valence bond theory and hybridization that is the topic of interest in this next lesson in my new organic chemistry playlist so in this first chapter just a review of general chemistry and it's just a reminder of where we've come from and where we're headed we just did lessons on lewis structures and formal charges we'll now hit valence bond theory and hybridization which will feed nicely into the next lesson on molecular orbital theory and then finally we'll finish this chapter off with a lesson on polarity and a lesson on intermolecular forces all right so valence bond theory so at the heart of valence bond theory just talks about what creates a covalent bond so we like to talk about the sharing of electrons and stuff so but this takes a step further and says that atomic orbitals are actually going to overlap and that's where the electrons are going to be shared so that's kind of the heart of it so we've got to remind ourselves what these atomic orbitals look like and we want to look at first of all your 1s orbital and it's just a nice spherical orbital so a nice solid sphere like a bowling ball not a basketball so it's solid so and it just gives you an idea of where you can find an electron around the nucleus so the nucleus at the center of that sphere so and somewhere in that sphere at least to the 95 probabilities what we're usually mapping uh that's what the actual three-dimensional equation would look like and again we call those wave functions now for a 2p orbital so these we say are dumbbell shaped and there is a what we call a node at the nucleus and a node is just a place where the function goes to zero now you probably remember your sine function and your cosine function and they also had nodes so for the sine function they have nodes at all the multiples of pi it's just where the function has a value of zero now your sine function your cosine function these were two dimensional wave equations but here we now have three dimensional wave equations that describe something related to where you find an electron in an atom so cool now this is the 1s and the 2p if you actually worked your way higher like the 2s or the 3p and higher orders which you find out is one they're bigger but they also start having these radial nodes areas at a set radius around the nucleus where you also won't find electrons so but i'm going to leave those out of the discussion i really just want to focus here but the big thing take away from those that as you go to higher orders of s and p orbitals higher shells if you will they're larger and they end up forming longer bonds which are typically weaker bonds and things of this sort all right one last thing to talk about with these wave functions so just like a sine function can be both positive and negative and notice from zero to pi your sine function is positive and from pi to two pi your sine function takes on negative values and every time you cross from positive negative you gotta cross through zero and that's your note and so same thing here if we look at that p orbital right at the nucleus whether it be the the p orbital on the y-axis the x-axis or the z-axis that's the difference in those three p orbitals so they all have a node right at the nucleus and the reason they have that node is that your function is going from positive to negative and it might be positive on top and negative on bottom or vice versa it's totally arbitrary for this lovely p oval on the y axis and so sometimes instead of showing plus and minus and again this is not charge this is the mathematical sign just the values of the function itself so in this case and sometimes instead of actually showing the plus and minus sometimes what we do is actually do a difference in shading we'll shade one side not shade the other or shade one side blue and shade the other side green or something along these lines so here i'm just using one side shading and one side not shading and it's not like one means plus and the other means minus but one of them does mean plus and the other minus it's just arbitrary which is which so this just shows you that there's two different signs for the different sides of this wave function and then again that node right at the nucleus cool so again at the heart of valence bond theory is overlapping orbitals to create these covalent bonds now if we take a look at a very simple molecule to start off with and we'll just start off with a molecule of elemental hydrogen here h2 so that lovely line represents a covalent bond and what we actually really have going on is so hydrogen's got its unpaired electron it's only electron in an s orbital and those s orbitals are going to come together and overlap according to valence bond theory and that's where in these overlapping orbitals that's where the electrons are going to live that are being shared here the ones described by that lovely line there representing the covalent bond so it turns out we would call this a sigma overlap so we'll get exactly what that means here in a second so often it's not going to be easy to identify what it means until you see something that's not an example we'll see pi overlap here in a little bit if we compare this to say hf so hydrogen again has an s orbital here so that it's 1s electron is only electrons involved in so but fluorine his valence electrons are in the 2s and the 2p so and in this case his unpaired electron surveillance bond theory talks about atoms using their unpaired electrons those are the ones they share well for fluorine its unpaired electron is in one of these 2p orbitals and so fluorine here is going to overlap its 2p orbital with hydrogen's 1s orbital i've probably drawn the 1s a little big or the 2p a little small truth be told but you get the idea and again in these overlapping orbitals that's