p2, so it's got four valence electrons. And if we look, only two of them are unpaired. And valence bond theory says that, again, an atom is going to use its unpaired electrons to make bonds. Well, that would mean, that would seem to imply that carbon is only going to make two bonds, but we know that carbon routinely makes four bonds. Again, only having four valence electrons, it's four electrons short of a filled octet, which is why we typically find it making four bonds. Well, again, valence bond theory here is having a problem and an issue with this. Well, valence bond theory does get around this, and it turns out that We're going to undergo what's called a promotion. So, and in this case, we're going to promote one of these electrons here up into a higher energy orbital. So just like when you get a promotion within a company, you get a higher position in the company. Well, here this electron is going to end up in a higher energy atomic orbital. Okay, so, so far so good. We now have four unpaired electrons and carbon is now ready to make four bonds. So now we're going to have a problem though. We know methane, so it's got four electron domains. We know the molecular geometry is going to be tetrahedral. We know all the bond angles are 109.5. And that's where we're going to start having a problem here. So, Let's say we take a look at these four unpaired electrons and the orbitals they're in, and I'm just going to ignore the s orbital for a minute because it's spherical and it could really be oriented anywhere, but these p orbitals are going to be the telling part that will help us kind of identify the issue. And so if we have one of these p orbitals, is going to be vertical, one of them is going to be horizontal, and one will be coming out of the board. They're all oriented 90 degrees apart, one on the x-axis, one on the y-axis, one on the z-axis. We often refer to them as px, py, and pz. So, but one of them will be oriented that way, another one's going to be oriented that way, and then again another one that I won't need to draw that'll be coming out of the board. But even if I just look at these two right here, well, again, that's where these unpaired electrons are, at least three of them are in these p orbitals. And if these are the orbitals that are overlapping with the s orbitals, the 1s orbitals of hydrogen, so we could kind of see where those bonds are going to form and say one of them could form on either side here. So we'd have a hydrogen bonding right there and maybe another one right here and have another hydrogen overlapping with part of the p orbital there. And the problem we get though is that this angle right here in this bond to the hydrogen here and the bond to the hydrogen here is going to be a right angle, 90 degrees. And so that is a huge issue because we know that the bond angles in methane are not 90 degrees. We can actually measure them. They come out to be 109.5, just like we've predicted with our molecular geometries, and they're not 90. And so the conclusion we come to is that these p-orbitals can't be the orbitals that are involved in overlapping to create these bonds, again, according to valence bond theory. And so it turns out what carbon is actually doing here is carbon is actually going to take all of his orbitals. And he's going to mix and combine them. And this process we call hybridization. And this is going to seem very weird, so a couple things we should talk about. So first of all, where do the shapes, you know, p orbitals being dumbbell shaped and s orbitals being spherical shaped, where does that even come from? Well, one, they're solutions to the Schrodinger equation, but they themselves are equations. They're three-dimensional wave functions, we call them, but they're just mathematical equations, three-dimensional equations. And so if you take these equations, it turns out you can combine them in a process we call linear combination. But just think of it. It is akin to like adding these wave functions in different ways. And we're going to mix and match and add them in different ways, combine them in different ways. And it turns out if you combine four different wave functions, i.e. four different orbitals, you can combine them four different ways. And it leads to the creation of four brand new orbitals. And in this case it turns out they're going to be a little higher energy than the s-orbital but lower energy than the p-orbitals because they're made from both. And we're not going to get crafty on the name here. They're made of 1s and 3p orbitals, so we're just going to call them sp3 hybrids. And the number of orbitals you mix together to create the hybrids, that's how many hybrids you're going to create. And so being sp3 hybridized, you have to have four of them. And that's where the electrons now reside in these sp3 hybrid orbitals. And if you take a look at what an sp3 hybrid orbital actually looks like, So it looks like kind of a fat p-orbital on one side and a rather small diminished one on the other side. So, but that's what an sp3 hybrid looks like. And again we have four of these and let me draw a second one in right here. And it's actually these that are overlapping with the s orbitals of our hydrogen atoms and Guess what the angle between these lovely sp3 hybrids is magically it's 109.5 degrees now There's two more of these sp3 hybrids, but I'm gonna really struggle to draw them because again the tetrahedral shape is three-dimensional but one of them would be coming out of the board over here, and then one of them would be going back into the board, and I'm just not the artist to be able to draw those. But rest assured, I've only drawn two out of the four SP3 hybrids, and they're all 109.5 degrees apart. And so this is kind of what gives credence to this idea of hybridization here, is that the different linear combinations, we call them, that we can do with the S and P orbitals would lead... to four brand new wave functions that do point indeed 109.5 degrees apart. So, and that's what we're going to use in the case of methane here. Now, if you take a look here, it turns out you can simply look at the number of electron domains and know exactly what the hybridization is. It turns out if you've got four electron domains, well, that means you're going to need four hybrid orbitals, one for every single electron domain. Well, if