Lecture 9: Electronegativity, Partial Charge, Polar Bonds and Polar Molecules

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What is this? I'm impressed. Good morning. I'm not Don Sadoway, as you can tell. He's at a conference. I'm not sure, I think it's in Halifax. What the heck can you have in Halifax? Education, OK.

A couple of announcements, the obvious, the first test is Wednesday. Maybe not so obvious, but it's posted on the website. There will be a review session for those of you who care to come given by myself in 26-100 tomorrow night starting at 7 pm going until the last question is answered.

That's why the infinity. Please don't show up at 10:30 or 11:00 and start asking questions. I just flew in from Beijing. For those of you who don't realize it, it's now about 12:00 in the evening tomorrow in Beijing.

Yeah, so anyway, I'll probably fall asleep by about 10:30. Anyway, OK, one little thing about the quiz. Professor Sadoway always gives some admonitions about how to take these quizzes. And, one thing I'd like to add to it, and that is, and I told this to my recitation sections that when you do these quizzes, in spite of the fact that it might be trivial in some cases, make sure you carry the units through.

If you've got a problem that has units associated with it, do the exercise of carrying the units through because, guess what? If the units are supposed to come out in meters per second and you get seconds per meter, what do you figure the chances of that problem being right are? Zero, all right? If the units come out in meters per second, you will quickly discover that the problems in 3.091 are just not that complicated.

And so, even by units analysis, if the units come out right, you've got a good shot that unless you've really, really messed up, that the answer is going to be right. The second thing is ballpark it.

That is to say, guess the answer ahead of time, strip all the decimal places off. Just go with powers of ten, and then see what the answer should be. And, you will be within 25 or 30% every time. And, that's a good thing to know because if you come out with an answer that's somewhere near the diameter of the universe and it's supposed to be the diameter of an atom, then you will know that you probably made a mistake.

So, those are two pieces of advice. OK, last day, you talked about the Born-Haber cycle, and octet stability via electron transfer. The Born-Haber cycle was designed to allow us to calculate the energetics of, in particular, the ionic bond.

And, the thing we need to remember, there are a couple things at least. And that is that the lattice energy as is depicted by the Madelung constant is dominant. And, the Madelung constant, what does it represent? It's a geometric factor that's unique for each crystal structure.

So that's something you go and look up. So, you go and look that up, and those are the key things. And as a result of that, the achieving of octet stability via electron transfer tumbled to the idea of an ionic bond where one atom donates an electron completely to the other atom, sort of like servanthood.

One donates yourself completely to another. OK, so that's where we are. But we've got a few problems. OK, sodium chloride works. Magnesium chloride works. Magnesium oxide works. All of these from the group one and two through the group five and six elements, but what about elements, what about molecules like hydrogen, or nitrogen, or maybe oxygen? Or we could keep on going: chlorine, right? We know these are stable.

And, if we wanted to try to fit, say, hydrogen, into this scheme that we have, we have to do what? We'd have to figure out a way to achieve octet stability by electron transfer. Well, we've got to hydrogen atoms here.

And, what would have to happen? Well, we would have to have one of these hydrogen atoms go to an H plus, plus an electron, right? **H --> H+ + e-** So, now we have a hydrogen ion here. But, at the same time, another hydrogen would have to do that.

**H + e- --> H-** And, clearly, we can't do both. This one here is what? Hydrogen with an added electron. That's isoelectronic with helium. This thing here, this is just a naked proton. So, it doesn't work.

It doesn't work. So, we need to find another scheme, and that solution was provided for us by G. N. Lewis. And, he asked the question, what if we could share -- -- electrons? And by now, I mean the valence electrons.

What if we could share electrons? Well, let's look at hydrogen see what would happen. Well, we know that hydrogen is 1s, right? So, if we take another hydrogen, we stick it over here, 1s, we know we have an electron here.

And, let's say the X denotes the other electron from this hydrogen. And now, we form a bond. And what do we have? Well, this is isoelectronic with helium, right, and so is this, isoelectronic with helium.

And so, each hydrogen has access to each electron, and now we have a satisfied system. And we can do the same thing with, well, we're going to do it with nitrogen in a minute, but this is a case where we have two atoms sharing electrons.

