Lattice energy | Molecular and ionic compound structure and properties | AP Chemistry | Khan Academy

You may already be familiar with Coulomb's law, which is really the most important or underlying law behind all of what we know about electrostatics and how things with charge attract or repulse each other.

But a simplified version of Coulomb's law is just that the force between charged particles—the magnitude of the force—is going to be proportional to the product of the charges. So, ( q_1 ) would be the charge of one of the charged particles—maybe this is an ion; ( q_2 ) would be the charge of the other particle—maybe that's an ion—divided by ( r^2 ).

And if we're talking about ions, ( r ) is going to be the distance between their nuclei. If the charges are different, it's going to be a force of attraction. If the charges are the same, it's going to be a force of repulsion.

We can use Coulomb's law to think about ionic compounds. So let's go with maybe the most common ionic compound in our daily life, and that is table salt. Table salt is sodium chloride.

So sodium chloride—we have talked about this in other videos—it is made up of positively charged sodium cations, so you have ( Na^+ ). Sodium is a group one element; it's very easy to nab an electron off of it, and then it has a positive charge. It's made up of a chloride anion, so ( Cl^- ). Chloride is a group seven element; it really wants to get that extra electron to have eight valence electrons in its outermost shell.

And so it's very likely to grab an electron, maybe from a sodium. These two characters are going to be attracted to each other; notice they have opposite charges. When you have a bunch of sodium and chloride together, you'll have a structure that looks something like this; in chemistry, we call this a lattice.

Now, in everyday language, you might associate things like lattices with kind of a crossing pattern like that. In chemistry, when we're talking about a lattice, we're talking about a three-dimensional structure of atoms or a three-dimensional structure of ions that have a repeating pattern to them. You can see that here, and in future videos, we'll go into more detail on lattice structures.

But you can see in this picture the purples are the sodium cations and the greens are the chloride anions. The reason why the sodium cations are so small, you can see that if you look at the periodic table of elements here. We have said that as you go to the right, your radius decreases.

What's happening is when sodium loses that outermost electron, then its electrons have a noble gas configuration of neon. So it really loses that third shell; it gets smaller. Not only does it lose that third shell, but it has 11 protons, so it's going to have a very strong pull on those electrons in that second shell.

Similarly, chloride is going to gain an electron, so it's going to have a noble gas configuration of argon, so it is going to be bigger. Now when we talked about covalent bonds, we talked about the bond energy—the energy needed to pull apart the atoms that were forming the covalent bonds.

There's a similar notion for ionic bonds like this, and that is lattice energy. That is the energy necessary to pull the ions apart so that they are infinitely far apart from each other. Lattice energy is usually measured in kilojoules per mole, which is also what we measure bond energy in because they're really the same notion.

Except lattice energy, you're breaking up a lattice of ions, while in bond energy, you're normally talking about covalent bonds. Now I want you to think about something: what's going to have a higher lattice energy? Would it be sodium chloride, or let's pick something else?

Let's say we had rubidium chloride. Which is going to have a higher lattice energy? What's going to take more energy to pull the ions apart? And I'll give you a hint with this periodic table of elements.

All right, well, rubidium chloride—that's made up instead of a sodium cation. That's made up of a rubidium cation, so you have ( Rb^+ ) and, of course, you have the chloride anion ( Cl^- ).

So what's the difference here? The anion is both chloride in both cases, but when you look at rubidium versus sodium, rubidium, when it loses an electron, is going to have a noble gas structure, electron structure of krypton, while sodium, once it loses an electron, is going to look like neon.

So the sodium cation is smaller. And what does that tell us? Well, if this one right over here—let me circle it like this—if this is smaller and we have similar charges on top, you have a plus one and a negative one on top; that's the charges between the two ions.

But now you have a smaller radius between the nuclei because sodium is smaller than rubidium. Well, as the radius goes down, the force goes up. So you're going to have stronger Coulomb forces in a lattice of sodium chloride than in the lattice of rubidium chloride.

Because the force of attraction is stronger, it's going to take more energy to pull it apart. So because of that, you're going to have a higher lattice energy for sodium chloride than rubidium chloride.

Now let's think about another ionic compound. Let's say we were to think about magnesium fluoride, ( F_2 ), and this is made up of a magnesium cation that has a positive two charge, so ( 2^+ ), in a lattice with a bunch of fluoride anions.

So, how would the lattice energy of magnesium fluoride compare to what we just saw up here? So magnesium has a larger charge than these cations up here. So if you viewed the charge of magnesium as ( q_1 ), you're going to have something larger up there, and that fluoride is a smaller anion than chloride.

We can see that if we look at the periodic table of elements again; fluorine is smaller than chlorine. And so even if you add an electron to both of them, fluoride is still going to be smaller.

And magnesium, when you take two electrons off of it, is going to have the noble gas configuration of neon, but it's going to pull even more on those second-shell electrons because it has 12 protons, whereas sodium only has 11.

So what we see here is not only does magnesium have a larger positive charge than the sodium cation does, but it's going to be smaller. And the fluoride has a comparable charge to the chloride, but it too is going to be smaller.

So we have a larger charge on top, at least for the magnesium, and you have smaller radii for the bottom. So in magnesium fluoride, the Coulomb forces between the ions and the lattice are even stronger.

And so the lattice energy—the energy necessary to pull it apart—is going to be higher. So out of the three we just looked at, the highest lattice energy is going to be magnesium fluoride, followed by sodium chloride, followed by rubidium chloride.