Lecture 12: Secondary Bonding, Metallic Bonding

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Settle down. I do want to draw your attention to the fact that the final exam schedule is out. It has been out for about a week. And the 3.091 final will be on Wednesday of finals week, which puts it on the morning of the 15th of December.

It will be a three-hour extravaganza, a celebration of learning where you all come to show you what you have mastered. And it is going to be just a grand, grand time. And it will be over in the Johnson Athletic Center.

I urge you to take a look at the final exam schedule and make your travel plans, as soon as you know what your last obligation is. Because things are going to get booked, and it is going to be harder and harder to get out of here, certainly to get out at a decent price.

Last day we looked at Electron Domain Theory which allowed us to predict the shapes of molecules. And this is taken from the book. This is Table 4.3. And I have highlighted in orange. We worked through some of these molecules last day, the SF6, BrF5, ICl4-.

And then we looked at the series CH4, SF4, ICl4-, and we saw how by counting the number of electron domains and then partitioning them into bonding versus nonbonding domains we could proceed in a systematic manner towards the deduction of what the molecular shape should be.

So that was a productive day. And I urge you to understand what is going on in Table 4.3. You can expect that you will be tested on that at the end of October. You will have an aid sheet so you will probably want to know how to work through this document here.

Today I wanted to continue this treatment of covalent compounds. And specifically I wanted to talk broadly about how we determine state of aggregation. In other words, how do we determine whether something is going to be a solid or a liquid or a gas? We have already seen that ionic compounds, by their nature, because they have unsaturated bonds and they continue to allow more ions to glom onto the initial starting point results in a large aggregate, tightly bound, leads to crystal formation.

The crystal is the regularity, but definitely solid formation. And when you are trying to answer the question is something a solid or a liquid or a gas under certain conditions, this is the subliminal message.

You have to compare the cohesive forces versus the disruptive forces. So the cohesive forces are the binding forces and the disruptive forces typically are thermal in origin. We have to compare the binding energy of the substance to the general thermal energy.

And that is shown here. Binding energy, then that gets back to the nature. If it is an ionic compound, this binding energy is that Madelung bearing crystal lattice energy, and it is very negative.

For sodium chloride it is about 787 kilojoules per mole. Whereas, the thermal energy in this room is about a 40th of an electron volt. That is small. Sodium chloride is a crystal at room temperature.

Now I want to turn to covalent compounds and ask the same question. What is the state of aggregation? But there is a fork in the road here. There are two types of covalent compounds. We saw, as is shown up here on the slide, the results when we have just the single molecules.

But we also saw, at the end of last lecture, it is also possible to talk about covalent networks. We looked at diamond and we looked at graphite. Now, in the case of diamond and graphite, we are in a situation that is similar to ionic solids.

In other words, we have large aggregates because the sp3 hybridization allows for carbon to bond to carbon to bond to carbon to bond to carbon. And so you end up with a large aggregate. In fact, it is an ordered aggregate.

It is a crystal. Diamond is a crystal, just as sodium chloride is a crystal, but both of them are large aggregates. And we saw also that the binding energy in diamond is very, very strong. Very strongly negative.

And so, therefore, it trumps the thermal energy of the system. So these are solids at room temperature. How about molecules? That's what I want to focus on today. What is the nature of binding in molecular systems? And specifically let's just take one of the molecules we looked at last day.

We looked at sulfur hexafluoride. And I told you, sulfur hexafluoride is a gas at room temperature, even though this thing has a very, very high molecular weight. The question we are really asking is what are the forces that would cause sulfur hexafluoride to bind to itself? And so far what we have been looking at, electron domain theory, doesn't answer this question at all.

Electron domain theory treats what is going on inside the molecule. It treats intramolecular bonding. This is between sulfur and fluorine. And this is a very strong reaction and is referred to as a primary bond because it is the first bond that forms.

