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Bond length and bond energy

A diatomic molecule can be represented using a potential energy curve, which graphs potential energy versus the distance between the two atoms (called the internuclear distance). From this graph, we can determine the equilibrium bond length (the internuclear distance at the potential energy minimum) and the bond energy (the energy required to separate the two atoms). Created by Sal Khan.

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  • stelly yellow style avatar for user lemonomadic
    Is bond energy the same thing as bond enthalpy?
    (15 votes)
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  • blobby green style avatar for user Ariel Tan
    Why do the atoms attract when they're far apart, then start repelling when they're near? Why is double/triple bond higher energy?
    (10 votes)
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    • blobby green style avatar for user 1035937
      they attract when they're far apart because the electrons of one is attraction to the nucleus (protons) of the other atom. however, when the charges get too close, the protons start repelling one another (like charges repel). the double/triple bond means the stronger, so higher energy because "instead just two electron pairs binding together the atoms, there are three. As a result, the bond gets closer to each other as well." found that from reddit but its a good explanation lol
      (7 votes)
  • male robot hal style avatar for user wael kilany
    How can energy be measured in negative ?
    (7 votes)
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    • leaf red style avatar for user Richard
      The idea is that you start at a reference point of 0 energy where the atoms are far enough apart that they do no interact. Then negative and positive energies are simply states with lesser or greater amounts of energy respectively to that 0 reference point. So -432 kJ/mol of energy isn't negative in an absolute sense, rather is has 432 kJ less energy than that 0 kJ reference point.

      Hope that helps.
      (7 votes)
  • aqualine ultimate style avatar for user asumesh03
    What is bond order and how do you calculate it?
    (7 votes)
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  • stelly blue style avatar for user mikespar18
    Because Hydrogen has the smallest atomic radius I'm assuming it has the highest effective nuclear charge here pulling on its outer electrons hence why is Hydrogens bonding energy so low shouldn't it be higher than oxygen considering the lack of electron shielding?
    (3 votes)
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    • leaf red style avatar for user Richard
      So a few points here

      First, the atom with the smallest atomic radius, as thought of as the size of a single atom, is helium, not hydrogen. Primarily the atomic radius of an atom is determined by how many electrons shells it possess and it's effective nuclear charge. Hydrogen and helium are the best contenders for smallest atom as both only possess the first electron shell. However, helium has a greater effective nuclear charge (because it has more protons) and therefore is able to pull its electrons closer into the nucleus giving it the smaller atomic radius. But here we're not really talking about atomic radii at all, instead we're talking about the internuclear distance between two hydrogen atoms.

      Second, effective nuclear charge felt by an electron is determined by both the number of protons in the nucleus and the amount of shielding from other electrons. Of the two effects, the number of protons has a greater affect on the effective nuclear charge. This means that even though both these effects increase as we do things like move down a group or left to right across a period and also conflict with each other, the positive attraction from the protons will win out giving greater effective nuclear charges. This would mean that hydrogen, even though it has minimal shielding, has the lowest effective nuclear charge of any element simply because it has the lowest number of protons.

      Third, bond energy (in a covalent bond) is primarily determined by how well the electron orbitals overlap from the two atoms. Greater overlap creates a stronger bond. Effective nuclear charge isn't as major a factor as the overlap. We can determine things like electronegativity or bond polarity with the help of effective nuclear charge however. Keeping the overlap of orbitals in mind, the bond in molecular hydrogen is average as far as covalent bonds go. Molecular oxygen's double bond is stronger at 498 kJ/mol primarily because of the increased orbital overlap from two covalent bonds. And this idea continues with molecular nitrogen which has a triple bond and a bond energy of 945 kJ/mol.

      Hope that helps.
      (7 votes)
  • blobby green style avatar for user charles.merriam
    I'm looking at the graph of distance versus potential energy and am confused about the energy when "squeezing" atoms together.

    As I squeeze harder, do the electrons give up on the covalent bond at zero, or does zero have no meaning on the 'squeezing' side of the graph?

    How hard do I push before I fuse to He? Something obscene?
    (3 votes)
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    • leaf red style avatar for user Richard
      Zero potential energy in this graph is the reference point from which we judge the energies of the distance between the two atoms. Zero potential energy represents the energy when the two atoms are infinitely far apart. On the left side of the graph where a potential energy of zero is reached again, this means there is a distance between the atoms where the potential energy is equivalent to as if they were separate atoms. This just means we have two distances with the same amount of potential energy value.