where our lovely two shared electrons are going to live that again is valence bond theory and again this is also described as sigma overlap now if i take a and highlight in blue where the nuclei are in both cases here what you find is that we say that the overlap occurs along this inter axis that's our technical term and it's just the line connecting the two nuclei and as long as your orbital overlap is occurring somewhere on that line that is sigma overlap and it turns out they give it the letter sigma here that's the greek letter sigma which corresponds to our english letter s and it's because all single bonds are sigma bonds as we'll find out in a little bit cool let's look at one more example of this and maybe if we look at a molecule of f2 so in this case both of them have their unpaired electrons in s orbitals and so your s orbitals are overlapped sideways here and once again that overlap is occurring along this internuclear axis and so once again we will refer to this as being sigma overlap cool now pi overlap is the only other type that we'll talk about in this course there's sigma and there's pi and that's it and so pi is nice so for a sigma overlap you can use any kind of orbital so you can use s's you can use an s and a p you can use a p and a p you can also use these hybrid orbitals that i'll reference a little bit later but we have sp sp2 and i didn't write it down here sp 3 hybrid orbitals those can also be used in in sigma overlap as well but pi overlap is specific and pi greek letter p essentially so it corresponds to our english letter p and you can only use p orbitals for pi overlap but we used p orbitals here and that was still sigma overlap so it's the key is it's not end to end overlap it's not overlaps that's going to take place on this inter nuclear axis it turns out it's going to be pi overlap is going to be when it occurs side to side let's do it where we got a little more room here so we got two atoms next to each other so again here's our nuclei so but the overlap doesn't occur along this internuclear line the overlaps occurring above and below that internuclear axis and so that is what we refer to as pi overlap cool and the only orbitals allowed to be involved are p orbitals and they overlap side to side not end to end we say so in summary the end to end overlap of any two orbitals that's going to be sigma overlap but the side to side overlap of p orbitals and only p orbitals that is our pi overlap and we'll find out we're only going to have pi bonds with double and triple bonds so it turns out uh when you start making multiple bonds it turns out you're only going to have one set of orbitals that actually point towards each other along this internal axis so just like here here here and so you can only make one sigma bond and that's the first one any two atoms always makes but if you're going to make any additional bonds then it can't be along this internal axis where you're already making a sigma bond any additional ones are going to have to be sideways overlap of p orbitals so a double bond would be one sigma and one pi a triple bond would be one sigma and two pi bonds all right so now i want to take a little bit deeper look at hybridization and so first off i just want to point out that you can just look at a lewis structure and determine an atom's hybridization without even understanding what hybridization is so i want to point that out first because you definitely have to be able to quickly determine hybridization and the truth is you don't really need to even understand hybridization to pull that off now you will have to have a little bit better understanding of hybridization and we will get into that in a little bit so but it turns out there's a simple relationship between the number of electron domains around an atom and its corresponding hybridization as well as its bond nickels and we related this back to like vesper theory in gen chem and things of this sort we said that so the farthest apart you could put two things is 180 degrees and so valence shell electron pair repulsion vesper theory says the electron domains around an atom want to spread out as far as possible and for two things that's 180 degrees for three things it was going to be 120 degrees so that corresponds to a trigonal planar shape whereas the 180 was linear and then finally for four things it spreads out into a three-dimensional shape instead of being nine degrees apart in three dimensions they can spread out a little further to 109.5 degrees apart in a tetrahedral shape and you can also relate this to corresponding hybridizations now again we'll get into what those mean a little bit in a little bit later and give you a little bit of understanding so but if we look at this we first got to talk about what is an electron domain an electron domain is one of two things it's either an atom that you're bonded to and i say you an atom that another atom is bonded to or it's a non-bonding pair of electrons that's it and when we say an atom that an atom is bonded to it doesn't matter if it's a single bond a double bond or a triple bond that is still just an electron domain so for example this carbon right here is bonded to four different atoms directly and has no lone pairs that's a total of four electron domains its hybridization will be described as sp3 and its bond angles would be 109.5 okay so we'll move on to nitrogen right here so nitrogen here's got three atoms that's bonded to and one lone pair also for a total of four electron domains so the nitrogen we'd say is sp3 hybridized and its bond angles are roughly 109.5 now the truth is though so with this 109.5 it turns out that the lone pair gives greater repulsion to the electrons in this bonds than they do to each other and so they get scrunched down a little