If I look at the world from the vantage point of sulfur, the first bond sulfur encounters is this primary bond to its neighboring flourines. But now I want to ask how does this molecule, which we know is net neutral, bond to another one like it? That now means we have to shift, so state of aggregation is not determined by this at all.

State of aggregation is determined by intermolecular forces. And they are different. What we want to do is look at the intermolecular forces. And, for that, we are going to go through this catalog.

That's last day. This is what we are going to do. We are going to go through this catalog. I am going to show you four different types of intermolecular forces, and I am going to go about them systematically.

The first one is dipole-dipole interactions. And, clearly, this interaction occurs only between polar molecules. Involves polar molecules. These molecules have a net dipole moment. We could model them as dipoles.

And so if this is, for example, an isolated molecule of hydrogen chloride, we know we have a strong covalent bond within the molecule and we know the shape of the molecule. It is linear. But how does this hydrogen chloride bond to another hydrogen chloride? Well, we can see that this is delta minus, this is delta plus, and so this delta minus end is attracted to the delta plus end of an adjacent molecule and so on and so on.

So this is a dipole-dipole interaction that, when the temperature is low enough, the thermal energy will not disrupt the bonds that are forming by this dipole-dipole interaction. So it is operative at low temperature.

And these are all weak interactions. Everything I am going to talk about today is weak by an order of magnitude in comparison to the primary reactions. If we compare ionic bonding and primary covalent bonding with this sort of thing, this is down at around on the order of about 10 kilojoules per mole.

Whereas, up here we are talking about hundreds of kilojoules per mole. These are very weak, which means that at room temperature HCl is a gas, sodium chloride and diamond are solids. And the energy in a dipole-dipole interaction, I am not going to give you the full formula, but I will just give you what it is proportional to.

Clearly, it is going to be proportional to the strength of the dipole. Stronger dipoles will bond more tightly than weaker dipoles. And, in fact, it goes as the fourth power of the dipole moment. If mu is the dipole moment, stronger dipole moments give much, much stronger interactions than weaker dipole moments.

And a dipole moment is proportional to what? It is proportional to the charge and the separation. If I have more charge separated by a greater distance, I construct a greater dipole, a dipole of greater strength.

And in the denominator we have the cube root of the interdipole separation. Really, what we want is very strong dipoles spaced closely together to give us the strongest reaction. The example HCl, I have used this in some of my own research.

This thing has a melting point -- HCl has a melting point minus 115 degrees C, and the boiling point at atmospheric pressure is minus 85 degrees C. If we go down below minus 115 degrees, see, the thermal energy is low enough that at temperatures below this value this weak interaction dominates and we have solid HCl.

Second form of interaction -- And these are all cataloged in Chapter 8 of your book, this one here is a little bit premature, but all the books do it so I will just, for completeness, go through it.

It is really involving solutions. This one was HCl to HCl. It is answering the question under what circumstances is HCl, solid, liquid or gas? This one here is called dipole-induced dipole. This is really two different species.

You can see in the cartoon that the left has HCl, hydrogen chloride, and the right has argon. So this is bonding between two different types of species. For example, if I were to mix HCl, which a gas at room temperature.

Argon is a gas at room temperature. I mix two gases at room temperature, I have a gas. But at low enough temperatures, I will get a liquid. And, at low enough temperatures yet, I will get a solid.

It will be essentially a solid alloy of HCl molecules and argon atoms. What holds that together? Whenever you see a solid, you must conclude that there are forces that bind the species together. Things don't just sit there because they are lazy.

They are bound. What are the forces that could bind a condensed form of argon and HCl together? And the answer is dipole-induced dipole interactions. This is a bit of a departure, but it will come in handy in a little bit.

This is present in solutions of what? You need one polar and nonpolar species. They could be atoms or they could be molecules, it doesn't matter. So how does this work? Well, here is the nonpolar molecule.

This is argon, helium or one such methane. Nonpolar. So it has uniform distribution, by definition. If it is nonpolar there is no net dipole. Here is the nonpolar entity, nonpolar species. If I bring up a dipole in close proximity, what can happen is the following.