you need four hybrid orbitals, then you need to mix four of your original atomic orbitals. And so, and in this case, an S, a P, a P, and a P, and you're SP3 hybridized. So if you have four electron domains, you're SP3 hybridized, done. Okay, so if you have three electron domains, well it turns out you have another way of combining these, and with three electron domains it turns out you wouldn't need to use, you'd still use the lowest energy s orbital first, and then you'd use two out of the three p orbitals, but you'd leave the last one alone. And in that case, that's not what methane does, but in that case... you'd end up just combining three of the orbitals and then leaving one of the p orbitals alone. And so in this case, because you just mixed an s and two of the p's, we just refer to the hybrids as sp2 hybridized. And then you just have an electron in an unhybridized p orbital, a plain p orbital that's not part of the hybrids, and we say unhybridized in that case. And it magically turns out that these three different sp2 hybrid orbitals would be exactly 120 degrees apart, part of a trigonal planar electron domain geometry. And so it turns out if you have three electron domains, you're going to be sp2 hybridized. You'll have three of those sp2 hybrid orbitals, and they will magically point 120 degrees apart. So, well, it turns out carbon has one more option here, and carbon, let's say, only has two electron domains. Well, if carbon only has two electron domains, well then he only needs two hybrid orbitals. And if he only needs two hybrid orbitals in the end, well then he only needed to mix two of the original atomic orbitals. And you'll always start with the S, the lowest energy one, and then it only needs to mix in one other P. And so instead of mixing the S with all three Ps, or mixing the S with two out of the three Ps, In this case, he's just going to mix the S with one of the Ps. And we won't get crafty on the name. We'll just call those SP hybrids. And then we'll have two unhybridized P orbitals in that case. And we'll kind of see where this fits into place when we start looking at multiple bonds and sigma and pi bonds in the next lesson. Now in this case, in this example with methane, carbon's fate looks like this. He was sp3 hybridized with four electron domains, and so he had four sp3 hybrid orbitals, and he had no unhybridized p orbitals left. So, but if you took a look at something, you know, maybe a case with carbon with three electron domains, like maybe we take a look. at a molecule of formaldehyde here, and this carbon right here just has three electron domains. He's bonded to three atoms. He has no lone pairs. So with three electron domains, he would be sp2 hybridized, and in the end, he would look like this. And it turns out with three electron domains, one sp2 hybrid orbital for each of the domains, and then we'd find out that that p orbital has a special purpose in making the double, the second of the double bond. Cool, and then finally sp hybridization happens when you have two domains. We might see this like in a molecule of carbon monoxide. In the case of carbon monoxide here, carbon again only has two electron domains. One is the atom he's bonded to over here in oxygen and the other is the lone pair. In this case, being sp hybridized, he's going to have two sp hybrid orbitals, one for each domain. One is going to be used in bonding to the oxygen, but the other one is going to be where the lone pair on the other side resides. That lone pair is actually going to be in one of these sp hybrids in the end. And then finally, we'll find out that the other two bonds in the triple bond, it's going to be the p electrons here in the p orbitals. They're going to be involved in making those. Again, we'll see that in the next lesson. But I kind of want to lay the groundwork here. for just basically seeing that once you know the number of electron domains coming off an atom, you can identify what its hybridization is. And again, two domains, sp hybridized. Three domains, spp, sp2 hybridized, we say. Four domains, sppp, sp3 hybridized. Now, if you've got an expanded octet and you have either five or six electron domains, you're out of p orbitals. There's no such thing as like sp4 or sp5. You've got to actually start adding in d's. And so with five domains, it would be sppp. and then a D, and so it'd be sp3d hybridized. And with six domains, it would be spppdd, a second D, so it'd be sp3d2 hybridized. And so really quickly from a Lewis structure, just count up the electron domains. And if you can count them up, you can indicate what the hybridization is. Even if you don't even understand this, you can still indicate what the hybridization of that atom is. But again, one thing you should realize is that if you're sp hybridized, you will have two sp hybrid orbitals if you're sp2 hybridized you will have three of those sp2 hybrids if you're sp3 hybridized you will have four sp3 hybrids in the end just like so if you are sp3d hybridized you will have five of those hybrid orbitals in the end and if you're sp3d2 hybridized you will have six of those hybrid orbitals in the end now it turns out a lot of classes will probably leave out talking about those expanded octets and for good reason they might not really be part of the good theory and stuff according to some people and uh Whether you have them or not, I put them on the list just to be kind of thorough and stuff like that, but some of you may not be introduced to them for a variety of reasons. So... Cool. I'm going to stop there. I put a lovely diagram on the study guide there showing kind of where an SP hybrid might come from and stuff like that. But I'm going to reserve talking about that in the last lesson in this chapter when we talk about molecular orbital theory. Now, if you found this lesson helpful, would you consider hitting that like button? And if you would rather not hit that like button, then I need you to call your mom and just remind her that you love her. So if you're looking for any sort of practice for your gen chem class, check out my general chemistry master course. Over 1200 questions, quizzes, chapter tests, practice final exams, lots of opportunities to put into practice what you've learned in these lessons. I'll leave a link in the description, free trials available. Happy studying.