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Chemical Science - Covalent Bonds - Lecture 11

Principles of Chemical Science/n * Email this page/nVideo Lectures - Lecture 11/nTopics covered: /nCovalent Bonds/nInstructor: /nProf. Sylvia Ceyer/nTranscript - Lecture 11/nOK. Great./nLet me pick up where we left off on Friday. And that is we were talking about some of the physical and chemical properties of the elements as we go across or down the Periodic Table. And one of those properties that we were talking about was the electron affinity, which I defined for shorthand just EA./nAnd we saw that, for example, if we add an electron to chlorine to make the anion, chlorine minus, that there is an energy change associated with that reaction. And that energy change was minus 349 kilojoules./nAnd what we saw is that the electron affinity is defined as the negative of this energy. So the electron affinity here is minus this delta E. So if you have a reaction that you write with something plus an electron to give the anion here, the change in that energy is this, in the case of chlorine, but the electron affinity is defined as minus that./nAll right. So chlorine we say has an electron affinity of 349 kilojoules per mole. And it is positive. Now, unlike the ionization energy, the electron affinity can be negative. For example, if you take nitrogen and you try to stick an electron on it to make n minus, delta E for this reaction is positive./nWhen delta E is positive it means, of course, that the anion, the product here is less stable than the reactant or the neutral atom. You cannot put an electron onto nitrogen. It won't stay there. It will fall apart./nIt is not bound. And, therefore, nitrogen here, the electron affinity of a nitrogen atom is minus 7 kilojoules per mole. So you can have a negative electron affinity. So nitrogen has a negative electron affinity./nAnd you can understand it in terms of the electronic structure of nitrogen. If you draw the states of nitrogen and put the electrons in the states here, here is the electronic structure of nitrogen, just nitrogen neutral./nBut now if you go and you try to add another electron to the nitrogen it's going to have to go into one of these filled states. There is a repulsion between these two electrons. That repulsive interaction is large enough so that the attractive interaction between the electrons and the nucleus is not great enough to overcome that negative interaction, that repulsive interaction./nAnd, therefore, the electron affinity here is negative or, in other words, this delta E here is positive. So you can understand that in terms of the electronic structure. The other atoms that have negative electron affinities are the inner gases./nHere is a plot of the electron affinities. Here are all the inner gases. They all have negative electron affinities, because you're trying to put an electron in the next shell. That's a higher energy state./nThe charge on the nucleus is not large enough to compensate for that extra energy to promote that electron, to put that electron in that higher energy state. All right. So let's look at what happens here as we go across the Periodic Table to the electron affinities./nAs you go across the Periodic Table, the bottom line is, in general, that the electron affinities increase. They get larger as you go across the Periodic Table. They get larger because the z on the nucleus is getting larger./nThe charge on the nucleus is getting larger. When that charge gets larger the Coulombic interaction between the nucleus and the electrons is greater. And if that's greater, well, then the electron affinity here is going to go up./nAnd it's greater because remember that potential energy of interaction is minus Z times e, the charge on the nucleus times Z over 4 pi epsilon knot r. If Z is going up, this interaction Coulombic attraction becomes greater./nBut at the same time we've got another parameter here, and that's r. And r, as you go across the Periodic Table, is remaining essentially constant because you're in the same shell. So if you're in the same shell, r is about constant./nAnd so the only thing really changing is Z. And so the electron affinity goes up. The same reason why the ionization energy goes up as we go across the Periodic Table, as we talked about last time./nAll right. But now, in general, let's look at going down the Periodic Table here. All right. Fluorine. Chlorine. Bromine. Iodine. Well, in general, the electron affinity actually goes down. And the electron affinity there goes down because r is, in general, getting larger./nYou're putting electrons in shells that are further and further away. Z is also getting larger, but not fast enough compared to r. So, in general, that electron affinity goes down. There are always some glitches, but in general that is the trend./nOK. So then the other property that I wanted to talk about is the atomic radius. And the atomic radius here is plotted on the side. And let's look at what happens as we go across the Periodic Table here./nWell, in general, as we go across the Periodic Table, the atomic radius is going down. The atomic radius is going down because again Z is going up. The charge on the nucleus is getting larger meaning that attractive interaction is getting larger, meaning that those electrons are pulled in closer./nNow, as you go across the Periodic Table again, your r is remaining roughly speaking the same in the sense that the electrons are in the same shell with the same principle quantum number. So, in general, that's remaining the same./nSo that's not changing. It's Z that is changing as you go across the Periodic Table. And that is the dominating factor, the change in Z. The change in Z brings those electrons in closer. And, therefore, the radius actually goes down./nAnd then what about down the Periodic Table, down a column? Well, in this case, as you go down the Periodic Table, again, Z is also increasing. But it's