This negative end of the dipole interacts with the electron cloud in the nonpolar species so as to cause repulsion. This cloud, it's in motion, the electrons are not potted, and so the presence of this negative end of the dipole actually causes the electrons to flee.

We get a maldistribution in the electrons. And, in fact, this end becomes a little bit electron lean, electron deficient, and the other end becomes electron rich. What started off minding its own business with this symmetric distribution of electrons in the presence of the dipole takes on a dipole moment itself.

So this dipole is induced by the presence of the permanent dipole. And now we have some bonding. This negative end here now is in a position to be attracted to the positive end of a permanent dipole and so on and so on.

This is how the system operates. And we know that the energy of the dipole-induced dipole interaction goes as one over the square of the interpolar separation. This is one over the square of the interpolar separation.

Whereas, here it is one over the cube of the interpolar separation. And, furthermore, we can talk about how susceptible elements are to this induction. I can give you two different elements. Suppose I have argon, and next to it I will put helium.

They both have inert gas electron configurations, but helium is small and has a few electrons. Argon is large and has many electrons. Which of these two, argon or helium is more susceptible to this electron displacement? You see that it is argon because argon is larger.

It's squishier. It is softer. This is hard. This is like a baseball. This is like a Nerf ball. It can be easily distorted in terms of its charge. And we call this distortion of electrical charge polarization.

Polarization is the official term for electrical charge displacement. And so we can quantify the ease with which electrons are displaced within a chemical entity by a quantity called polarizability.

And give it the symbol alpha. And this is a measure of ease of electron displacement. And, clearly, polarizability is affected by -- Now watch the fonts here. This is alpha. And then I want to say alpha is proportional to, I don't know how you differentiate the two.

Alpha is proportional to the number of electrons. In other words, the more electrons the more there are to move. If I only have a couple of electrons and I have a couple of protons, those electrons are more tightly bound.

They are less flexible. So the number of electrons and also the size. For equal numbers of electrons, a larger entity will be softer and squishier than a smaller entity. So polarizability scales with electron number and with size.

We reason that helium is going to be low polarizability. Whereas, argon will be high polarizability. Because we have a lot of electrons, they have to, by necessity, you know what the filling sequence is.

The more electrons you have, those last electrons are farther out, so the positive charge in the nucleus has a weaker hold on them. Therefore, while they are bound, they are a little bit friskier. They don't sit in their place.

They move around. Now, let's get back to homonuclear species. This is induced dipole-induced dipole. That is the third type of interaction. Induced dipole-induced dipole. This is a really fascinating one.

It puzzled people for a long time. And it is dominant in nonpolar molecules. Dominant in nonpolar everything. It is dominant in nonpolar species, atoms and molecules. And here are some examples.

Let's go back. Here is argon. Now, if you look on your Periodic Table, argon has a melting point of 84 Kelvin. And it has a boiling point of 87 Kelvin. And I told you, whenever you see a solid, that you have to conclude that it is held together by some force.

Let's imagine that we are at liquid nitrogen temperature. We take some argon out of an argon gas cylinder and we flow it through a tube. And that tube is immersed in liquid nitrogen. Liquid nitrogen is 77 Kelvin.

Well, that is below 84. The argon is going to solidify. It is going to deposit on the walls of the tube. And after a while I will have argon ice. I am sitting there and looking at argon ice. What binds argon to argon? Well, it is not ionic.

It is not primary covalent. It is not dipole-dipole. They are all the same. What could possibly bind argon to argon? Was it just adhesion because it is sticky? Why? Well, the answer was given to us by a German scientist by the name of Fritz London.

And London said I think I can explain this. He looked back over here at dipole-dipole and said we have already come to the conclusion that electrons are in motion and are not stationary. He said imagine if we could zoom in here with a femtosecond camera and take a snapshot.

Instead of having a uniform distribution of electrons, suppose at this instant in time there is a slight excess of electron density here at around 2:00. Therefore, conservation of charge dictates that there must be a slight electron deficiency at 8:00.