And, in general, what we have is sharing to -- -- sharing to achieve electron, oh, octet stability. Let's look at nitrogen to see if it applies there as well. Well, we know nitrogen has what? Nitrogen is 1s2, 2s2, 2p3, so, we've got five electrons here in the valence shell.

If we take nitrogen, we've got N2, and we've got one, two, three, four, five. One, two, three, four, five, one, two, three, four, five, six, seven, eight, right, one, two, three, four, five, six, seven, eight.

Here we go. We've got two cases where each one of those things now is isoelectric with neon. And, we have achieved octet stability in the same way. So, Lewis called this, what did he call it? He called a cooperative use of valence electrons.

Right, so you take the co here, and we take the valence here, and out of that comes covalent. And, let's be a little, now we need to put a little terminology here. This region in here contained the bonding domains.

Right, and the non-bonding electrons are non-bonding domains. And this structure that I've depicted here using the X's and O's is called the Lewis structure. Right, it's called the Lewis structure.

And, let's see, this is actually from Lewis' notes. Now, remember, this is 1902. So, there wasn't a whole lot going on. There was a lot of physics going on, but we didn't know a whole lot about atomic structure back in those days.

But, you can see, this is right out of his notebook, and you can see he's arranged the atoms by row. And, he's trying to figure out, see, lithium has one. Beryllium, magnesium have two. Boron, aluminum have three.

And, he's trying to figure out how to arrange these things. This is right out of his notebook. And, look up at the top here. He's got a bit of a mistake. He's trying to make helium octet stable.

He's trying to put eight electrons around helium, and it isn't working. But look down here. He's got a box within a box. This is 1902. This is reminiscent of what? The shell structure which people hadn't even thought of.

So, this is in his notes. He didn't publish these notes. And, he didn't publish anything related to the Lewis structure until about 1912 or 1913. But, you can see that he was thinking about this structure for all along.

Whoops, let's see if I can get this. OK, now, this is a more formal look at that structure. And you can see what he's done. I don't know what the dates say, 1916, excuse me, and you can see what he's done.

He's taken the elements, and he's arranged them. And he's stripped off all of the non-valence electrons. And, all he's done is leave the valence electrons associated. So, you can see the alkali metals here: lithium, one electron, and then beryllium, magnesium, two electrons, all the way over here to neon and argon where you have stability.

There is fluorine and chlorine where you have seven electrons. So, that's his gift to us: the Lewis structure, and the idea that you could share electrons and form a covalent bond. Now, we need to go a little bit further to put some more meat on this thing because we haven't quantified it.

We've got the concept, but we haven't quantified it yet. But, let's take a look and see about water. These are so-called homo-polar molecules. The atoms are the same in each one. And, let's try one with two different atoms.

Let's take a look at water. We know that hydrogen is 1s1, and oxygen is 1s2, 2s2, 2p4, so, there's six electrons in the valence shell. And, let's try oxygen. Well, oxygen, we'll put a hydrogen here, hydrogen here, and one, two, three, four.

We've got to put six electrons around it. So, let's put one here, and one here. We've got an electron from each of the hydrogens. So, let's put that here, and that's there. And that works. So now we have what? We have two, well, let me draw this is as a square.

We have two bonding domains. And, we have two non-bonding domains. Now, we know that there's more structure to this molecule. Water is a very unique molecule. It's one of the only compounds, there's only I think three, where the density actually goes down when it freezes.

Think about that. Think of anything else with the density goes down when it freezes, and think about where we would be if that wasn't the case. Ponds would freeze from the bottom up. That would be a bummer.

All the fish would freeze in the wintertime. Water has some pretty unique properties, which we'll deal with a little bit later. But, it all relates to the bonding, all relates to the bonding. And now, Lewis actually listed some rules.

And, what we want to do is go by example here. And these, by the way, are called Lewis structures. All right, and so, he came up with a set of rules. And, let's take an example, and see how these apply.

And as an example, let's take sulfuryl chloride, SO2, make it a little complicated, Cl2, right, so don't worry about these compounds. And, we'll tell you all you need to know except for how to draw them.

