Molecular Bonding: Questions & Answers

[sci-guy]

I have some questions about molecular bonding. I understand that intramolecular bonds (forces holding a molecule together) are stronger than intermolecular bonds (forces between molecules). I also understand that the strength of intermolecular bonds determines whether something is gas (no bond), liquid (weak), or solid (relatively strong). All these various types of bonds between the many chemical elements account for the myriad diversity of matter in creation. Last, I understand that some types of molecular bond have a special order to them, called crystal structure or lattice.

From what I can gather, all molecular bonding stems from electron sharing, exchange, etc. Here are my questions:

1) Is it correct to say that all molecular order (i.e. bonding arrangement) results from the most efficient energy state (i.e. electron configuration) of the material?

2) What about metallic bonding, involving the sharing of free electrons circulating through the material -- is that also the most efficient energy state?

3) Since all molecules of the same type have the same structure, when like molecules join, it seems like there must always be an ordered, repeating pattern (though often complex). Is the only distinction in crystals that the repeating order is identical in all three dimensions (as suggested here: http://en.wikipedia.org/wiki/Crystal_structure)?

 

[DrDu]

to 1. Energy is an important factor, but generally, the driving force between all reactions is entropy. I.e. the energy released in bond formation leads to an increase of the entropy of the surrounding. However, e.g. in the process of the formation of a crystal, not only the energy of the crystal is lower than that of its constituents but also its entropy. Hence crystal formation (and bond formation in general) is only favourable at sufficiently low temperatures. This concepts are formalized considering the thermodynamic potentials "free energy" and "free enthalpy".

to 2. Yes, electrons in a metal also have lower energy than electrons in the isolated atoms. See my explanation in this thread which also applies here:
https://www.physicsforums.com/showthread.php?t=476675

3. is a very complex question. Usually, the ordered structure has a low entropy which thence is favourable at low temperatures.

 

[sci-guy]

[from http://en.wikipedia.org/wiki/Introduction_to_entropy ]: "Entropy is a measure of how evenly energy is distributed in a system."

Isn't that another way of saying that the energy (of the two atoms) is most efficiently distributed by the bond that forms the molecule?

Maybe my phrase "most efficient energy state" wasn't clear (I don't know the precise scientific terminology), but efficient energy distribution, organization, or exchange is what I meant.

However, I was surprised by your statement "the energy released in bond formation leads to an increase of the entropy of the surrounding." I'm completely new to this, but I see where, after a bond, the previously unbonded electron is no longer available for "work" according to the definition of entropy, if that's what you're referring to. But I don't understand how energy is released in bond formation. Can you give a simple explanation of that, say, what happens when two hydrogen atoms bond? What energy is released and where does it go?

 

[DrDu]

When two atoms of hydrogen form a bond, an enormous amount of energy is released (420 kJ/mol if I remember correctly), usually in the form of heat. This is technically exploited e.g. in MIG welding.

 

[sci-guy]

Forgive my ignorance of what is probably basic science, but why/how is energy released? There were two electrons before (one in each atom) and there are two after, shared by the H2 molecule. What's changed?

 

[DrDu]

Read my basic explanation about how a bond is formed in the thread I cited in answer #2.

 

[sci-guy]

I read the thread and followed up on a few terms and concepts I didn't know. Wow -- I thought molecular bonding was a fairly basic process; there's more going on than a simple sharing of electrons. I understand most of it, but I still don't have a clear answer to my question. The best description of bonding I could find was this (from http://en.wikipedia.org/wiki/Antibonding_orbital):

"Consider two hydrogen atoms that are initially far apart and are brought together. When they are far apart and isolated the atoms have identical energy levels. However as the spacing between the two atoms becomes smaller the electron wave functions begin to overlap. The Pauli principle dictates that no two electrons in an interacting system may have the same quantum state. Therefore, each energy level of the isolated atoms splits into two molecular orbitals belonging to the pair, one lower in energy than the original atomic level and one higher. For example, the ground state energy level, 1s, splits into two molecular orbitals. Since the lower orbital is lower in energy than the original atomic orbitals of the separate atoms, it is more stable, and promotes the bonding of the two H atoms into H2. This is the bonding orbital. The higher orbital is higher in energy than the original atomic orbitals and is less stable, and therefore opposes the bonding, this is the antibonding orbital. In a molecule such as H2, the two electrons normally occupy the bonding orbital since it is lower in energy, and therefore the molecule is more stable than the separate H atoms."

My first question is about how the bonding orbital of a hydrogen molecule can be at a lower energy level than the orbital of a single atom. I thought the single electron of a hydrogen atom, being in the 1st shell, is already in its lowest energy state. In researching this, I see that my understanding of electron shells and subshells was too simplistic, but I still don't see where a lower energy orbital comes from.

That said, is this the release of energy you describe? If so, in what form and to where is the energy released?

 

[asheg]

you can look it from this point of view that metals are favorable state (in respect to energy) because the electron wave function can expand all over the metal and momentum is inverse of wavelength so momentum decreases and as a result the energy decreases. The same thing is true for crystal creation but when you increase the temperature the Entropy comes in and no longer crystal structure would be favorable (Concept of free energy ...).

 

[sci-guy]

Aside from my main question, which I still don't think has been answered, I don't understand why the larger orbital space in a molecule decreases an electron's momentum (and hence, energy). I understand the inverse relation of position and momentum due to the uncertainty principle, but how is a decrease in the CERTAINTY of the electron's momentum the same as a decrease in its momentum itself? It just means we have less knowledge of what it is, not necessarily that it's actually less.

