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Worked example: Interpreting potential energy curves of diatomic molecules
The length and energy of a bond are influenced by both the bond order and the size of the atoms in the bond. In general, the higher the bond order and the smaller the atoms, the shorter and stronger the bond. As shown in this video, we can use these relationships to match diatomic molecules to their potential energy curves.. Created by Sal Khan.
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How do you know if the diatomic molecule is a single bond, double bond, or triple bond?(10 votes)
I know this is a late response, but from what I gather we can tell what the bond order is by looking at the number of valence electrons and how many electrons the atoms need to share to complete their outer shell.
Both N atoms have 5 electrons on its outer shells so they can both share 3 to complete their shells (so they form a triple bond).
Both O atoms have 6 outer electrons so they can share 2 electrons to complete their outer shell (thus forming a double bond)
Similarly, the H atoms have 1 valence electron - they can each share their electron to complete their 1n shell, thus form a single bond.(14 votes)
4:45I don't understand one thing: The atomic radius of oxygen is smaller than nitrogen, so it makes sense even considering radii that oxygen would be the purple-coloured line. As the atom gets bigger it has a bigger potential energy curve, and since nitrogen is bigger than oxygen, Sal's thought process that oxygen may be the red coloured line when considering atomic radii doesn't make sense. Am I confusing something here?(9 votes)
Careful, bond energy is dependent not only on the sizes of the involved atoms but also the type of bond connecting them. As mentioned in a previous video, the smaller the individual atoms, and the higher the order of the bonds, the higher of a bond energy you're going to be dealing with.
In the case of oxygen vs. nitrogen, the fact that oxygen has a smaller atomic radius (due to a larger effective nuclear charge) may lead you to believe that it has a smaller stable internuclear distance than nitrogen, and a curve with its minimum potential energy situated closer to the origin of the axis (the red one).
However, the triple bond between two nitrogen atoms brings the nitrogen atoms closer together than two oxygen atoms, which are connected by a weaker double bond. This causes nitrogen to have a smaller stable internuclear distance than oxygen, and thus a curve with its minimum potential energy closer to the origin (the purple one), as the bond order generally trumps factors like atomic radius.
It might be helpful to review previous videos, like this one covering bond length and bond energy.
https://www.khanacademy.org/science/ap-chemistry-beta/x2eef969c74e0d802:molecular-and-ionic-compound-structure-and-properties/x2eef969c74e0d802:intramolecular-force-and-potential-energy/v/bond-length-and-bond-energy
Hope this helped!(14 votes)
Won't the electronegativity of oxygen (which is greater than nitrogen )play any role in this graph?(4 votes)
No electronegativity doesn’t matter here, the molecule has two oxygen atoms bonded together, they have the same electronegativity.(7 votes)
How come smaller atoms have a shorter stable internuclear distance in a homonuclear molecule?(2 votes)
An atom like hydrogen only has the 1s orbital compared to nitrogen and oxygen which have orbitals in the second electron shell which extend farther from the nuclei of those atoms. So basically a small atom like hydrogen has a small intermolecular distance because the orbital it is using to bond is small.
Hope that helps.(3 votes)
- "your radius for an atom increases as you go down a column. But as you go to the right on a row, your radius decreases."
-- Why? In both cases the numbers of protons & electrons are increasing. Why the atom size changes oppositely?(1 vote)- As you go from left to right along a period of the periodic table the elements increase in their effective nuclear charge meaning the valance electrons are pulled in closer to the nucleus leading to a smaller atom. As you go from top to bottom along a group then the number of electron shells increases meaning the valance electrons occupy a greater distance from the nucleus leading to a larger atom.
Hope that helps.(4 votes)
- I don't get why at3:54Sal attributes the cyan line, with the shortest bond energy 'distance', to H2 after explaining that the H atom is the smallest. Since hydrogen atoms are the smallest, shouldn't it have the longest bond energy 'distance'? According to what I understand, for smaller atoms, we need to supply more energy to separate them. So shouldn't H2 be attributed the red line?(2 votes)
- The bond of H2(H-H) is happening at the 1s shell, the closest shell to the nucleus, that's why the distance is so short.
But what about the nucleus charge?
If we had a Li2 (Li-Li) and a C2 (C=C), then we would see that C2 has a shorter distance because it has a stronger charge.
For the energy, both distance and bond is considerable, that's why that H2 with a single bond has a similar energy to O2 with a double bond. H2 bond is close to the nucleus but it's a single bond, the energy required to unbound it is for only one electron, while for O2 the energy required is for 2 electrons.(1 vote)
Is it possible for more than 2 atoms to share a bond?(1 vote)- If I understand your question then you asking if it's possible for something like three atoms to be connected to each other by the same bond. The best example of this I can think of is something called hapticity in organometallic chemistry.
In transition metal coordination complexes (molecules with a transition metal as their central atom) it is possible for a ligand like an alkene to bond to the metal using its pi-bond. An alkene (like ethene) has a carbon-carbon double bond formed from a sigma and pi bond. The pi electrons from the alkene can bind with the metal (and there's also some back donation of electron density from the metal back to the alkene) and still have the bond between the carbons remain. So the two carbon atoms and the metal are essentially sharing electrons in a bond.
A relatively simple example of this is Zeise's salt where a platinum atom binds to an ethene ligand using this type of bonding.
Hope that helps.(1 vote)
- So, if you pull diatomic molecules apart, eventually the amount of energy needed to pull the atoms apart diminishes, but as you push them together, what happens?