And, it says, OK, center the element with the lowest average valence electron energy. Well, if you look, sulfur is less than chlorine, which is less than oxygen. So, sulfur has the lowest average valence electron energy.

So, that says, put the sulfur in the center. So, put the sulfur in the center. Then it says, count all the valence electrons. Well, sulfur has six. That's 3s2, 3p4. Oxygen, two times oxygen, that's 12 because sulfur is 2s2, 2p4, and chlorine, there's two of those.

That gives us 14, and that's 3s2, 3p5, and so we've got to come up with, we have 32 electrons that we have to use. OK, then it says draw a single bond from each surrounding atom to the central atom, and subtract two valence electrons.

OK, and let's just put chlorine here, chlorine here, oxygen here, oxygen here. So, two, four, six, eight, minus eight, that gives us 24. So, we have 24 electrons that we have to come up with. And then it says, OK, distribute the remaining electrons in pairs so that each atom has eight.

Place the non-bonding pairs on peripheral atoms first, which the higher average valence electron energy. All right, well, oxygen has the highest valence electron energy. So, let's go and put the one, two, three, four, five, six here.

Let's do one, two, three, four, five, six here. And, OK, and let's put the atoms around. Now we'll do the chlorines. Chlorines have seven. So, one, two, three, four, five, six, seven, right? One, two, three, four, five, six, seven.

OK, so now we've got, taken an electron from that sulfur, put it here, an electron from that sulfur, put it here. So, how many have we got in the sulfur? We've got one, two, three, four, five, six, seven.

Well, son of a gun, one, two, three, four, five, six, sulfur, one, two, three, four, five, six. We've got six. We've used all the electrons. But what do we have here? Well, this chlorine has taken one electron from the sulfur.

But, the oxygen has taken two electrons from the sulfur. This is a kind of a special, and you might expect that. Oxygen has the highest average valence electron energy. So, it's going to want to scarf, and take these electrons.

This is called a dative bond. It's what it's called when an atom takes both electrons in the bond. So, what do we have? We have one, two, we have four bonding domains. And, how many non-bonding? Well, one, two, three, four, five, six, seven, eight, nine, ten, 11, 12.

12 non-bonding domains. OK, so this is looking pretty good. We now have octet stability. We've got each. Each one has an inert electronic structure. But, a few things to note. We know that because the sulfur and the chlorine in the oxygen have different average valence electron energies, they'll have different electron affinities.

So, this bond is going to be a little bit different than this bond. We have to account for that in some way because we know that they don't have identical average valence electron energies. OK, let's start over here.

OK, let's try another one. Let's try something like four, which is what? Methane. What do we know about methane? Well, we know it's stable. But, we also know that it's symmetric. Right, it's symmetric.

We know that it's non-polar. All right, so those are the things that we know about it. We also know that carbon is 1s2, 2s2, 2p2, and we know what hydrogen is. And so, if we look at our box notation, we've got three states in the p orbital.

We've got one in the s orbital. If we apply the Hund rule, we've got up arrow, down arrow, right? But, there is something else that we know. We somehow have to take hydrogen, attach it to carbon, and we have to make it symmetric, and we have to make it nonpolar.

And yet, we know that the shape of the s orbital is spherical. The shape of the p orbital is, however, not spherical. It's asymmetric. And, moreover, they are at right angles to one another that we've learned.

So, somehow we have to figure out a way to take orbitals that are non-symmetric, and convert them into orbitals that are symmetric. Now, what does that mean? If it's symmetric, that means that each bond has exactly the same energy.

Same bond, symmetric bonds means equal energy, which means equal links. If we can do that, we'll end up with a symmetric nonpolar molecule. Well, this stumped people for awhile until another fellow came along: Linus Pauling.

He's famous for a lot of things, one of which is covalent bonding. And, he said, well, let me take a look at this. What if I were able to mix the orbitals? All right, what if I were able to mix these orbitals and produce what he called hybrid bonds? And, how would he do that? Well, this is where the thinking comes in.