r that is changing faster than Z because you're having electrons in shells that, on the average, are a farther distance away from the nucleus./nAnd that is increasing more rapidly than Z is increasing so, therefore, this radius here is getting larger. All right. So those are the three big trends across the Periodic Table that you should know./nIonization energy and electron affinity increase as you go across, radius decreased. Ionization energy and electron affinity decrease as you go down a column, radius increases. That is something that you do need to know./nOK. Now there is one other concept or quantity that I want to make you familiar with, and that is something called the electronegativity. And the electronegativity is really an empirical concept. We're going to use the definition gave by Mulliken in 1934 as opposed to Pauling's definition./nMulliken's definition is a little bit more straightforward. And the electronegativity is often just labeled chi, and it is given by one-half times the quantity ionization energy plus the electron affinity./nThat is out electronegativity. So the electronegativity here is kind of some average of the ionization energy plus the electron affinity. The electronegativity is some measure of the tendency of an atom to accept an electron or to donate electrons./nSo if the electronegativity of an atom is high that's a good electron acceptor. If the electronegativity of an atom is low, well, that's a good electron donor. For example, if you look at the Periodic Table here and you look at electronegativities, the elements that have high electronegativities, high chi here, are in the upper right-hand corner./nThese atoms have large electronegativities because they have high electron affinities and high ionization energies. These atoms are good electron acceptors. They're good electron acceptors because their electron affinity is high./nThe change in the energy when you add an electron is very large and negative meaning the electron affinity is high. They're good electron acceptors. They're also good electron acceptors because their ionization energy is high./nIt is difficult. You have to put a lot of energy into the system to remove the electron. They're good electron acceptors. On the other hand, if you look at the elements down here in the left-hand lower corner, these elements have low chi./nThey have low electronegativities. They are not good electron acceptors. Their electron affinity is low and their ionization energy is low. So these elements here are good electron donors. Their ionization energy is low./nYou don't have to put in as much energy to pull an electron off as you do for some of the other elements. They have low ionization energy and low electron affinity. All right. So you can already suspect that some of the strongest ionic bonds are going to be made between those elements with high electronegativity and those with low electronegativity./nBecause in an ionic bond, as we're going to talk about, there is this unequal sharing of electrons. So strong ionize bonds are typically made between elements of high electronegativity and elements of low electronegativity./nAll right. And then finally one other concept, or one other definition that I just wanted to make sure everybody was on the same page with is this term here, isoelectronic. Isoelectronic means having the same electron structure, having the same electronic structure./nAll of these atoms and ions have the 1s2 2s2 2p6 electron structure. So nitrogen here. Nitrogen has added three electrons. That makes it minus three to get this electronic structure. Aluminum has pulled three electrons off to get this electronic structure./nThese are isoelectronic. And typically the common ions that are found in nature are ions that have this octet, this inner gas kind of structure to it like the neo structure. So, for example, typically you will see a nitrogen minus three ion./nYou won't see nitrogen minus two because that doesn't have the inner gas configuration. You will see oxygen minus two but you won't see oxygen minus one because that doesn't have the inner gas configuration./nAll right. So common ions in nature are ions that have either added or removed electrons to obtain that inner gas configuration. OK. So those were a little bit of the odds and ends that I wanted to just make sure that we all understood each other about them./nAnd now what we're going to do is we're going to move on, and we're actually going to start talking about what chemistry is all about. And that is the formation of bonds. We're going to take these atoms now and we're going to put them together and we're going to make some chemical bonds./nSo I am going to start to talk about this just in terms of what are the fundamental interactions that are taking place in a chemical bond. So that's what I will do for most of the rest of the hour today, is to talk about those fundamental interactions that are common to all chemical bonds./nAnd then at the end of the hour, I'm going to tell you about one very simple model for bonding which are these Lewis diagrams. And then in the next few days we will look at some more sophisticated models./nWe'll look at molecular orbital theory and we'll look at hybridization. That is the plan. So today just the elementary principles behind chemical bonds, the elementary interactions and a start on Lewis structures./nLet's take hydrogen. That is going to be our prototypical molecule. If we have two hydrogen atoms that are far apart, well, we have the hydrogen nucleus here which is positive and its electron, which we'll call electron A./nAnd they're sort of attached. And way out here is another hydrogen atom. Here is the nucleus and its electron, electron B. And so in the separated atom limit, the interaction that we've got is the electron-nuclear attraction./nThis electron is attracted to this nucleus and visa versa. It's that electron-nuclear attraction that is operable in both of