bit and you should know that that occurs and so the bond angles here the angles between the actual bonds instead of being 109.5 exactly is just a teeny bit less turns out right around 107 degrees in the case of ammonia and you wouldn't be responsible for knowing that it's 107 but you should know that instead of being exactly 109.5 it is just slightly lower than 109.5 cool look at the next example here this is formaldehyde in this case the carbon is bonded to three atoms it doesn't matter this is a double bond we're just going to count that as one electron domain so one two three electron domains total because there's no lone pairs around the carbon and with three electron domains we'd say that that carbon is sp2 hybridized and that the bond angles around it are going to be 120 degrees now here's another place where the bond angles won't be exactly the number listed here because this double bond has greater electron density than these single bonds and so there's going to be a greater repulsion and so the angle between the double and the single actually slightly bigger than 120 on both sides and that forces this which gets scrunched down just a little bit to be a little bit smaller than 120 degrees now we could say again that the bond angles are approximately 120 and that's a true statement but they're not exactly in this case as well because one of the electron domains was a double bond whereas the others were singles cool we could also look at it from auction's perspective oxygen is bonded to one atom and has two lone pairs also for a total of three electron domains the oxygen's sp2 hybridized and the bond angles if it had multiple bonds in this case would be 120 well in this case it doesn't actually have multiple bonds but the angle you could say between the lone pairs is 120 or between a lone pair and a one would be 120 but that technically wouldn't be a bond angle but it would be roughly 120. finally on this last one we could look at a few different atoms we could look at the carbon on the left which is bonded to four different atoms and as sp3 hybridized 109.5 we can look at this carbon right here which is bonded to two atoms and is sp hybridized in bond angles of 180 and then we can look at the nitrogen which is bonded to one atom and has one lone pair also sp hybridized cool that's how you can identify an atom's hybridization simply by looking at it and counting the number of electron domains we'll see where this comes from in a little bit okay so i want to take a little closer look at methane here to kind of get the idea of where this you know idea of hybridization even comes from so in this case we see that carbon is bonded to four different hydrogens so and for bonding theories i'll explain that it's the valence electrons that are used in bonding so if we take a look at carbon's electron configuration it's 1s2 2s2 2p2 and if we kind of show that in diagram form here we're going to focus on the 2s and 2p electrons because those are the valence so we've got two electrons in the 2s orbital and then we've got two unpaired electrons in two different 2p orbitals now classic bond theory say that it's the unpaired electrons that are used in bonding and so we look at this and say well carbon's only got two unpaired electrons therefore carbon should only be able to make two bonds but we know that carbon makes four bonds so there's problem number one so and there's an easy solution to this problem carbon is going to promote one of the two s electrons and put it up into a p orbital and we call this a promotion cool the result is that carbon now has four unpaired electrons and now can make four bonds so when electrons are shared in a bond that lowers their energy and makes them significantly more stable so you might be like well chad why would this electron go to a higher energy orbital well it looks like that's really just going to be an investment because now by making two additional bonds there will be a significant lowering significant reduction in the energy of the electrons so in the molecule and therefore it'll be a much more stable arrangement so which is kind of the idea of why atoms make bonds to begin with but we still have a problem here so we've still got an electron in a 2s orbital and then 3 in the 2p orbitals and if you recall those two p orbitals are ones on the x axis ones on the y axis ones on the z axis and if you recall valence bond theory says that orbitals are overlapping to make these bonds well hydrogen's a valence electron it's only electrons in the 1s orbital we know what he's going to be using to overlap in all four of these cases the question is what's carbon going to be using well if we think this is what's carbon's using we're going to have an immediate problem here so let's say we got carbon here with one of his p orbitals right there and let's just say on top that's where it overlaps with the s orbital of hydrogen cool and let's say that's p y now we take a look at say p x and p x on the x axis overlaps with the s orbital of another hydrogen and the problem is is that the y-axis and the x-axis are only 90 degrees apart and that makes it appear as if the bond angles should end up being 90 degrees except we know that they're not we can look at a molecule of methane and actually measure the bond angles from electron density maps and stuff and we know they're 109.5 degrees and so what we figured out is that you know carbon's not actually using his s and p orbitals to make his bonds what carbon is actually doing is combining these orbitals to make new ones and so it turns out carbon is going to take and combine all of these four orbitals so it turns out again these orbitals are just math equations they're wave functions and when you start combining math equations well you guys have