The material for this lecture is in Concept Development Study 9 entitled Energy and Polarity of Covalent Bonds. Recommend that you want to read this material book before and after listening to this lecture. There's a lot of important information content in here, some of which can be fairly challenging. We're going to go back in and revisit this concept of the covalent bond. We'll go back to concept development study seven. We located a covalent bond as being the primary way in which atoms bond together by sharing a pair of electrons. We didn't say much more abuot it than that, but we did use that to develop the whole meachnism by which we could talk about molecular bonding. But what does it actually mean to share an electron pair because we don't really know where electrons are. We don't understand how atoms can share the electrons. We might actually also then ask what if we bonded together two unlike atoms say carbon and oxygen do they actually share the electrons. After all the properties of a carbon atom and the properties of an oxygen are not the same. Perhaps they don't share. And ultimately, actually sort of the big question, what is a bond anyway? We've sort of taken it for granted. But somehow or another the atoms hooked together, and we call that hook a bond. We haven't really described it, or even what it means for two atoms to bond together. Other then the fact that in someway or another then they form a molecule. To answer these questions, I'm going to make some experimental measurements having to do with the very, very simplest possible molecule H2 plus. This is why that's the simplest molecule. Each hydrogen of course typically would bring one electron into the molecule and H2 should be neutral. But H2 plus apparently missing one electron. So it's only got one electron. So if we have H2 plus then it has a rather simple structure. It has a plus 1 nucleus for one hydrogen and a plus 1 nucleus for another hydrogen and then a single electron. That we guess is probably somewhere between those two, since we believe that the electron would be shared. Now, our idea of a covalent bond was that there were two electrons being shared. In H2 plus there's clearly only a single electron. We might have thought, perhaps, that wouldn't form any kind of a molecule, or in this case a molecular ion, but it does. And the proof of that is, in fact, experimentally that it costs energy to pull the two nuclei farther apart from each other. If I actually wanted to separate this into a a, a hydrogen atom. And the hydrogen nucleus just an h plus charge to go from this down to this would require breaking the bond. And the amount of energy required to break that bond turns out to be a decent amount 269 kilojoules per mole. Why does it cost us energy? Well keep in mind that any time we're going to break a relationship to two things that are attracted to each other cost us energy. I have a couple of magnets here and you can get your own magnets and figure this out. But if you'll notice if I actually try to pull the two atoms apart it takes some effort on my part. If I let them come back together they do so without any effort on my part, in fact they release energy to me. But to break the bond, costs me energy. Correspondingly then, the energy here for the H2 plus is the energy required to pull the two atoms apart from one another. but if I'm putting energy in to break that bond. Where does that energy actually go? When I actually pull them together, what energy has been elevated in the process of pulling the two atoms apart? Why does it cost us energy? To answer that question, let's think about the coulombic interactions here amongst the charged particles. Let me do another drawing of the H2 plus here. Well, we draw this. Here's a positive charge. Here's a positive charge. And if the electron is located, perhaps, somewhere between the two, what we wind up with is a. Positive or a strong attraction actually a negative potential energy of attraction. For the electron not just to one nucleus but rather two two nuclei. If you think about Coulomb's Law, an attraction of an electron to it's nucleus lowers its potential energy. So attracting of the electron to two nuclei simultaneously lowers the potential energy even further. So the electron itself lowers its potential energy as a consequence of the sharing. What is sharing in this case mean It means that the electron is in fact located in this region between the two nuclei. That deals with the potential energy, turns out that also the kinetic energy is also lower for reasons that we won't discuss until a little bit later. So what does that mean? It means if I'm going to pull these two atoms apart, I'm going to have to elevate the energy of the electron to get it to be simply with one of the nuclei and not the other. So the bond actually forms as a lowering of energy for the shared electron. In order to pull the atoms apart I have to add energy to the electrons so that it has enough energy to be with one nucleus instead of both of them. That's where the energy actually goes as I attempt to break the bond. Let's think about more detail now because we're not all that interested in H2 plus. That's a pretty unique molecule. What we're probably really interested in is H2. And in H2 of course, we have two electrons forming the usual shared pair of electrons. And in H2 of course, we have two electrons forming the usual shared pair of electrons. In that case, I might have a second electron here, which is strongly attracted to the two nuclei. Of course there's also electron, electron repulsion here. Or would it be the case that two electrons is better than one, because we've got the two electrons being attracted to the two nuclei. Or would it be the case, that two electrons might be worst then one, because they repel each other. And for that matter, if two is better then one, is three better then two? Could I add a third electron in here, and somehow lower its energy as well? With a good covalent bonds are formed by two electrons, being shared, but maybe you could actually have them three. Why is two actually the appropriate number? To answer this question we actually have to go back and remember something that we know about the motion of electrons. Remember that the motion of electrons is determined by two descriptions having to do with the fact that it has wave like motions. First, it has to do with the uncertainty principle. In other words, the drawing that I've drawn here is actually not a good drawing at all, because I've localized the electrons in space. But we know we can't localize the electrons in space. We cannot know where the electrons are, because the electrons move like waves, and by moving like waves, their location is uncertain. We actually don't know where they are. So what can we know? We recall what we can know, is a probability map for where the electron might be found. And this probability map, as you recall, we referred to as orbitals, and orbital is a probability distribution that tells us where the electron is most likely to be, and where it is unlikely to be. Remember that we get the molecular, or, I'm sorry mechanical orbitals out of quantum mechanics. We do a quantum mechanical calculation for the molecular orbital in H2. We get a diagram that looks something like this. Remember that this is a dot diagram and the more dots there are the higher the probability for the electron to be in that region of space. So we have very limited probability for electrons out here in the outer regions of, of this space. So out here not so much, in here, oops, in here quite a lot. So we actually see then a build up of probability in the region between the two nuclei. But why is that significant to us? If the electrons are in the region between the two nuclei, then in fact, they're going to have their potential energy lowered because they're attracted to two centers rather than one. Just as we just described a minute ago. Furthermore, if we look at essentially the extent of this orbital. How much space it has in both x and y and actually in a third coordinate here, if we could see it. We see that the electron has more room to move around. You should recall when we confined an electron, it's kinetic energy goes up. So within the molecular orbital is actually less confinement. So what we can say, if we look at the molecular orbital for H2, that's this diagram here, we have two properties that are very important. One is a build up of probability between nuclei. And the second is a decrease in confinement particularly along the bond axis. Both of these factors actually lower the total electron energy relative to the seperated atoms. Meaning that if I wanted to separate the atoms, I would have to add quite a lot of energy to elevate the energy of the electrons. And now the question is, why two? And the answer is, we remember from our quantum mechanical description of atoms that we can put two electrons into a particular orbital. And if we put two electrons in, then if one electron has its energy lowered. Two electrons will have their energy lowered even further. But we can't put a third in because the exclusion principle tells us that in this particular molecular orbital. There can be only two electrons, which move in that particular fashion, in that particular probability distribution. As a consequence, lowering the energy of the electrons is what creates the chemical bond. And two electrons are better than one, which is why we share a pair of electrons and a molecular orbital which has the properties here of a build up in probability between the two nuclei. And a decrease in confinement along the bond access. The remaining questinos had to do with what if the atoms are not the same. In this particular case, we've only considered atoms of like type. In the next lecture, we're going to consider atoms of different type.