Well, if this is the case, what is the consequence for the adjacent argon? Well, this adjacent argon says if this is electron deficient it is going to pull electrons in this argon and make the bottom right here electron rich leaving the top left electron deficient which then causes "she told her and he told him", etc.

So what is the result here? The result is we have dipoles. Time averaged, it is nonpolar, but it is always dipolar. And this is a tiny, tiny dipole. He called this the time fluctuating dipole. And it is present in all systems.

Even a sodium ion has an electron cloud that is in motion, and we don't see this in sodium because the action of this in sodium is dwarfed by the Coulombic force which is a thousand times stronger. But this is the only game in town.

When you are at 77 Kelvin there is nothing left so this is dominant. And the force that comes out of this, this attractive force has been termed the London Dispersion Force. And the London Dispersion Force is a very weak force.

And, as you would expect, it is proportional to the polarizability. Elements that have big electron clouds that are weakly held are going to be more mobile than small atoms that have small electron clouds that are tightly held.

The London Dispersion energy goes as the square of polarizability. And, as you would expect, it is a very weak force analogous to the repulsive force. We are talking about electron-electron repulsion.

Where did you see that before? You saw that in the Coulombic derivation with the Madelung Constant. That is the Born Exponent. It is a very high number because this is a very weak force. If this is the interspecies separation, this goes as r to the 6th, which makes sense.

It is sort of Born-like. Now, this actually has another name. This is not a secondary bond for argon. This is the only bond for argon, so this is a primary bond. As a primary bond, some people call this a Van der Waals bond.

It is a time fluctuating dipole which leads to a London Dispersion Force resulting in a Van der Waals bond, which for some systems is the primary. And it is not that I cannot spell Van der Waals. He was a Dutchman, and that is how you spell Van der Waals.

Here is the situation. This is the primary bonding in argon. Go to your Periodic Table and look up iodine. It exists as the diatomic molecule. It has a melting point of plus 114 degrees C and has a boiling point of 184 degrees C.

Iodine, at room temperature, is a deep purple crystal. What holds iodine together? You're looking at it going, I know, I am going to go back to that Table 4.3 and will tell you about iodine-iodine.

I am going to write the Lewis structure. That is wrong. That has nothing to do with it. How does this iodine bond to another iodine? Well, what is the catalog? Is there a net charge? No. Is there a local dipole? This is a homonuclear molecule that is 100% covalent.

What's left? You have electron clouds here around the two iodines. Iodine is big. It is huge. First of all, there are lots of electrons. And they have a giant corral to run around. And so they are running around all over the place.

And, at any given moment, the right side might be a little bit electron-excessive and the left side might be a little bit electron-deficient. Net neutral of course. And then that is what causes the next iodine and the next iodine and the next iodine.

This is the way you describe. How about this one? Methane. We saw methane. How do I form solid methane? When you look at Jupiter you are seeing solid methane. Do you ever sit there and think, how is that solid methane held together? I bet you never thought about that.

Well, I am inviting you. Think about it. How does this methane bond to this methane? I can see everybody go I know, carbon, hydrogen. It is a polar bond. I've got it, it's a polar bond. And you proudly trot out your electronegativities and you tell me what the percent ionicity is.

And I go no, no. That is wrong. It has nothing to do with it. I am asking about foreign policy and you are talking about some state budget. I want foreign policy. How do they negotiate with one another? Well, what is the list? Net charge? No, they are neutral.

Dipole? No, they are symmetric. What is left? Solid methane is held together by Van der Waals bonds, London Dispersion Force. Remember that the next time you look up at the sky and you see Jupiter.

It is solid methane. Here is a good example of this in compound. These are three different hydrocarbons. It is just carbon and hydrogen. Here is propane, octane, eicosane. Look, it is just CH2, CH2, CH2 with methyl terminals.

