Lecture 7: Octet Stability by Electron Transfer: Ionic Bonding

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Chemical properties: so let's put something up as a hypothesis. Let's say, well, maybe it has to do with the energy that it takes to remove electrons. And, one other thing that I failed to point out, if you take a look at the energies associated with the outermost electrons, in this case, lithium, you see it's 0.5 megajoules per mole, and then what's the 6.26? That's associated with one, n equals one, inner shell.

There is a huge difference between the energies in the outermost shell and the inner shells, which tells you that it's unlikely that any electrons except those in the outermost shell are going to be active.

The inner electrons are so tightly bound that they are for all intents and purposes, immobilized when it comes to reactivity. Again, boron is a good example. Look, 0.8, 1.36. This is 2p. This is 2s.

Yeah, they're different but they are roughly on the order of about 1 MJ per mole. If you go down to 1s, it's 20 MJ per mole. So, the chances of getting any activity from these inner shell of electrons are vanishingly small.

So, let's focus on the outer shell electrons. And, these outer shell electrons are termed valence electrons. So let's construct a model here that suggests that chemical reactivity is somehow related to the electron binding energies of the outermost electrons of the outermost shell.

And, this outermost shell is termed the valence shell. So, in a first blush, you might say, well, why don't we just take the first ionization energy? And, that's not a bad first guess. But, we know for example that magnesium, when it reacts, it reacts with both of its electrons, not just one of its electrons.

So, taking just the outermost electron might give us some false readings. So, what if we capture all of the valence electrons. Is there some way of handling that? Because that will take care of all of the electrons that are capable of reacting, none of the inner shell electrons.

And we do so by a quantity called the average valence electron energy. In other words, if the average energy of all the valence electrons. So, let's take a look at an example. An example of that might be, oh, let's look at something like oxygen.

If you look at oxygen, oxygen is 1s2, which is an inner shell electron. Just putting it up for completeness. 2s2, and 2p4, and so here's the valence shell. If I want to take the average energy of all of those, what I can do is go over to my data set.

Here's a data set. There is oxygen. The 2p is 1.31. The 2s is 3.12. So then, I could say that the average valence electron energy for oxygen would then be, I've got two s electrons. So, it's two times 3.12 plus four times 1.31, all divided by six.

I'm averaging it over the entire set of valence electrons which gives me 1.91 MJ per mole. Or, in my favorite unit, 19.80 electron volts. This is electron volts per atom. So, how does average valence electron energy very across the periodic table? Let's take a look at that.

So, we see it here. We see that it varies monotonically from left to right as we move along a row. So, this is a constant n number. Within a constant shell, it varies from left to right, maximally taking value at the right extreme.

And, within a column, it decreases down a column. It rises up a row. It decreases down the column. And, the values that it takes can be broken into three groups. Over here in the lower left corner, we have elements that as a group have very low values of average valence electron energy.

These are elements that are good electron donors. They are good electron donors because the electrons aren't tightly bound. OK, elements with low average valence electron energy, and here I'm saying below 11 electron volts, these are good electron donors.

And, we call these in simple English, metals. And, it turns out that about 75% of the periodic table falls into this category. So, the vast majority of elements in the periodic table are metals. And, at the other extreme, we have elements with very high value, elements with high average valence electron energy.

Well, we just did the calculation for oxygen. This is almost 20 eV, high average valence electron energy, greater than 13 electron volts. So, that means the electrons are tightly bound. So, these are poor electron donors.

And, in fact, if any electron comes in their midst, they'll capture it because the binding energy is so high. So, these are poor electron donors but also a good electron acceptors, and we call these non-metals.

And you see those. And then there is this group of about half a dozen right down the diagonal middle. And, they have intermediate values. So, when the value of the average valence electron energy lies between 11 eV and 13 eV, we have these elements that are neither fish nor fowl, and you'll see in a little bit their unique electrical properties.