He says let's just makes the 2s and 2p orbitals. And, I know I need to come up with four symmetric equi-length bonds, and let's just see, let's draw the structure here. And, if I take and I mix the 2s and the 2p's, and by the Hund rule, if I can come up with four, what have I got? I've got two states here, three states here, two here, I need four, and if I can come up with these bonds, four, by the Hund rule I'd fill them like this.

And there I have it. I have four bonds that are of equal energy, and he called this an sp3 hybrid. And now, I can't do the drawing justice. But let's take a look at how we do this. The graph to the left, this is the s orbital, symmetric.

These are the p orbitals. And, these are what? These are the probability densities, right? Our friend Schrödinger told us that if you solve for the wave function, this is what the probability densities look like.

If I now hybridize these, if I take these and I make four symmetric, now, these are just the sp3 orbitals. The hydrogen's not on there yet. Notice, the orbital looks kind of funny. It's got a big lobe and a little lobe.

And, they are sort of backed into it. So, this forms a tetrahedron, which forms the sp3 hybrid orbitals. Now, the hydrogen, on the other hand, the hydrogen has symmetric s orbitals, and now if we take, and this is just another way to look at it, you take these sp3 hybridized orbitals, and you add a hydrogen to each one.

And now, what do you have? You have a symmetric molecule, and let's see. You have a molecule where we put the carbon in the center, and we go up like this, like this, and out the back. And now you have a tetrahedron with equal length bonds.

And, it's going to be symmetric. Now, will it be polar or nonpolar? We are getting a little ahead of ourselves. What makes something polar versus nonpolar? Well, if this bond has completely identically equal sharing of electrons, then this bond will be nonpolar.

However, we're going to see that that's not the case for hydrogen and carbon. This bond will be nonpolar. So, that means we've got one, two, three, four nonpolar bonds in here. And yet, the molecule is symmetric and nonpolar.

What's going on? Well, what's going on is the carbon is at the exact center of the tetrahedron. So, the nonpolar bonds cancel each other out. The two sources of charge cancel each other out. And, you get a nonpolar molecule.

OK, so that's what Pauling did. But, he did a little bit better. Lewis, by the way, didn't get the Nobel prize. But Pauling did get a Nobel prize. So, you say to yourself, well, Lewis is the guy that came up with the idea.

Why didn't he get the Nobel prize? Well, he came up with the theory. But he didn't reduce it to something quantitative. Pauling did that. And so, let's go back and take a look at the energetics again.

Let's take another look at the energetics. Now, last day, we looked at the energetics of the ionic bond, right? And we wrote something that looks, the energy is equal to minus the Madelung constant times Avogadro's number, q1 q2 over 4 pi epsilon zero R zero.

**E = -M*NAv*q1*q2/(4*pi*epsilon0*R0)** And, we knew that if we know the crystal structure we can get the Madelung constant, not a problem. And, what we need to do is to get this. Well, how do we get that? Well, if we just take, for example, MgO, and let's try Mg, magnesium chloride just as an example.

We put the magnesium 2 plus here, and then we put the oxygen here, O 2 minus, and we know that this gives us our R zero, right? So, we can go and measure that. We haven't said much about how to measure it, but you can measure it.

If we wanted to get the chlorine, we could just put the chlorine over here, and we'd measure another radius there. And, we could easily calculate the energies. Well, with covalent bonding, it's not so simple.

It's not so simple, and so let's see how, let's take an example. And let's take an example, HF, hydrofluoric acid, all right? Well, if we wanted to draw that, we have HF, whoops -- It looks something like that.

But let's say we wanted to calculate the energy. Now, Pauling was trying to figure out how to do this. And he said, well, what if I were to take, and just somehow add up bonds, the energies of bonds, or derive this energy from energies that I do know? And so, let's take HH, the HH bond.

More particularly, the HH bond, right, and let's ask what the energy of that is. Well, we can look that up, and that's table in your text, by the way, B14 in your text. And, we can come up with a number of 435 kilojoules per mole.

Well, if we want to get HF, let's see what the FF bond is. Well, you go look in your table and you come up with 160 kJ per mole. So, if I had to guess, what would you guess the bond energy would be in HF? Well, 435, 160, take 435, add it to 160, divide by two.