combined math equations before so we're doing something similar here it's not quite so simple as that but it's along those lines but the number of wave functions you combine is the number of different ways they can be combined as well so in this case i'm going to combine an s and all three of the p's i'm combining four orbitals it creates four brand new wave functions four brand new orbitals and since they're combinations of both s's and p's we'll call them hybrid atomic orbitals and so in this case they're going to be a little lower in energy than p orbitals but a little higher energy than the s orbital since it's a combination of the two and we don't get crafty on the name they're just based on what they're built from built from an s and three p's call them sp3s so if you're sp3 hybridized you've mixed an s and three p orbitals four orbitals total you're always going to have four of these hybrid orbitals and these still all have an unpaired electron so life is good and now we just look at what do these actually look like if we actually combine the mathematical wave functions those equations in four different ways we call it linear combination of atomic orbitals if you care so if you actually map them out so what you end up with you got carbon and then you get this long kind of funky kind of orbital that looks kind of like a pu orbital but kind of like with an extended s orbital and it's a little bit strange but it's a combination of three p's and a single s orbital to make this and it can overlap with the s world of hydrogen then you get another one that would point down over here down at an angle and it turns out this angle right here is going to be degrees turns out exactly what we see in the molecule it's not 90. it really is 109.5 degrees and the hybrid orbitals that we can create by linear combination atomic orbitals are exactly 109.5 degrees apart now it's going to be difficult for me to draw the other two of these orbital i've driven you know drawn two of them to draw the other two would be a challenge because there it's a three-dimensional shape one of them would be coming out of the board one of me going back into the board so but it would be a much better drawing if i could but i've only driven you know only drawn driven when we're getting that only drawn half the drawing here so cool but you get the idea is that now this actually is a better reflection of what we see in reality for the actual molecule of methane than trying to use the original just plain old s and p orbitals cool now it turns out that the truth is though this is kind of a lie as well it actually is even more complicated than this and we talk about molecular orbital theory in the next chapter it turns out that this idea of hybridization stuff like that it's not really a com perfect reflection of the truth either but we'll get closer to that in molecular orbital theory in the next lesson so i'm going to take a little more thorough look at hybridization we'll look at it from the perspective of carbon being that this is organic chemistry but this happens with other elements as well and again carbon has four valence electrons only two that are unpaired it promotes one so that it now has four unpaired electrons but we see if we use these regular atomic orbitals we don't get the right geometries that correspond to reality and that's again the idea behind why hybridization where that theory kind of took hold and why we suggest that it occurs now we got really three different options for carbon in this case he can mix his s and all three p's and make four sp3 hybrids that's one option and if you have four electron domains that's exactly what you want to do because those sp3s all point 109.5 degrees apart now your other option is to only combine an s with two of the p's and if you combine an s with two p's one s two p's you're only combining three orbitals you only make three hybrid orbitals and we call them sp2 hybrids just based on what they're you know what they're composed of but that leaves you with an unhybridized p orbital that last p orbital not part of the hybridization process at all left behind still unhybridized cool and that's perfectly the case these sp2 hybrids it turns out point magically 120 degrees apart so but the p orbitals left behind that electron right there because that's what you'll need to make a pi bond so keep in mind in this kind of a structure where carbon's got one double bond and two single bonds all single bonds are sigma bonds so when you've got a double or triple bond the first one is also a sigma but any additional bonds past that point are going to be pi bonds and so you can see that the hybrid orbitals are going to be used to make all the sigma bonds but it is an unhybridized p orbital that is needed to make pi bonds keep in mind again that a pi bond is always the sideways overlap of plain old p orbitals nothing else can be involved in a pi bond that's why we had to have a p over the left over to make that pi bond cool now the last option is if we just mix one s and one p orbital so if you mix a single s and a single p you're only mixing two orbitals you only create two hybrids we call them sp hybrid orbitals they magically point 180 degrees apart so and that leaves you with the last two p orbitals still in existence and they're used to make pi bonds and so when you see a carbon having a single bond and a triple bond again the single bond is a sigma bond and the first bond of the triple bond is a sigma bond as well but the other two bonds are both pi bonds and that's why we needed these two different p orbitals one for making each of those pi bonds this also happens it turns out much less commonly but if carbon's got two double bonds so the first bond on either double bond is a sigma bond but the additional