So they are net neutral. There is no dipole moment. They are symmetric molecules. And you all know what propane is. It is a gas at room temperature. It is used as a low-grade fuel, boils at minus 42.

Octane is the principle constituent of gasoline, which we know is a liquid at room temperature. And eicosane is a solid. It looks like paraffin. Three different molecules, all nonpolar. How do I describe the fact that propane is a gas, octane is a liquid and eicosane is a solid? Right here.

Polarizability, which is proportional to the number of electrons inside. As these molecules get bigger, the electrons have a bigger corral to run around in. It is sort of like a small tank gives rise to small waves and a big tank gives rise to big waves.

And that is what you are seeing. Big waves mean bonds. Small waves means the thermal forces present at room temperature disrupt. That is a good one. I really like that. That's a vivid one. Actually, this is out of your book.

This is the whole series. I just chose a few extremes. Here is methane, ethane, propane, butane, on and on and on. And as the molecule weight increases the boiling point increases. Why? Because the polarizability is increasing.

But I don't want anybody telling me that the reason something has a higher boiling point is it has a higher molecular weight. That is not expository. It is not mass. It is about polarizability, because mass alone will not get you the time-fluctuating dipole.

That is what is shown up here. And now the fourth one. The fourth type of secondary bonding is hydrogen bonding. And it occurs between, as the name implies, hydrogen and only the most electronegative elements.

And that is fluorine, oxygen and nitrogen owing to their high average valence electron energy. There is something peculiar here about the combination of high average valence electron energy and the lightest element.

And here is what I want you to first be reminded of. I am showing here that average valence electron energy in order. And we see fluorine has the highest of the active. I know neon has a higher, but neon doesn't participate in chemical reactions to speak of.

I know there are subtle differences in the electronegativity scales. One of them has fluorine at 3.98. This has it at 4.19. It is a self-consistent set. So what do we see? Here we are up at around 20 electron volts for average valence electron energy, and then it tapers off.

Something magical happens at around 18 electron volts. What happens? When we put hydrogen in the presence of something that is that strongly electronegative, so let's work with the most powerful example, fluorine.

Hydrogen donates its electron to the covalent bond. Fluorine donates one of its seven valence electrons. And here are the other six. And we know because fluorine is strongly electronegative. This bond is very polar, and we can designate the fluorine end as delta negative and the hydrogen end as delta plus.

And let's look at this in greater detail. When we start pulling hard on the electron associated with hydrogen, what is left? It is not an atom that has its protons in the nucleus and n minus one electrons.

In the case of hydrogen, it only had the one electron. And when you pull that electron hard, what you are leaving is something that is essentially a proton. If, hydrogen is denuded of its electron, it is a proton.

The proton is very special because the proton has a charge of plus one but it has a volume that is tiny, tiny, tiny. So the charge density is very, very high. Now let's bring up another HF. Here is a second HF.

We know that dipole-dipole interactions happen. That was category number one. So let's start with a simple dipole-dipole interaction. The negative end of the left HF molecule sidles up to the positive end of the right HF molecule.

Then the magic happens. You see this nonbonding domain sitting here on the right side? Those nonbonding electrons are dangling way, way out there. And here is this hydrogen over here. And its electron is being pulled so hard by the fluorine on the right, I mean this hydrogen hardly gets visitation rights to see this electron.

Here are these two electrons sitting over here, and hydrogen is looking over there and said I hardly get any time with my electron. But there are these two lone pair electrons sitting there. And so can you imagine that there is a force that is set up between this lone pair of electrons? Because this fluorine, because it has so many electrons, tends to neglect its electrons.

It does not pay close attention. If you come from a big family, you don't get as much attention as if you were an only child. Fluorine has electrons all around. If two kind of stray off, fluorine doesn't care.

That is what is happening. Here is hydrogen that does not have the full impact of its single electron. Here are two electrons dangling way, way out. This is a recipe for attraction. And that is exactly what happens.

