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Worked example: Interpreting potential energy curves of diatomic molecules

AP.Chem:
SAP‑3 (EU)
,
SAP‑3.B (LO)
,
SAP‑3.B.1 (EK)
,
SAP‑3.B.2 (EK)
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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  • blobby green style avatar for user comet4esther
    How do you know if the diatomic molecule is a single bond, double bond, or triple bond?
    (8 votes)
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    • stelly yellow style avatar for user lemonomadic
      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.
      (8 votes)
  • aqualine ultimate style avatar for user inirah
    I 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?
    (7 votes)
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    • leafers ultimate style avatar for user SJTheOne
      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!
      (6 votes)
  • leaf green style avatar for user Shlok Shankar
    Won't the electronegativity of oxygen (which is greater than nitrogen )play any role in this graph?
    (3 votes)
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  • leafers seed style avatar for user kristofferlf
    How come smaller atoms have a shorter stable internuclear distance in a homonuclear molecule?
    (2 votes)
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    • leaf red style avatar for user Richard
      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)
  • blobby purple style avatar for user John Smith
    Is it possible for more than 2 atoms to share a bond?
    (1 vote)
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    • leaf red style avatar for user Richard
      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)
  • blobby green style avatar for user Frank Wang
    "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)
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    • leaf red style avatar for user Richard
      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.
      (1 vote)
  • duskpin sapling style avatar for user allie
    can two atoms share a bond? sorry dumb q
    (1 vote)
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  • stelly green style avatar for user Taimas
    If diatomic nitrogen has triple bond and small radius why it's not smaller than diatomic hydrogen?
    (1 vote)
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  • aqualine ultimate style avatar for user Morgan Chen
    Why don't we consider the nuclear charge of elements instead of atom radii? Like, if the nucleus of the atom has a higher nuclear charge, then they repel each other more, and so less likely to get closer, so the optimal diatomic distance is longer. This makes sense much more than atom radii and also avoids the anomaly of nitrogen and oxygen.
    (1 vote)
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    • sneak peak blue style avatar for user blitz
      Considering only the effective nuclear charge can be a problem as you jump from one period to another.
      Even though sodium (Na) has two extra protons, its atomic size is much larger than fluorine (F) because of an extra shell
      (1 vote)
  • leaf green style avatar for user dpulscher2103
    What is "equilibrium bond length"? The help section on this chapter's quiz mentions it as either being "shorter or longer" when comparing two diatomic molecules, but I can't figure out what it's referring to i.e.

    "According to the two potential energy curves, the unknown diatomic molecule AB has a "shorter equilibrium bond length... than O2"

    In that example, the AB bond energy level (the "valley" on the graph) was significantly deeper (higher energy) than the O2 but all other aspects looked similar.
    (1 vote)
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    • leaf red style avatar for user Richard
      When considering a chemical bond it's essentially the distance between the atoms when the potential energy of the bond is at its lowest.

      It's easiest to visualize this concept in a metal spring. If the spring is undisturbed without any masses attached to it at either end, then it is at its equilibrium bond length. If we apply a force to the spring by either stretching or compressing it we are disturbing it from its equilibrium bond length by making it longer or shorter respectively. What we're also doing is putting more energy into the spring than it originally had resulting in the spring stretched/compressed to have more energy than when it was at its equilibrium bond length. The same logic applies to the bond energy of a diatomic molecule.

      Hope that helps.
      (1 vote)

Video 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.