bonds are also pi bonds but having a triple bond will be much more common occurrence that you'll see throughout the course cool but these are the kind of three results for carbon and it just magically works out that with sp3 hybrid orbitals they're all 109.5 apart that with sp2 hybrid orbitals they're always 120 apart and with sp hybrid orbitals they're 180 degrees apart so explaining you know how this matches up with what we know from vesper theory and how molecules really look all right so we want to visit these molecules we had on the board just a second ago and if you look at the the study guide they're in that as well so we'll look at them one more time and talk about a common question you're going to see in organic chemistry examine so what they might do in light of everything we've just presented now is talk about what orbitals are overlapping in any given bond or what orbital is a particular lone pair of electrons in so now first we want to do is go back and just you know designate hybridizations for all these lovely atoms here and so in this case carbon right here is sp3 hybridized having four electron domains nitrogen here is also sp3 hybridized having four electron domains carbon here is just sp2 hybridized oxygen was as well both having only three electron domains so the carbon on the left here is sp3 hybridized so carbon on the right is sp hybridized having just two domains and then nitrogen also sp hybridized having just two domains now the way this works if an atom is hybridized it will always use hybrid orbitals to make its sigma bonds it will also put lone pairs in those hybrid orbitals as well so if we take a look here so carbon here in this case has four sigma bonds one there one there one there and one there and he's going to use an sp3 hybrid orbital for his half of all four of those now hydrogen on the other hand is not hybridized at all he's just got that one unpaired electron only going to make one bond when that's the case he just uses the plain old regular atomic orbital not the hybrid atomic orbital and for hydrogen that's just a 1s orbital so if the question said hey for that bond right there what orbitals are overlapping to create it will carbon you'd look at and say well he's sp3 hybridized and that's a single bond so he's going to use one of his sp3 hybrids and hydron is just going to use an s orbital and those are the orbitals that are overlapping to create that sigma bond cool if we take this a little further we could also point at any one of these nitrogen hydrogen bonds and you should be like okay nitrogen's hybridized so since that also is a sigma bond the nitrogen being hybridized is going to use one of his sp3 hybrid orbitals and hydrogen once again just going to use an s orbital not hybridized at all you could also be asked well what kind of hybrid orbital is that lone pair in right there and again nitrogen is hybridized and so he's going to put that lone pair in one of his sp3 hybrid orbitals as well okay moving on to the next one here so if we were asked about one of these lovely sigma bonds between carbon and hydrogen the carbon being hybridized will use an sp2 hybrid orbital and the hydrogen's just going to play and again use his s orbital now things get interesting if we look at the carbon oxygen bonds because there's both a sigma bond as well as a pi bond and if you had your choice on which one you want to be asked about you should choose the pi bond every time because if it's a sigma bond any orbitals can be involved and you have to figure out which ones but if they say what orbitals are overlapping to form the pi bond you're just like p and p done same two every time p orbital with a p orbital carbon's got a p orbital oxygen's got a p orbital and they're going to overlap side to side not end to end but it's just going to be p orbital overlapping with a p orbital every time for a pi bond so that's like the preferred question now if we look at the sigma bond we'd have to say okay the carbon is definitely hybridized so he's going to use one of his sp2 hybrids the oxygen's also hybridized and so he also will use a hybrid orbital another sp2 and so in this case to make the sigma bond between carbon oxygen it'd be an sp2 from carbon overlapping with an sp2 from oxygen cool one more question we could ask is what kind of orbital is either lone pair on oxygen in and we have to say oh is oxygen hybridized and yes he is he's sp2 hybridized then the lone pairs will both be in sp2 hybrid orbitals as well cool and that's generally the way this works let's just look at one more example here so if we look at that triple bond yet again keep in mind that the first bond again is always a sigma any additional bonds past that are pi bonds and again if they said what orbitals are overlapping to make either one of those pi bonds p and p done but my question for you is what orbitals are overlapping to make that sigma bond so in this case we've got to look and say wait oh carbon's sp hybridized the nitrogen's sp hybridized and they're both being hybridized they're going to use one of their hybrid orbitals to make that sigma bond and so in this case that's going to be an sp hybrid with an sp hybrid from nitrogen as well those are the orbitals overlapping to make that particular sigma bond and this is how it works so you could be asked this in kind of any context they'll just give you some random lewis structure and either ask you what two orbitals are overlapping to create a bond or maybe possibly less likely but possibly what orbital is a lone pair of electrons residing in cool hopefully this makes a little more sense than it did when you got it in gen chem it's a place we often scrimp a little bit and students just often don't come away with quite as good of an understanding as they could