And so a weak force is established between this nonbonding pair and hydrogen, when hydrogen is found in a molecule where there is this very, very strong pull on its lone electron. The hydrogen bond is established in this following manner.

And this is a very important bond because it is found in compounds involving hydrogen fluorine, hydrogen oxygen, hydrogen nitrogen. And let me show you what the manifestation of this is. Here is, first of all, a cartoon from your book that shows this weak force.

You see the hydrogen where its electron has been pulled. In this case, they are showing water so this is hydrogen-oxygen. The electron of hydrogen has been pulled towards oxygen. And this distance is about 1 angstrom and this is distance is about 1and æ angstroms.

So it is greater. I am not suggesting that this is a double bond off the hydrogen, but it is not something to be ignored. It is very, very strong. And, in fact, it is about twice as strong as the next strongest force here.

It is about two to four times the intensity of a dipole-dipole interaction, so it makes a huge difference. And let me demonstrate that with data. This is a plot that I inked in. This is out of your book.

It shows the series that I am going to show, but I kind of like this one because I had a chance to color. As you know, that is very therapeutic for me so I needed to do this. First thing I want do is I want to go across the groups and show you the impact of hydrogen bonding.

I used colors of the T, so let's start with Green Line here. The Green Line is group 14. And what do we find? Here is methane, silane, germane, stannane. The four tetrahydrides, if you will, of carbon, silicon, germanium and tin.

And what do you find? As the size of the molecule increases, its number of electrons increases, its polarizability increases. Therefore, its induced dipole-induced dipole interaction increases. And, therefore, the greater the atomic mass the greater the boiling point.

Everything makes sense. Now, let's go to the next one. The next one I am going to go over is, this is group 14, so what I want to do is go to group 15. That's the Blue Line. The Blue Line is up here.

This is stibnite. This is the antimony compound. This is arsine, which is the trihydride of arsenic, which is used in CVD and precursor to making gallium arsenide. They use this over here in Building 13.

Occasionally, you will hear the sirens wailing and people have to evacuate the building. It is usually a gas leak of this stuff. It's good the sirens go off. It could be worse if they didn't. And then we have phosphine.

This is following the same trend. As the size of the molecule shrinks, the polarizability shrinks. Therefore, the Van der Waals bond weakens. By this analogy -- Plus, these are dipole interactions.

These are all trigonal pyramids. Its sp3 hybridization with a lone pair, so these all have a net dipole moment. And the dipole is getting stronger and stronger according to this formula. And everything is going great.

All of a sudden ammonia has got this abnormally high boiling point. What is going on? Well, in the case of ammonia, it is not just -- Here is ammonia. It is not just ammonia with its net dipole moment that is sticking to other ammonias.

What is happening in the case of ammonia is when another ammonia gets in the vicinity hydrogen bonds are forming. And those hydrogen bonds swamp everything. And, therefore, they give strength to the system that trumps the thermal energy and thereby raises the boiling point of ammonia to values that are higher than arsine and phosphine.

Let's go to Group 16. We start with hydrogen telluride, hydrogen selenide, hydrogen sulfide fitting the pattern. Smaller molecules, lower polarizability, smaller dipole moments, everything is fine.

Then we get to H2O and it is up at 100 degrees C which is higher than even hydrogen telluride. Why? Because the hydrogen bonding is present in water. It is not present in the compounds of hydrogen and any of the other members of this homologous series.

If it were not for hydrogen bonding, water would not boil at 100 degrees C, it would not melt at zero degrees C, and this conversation would take on a very different character. We wouldn't exist. So we need hydrogen bonding.

Lastly, let's look at HI. This is Group 17. These are just simple linear molecules. Hydrogen iodide, hydrogen bromide, hydrogen chloride. There is our prototypical hydrogen chloride. We are just getting bigger and bigger dipoles, higher and higher boiling points.

Finally, we get down to HF which should be the tiniest. It should have the weakest interaction. And we have a very, very abnormally high boiling point because hydrogen bonding is operative. You can see hydrogen bonding and the impact that it has on boiling point and properties.