Maybe that would be a guess. Or, I could come up with some other scheme. But, you would kind of guess that it would be somewhere in between. It would be somewhere in between. Well, what's the actual value? Well, the HF bond energy is actually 569 kJ per mole.

So, we have a problem. The problem is we can't add these two together. There's no way that we can get from here, to here, to here without knowing a little bit more information. And, we get that information by going back to the definition.

What's the definition of the covalent bond? Sharing of electrons. Well, they don't have to share equally, do they? And, if they don't share equally, then the individual bonds might have different energies.

And so, that's exactly what Pauling proposed, right? And he actually proposed sharing -- -- unequal sharing of electrons. And, he needed to get quantitative. And, he defined a term called the electronegativity.

And, in your text, it's E sub N. But, in most chemistry texts, it's also chi. That's the more common term. And, it represents the ability of an atom to attract electrons in a bond, all right? The ability of an atom to attract electrons, and in particular, in a covalent bond.

All right, and he came up with a scheme, and this is how he ranked things. And, you can see a parallel. If you take a look at the last day, or the day before, you will see that we talked about average valence electron energy.

There is a striking parallel here in that the group one elements have a tendency to want to give up electrons, whereas the fluorine, chlorine, bromine, have a tendency to attract electrons. And so, this is a schematic of the electronegativity scale.

Now, Pauling originally assumed that fluorine was the most electronegative element. So, he assumed, he referenced or normalized everything to fluorine. Since that time, we've been able to actually measure these bond strengths by PES, photoelectron spectroscopy.

And, when you do that, it turns out that fluorine doesn't come out to exactly four. And, this is a figure out of your text. And, you can see that fluorine, instead of four, it's about 4.19. But, it's as you would expect.

The most electronegative elements, fluorine, chlorine, oxygen, are over here. The highest one is neon. But the lowest one is way down here, cesium. I mean, you would expect that the group one, absent hydrogen, would be the ones that would have the least.

Now, remember, the formation of the ionic bonds was from group one and group two, and over here with group six and seven. So, those are the ones that most likely form ionic bonds. OK, not only did he propose it.

He quantified it. And, he did something even better. Let's see -- He defined something called, how much time do we have, partial charge. Now, this is what got him the Nobel prize. And, he defined partial charge, I'll give you the formula: G sub x, this is in your text, N sub x -- -- in an XY bond, right? Chi sub x plus chi sub y, right, where G sub X is the group number.

N sub X is the number of non-bonding electrons. And, B sub X is the number of bonding electrons. OK, now let's take this and look at what we get if we try HF. All right, we know this is what it comes out to.

This is H. We've got one "x" here. We know that this is going to be, by measurement, this is going to be plus and this is going to be minus. It's going to be a dipole. This is plus; this is minus.

And, we know that chi of the fluorine is 4.19, and chi of the hydrogen is equal to 2.30. OK, well, if we plug that in, let me just do one of them, just do the fluorine. And, by the way, if you do this for the hydrogen, it ought to come out the same.

That's equal to seven minus six minus two times 4.19, or 4.19 plus 2.3. And, that gives you a number for the fluorine, minus 0.29. Now, if you do the same for the hydrogen, you'll come up with the same number.

But, it will be plus, all right? But, it will be plus. And, so, what that tells us is HF is polar. So, we did that. And, now let's go back to, whoops, I'm running out of space. Let's go back to methane and see what happens there.

Let's go back to methane. Well, the chi of the carbon is equal to 2.54. The chi of the hydrogen, again, is what, 2.3. And, so what this tells us, since these aren't equal, that tells us that the carbon-hydrogen bond is polar.

And so, if we go and we draw this again, if this is the carbon here, hydrogen, hydrogen, hydrogen, hydrogen like this, then this is going to be a little bit plus. And this end is going to be negative.

So, we know from our calculation that we can do over here, that this bond is polar. This bond is polar, but again, as I alluded to earlier, because the carbon is centered in the tetrahedron, because of the sp3 hybridization, the molecule itself is symmetric and nonpolar.

