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Course: AP®︎/College Chemistry>Unit 2

Lesson 2: Intramolecular force and potential energy

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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• Is bond energy the same thing as bond enthalpy?
• Yep, bond energy & bond enthalpy are one & the same!

Sometimes it is also called average bond enthalpy: all of them are a measure of the bond strength in a chemical bond.

Hope this helps! :-)
• Why do the atoms attract when they're far apart, then start repelling when they're near? Why is double/triple bond higher energy?
• 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
• How can energy be measured in negative ?
• 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.
• What is bond order and how do you calculate it?
• Bond Order = No. of Bonds / no. of surrounding atoms
• 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?
• 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.
• 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?
• 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.
• 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?
• 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.
• what is potential energy?
• 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.
• Does bond energy increase with the length?
• 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!
• 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?