And we will return to this when we talk about conformality in polymers, in nylons in particular. And certainly when we get to biochemistry because our proteins consist of, among other things, hydrogen and oxygen and nitrogen.

And those hydrogen bonds help hold the system together. At this point, just to summarize, we have seen three types of primary bonding. We have seen ionic bonding, covalent bonding and, in certain instances, Van der Waals bonding.

And things seem to be working fairly well, but then there is data. And here is some data that I want you to look at. These are data of electrical conductivity. And up here we have metals, silver at 10 to the 7th Siemens per centimeter, copper at 10 to the 7th Siemens per centimeter.

I mentioned last day that graphite has some delocalized electrons. It is 10 to the 4th Siemens per centimeter. And then we get down to the insulators. I said diamond was a good insulator. It is 10 to the minus 11th.

There is aluminum oxide, a good ionic compound. And here is PTFE, Teflon, 10 to the minus 16th. The first thing that you notice is look at the range. I mean if you look at the range on the Periodic Table, look at the range of something like density.

Lithium has a density of 0.53, and you have osmium that is around 22. It is a range of about 40. Look at this. 10 to the 7th, 10 to the minus 16th. A range of 10 to the 23rd. Secondly, what do we know about the compounds we have seen so far? Ionic compounds, conductors or insulators? We know they are insulators.

They have tightly bond electrons in stable octet configurations, so that is not going to help us. Covalent compounds. Well, the network ones are like diamond, very, very good insulators. Van der Waals compounds, let's look at that.

How about argon? Do you think argon is going to be a good conductor of electrons? No way. It has inert gas configuration. Those are the three types of primary bonding. And I cannot explain how three-quarters of the Periodic Table has this abnormally high value of electrical conductivity.

It sounds to me like we need to come up with yet another form of bonding. And the answer is metallic bonding. Why is it metallic bonding? Because it is practiced in metals. Let's look at metallic bonding.

The need for metallic bonding was brought on by the observation of electrical conductivity. If we are going to be true to form in 3.091, we have to look at the electronic structure. And the first model that attempted to account for the high observed value of electrical conductivity was enunciated in 1900 by a German physicist by the name of Paul Drude.

What he said was he could model a metal as a mixture of positive nuclei plus the inner shell electrons, which he called this whole mix of the positive nuclei and all the inner shell electrons, he called that the atomic core.

And then the valence electrons, he said, were separate. You have the atomic core plus valence electrons which he assumed were free. That is to say they could move about the material. In other words, they were not associated with any single atom.

We call them delocalized. I think last day I used the term delocalized. And we will come back to that in a bit. This is, in essence, modeling the metal as a solid consisting of cores and the electrons freely moving, much in the same way as a gas.

This was termed the free electron gas model. In other words, a gas of free electrons. And with this they had some success. They were able to account for such things as the heat capacity of solids.

The heat capacity of solids they could model. That was good. And I think there was something else they were able to do. But, by and large, this did not stand up because it was not quantitative. If it is not quantitative, what does that mean right off the bat? No Nobel prize.

You got it. No Nobel prize for Paul Drude. No quantitative, no Nobel prize. We will just put this here. "No Nobel." And it is true. The people that made really important insights but they were not quantitative, no Nobel.

So it is not quantitative because it cannot be tested. And the second thing is it was not discriminating. In other words, if you said assume that something is metallic, then you continue with the atomic core and the gas of free electrons.

But that is like saying silver is a metal and this is how a metal behaves. But what about the earlier question? Why is silver a metal and diamond not acting as a metal? Doesn't diamond have a set of positive nuclei with inner shell electrons? Why do you choose to have the valence electrons of silver moving around but the valence electrons of diamond not moving around? Well, we know a little bit that he didn't know because we have the benefit of Linus Pauling and the understanding of covalent bonding.

But, even so, he could not help classify insulators and metals. And so that did not work. We had to wait almost 30 years for the next installment. And so when we return next day we will look at the next installment of the attempt to explain metallic bonding.

