Bond length and bond energy | AP Chemistry | Khan Academy

If you were to find a pure sample of hydrogen, odds are that the individual hydrogen atoms in that sample aren't just going to be separate atoms floating around. Many of them, and if not most of them, would have bonded with each other, forming what's known as diatomic hydrogen, which we would write as H₂.

Another way to write it is: each hydrogen in diatomic hydrogen would have bonded to another hydrogen to form a diatomic molecule. Like this, this molecule is only made up of hydrogen, but it's two atoms of hydrogen. This makes sense why it's stable because each individual hydrogen has one valence electron if it is neutral. So, that's one hydrogen there, that's another one there. And if they could share their valence electrons, they can both feel like they have a complete outer shell.

So, this dash right over here you can view as a pair of electrons being shared in a covalent bond. Now, what we're going to do in this video is think about the distance between the atoms. So just as an example, imagine two hydrogens like this. So that's one hydrogen atom and that is another hydrogen atom. It turns out that at standard temperature and pressure, the distance between the centers of the atoms that we observe, that distance right over there is approximately 74 picometers.

And just as a refresher of how small a picometer is, a picometer is one trillionth of a meter. So this is 74 trillionths of a meter. We're talking about a very small distance. But one interesting question is: why is it this distance? What would happen if we tried to squeeze them together? What would happen if we tried to pull them apart?

To think about that, I'm going to make a little bit of a graph that deals with potential energy and distance. So in the vertical axis, this is going to be potential energy. I won't give the units just yet; I'll just think in very broad-brushed conceptual terms, and then we could think about the units in a little bit.

Then this over here is the distance, the distance between the centers of the atoms. You could use the distance between the nuclei, and let's give this in picometers. Now, potential energy, when you think about it, is all relative to something else. So let's just arbitrarily say that at a distance of 74 picometers, our potential energy is right over here.

I'm not even going to label this axis yet. Now, what's going to happen to the potential energy if we wanted to pull these two atoms apart? Well, this is what we typically find them at; this is probably a low point or this is going to be a low point in potential energy.

So if you make the distances go apart, you're going to put energy into it, and that makes the potential energy go higher. To think about why that makes sense, imagine a spring right over here. If you want to pull it apart, if you pull on either sides of a spring, you are putting energy in, which increases the potential energy. Because if you let go, they're going to come back; they're going to accelerate back to each other.

So as you pull it apart, you're adding potential energy to it. As you have further and further distances between the nuclei, the potential energy goes up. And if you go really far, it's going to asymptote towards some value, and that value is essentially going to be the potential energy if these two atoms were not bonded at all.

If they, to some degree, weren't associated with each other, if they weren't interacting with each other. And so that's actually the point at which most chemists or physicists or scientists would label zero potential energy—the energy at which they are infinitely far away from each other. And that's what this is asymptoting towards.

So let me just draw that line right over here. So let's call this zero right over here. And actually, let me now give units. Let's say all of this is in kilojoules per mole. Now, once again, if you're pulling them apart as you pull further and further and further apart, you're getting closer and closer to these two atoms not interacting.

Why is that? Because as you get further and further and further apart, the Coulomb forces between them are going to get weaker and weaker and weaker. And so that's why they like to think about that as zero potential energy.

Now, what if we think about it the other way around? What if we want to squeeze these two together? Well, once again, if you think about a spring, if you imagine a spring like this, just as you would have to add energy or increase the potential energy of the spring if you want to pull the spring apart, you would also have to do it to squeeze the spring more.

And so to get these two atoms to be closer and closer and closer together, you have to add energy into the system and increase the potential energy. Why? Why are you having to put more energy into it? Because the more that you squeeze these two things together, you're going to have the positive charges of the nuclei repelling each other.

So you're gonna have to try to overcome that, and that puts potential energy into the system. And these electrons are starting to really overlap with each other, and they will also want to repel each other. So what we've drawn here, this is just conceptually, is this idea of if you wanted them to really overlap with each other; you're going to have a pretty high potential energy.

If you're going to have them very separate from each other, you're not going to have as high of a potential energy, but this is still going to be higher than if you're at this stable point. The stable point is stable because that is a minimum point; it is a low point in this potential energy graph. You could view this as just right, and it turns out that for diatomic hydrogen, this difference between zero and where you will find it at standard temperature and pressure, this distance right over here is 432 kilojoules per mole.

So this is at the point negative 432 kilojoules per mole. One interesting thing to think about a diagram like this is how much energy would it take to separate these two atoms to completely break this bond? It would be the energy of completely pulling them apart.

So it would be this energy; it would be this energy right over here or 432 kilojoules. And that's what people will call the bond energy—the energy required to separate the atoms. And we'll see in future videos that the smaller the individual atoms and the higher the order of the bonds—so from a single bond to a double bond to a triple bond—the higher order of the bonds, the higher of a bond energy you're going to be dealing with.