      Pushing atoms of hydrogen, and any two atoms, so they form a single, larger atom is called nuclear fusion. The energy required to do this is quite large because of the electric repulsions of the protons of the two nuclei. Nuclear fusion happens naturally in the cores of stars and is how they produce light and energy. Only in the cores of stars though (in nature at least) is the density and temperature sufficiently high enough to facilitate nuclear fusion. Our own sun for reference has a core density of 150 g/mL and a temperature of about 15.7 MK (million kelvin). The minimum requirements for stellar nuclear fusion is a core density of 100 g/mL and a temperature of about 4 MK.

      Hope that helps.
      (6 votes)
  • blobby green style avatar for user Amelie S.
    Why is the potential energy higher for atom bondings that are getting squeezed together than the potential energy for atom bondings that are getting pulled apart?
    (3 votes)
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    • leaf red style avatar for user Richard
      If we push the nuclei of two bonding atoms together, then their protons get closer together. The protons are positively charged and like charged particles repel each other, so the closer we bring them together the more they repel each other. The stored desire to repel each other is potential energy.

      We still have a force of attraction between the electrons and the protons of the same atom which is also some potential energy. When we pull the nuclei farther apart then they gradually lose that proton-proton repulsion and only feel those proton-electron attractions. If we pull them far enough apart then we have separate, unbonded atoms which is being defined here as zero potential energy.

      Of course the protons and electrons of separate atoms also have attractions for each other. Allowing them to come closer reduces the potential energy of the two atoms in the same way that an electron bound to a proton in the same atom reduces the potential energy compared to if they were separate particles. There’s an optimal distance where electron-proton and proton-proton interactions of the two atoms yield the lowest overall potential energy.

      Hope that helps.
      (5 votes)
  • blobby green style avatar for user kumaar
    what is potential energy?
    (3 votes)
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    • leaf red style avatar for user Richard
      Potential energy is a main type of energy which is possessed by an object which allows it potentially do work with it later. Work, in a physics context, is essentially a useful action an object can perform like push or pulling something else. We can also think of potential energy as stored energy which an object can use. In a chemistry context here, the potential energy is due to the attraction and repulsion of the charged particles in the atoms; the protons and electrons.

      The electrons of one atom are attracted to the protons of the other atoms (because of the different charges) and so moving closer together reduces the potential energy of the atoms. But too close of a distance and the repulsion by the two atom’s protons begins to increase the potential energy. So that’s why bonding atoms are at a certain distance from each other so that their potential energy is at a minimum.

      Hope that helps.
      (4 votes)
  • eggleston yellow style avatar for user eman
    Does bond energy increase with the length?
    (2 votes)
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    • hopper cool style avatar for user obiwan kenobi
      Actually, it would be the other way around. If the bond length increases, the bond energy would decrease. If the two atoms bonded are closer together, then by coulomb's law, there should be a stronger force due to a smaller distance. Therefore, a shorter bond length would make it harder to break the bond, resulting in a higher bond energy. Accordingly, a longer bond length would make it easier to break the bond, resulting in a lower bond energy. Hope this helps!
      (5 votes)
  • piceratops ultimate style avatar for user Tanzz
    At , Sal says, "You're going to have a pretty high potential energy." What can be termed as "a pretty high potential energy"? Is it like ~74 picometres or something really larger?
    (2 votes)
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    • leaf red style avatar for user Richard
      Well picometers isn't a unit of energy, it's a unit of length. Here Sal is using kilojoules (specifically kilojoules per mole) as his unit of energy.

      Whatever the units are, that higher energy value we don't really need to know the exact value of. Instead we just need to know it is both greater than the reference point of the two atoms being infinitely far apart feeling no attraction having 0 potential energy and also energetically unfavorable to that 74 picometer distance.

      If we really wanted an actual number, we would just have to push those hydrogen atoms together and essentially measure their repulsion to gauge the potential energy.

      Hope that helps.
      (5 votes)

Video transcript

- [Instructor] 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, that 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 you have each hydrogen in diatomic hydrogen would have bonded to another hydrogen, to form a diatomic molecule like this. This molecule's only made up of hydrogen, but it's two atoms of hydrogen. And 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. And 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, at standard temperature, 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, so 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? And to think about that, I'm gonna 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, potential energy. And I won't give the units just yet. I'll just think in very broad-brush conceptual terms, then we could think about the units in a little bit. And then this over here is the distance, distance between the centers of the atoms. You could view it as the distance between the nuclei. And let's give this in picometers. Now, potential energy, when you think about it, it's all relative to something else. And 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 have to put energy into it, and that makes the potential energy go higher. And 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 just going to come back to, they're going to accelerate back to each other. So as you pull it apart, you're adding potential energy to it. So 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's 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, and 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, 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 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. And 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. 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. And so what we've drawn here, just as 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. And 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. This 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. And so 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? Well, it'd be the energy of completely pulling them apart. And 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, 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.