And what happens in the 30 years between 1900 and 1930? The quantum revolution. Clearly, in 1900, in respect of Professor Drude, absent quantum mechanics, there was not much else they could have done.

But the next people are going to stand on the shoulders of people who gave us quantum mechanics and explain why we have metals as we do. Let's take a look at a few things before we leave. The unit of conductivity is the Siemens named after Charles Williams Siemens who was quite an inventor.

He was born in Germany but spent most of his life in the UK. He gave us the open-hearth furnace which dominated steel-making for a century, laid the first trans-Atlantic telegraphy cable in 1985, and something dear to my heart was an early proponent of electric traction for automobiles, no internal combustion engine.

Siemens is this. And so the unit of Siemens is the reciprocal of the ohm, which when I was your age actually was called the mho. That is ohm spelled backwards. This is electrical engineering. That is supposed to be funny, but obviously the SI commission decided mho just does not cut it.

We are going to give it a proper name with a proper recognition. And, oddly enough, Ohm, whose unit is the reciprocal of the Siemens, was also a professor in Germany. But, when he enunciated his law in 1827, the linearity between resistance and the voltage required to drive a particular current, he was so badly ridiculed at his university that he resigned his position.

As I told you in the past, scientific change does not come easily. I know Professor Ballinger talked to you a little bit about Midgley. I want to talk to you about one other invention of Midgley's and refer back to all of these shapes of molecules.

I call him sp3 Midgley because most of his work that we know today involved sp3 hybridized molecules. And I know Professor Ballinger talked about Freon which was a refrigerant. Midgley at one point joined the Dayton Engineering Company, which is DELCO, which eventually was bought by General Motors.

And in 1921 he discovered this anti-knock agent for gasoline called tetraethyl lead. You know the structure is 6s2p2. You can hybridize this to give us 6sp3. And there are four unpaired electrons there.

And then we can take the ethyl radical and put four of those on. And so this gets diluted in the gasoline and goes through the combustion process. And what it does is actually reduces the potency of gasoline.

If the potency of gasoline is too high, when the fuel first goes into the combustion chamber and then the piston compresses, remember everything is hot from the previous combustion, the chamber could explode of its own accord.

And, if it does so, it with ram the piston up. Everything is supposed to be moving synchronously. What you want to do is put something in the gasoline to delay the combustion until the spark plug fires.

The sad thing is that there was a superior chemical known already back in 1920 which was ethyl alcohol. If ethyl alcohol had been used, we wouldn't have all the lead in the environment that we have thanks to the use of leaded gasoline for about 50 years.

Anyway. This is tetraethyl lead, and this was an invention of Midgley. Now, in the 1970s along came catalytic converters which we have to this day. And these are precious metal catalysts, platinum, palladium and rhodium.

But when tetraethyl lead burns the carbon forms CO2, the hydrogen forms H2O and the lead forms lead dioxide. And lead dioxide is volatile. And it goes with the exhaust gases. And it will pass over the catalyst.

And the catalyst's job is to break bonds. And so it breaks the lead-oxygen bond and reduces it to lead. And now the lead alloy is with the catalyst. Now you have platinum alloying with lead. What do you think the catalytic activity of lead is? Considering the difference in cost, I am willing to wager that if lead had any catalytic value we wouldn't be using platinum.

So when the lead alloys with the catalyst, it poisons the catalyst. Hence in the ë70s the advent of lead-free fuel. All of these things came together as a result of the need to deal with the absence of the tetraethyl lead necessitated by the onset of catalytic converters.

Again you see where the sp3 hybridization comes into play in a chemical that was used for about two generations. When it came along, people thought it was fantastic to stabilize internal combustion engines.

In the end it was dismissed for its toxicity to the environment. The same thing happened with Freon 12, dismissed after two generations for its toxicity to the environment. Midgley died about 30 years ago.

He doesn't know any of this. OK. We will see you Friday.

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