these hydrogen atoms. But now, as these two atoms come closer together, well, this nucleus here is bringing its electron along and this nucleus here is bringing its electron along./nBut what happens is, as they get closer together, this electron that was only attracted to this nucleus, nucleus A, now begins to experience an attraction to nucleus B. And this electron that was attached only to nucleus B experiences an attractive interaction here with nucleus A./nAnd it is that mutual attraction of the electrons for both nuclei that actually is the force, the energy of interaction that brings the two nuclei together, and ultimately a chemical bond is formed./nHowever, at the same time that you now have this additional attraction, this attraction, say, of electron A not only to its original nucleus but to the other nucleus, at the same time as you bring those two together, well, you're bringing the electrons together./nAnd the electrons have like charges and they repel. So, at the same time now, we've got a repulsion, an electron-electron repulsion that is coming into play. And, at the same time to that, we're bringing the two nuclei together, which are both positively charged./nWe've got a repulsion coming up there also. And so the formation of a chemical bond here is an interplay between three very strong interactions, this electron-nuclear attraction, the electron-electron repulsion and the nuclear-nuclear repulsion./nAnd so what we want to take a look at is how those energies actually change. And the components change as a function of the distance between the two nuclei. That's what we are going to look at today./nSo I am going to take two hydrogen atoms here, H, H, and I am going to plot the energy of interaction as a function of the distance between those two hydrogen. So that distance between the two hydrogen here is r./nThat's the distance between the two nuclei. Now, I've changed my definition of r. Up until now we've been talking about r as the distance between the electron and the nucleus, but I just changed it in this discussion of the chemical bond./nIt's the distance between the two nuclei. This is important. Now let me plot this energy of interaction here. And I am going to write this as energy. This is the energy of interaction. It's going to be in kilojoules per mole./nAnd I am going to plot it as a function of r, this distance between the two nuclei. And what I am going to find, this is going to be zero of energy here, is that way out here where the two hydrogen atoms are separated, this energy of interaction is going to be minus 2624 kilojoules per mole./nSo this is hydrogen plus hydrogen. Hydrogen atoms infinity separated. But now I am going to bring those two hydrogen atoms together. And what happens is that the energy will go down. The energy of interaction will go down, it will keep going down until some point, and then it will start going up./nAnd that energy of interaction will be actually at some value r here greater than what it was in this separated atom limit. Now, everywhere where this energy of interaction is lower than the separated atom limit -- Everywhere along these values of r we have a chemical bond./nThe two hydrogen atoms are bound because their energy of interaction is lower than that of the two separated hydrogen atoms. Where it is the lowest, where that energy of interaction is the lowest is the equilibrium bond length./nThat's what defines the bond length, is the value of r at which that energy of interaction here is the lowest, is the most negative. That's the equilibrium bond length. In the case of H2 that bond length turns out to be 0.4 angstroms./nEverywhere here, where that energy of interaction is lower than that of the separated hydrogen atoms, from here to here, we call that the attractive region of the potential energy of interaction. We call that the attractive region, because everywhere here, from here to here two hydrogen atoms are bound./nThey are lower energy than that of the separated hydrogen atoms. So, in other words, they are bound if they are at this value of r. They're bound if they're at this value of r. It's just that they are most strongly bound at the equilibrium bond length./nSo that's how you read the curve. This well here, if you will, we call this sometimes a well, that's the attractive region of this energy of interaction curve. Sometimes we call it the potential energy of interaction./nAnd then another important definition here is the change here from the bottom of this well to the separated atom limit, as you measure it from the bottom to the separated atom limit that energy change I'm going to call delta e sub d./nThis is the bond association energy. This is how much energy it's going to require to dissociate the H2 molecule if it's sitting in its equilibrium position from here to here. That turns out to be, in kilojoules per mole, 432 kilojoules per mole./nThat's the bond association energy. But you also notice here something a little peculiar in the sense that you can bring these two hydrogen atoms in. And if you bring them in too close, that is if you start to push them in closer than their equilibrium bond distance the energy of interaction goes up./nAnd you can keep pressing them in. And the energy of interaction will go even further up. In other words, will increase more as you push those two hydrogen atoms in. The energy of interaction can get above that of the separated hydrogen atoms./nAnd it's this region of the potential energy of interaction that we call the repulsive region. It's repulsive because if you push those two hydrogen atoms closer than about this point right here, those two hydrogen won't stick together./nThey're even closer than the bond length, but they're not going to stick together because their energy of interaction is greater than the separated hydrogen atom limit. So that is, in general, what the energy of interaction looks like for every chemical bond./nBut this curve