OK, and for this, he got a Nobel in, I think, 1954. OK, now one last thing that he did is that he said, OK, what's going on here? Well, on the one hand, we have ionic bonding where we have complete sharing.

On the other hand, if we have a perfect covalence bond, we have identical equal sharing. But we know that just by this calculation, that we don't have equal sharing. So, somewhere in between, the bonds are, we have a range of bonds between ionic on the one hand, and perfectly covalent on the other hand.

But, there's a whole range in between. So, what's going on there? Well, Pauling also suggested that for that case, that the bonds are partially ionic and partially covalent. And, he came up with a relationship to calculate the percent ionic character.

And, I'll just give it to you. This is a squared, give you a percent. All right, so this is a relationship. And so, you can see where chi comes in here. And, this is the difference in electronegativity between the two elements, all right? Let's see how much time.

OK, he also, let me see, he also, lastly, to close us out, he also developed an analytical expression for the energy of that covalent bond, which is really what we want. All right, so the type of bond energies that we can go and look up in tables are individual atom bonds, H-H, F-F, and the like.

But he said the energy of an X-Y bond is going to be equal to the square root. Right, so the X-X bond and the Y-Y bond, we can look up those energies, plus 96.3, delta chi squared, and kilojoules per mole.

Where does the 96.3 come from? Well, it's a conversion factor. So, this gives you the energy of the bond. Now, if we plug in the numbers, we plug in the numbers for HF. What do we get? Well, we get square root of 435 times 160 plus 96.3 times chi H minus chi carbon, whoops, squared, and you get this number here is 2.3.

This is 4.19. You get the E of the HF is equal to 608. OK, now, where is my other one? Somewhere here, 569 over here, kilojoules per mole, and by his formula he gets 608, which isn't bad, which really isn't bad at all.

OK, so what we've gone through today is we've introduced covalent bonding, and we've figured out a way to quantify it. Not only did we figure out a way to describe how we quantify it, but we've also quantified how we tell the difference between covalent and ionic, and percent ionic character.

So, those are the key things to remember for today. But hold on a minute. What have we got? We've got a few minutes here. I'm just going to give you an example of sp3 hybridization. There's a scientist, Thomas Midgley, and Professor Sadoway calls him sp3 Midgley.

He developed a whole lot of compounds based on sp3 hybridization. And, this one here, some of you might recognize, is dichlorodifluoromethane. It's also known as a CFC. And, this is the shape. It's SP3 hybridized.

Now, it's not going to be symmetric is it, because there's two fluorines and two chlorines. So, it's a nonsymmetric molecule. But, what is so unusual about this? Well, up until probably ten years ago, this was the primary propellant in just about every kind of spray thing that we had, hairspray, everything.

It's called freon. It's also used in air conditioners. What was neat about it is before that time, the predominant species to use for air conditioning or refrigeration was ammonia. And, not too many people, actually, if you talk to your grandmother or grandfather, there were some refrigerators that were actually made that used ammonia.

But, when they sprung a leak, you had a problem. And so, by and large, until this freon was invented by Midgley, there wasn't a good gas that had the right properties to be used for a refrigerant. And so, this was good as a refrigerant.

But, something else can happen with these things. And, I think you hear about this in the news a lot. If you get some of these in the upper atmosphere, a photon, an ultraviolet photon, has the energy capable of breaking this bond.

When it breaks this bond, that chlorine atom, a free chlorine atom comes down and reacts, this is ozone, with the ozone in the upper atmosphere. And you end up with the destruction of the ozone layer.

And, this is what you hear a lot about in the news, Kyoto, and all this kind of thing about destruction of the ozone layer. Well, Mario Molina, who was a faculty member here at MIT, won a Nobel prize for describing this process.

He wasn't here at MIT when he won the prize, but here's the actual paper. Now, you think you can make a mistake on your exam, take a look at this up here at tell me what that all is. I have no idea.

That's exactly the actual paper. It actually should be chlorine catalyzed shouldn't it? But, who cares, he got the Nobel prize. And, I'm sure he's not worried about it at all. OK, good luck on your tests, and remember the review session if you care.

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