And, these are called semi-metals or metalloids. And, in some instances, they can be made to behave more nearly metallic. And in other cases, they behave more nearly as insulators. So, now with this framework, I said that talking about these valence electrons might give us some insight into chemical reactivity.

What can we say about chemical reactivity? Well, what do we know about extremes of chemical reactivity? See if we can grab onto something. We know that at one extreme we have no chemical reactivity.

We have elements that are totally inert, and we have examples of this, the noble gases, dominantly inert. I know it's possible to induce chemical reactions, but these are exceptions. This is not the norm.

So, we have an inertness. And at the other end we have explosive reaction. OK, so do we know anything so far that we can point to that would give us a departure? And the answer is yes, we know something about the noble gases.

What do we know about the noble gases? They are chemically inert. They have the highest values. They have the highest average valence electron energy in any shell. And, the electron configuration is always ns2p6.

Whatever the n number is, with the exception of helium, helium is the oddity because there's only two elements in n equals one shell. But, once you get beyond n equals one, it's always 2s2, 2p6, 3s2, 3s6.

So, we have an octet of the electrons that seems to be associated with chemical inertness. Octet stability is the term applied to this feature. So, all right, let's go with this. Let's say, suppose we hypothesize that an octet of the electrons is going to lead to stability.

Is there some place we can go next with this? And I say, well, let's look at something like sodium. Let's look at sodium. Sodium has the electronic structure 1s2, 2s2, 2p6, 3s1. Now, that's not an octet, but it's not far.

This is the electronic structure of neon. So it's really sodium you can think of electronically as neon plus the 3s1 electron. It's so close. And, I also know something else about sodium. It's got a very low average valence electron energy.

Its average valence electron energy is 5.2 electron volts, which is a heck of a lot less than 11. So, this is a good metal. It's a good electron donor. So, I've got something that's one electron away from the electronic structure of neon.

It's a good electron donor. If it could only ditch this electron, it could have the same electronic structure as neon. But you can't just ditch an electron. Charge neutrality won't allow for it. If you want to lose electron, you have to find someplace for that electron to go.

In other words, for an electron donor to give up its electron, the electron donor needs to have an electron acceptor. So, that's sort of half the story. Now, let's go over to the other side. Let's look at chlorine.

Chlorine is 1s2, 2s2, 2p6, 3s2, 3p5. The chlorine, it's not an octet here. This is five plus two is seven. But, when I went to school, seven was only one less than eight. So, this needs only one more electron.

If it could gain one more electron, then chlorine would be iso-electronic with argon. So, it would achieve octet stability. And we know that chlorine is very aggressive when it comes to electrons. It's got an average valence electron energy of about 16 eV, 16.5 eV, which is a lot greater than 11.

So, what if we were to put the two of these in the same room? You've got an electron donor with a powerful urge to become neon-like. You've got an electron acceptor with the powerful urge to become argon like.

What if we were to take this electron and send it over to here, in other words, engage in electron transfer. What will we achieve? Sodium would become sodium plus. Chlorine would become chlorine minus.

So, I've got ion pair formation, and I've got a huge decrease in energy because a donor is able to express that urge, an acceptor is able to express that urge. And, I've achieved octet stability in a new way.

But there's more because now I've got pluses and minuses. This is all gas phase. It's all gas phase. So, what happens if I put pluses and minuses in a gas phase? There is a Coulombic force of attraction.

So, the sodium over here and the chlorine over here, they will be attracted to one another. So, let's start. So, sodium, chlorine attaches. But there's more sodiums. There's more chlorines. So, maybe another sodium will attach.

And, this will go on and on and on without limit. So, what's the consequence of forming these gas ions? These gas ions, if you take gas ions, these gas ions, if you take gas ions, gas ions of opposite charge will necessarily agglomerate without limit.

And, what happens if I put a gazillion of these things together? What's the resulting form? The resulting form is a solid. A solid will form. So, if you start with sodium vapor and chlorine gas, electron transfer will occur.