here is really given by the competition and the interplay between these three interactions that I started talking about right here. And so I want to try to decompose this curve into those three interactions./nAnd that is what we're going to do now. We're going to try to explain why that curve has the shape that it actually has. I started out saying that this energy of interaction, I will just call it energy of I here, was really the sum of three interactions./nOne of those interactions was the nuclear-nuclear repulsion between the two nuclei. That's one. Another one of those interactions was the electron-nuclear attraction -- -- between the electron and both nuclei, or between both electrons and both nuclei./nAnd the finally, the third, is this electron repulsion between the two electrons as we bring the two hydrogen atoms closer together. So those are the three components. Now, what I want to try to do is I want to try to figure out an r dependence for each one of those components./nI want to see how each one of those components change with r. And then when I add that up, I should get something that looks like that. OK? All right. So how are we going to do that? Well, first of all, I am going to realize that with a nuclear-nuclear repulsion, what is that r dependence going to look like? You want to guess? Coulomb interaction, right? Coulomb interaction between like charges./nThat's what that r dependence is going to look like. So that's e squared for the hydrogen atom, the charge on the nuclei. Each hydrogen atom is e over 4 pi epsilon knot times r. In the case of the nuclear-nuclear repulsion right here, I've got a very good handle on what that r dependence for that interaction energy should look like./nHow come I ran out of board here? Oh, wait a minute. All right. Let me draw that. So I have the energy of interaction here. And I've got a zero of energy. And so I'm drawing a one over r dependence there./nWell, one over r looks like it starts at infinity and drops off to zero for very large values of r. So this is my nuclear-nuclear repulsion. That is this dependence right over here. I have one of the components, but now what about the electron-nuclear attraction and the electron-electron repulsion? Well, it turns out that I have no simple way to predict the r dependence for the electron-nuclear attraction or the electron-electron repulsion./nI have no simple way to do that without doing a sophisticated calculation. And, in fact, I don't even have a simple way of doing that if I want to sum these two terms. These two terms are really the electron interactions./nThese two terms involve the electron-electron repulsion, electron-nuclear attraction. This one didn't have any electrons in it. So I have no simple way to do that. However, what I can do is that I can evaluate the sum of these two energies at two extremes./nI can evaluate the sum of these two energies when r is infinity way over here, and I can evaluate the sum of those two terms when r is at zero way over here. So I am going to have two points, and then I am going to interpolate between those two points to get my r dependence./nThat's what I'm going to do on my graph over there. So let's do that. I am going to erase this here. Let's start by looking at what that energy of interaction is at r equal infinity. At r equal infinity, what is the electron-electron repulsion equal to? Zero, because the electrons are very far apart./nThere is no interaction there. When r is equal to infinity, what is the electron-nuclear attraction? I'm sorry? What is the electron-nuclear attraction? I'm over here. When r is infinity, what is the energy of interaction for the electrons in the nuclei? It's not zero because when the two hydrogen atoms are separated, in each hydrogen atom the energy of interaction is? How about the binding energy of an electron to a nucleus, right? It is the binding energy of the electron to the nucleus./nThat's the binding energy of the electron in the ground state. It's the binding energy of the 1s electron. Make sense? Does this make sense to you? No it doesn't. No. OK. What's confusing? You don't know./nDo you understand what I am plotting here as a function of r, the distance between the two nuclei? OK. When the two nuclei are very far apart -- Right over here they're really far apart. There is no electron-electron repulsion./nBecause each electron is attached to each nucleus and they're too far apart for there to be any repulsive interaction. That makes sense, right? But when they are far apart here the electron-nuclear attraction, between this electron and its nucleus here, that electron-nuclear attraction, that energy of interaction is the binding energy of the electron to the nucleus./nIn the case of the ground state hydrogen atom it is the binding energy of the 1s state. Does that make sense? Yes? No? Good. But we've got two hydrogen atoms so there is a two in front of this. We've got two hydrogen atoms so there is a two in front of that./nAnd now you know that the binding energy of an electron to a nucleus is minus 2.18 times 10 to the minus 18 joules, right? Yeah, you know that. I am going to turn that into kilojoules per mole instead of joules per molecule./nWhen I turn that into kilojoules per mole, it is 1312 kilojoules per mole. If I multiply that by two, I am going to get 2624 kilojoules per mole. And so way out here at r equal infinity I've got one point minus 2624 kilojoules per mole./nThat is where that number came from in this original graph. Do you understand that? This is important because these are the interactions present in all chemical bonds. So we've got that. Now we're going to estimate what the sum of these two terms are at r equals zero./nAt r equals zero we've got the electron-nuclear attraction and we've got the electron-electron repulsion. How are we going to do this? Well, at r equals zero, what we've got are two hydrogen atoms with the nuclei right on top of each other