 

[zincshow]

Forgive my ignorance of what is probably basic science, but why/how is energy released? There were two electrons before (one in each atom) and there are two after, shared by the H2 molecule. What's changed?

I assume energy would be released in the form of a photon when the h2 molecule forms from the 2 h molecules. Whats changed is that there is now a photon shooting off somewhere that may well break up some other h2 molecule into 2 h molecules sometime in the future.

 

[Drakkith]

I don't know the why, but I do know that it is more stable for an atom to fill its orbitals to reach the same state as the noble gases occupy. IE to "close" the shell. So two hydrogen atoms can reach the Helium electron shell configuration by sharing an electron each. This fills up their 1st shell, just like Helium is.

 

[asheg]

Aside from my main question, which I still don't think has been answered, I don't understand why the larger orbital space in a molecule decreases an electron's momentum (and hence, energy). I understand the inverse relation of position and momentum due to the uncertainty principle, but how is a decrease in the CERTAINTY of the electron's momentum the same as a decrease in its momentum itself? It just means we have less knowledge of what it is, not necessarily that it's actually less.

For a moment forget the uncertainty principle, my discussion doesn't depend on it.
In a single atom the wave function of electron is confined to a region near it so the wavelength of electron is short hence its momentum is high. when you have a metal, there exists many states which their wavelength are near metal's width, so their wavelength are very larger in compare to a single atom and their momentum are very smaller.

 

[sci-guy]

Thanks, that helps. Now that I'm a little clearer about the process, I want to return to my original question, which is whether a bonded molecule represents the most efficient energy state (or exchange/distribution/arrangement/etc. -- whichever term is best, and please TELL me which is best) vs. the energy state of two separate atoms. In other words, do molecules basically form because it's a way for electrons to fall into a lower (i.e. more restful) energy state?

DrDu mentioned entropy as the driving factor. Entropy is commonly viewed as disorder, but physics is moving away from that misleading term in favor of equal energy dispersion. Electrons want to spread out (i.e. orbit two atoms rather than one) so that they can do so at a lower energy level. They are more widely and evenly distributed, so it is really a more orderly state of the system. Is this a correct view?

This is also a good point; where does it fit in:

I don't know the why, but I do know that it is more stable for an atom to fill its orbitals to reach the same state as the noble gases occupy. IE to "close" the shell. So two hydrogen atoms can reach the Helium electron shell configuration by sharing an electron each. This fills up their 1st shell, just like Helium is.

 

[asheg]

The entropy also can be considered in energy like in Gibbs free energy:
G = H - TS (Equ_1)
Where H is enthalpy and T is Temp and S is entropy.
As far as I know every system in the world behaves so that its G becomes minimum.

When temp is very low the second term in equ 1 would be low and we can neglect it. So G = H and when 2 atoms be there, they attach to each other and decrease the total energy by expanding electron wave functions.

But when the temp is high (According to equ 1) the second term becomes more important and the energy would be lesser if entropy is higher. So the molecule will breaks into parts which increases entropy. It's a trade off between first and second term.

 

[sci-guy]

As far as I know every system in the world behaves so that its G becomes minimum.

That's essentially the same as what I'm saying, right? So a molecular bond is an example of a system tending toward its lowest energy state. Is that right?

 

[asheg]

Yes, I think you're right (just change energy -> free energy).

 

[alxm]

Thanks, that helps. Now that I'm a little clearer about the process, I want to return to my original question, which is whether a bonded molecule represents the most efficient energy state (or exchange/distribution/arrangement/etc. -- whichever term is best, and please TELL me which is best) vs. the energy state of two separate atoms. In other words, do molecules basically form because it's a way for electrons to fall into a lower (i.e. more restful) energy state?

Yes. Why would they otherwise form bonds? The ground state energy of a molecule such as H2 is lower than the ground state of two hydrogen atoms separated by infinite distance. If you have two helium atoms at the same distance, or any distance the energy is higher, so they repel. (well, actually they attract very weakly due to dispersion forces, and have a shallow energetic minimum at over 40 Å separation, but they certainly don't form a bond).

The electrons don't 'fall' into a lower state. In fact, most of the time they don't change states at all; many/most chemical reactions occur in the ground state. What happens is that the ground state itself changes, because you're changing the potential. If you were to plot the ground-state electronic energy in terms of the distance between the nuclei, it looks like http://www.hasdeu.bz.edu.ro/softuri/fizica/mariana/Atomica/Covalent/covalentH.gif" .

That's for H2. The ground state has both electrons in the σ bonding orbital (electronic state). The blue curve is for the triplet state, where one of the electrons is in the σ* anti-bonding orbital - there is no minimum there. If an electron is excited to that state, the molecule will fall apart. With helium, you have four electrons, fully occupying both the σ bonding orbital and the σ* anti-bonding orbital. So as with the excited hydrogen atom, they don't bond.

The bonding orbitals of the electrons are always lower in energy than the anti-bonding ones. (Which doesn't mean every anti-bonding orbital has more energy than every bonding one) But the Pauli Principle only allows you to have two electrons in each orbital. You might want to just borrow a general or physical chemistry textbook and read that, though. They all explain it better and in greater detail than I have here.