And you will form a crystal of sodium chloride as a result of this need to form crystal expressed through the Coulomb's Law. So now, I want to take a look at the energetics of that. Let's look at the energetics of Coulomb's Law.

I want to talk a little bit sort of at a general level about modeling. How would I model this system? Well, there's levels of models. And, the bottom line in modeling is make it only as complex as you need to.

Don't put in extra bells and whistles if it's not necessary. So, for example, if I have a sodium ion over here, and I have a chloride ion over here, where the distance from center to center I'm denoting as r, this is nucleus to nucleus separation.

And let's say that sodium has a radius, r plus, and chlorine has a radius, r minus, when r is very large in comparison to the radii of the ions, I don't need to draw them this way. I can model this whole thing as point charges.

I can model it as point charges. This is a point that's negative, and this is the point that's positive. And, that's all we need to do. And, a lot of the derivations you will see in physics rely on this being able to model as point charges.

But, what happens when these two start to get really close together? When they start getting close together, there is more complexity. More complexity takes on this form. So now, let's get a sodium here, and the chloride ion next to it to the point where they are touching.

So now, I'm going to show some fine structure. Yeah, this is net positive. The sodium is net positive. And the chloride is net negative. And so, there is an attractive force between the two of them, the positive and the negative.

But, let's look more carefully. Sodium is net positive. But, I've got a nucleus with 11 protons in it. And, I've got ten electrons around it. And, here, I've got 17 protons in the nucleus. And, I've got 18 electrons around it.

So, when we get really close together, granted, there is a net positive negative charge with a Coulombic force of attraction. But, can you see that as you get really close together the negative electronic cloud surrounding the two ions start to sense one another.

And, there is a mutual repulsive force here. There is a repulsive force, the attractive force between ions of opposite charge is offset by a repulsive force due to electron cloud interactions. This is the clouds or the orbitals, electron cloud interactions.

And, this is what prevents them from collapsing into one another. They reach a certain equilibrium. So, what we're going to do now is look at the energetics associated with that. And that's given as follows.

I want to plot energy in the system as a function of interatomic spacing. So, the x axis is interatomic spacing, and the y axis is energy. Positive energy is repulsive, and negative energy is attractive.

And, I'm going to put the sodium atom at the center. So, here's sodium. And, I'm going to ask what happens when chlorine comes in. So, we'll put chlorine over here. So, this is the chloride ion. It's over here.

And, we're going to look at what happens as the chloride ion moves from infinity in towards the positive ion. So, let's first go with the attractive because you know this already. The attractive energy is just the potential energy, Coulombic potential.

That's simply q1, q2 over 4 pi epsilon zero R. And, q1 is equal to the charge on sodium. q2 is the charge on chlorine. So, this is positive E on the sodium, negative E on the chlorine over 4 pi epsilon zero R, which is going to give us minus E squared over 4 pi epsilon zero R.

And, this is just a rectangular hyperbola, and it's going to look like this. So, this is the E attractive. At infinity, there's no stored potential energy, and it drops off more and more negative as one over R.

Now, how about this repulsion between electrons? This is not a Coulombic force. It's very different. The repulsive term goes as some constant lower case b divided by R to the n. N is not the quantum number.

N is a power law factor in here. And, it's given by what is called the Born exponent. And, it's a very high number. Why is it a high number? Because it has to drop off precipitously. When you get one over R, you get a gradual fall.

If you get one over R squared, it'll be a little steeper. One over R to the sixth will come in, and then jump off precipitously. And that's what you want because the electron repulsion is only felt when you are in really, really close.

And then, it's, for all intents and purposes, falls to zero. So, the Born exponent typically takes values of between six and 12. And, B is some constant that we have to determine. So, what's one over R to the 8th going to look like on this scale? It's going to look like this.

