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Where does the required energy for Na + Cl -> NaCl come from?

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Roxo:
Corribus thanks very much for your detailed explanation. It sort of confirmed what I’d more or less figured out regarding the kinetics but it’s good to have it confirmed by an expert.
I’m still in high school so I’ve not come across the quantum effects which you mention. That sounds really interesting, I’ll look into that. If you can give me a link to something which would get me started on those quantum effects you mentioned that would be really helpful. We don’t do any QM in school so I’m trying to teach myself ; it’s really interesting but pretty challenging trying to get my head around four vectors and stuff 🙃

Corribus:
Sure. Not sure exactly how much you know, but here's the five minute version:

An unpaired electron is a fermion and has a spin angular momentum of +/- 0.5 (in units of the reduced Planck constant ħ). As you probably know, orbitals hold two electrons, and when an orbital is filled, the electrons pair, such that the total spin (S) of the pair is zero (one is +0.5ħ and the other is -0.5ħ). A state where all the electrons are paired has S = 0 and is called a singlet state*. Most stable molecules are singlets because unpaired electrons are usually reactive. Molecular oxygen is a little unusual in that it has two unpaired electrons. Each electron contributes an S = 0.5ħ for a total S = 1ħ. This is called a triplet state.

Formally, any process in quantum mechanics has to have a net change in particle spin angular momentum of zero. This is sometimes called the Wigner spin conservation rule. It is basically a statement about conservation of momentum.

So, consider the reaction 2H2 + O2 :rarrow: 2 H2O

The reactants have a total spin momentum of 1 equivalent (S = 0 for the two singlet hydrogen molecules and S = 1 for the oxygen molecule) and the products have a total spin momentum of 0 (for the two singlet waters), for a net change in spin angular momentum of 1 equivalent. This violates the conservation of angular momentum.

Of course, this reaction still occurs. Formal quantum mechanical rules often outlaw certain processes (we call these processes "forbidden"). In practice, these processes are only "mostly forbidden". You might think of it as being due to certain quantum mechanical loopholes that provide avenues to get around the rules. For instance, if molecules vibrate in a certain way, stretched structures that exist for fractions of a nanosecond may not be subject to the same formal rules that the idealized symmetric structure is subjected to, giving a brief window for "forbidden" processes to occur. That sort of thing. The effect is that nominally forbidden processes are observed to just occur slowly on macroscopic scales.

In the case of combustion reactions or other reactions involving oxygen, there are lots of ways the formal rules may be bypassed. One is that while oxygen is a triplet in its most stable state, a certain highly energetic form called singlet oxygen exists. Singlet oxygen has about 94 kJ/mol more potential energy than normal ground-state triplet oxygen. That's a lot. A sudden concentrated burst of energy, such as from a spark or a blast of light, can transform triplet oxygen into a singlet oxygen. Now the Wigner rule is no longer violated, and thermodynamically favorable processes can occur quite rapidly. Now, you may also notice that transformation of triplet oxygen to singlet oxygen also violates the Wigner rule. True! How does it happen? Honestly I don't think these things are necessarily well-understood in practice. But one possibility is that in a hydrocarbon fuel mixture, there may be small amounts of aromatic compounds whose conjugated electron systems are known to be good photosensitizers of singlet oxygen production when they are electronically exited (for reasons that would far exceed the 5 minute version to explain). You may read more about that here:

https://pubs.acs.org/doi/10.1021/acs.energyfuels.8b02312

In biology, certain enzymes or pigments can photosensitize singlet oxygen production. In fact, some enzymes are specifically designed (well, I don't like that word... evolved?) to help bypass all kinds of quantum mechanical rules and turn slow "forbidden" reactions into fast "not forbidden" ones. Just so, a large drive in (man-made) catalyst research is to try to develop new catalysts that can better play quantum mechanical tricks to get around the Wigner rule and make reactions go faster.

Anyway, I hope you get the idea.

Spin: https://en.wikipedia.org/wiki/Spin_(physics)
Spin multiplicity: https://en.wikipedia.org/wiki/Multiplicity_(chemistry)
Spin-forbidden reactions: https://en.wikipedia.org/wiki/Spin-forbidden_reactions

*Singlet and triplet derive from a quantity called multiplicity, M = 2S+1. It's a historical term that basically describes the total number of ways the individual spins can combine.

Roxo:
Thank you so much for taking the time to explain all that . Very interesting and lots for me to follow-up.

Enthalpy:
Ionization energy:

It's the energy needed to take the electron far away. Such an event is too rare under normal conditions. 496kJ/mol and 2478J/mol=298K result in a Boltzmann probability of e-200.1 or 10-89.6, not compensated even by Avogadro's N. It happens in situations far from equilibrium, say in a sodium gas discharge lamp, or for instance at 6000K at star surfaces, where the probability increases to exp(-10), or in star cores (10MK) or tokamaks (100MK) where it's the normal state.

The OP notes that the electron affinity of a chlorine atom is less than the ionization energy of a sodium atom. But as the nuclei stand close to an other, the electron doesn't go far away, so the ionization energy is an excessive value. Or if you wish, the diatomic molecule has the equivalent of some lattice energy too. The CRC handbook of Chem&Phys claims that NaCl boils without decomposing, so the gaseous diatomic NaCl molecule exists - or maybe the gas molecule contains more atoms, but I suppose that would be known for NaCl. For C it's still incompletely known.

Even some sort of ionization energy to a short distance would be an excessive value. Bound atoms are "in contact" in molecules, ionic bonds are a conceptual simplification, and the electron isn't fully ripped away, but remains partly at the Na atom. As the atoms (or rather molecules! Lone Na or Cl atoms need much heat) met to form a molecule, the electron needed to cross no distance, so ionization energies and electron affinities don't determine an energy hurdle or an activation energy.

The energy of NaCl is much more favorable in the solid because each Na ion has 6 Cl neighbours, so the electric flux resulting from the charge spreads over more area around the ion, the electric field is smaller, and the energy too.

Or in fact, as the Cl ions are "in contact" (the limit of an atom or ion is fuzzy) with the Na ions, the valence electrons move very little to make a bond. My present and imperfect understanding is that near the "contact" surface of the ions, very little happens, as the surface of Na is also the surface of Cl; the probability density of these valence electrons drops only close to the nuclei when the bond forms, for the electrons that had a significant probability density, that is the S layers.

The situation is very similar in a solvent, say H2O. There Na+ can separate from Cl-, but only because several negatively charged O surround each Na+ and several positively charged H surround each Cl-. That is, isolated ions aren't present because they're energetically impossible.

Corribus:
@Enthalpy

The webbook @ NIST provides gas phase thermochemistry data as well as spectroscopic constant for diatomic NaCl molecule, which I assume are determined in the gas phase.

https://webbook.nist.gov/cgi/cbook.cgi?ID=C7647145&Mask=1E9F

A brief search shows that dimers and linear polymer chains also form under certain conditions.

https://aip.scitation.org/doi/10.1063/1.471389

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