because that's what r equal zero means./nThere is no distance between the two nuclei, right? So we've got two protons right on top of each other. And, as far as we're going to be concerned here, if you've got two protons right on top of each other that looks like a helium nucleus./nIf we've got two protons right on top of each other at r equals zero, Z is going to be plus two. That is going to look like a helium nucleus. This is a thought experiment. We're taking two hydrogen and we're putting them right on top of each other./nSo you've got something that looks like a helium nucleus, Z=2. And now, because r is equal to zero, we've got two electrons around that helium nucleus. So all of a sudden what we've got here is something that looks like a helium atom./nThis looks like a helium atom in this thought experiment. How can I estimate the sum, not these individuals but the sum of these interactions in the helium atom? In the helium atom we have the electron-nuclear attraction, the attraction between this electron and the helium nucleus, this electron and the helium nucleus, and we've got the repulsion between these two electrons./nHow can I estimate that? Well, experimentally I can estimate that by taking the first ionization energy, making that minus, plus minus the second ionization energy. That will be my total energy of interaction as far as the electrons are concerned./nSo I go and I look up the first ionization energy of helium. Remember the first ionization energy was the energy required to pull off the first electron? I find that number. The binding energy is minus that ionization energy so that's why I put that minus sign there./nI do that, and that removes one electron. And now I want to know how much is this electron bound to the nucleus. I go up and I look up my second ionization energy for helium where I solve the Shrˆdinger equation for a one electron atom./nI look that up. That's minus the ionization energy. It turns out that the sum of those two is minus 7622 kilojoules per mole. Does this make sense? The electron-nuclear attraction plus the repulsion./nI cannot separate those two terms, but I know what they are experimentally as a sum because I go and I measure how much energy is required to pull the first electron off, add it to the energy required to pull the second electron off./nThat's totally the electron-nuclear attraction plus the electron-electron repulsion. That's what that is. And I have to make it negative because the binding energy, the energy interaction is minus the ionization energy./nSo way over here on this plot I've got another point for r equals zero. That is minus 7622 kilojoules per mole. And so now what I'm going to do is I am going to just draw a line here between the two./nI just interpolate it because I don't know what else to do. I don't know how to get that energy of interaction in a simple way as a function of r in any other way. But now what I've got are the three components./nHere is one, the r dependence. Here is my approximation for the r dependence of the sum of the other two components. I am going to add them up. Because my total energy of interaction I said was the sum of those three./nAnd when I add them up, well, what I am going to get, if I add this curve to that curve, I'm going to get something that looks like that. This is going to bring it down. This goes to infinity so this will go high up to infinity here./nI am going to get a potential energy of interaction that looks something like that. The point of all of this was to illustrate that a chemical bond is really a result of the competition between the electron interactions./nThe electron interactions are this green line here. It's a competition between the electron interactions, which is always negative. Even though you have an electron-electron repulsion here, which is a repulsive interaction, the overall energy of interaction is negative./nIt's attractive. The electron interactions overall are attractive. They're negative. So this chemical bond is a competition between the electron interactions, which are attractive, and the nuclear-nuclear repulsion, which is always repulsive./nThis was always positive. It's always repulsive. And what you can see here is that there is some optimal distance which ends up being the bond length where the total energy of interaction is a maximum negative number./nWhere the total energy of interaction is the greatest. In other words, what you have to do is you're going to make a chemical bond. You have to bring the two atoms in close enough so that the electron attractions are present, which bring the two nuclei in./nBut you cannot press them so close together such that the nuclear repulsions take over. So there is some intermediate distance here where you have enough electron attraction, but you don't push them so close that the nuclear repulsion takes over./nAnd it is that optimal distance here that is the equilibrium bond length. Now, there is one other very important point. And that is that what we often do is we shift this zero of energy when we talk about a chemical bond./nThis zero of energy right now is 2624 kilojoules above the energy of the separated hydrogen atoms. But we already saw that this energy of interaction is the energy of interaction between the electron and the nucleus in the separated hydrogen atom limit./nWhen we talk about a chemical bond, we really want to know what the energy of interaction between the two hydrogen atoms is. And so it is useful for us to take for us to take this zero of energy here and just shift it down and set it here, make this the zero of energy./nNow our zero of energy is when the two hydrogen atoms are separated from each other. That is just the convention. It is often useful to talk about chemical bonds when you set the two atoms. When they are far apart and you set that energy of interaction equal to zero./nSee you on Wednesday.

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