It's going to hug the x axis until it gets a very, very close. And then, it's going to take off like a shot. So, this is the repulsive energy term. And so, what's the net energy? The net energy is the sum of the repulsive and the attractive.

And, see, out at very, very high separations, it's essentially all repulsive, excuse me, all attractive. And at very, very low separations, it's all repulsive. And in between, it goes through a minimum.

And, this minimum here is what gives us the value of the inter-electrode separation, the inter-ion separation. And so, I need to cheat a little bit on the drawing and make sure that this minimum occurs right here.

OK, so R minimum, the minimum separation occurs when the energy is at its minimum. And, that's given by the balance between the attractive force of the ions offset by the repulsive force in the electronic shells.

And, what we will do next day is we will look at the consequences of such an energetic set up, and rationalize that when ions form, by necessity we must form ionic crystals. So, I think with that I'll shift over to some external matters.

We've seen so far that we can have a neutral plus neutral sodium plus chlorine goes to cation plus anion. That's what we've just been looking at. And this occurs in order to achieve octet stability.

Well, it's possible to reverse this. It's possible to take the cation and anion and restore them to their neutral states. So, for example, in an electrochemical cell, it would be possible to take the sodium ion, give back its electron, and convert it into a metallic sodium, take the chloride ion, remove its electron, and restore chlorine gas.

So, this is what goes on in an electrolysis cell, and it works thanks to input energy from a power supply shown here. So, that's point number one. Point number two is that ionic solids at high temperatures make ionic liquids.

So, one such ionic liquid is magnesium chloride. Magnesium chloride is the raw material for the production of magnesium. This is magnesium. It's the lightest of the structural metals. It's got a density of about 1.76 at room temperature.

For comparison, aluminum is 2.7. So, aluminum is about 50% denser than magnesium. Steel is 7.87. So, this is about a quarter of the density of steel. So, if you could make automobiles with a high magnesium content, you would reduce the mass, reduce the energy required, and thereby reduce the environmental impact.

Clearly, if I did nothing more, but I took every car, doubled its fuel economy, its emissions would go to 50% of what they are now, no other changes being made. So, fuel economy and environmental conservancy make a lot of sense if you care about such things, of course.

So, here's magnesium. It's very light. It takes energy, and this is how it's made. Electrolysis of magnesium chloride in a cell where the one electrode we would make magnesium. The other electrode, we'd make chlorine gas.

So, the question becomes, well, what are the resources for magnesium? Do we have magnesium to do this? So, I went to the library and I looked up Advances in Molten Salt Chemistry volume six because there's an article in there about the chemistry and electrochemistry of magnesium production.

So, I went to go look up the authoritative source on this, and so I looked this up, and I want to give you a sense of what the truth is. People tell you that we are resource constrained, that we are running out of resources.

Well, think about this. Where are the data? A cubic kilometer of seawater, go into the ocean and imagine a box 1 km x 1 km x 1 km. That's a cubic kilometer. It contains an million tons of magnesium, 1,000,000 tons, which is more than has ever been produced in one year by all the magnesium plants in the world.

Annual production of magnesium is about 600,000 tons per year. You get that out of 1 cubic kilometer of seawater. And, seawater contains only 3.7% of the total magnesium present in the Earth's crust.

So, clearly magnesium resources are ubiquitous and virtually inexhaustible. There's lots of magnesium. So, if magnesium is so abundant, why is it so expensive? Steel is about 10 cents a pound. Aluminum is about 70 cents a pound.

And magnesium is over a dollar a pound. Why is it so expensive? It's not because of scarcity. It's expensive because the process by which we produce it is energy intensive and resource intensive. So, if we want to get more magnesium into the marketplace at an affordable price, not by government edict, what do we have to do? We have to invent a process, a chemical extraction process that will make the production of magnesium cheaper so that we will have the opportunity to avail ourselves of energy-efficient materials.

And so, maybe somebody in this room working with me will invent such a process. All right, I'll see you on Friday.

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