Is this explained in another video somewhere? it seems the potential energy reverses(1 vote)- For the graph shown, it represents the amount of potential energy the molecules have based on their intermolecular distance. Zero here being the reference point and is the energy of two atoms infinitely separated from each other. Essentially the energy the atoms would have if they had no interactions at all with each other; or two individual atoms. Negative energies therefore would be a decrease in energy from this zero reference points, and positive energy would be increases in energy from the reference point.
If the atoms are so far apart from each other then they’re essentially just two separate atoms and there is no molecule. Therefore, the potential energies of the atoms would approach the zero reference point. If you put them together then the repulsions from the protons in the nuclei between so great that it increases the potential energy of the molecule. The valley (or most negative energy) represents the ideal distance the two nuclei are from each other in the molecule. It’s at that distance that the molecules have the least energy and are the most stable.
Hope that helps.(1 vote)
- @0:30, how come H2 is the 0 on the scale? It's a gas in natural form, not solid or liquid. Gases are atoms drifting around; why not atoms that are more containable?(1 vote)
- Not sure what you mean by H2 having 0. Zero what?
Gas can also be molecules too, not just atoms.
Are you asking about why are particles in the gas phase not condensed in a single spot?
The video is talking about the intranuclear distance of the two bonding atoms, essentially the length of the bond. Whether it is a gas is a question about the physical state, which is a different concept.(1 vote)
If diatomic nitrogen has triple bond and small radius why it's not smaller than diatomic hydrogen?(1 vote)- Hydrogen has a smaller atomic radius compared to nitrogen, thus making diatomic hydrogen smaller than diatomic nitrogen. Sal explains this at3:32.(1 vote)
4:45Video transcript
- [Instructor] In a previous video, we began to think about
potential energy as a function of internuclear distance
for diatomic molecules. What do I mean by diatomic molecules? Well, we looked at
molecular hydrogen, or H2, which is just two hydrogens
covalently bonded to each other. And at standard temperature and pressure, there, they would naturally, the distance between the two nuclei would be based on where there is the lowest potential energy. And if you were to squeeze them together, you would have to put
energy into the system and have a higher potential energy. Or if you were to pull them apart, you would have to put
energy into the system and have a higher potential energy. What I want to do in this video is do a little bit of a worked example. Over here, I have three potential energies as a function of
internuclear distance graphs. And what I'm going to tell you is one of these is molecular hydrogen, one of these is molecular
nitrogen or diatomic nitrogen, N2, and one of these is diatomic oxygen. And what I want you to think
about, pause this video, is which graph is the potential energy as a function of internuclear distance for each of these diatomic molecules. And I'll give you a hint. Look at the low point in potential energy. The low point in potential energy is what you would typically observe that diatomic molecule's
internuclear distance to be at standard
temperature and pressure. And this distance right over here is going to be a function of two things. It's going to be a function of how small the atoms actually are, how small their radii are. So smaller atoms are, in general, going to have a shorter
stable internuclear distance. But the other thing to think
about is the bond order between these atoms, and I'll give you a little bit of a hint. Diatomic hydrogen, you just
have a single covalent bond. For diatomic nitrogen,
it is a triple bond. And for diatomic oxygen,
it is a double bond. So the higher order the bond, that will also bring the
two atoms closer together, and it also makes it have
a higher bond energy, the energy required to separate the atoms. Remember, we talked about
it in the previous video. This right over here is the bond energy. And so with that said, pause the video, and try to figure it out. Which of these is the graphs of H2, which is N2, and which is O2? So let's first just think about
it in terms of bond energy. If you look at it, the single bond, double
bond, triple bond here, you would expect the
highest order bond here to have the highest bond energy, and the highest bond energy is this salmon-colored
one right over here. So just based on that, I would say that this is
a good candidate for N2. So this one right over here, this looks like diatomic nitrogen to me. Then the next highest bond energy, if you look at it carefully, it looks like this purple
one right over here. And so just based on bond order, I would say this is a
good candidate for O2. And then the lowest bond energy is this one right over here. And so just based on the bond order here, it's just a single covalent bond, this looks like a good
candidate for diatomic hydrogen. But let's also think about
the radii of these atoms. If we get a periodic
table of elements here, we can see that hydrogen
only has one electron in that first shell, and so it's going to be the smallest. So that makes sense over
here, that your distance, where you have the
lowest potential energy, is shortest for the diatomic molecule that's made up of the smallest atoms. But then when you look at the other two, something interesting happens. Remember, your radius
for an atom increases as you go down a column. But as you go to the right on
a row, your radius decreases. 'Cause you're adding
more and more electrons to the same shell, but the
Coulomb forces are increasing between that outermost
shell and your nucleus. And so if you just look at that trend, as you go from nitrogen to oxygen, you would actually
expect your atomic radius to get a little bit smaller. They're right next to each other. They might be close, but
you say, okay, oxygen, you have one extra electron
in that same second shell, maybe it's going to be
a little bit smaller. So if you were to base
things just on that, you'd say, all right, well,
the internuclear distance for this salmon-colored one
is a little bit shorter, maybe that one is oxygen, and
maybe this one is nitrogen. But they would be close,
and I would say, in general, the bond order would trump things. And the bond order, because
you see this high bond energy, that's the biggest
giveaway that this is going to be the higher bond order
diatomic molecule or N2. They're close in atomic radius, but this is what makes
all of the difference. And we'll take those two nitrogen atoms and squeeze them together
just a little bit more, even though they might
be a little bit bigger. And so I feel pretty
good with this labeling.