Where does the energy in a chemical bond come from...

The bond is actually just an energy potential.

Reactions occur because it minimizes the action of the system.

I.e. it causes the system to form new bonds at the most stable energy, which is usually the lowest possible.

All of these answers suck. I will explain things as clearly as I can.

Starting off, a good way to think of a chemical bond, is two masses connected by a spring. The potential energy of this system is simply a function of the distance between the two masses, pic related. Notice that if you "stretch the spring" past a certain point, the bond is just broken, the potential energy does not just increase indefinitely.

As other posters pointed out, the chemical bond is the attraction for electrons to the protons of other atoms, and this is true, though the energy is usually thought of mathematically in terms of Re, or the equilibrium distance between the two bonded species. There are a myriad of things that can effect the stability and energy of a chemical bond, like the mass of the two atoms, the principle quantum number of the bonding electrons, and several other things I am not going to bother typing out unless you ask.

At its core, chemical bonding is essentially like snapping very small magnets together. The biggest difference is that in the middle of "snapping together" they stop, because there is a second pair of magnets repelling each other (atomic nuclei).

That is pretty much all you need to know without going into obnoxious detail.

Also, to clarify the picture, the x-axis is bond length in angstroms, the y-axis is energy, and each n represents a vibrational energy level. You do not really need to worry about that, just notice the shape of the potential energy surface, and note that it represents the distance between two bonded species.

okay, so where does the energy in a chemical bond come from?

The separation of the electron and the nucleus. They experience a very attractive force, separating them creates potential energy. Same way that gravitational potential energy is a result of being farther from the center of the earth.

>he thinks position is a variable/number and not an operator on a Hilbert space

laughingsluts.tiff

...an operator whose eigenvalues are the "variable/number". Not sure what point you thought you were making, but it is not even particularly relevant to the thread.

I am officially asking for the myriad of things

Please explain the n bars.
Is this saying that the bottom of the potential well is not as low for atoms with a higher principal quantum number?

Would you say it is necessary to take a course in linear algebra to be a competant chemist? Or is there a select few topics that would be good to know.
How much linear algebra do I need to know to understand eigenvalues

Bond order, whether it has more bonding or anti-bonding characteristic, covalent or ionic characteristic, resonance for multiple bonds, things like that.

Keep in mind, for that picture the n is NOT the principle quantum number, it is a quantum number that deals with the vibration of the bond. That is one thing that can be difficult with quantum physics, no one uses the same terminology twice, it seems. No, the principle quantum number is basically whether it is an electron in the s shell, p shell, etc. On the graph, it is showing the energy as vibrational frequency increases.

For example, lets thing of H-Cl gas. At n=0 it vibrates somewhat and has a relatively low energy (no bonded species can ever NOT be vibrating, for various reasons), if we excite the H-Cl molecule with light, it might go to the n=1 energy level, corresponding to a vibrational frequency of 1589.95 wavenumbers (I think this is correct, could be plus or minus 20 wavenumbers. Immaterial really, I just want to get the point across). Because energy is quantized, the H-Cl molecule only has specific frequencies it can vibrate at, so each "n" refers to an energy level corresponding with one of these allowed frequencies. If the molecule is vibrating at the n=3 frequency for example, you can think of it sliding up and down the walls of the potential energy surface--i.e. it does not have a constant potential energy, it just has an average value that is extremely reliable.

Now, the bottom of the potential well CAN be less deep for atoms whose valence electrons have higher principle quantum numbers, but this is not always the case, per se. A good way to think of it is the spring example. If you have two light weights and a normal spring, things behave pretty normally, but if the weights are heavier, then you start seeing the effects of inertia, and so on. Basically, the bond is easier to break in almost all cases, but there are exceptions.

Is this what pchem is?

Also, how the fuck does one even begin to measure angstroms and atomic radii and such?

Depends on what you want to do. Computational or quantum chem, yes you need a background in linear algebra. Any other type of chem? No, not really, but I would recommend it just because it is useful. Eigenvalues are very very easy, they just take some getting used to. An intro to diff eq. would cover all you would need to know for chemistry purposes. I know incredible chemists who have never even sat courses in multvariable calc. Mathematical ability is very important and useful, but not all of it is applicable to all fields in chemistry.

Can you post a textbook recommendation

Yes, basically. It is actually very easy once you have a good theoretical background. Did a lab where I measured the bond length and atomic radii of H-Cl and D-Cl with nothing but a quartz tube and an FTIR from the 70's. Took about 2-3 hours. It is not difficult per se, you just need a good grounding in what you actually need to look for.

Not really. I had a textbook that was awful, and ended up referencing several different books. I have not actually found one single book that is good for everything.

Nobody in this thread has even mentioned that the force carrier for the electromagnetic force is virtual photons, which can be 'blocked' by opaque nuclei in the same way that sunlight is blocked by a curtain. This is the source of 99% of the potential bonding energy for the electronic nuclei.

Now, is this vibrational frequency in a way analogous to the energy well of intermolecular forces and the energy required to overcome these forces? I suppose what I am trying to say is if enough vibrational energy is put into the molecule, will the bond break? Just as a molecule in the liquid phase will escape to the gas phase when the energy of the molecule is higher than the potential energy of the intermolecular forces it is participating with.
Also, how can these vibrational frequencies be discrete values of they are averages? Are they averages of the potential energy of the bond and the kinetic energy of the vibrating atoms?
Thank you by the way. You are very lucid with your explanations.

being this retarded

You see how the curve levels off on the right side in the picture? That is the bond breaking. Basically if it vibrates enough, it will get to that plateau, and it effectively no longer interacts with the other atom. They are no longer bonded.

As for the whole "averages" thing, I somewhat mislead you with poor word choice, I think. The frequency at a given n value do not change, they are constant and discrete and so on, but the potential energy varies a small amount depending on where it is in the period of oscillation. When you report the potential energy of a bond, you average the potential energy at every point along the period of the vibrational frequency, and this gives a good workable value.

I scored in the 95th percentile on my ACS exams. Is that dog shit for someone looking to get into a good chemistry grad program? Does it even count for anything?

ACS is pretty much useless. Most of their journals are awful, they are an inane organization, and most people dislike them quite a bit. If you are getting into a grad program, all that matters is your chemistry GRE.

ikr, they're a fucking undergrad and they still don't know why bonds work

What the fuck that donut is fake.

You should definitely take an introduction to linear algebra, and introduction to quantum mechanics, and finally a quantum chemistry course.

The insight into how and why molecules form is invaluable to any chemist.

If you are a chemical engineer on the other hand, all you care about is how hot the reactor needs to be in order for the 10000 liters of mayonnaise per hour not to seize up and jam the extruder mechanism.

>linear algebra, and introduction to quantum mechanics, and finally a quantum chemistry course.

don't most chemistry programs include mathematics and physical chemistry?

As a chemist I say, believe the physicists. Theoretical chemists know it, alright, but synthesists? I wouldn't count on it.