[PaulC4]

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

"The energy required to transfer an electron from a sodium atom to a chlorine atom (the difference of the 1st ionization energy of sodium and the electron affinity of chlorine) is small: +495.8 − 349 = +147 kJ mol−1. This energy is easily offset by the lattice energy of sodium chloride: −783 kJ mol−1. This completes the explanation of the octet rule in this case."

Where do these +147 kJ/mol come from in reality that are needed for the start, so to speak? And I don't quite understand the formulation that in the end it is compensated by the lattice energy, it's not as if the 147 kJ/mol uptake and 783 kJ/mol release of energy take place simultaneously so that the 147kJ/mol can be taken from the 783kJ/mol, is it?

Chronologically, this small amount of energy must be put in first and only then can 783 kJ/mol be released through the ionic bond (?)

Similar problem with the ionisation energy, which is offset against the released electron affinity energy, how can that work? Is the release and absorption of energy there also somehow simultaneous? In principle, I would have to put in the full +495.8kJ/mol first, then only 349kJ/mol are released (and then of course the 783kJ/mol) (?)

For me, "compensation" means something like I vary the outflow of my washbasin so that the water inflow is compensated and therefore no back-up builds up, both must happen at the same time, inflow and outflow.

[Corribus]

In principle there is almost always some sort of activation energy for any chemical process. For the process to occur, the system components must have enough energy to surpass this barrier*. This energy usually takes the form of thermal (kinetic) energy of participating particles/atoms/molecules in the system. If the reaction barrier is small enough, the reaction may still occur even at very low temperatures. The reaction rate for temperature driven equations is related to the ratio of the activation energy and the average kinetic energy in the system (Ea/RT, say), as well as a few other factors (Arrhenius eqn). In other cases, light, sound, etc., may also supply the energy to drive the reaction rate, and in those cases other rules determine the rate. And of course, when we are dealing with systems of large numbers of participating molecules, we have to consider the reverse reaction (with its activation energy) as well, and the final state of the system at equilibrium depends on the enthalpies and entropies of both the reactants and the products. The reaction barrier only determines how long it takes to get to that point.

I don't know what the activation energy is for the reaction between a sodium atom and a chlorine atom, but it is likely sufficiently small that the reaction readily occurs even at fairly low temperatures. And the stability of the NaCl lattice clearly drives the reactants strongly in favor of products.

*For some processes surmounting the energetic barrier is not strictly necessary. Certain quantum mechanical effects like tunneling may come into play.

[Roxo]

I’m very interested in the concept of activation energy. Considering a mixture of hydrogen and oxygen gases at room temperature they do not react but we know that supplying some activation energy in the form of a spark or a flame they react violently. The thing I don’t really understand is this: the well known Maxwell Boltzmann curve indicates that all energies are available and we are taught that the curve never reaches the x-axis. This seems to suggest there must be at least some particles which do possess the required activation energy. If they collide they will react and release a large amount of energy which would then trigger further reaction. However the mixed gases can be kept in the lab pretty much indefinitely without reaction (in the absence of a catalyst ) . In trying to rationalise this to myself I thought it must be that two such molecules of the gases with sufficient kinetic energy must exist but have zero likelihood  of colliding due to their rarity. But in a mole of gas there’s >10^23 particles so it seems pretty unlikely that higher energy ones are so rare they never collide and initiate the reaction. I would much appreciate if Corribus or some other expert could help me understand this better.

[PaulC4]

But you also have to consider that 1 mol of gas has a volume of ~22 litres. These are enormous distances that the particles have to travel. And even if two particles with enough energy exist, this does not mean that they will meet. On their way through the gas, they can quickly release their energy again through collisions. Moreover, a collision does not mean that the particles will react. This makes a reaction highly improbable.

In addition, the assumption that a single reaction directly triggers a chain reaction is also incorrect. The energy of a reaction is ultimately released into the surrounding gas, where it is probably not sufficient in this case to trigger further reactions. That means you might need two or three or even more reactions in close proximity to start a real chain reaction.

[Corribus]

Well there are few things here worth mentioning.

First, considering reactant molecules on an individual basis for a moment: if a hydrogen molecule and an oxygen molecule come together, having sufficient kinetic energy is not the only factor that determines their likelihood of undergoing a chemical transformation. Other considerations include the need to collide with the right geometry and quantum effects. The latter are particularly important for oxygen, which is a ground state triplet and is formally forbidden from reacting with another ground state singlet to form two ground state singlet molecules as products. Hydrogen is a ground state singlet and oxygen is a ground state triplet, the products (two water molecules) are both ground state singlets. So, spin conservation is violated by this reaction. Likewise with virtually every combustion reaction. This is why gasoline and oxygen don't spontaneously combust despite the apparent massive thermodynamic favorability to do so. We call this a kinetically unfavorable process. From an Arrhenius model standpoint, these types of factors are usually all lumped together in the pre-exponential factor, such that Ea/KT (barrier height) may be favorable for a reaction but still the reaction rate is vanishingly small without some massive energetic input.

Second, you are right that the Boltzmann distribution of energy is just that, a distribution. Meaning that even at low temperatures, there will be some molecules that have far higher kinetic energy than the mean. But two such molecules have to come into close proximity in order to react. So, rare circumstance times rare circumstance = very rare circumstance. Even then, while a single reaction event will occasionally occur just on the basis of probability, and those occurrences would each result in a gain of kinetic energy to the products, that tiny amount of released energy is distributed throughout the ensemble according to some molecule-scale energy transfer rate, and also outside the system (if it is not well-insulated). So while you are technically correct that each reaction event increases the probability of subsequent reaction events (because the average kinetic energy of the system increases), the effect is probably too small to be noticed and just gets washed out - for every slight gain in kinetic energy due to spontaneous reaction events, some is also lost to the surroundings with little net change. This is the nature of equilibrium.

If you increase the average kinetic energy of the system (increase the temperature), individual reaction events become more likely. Each one of those events releases a bit of energy, which increases the likelihood of subsequent reaction events nearby, a kind of exponential feedback effect. At some point the rate of kinetic energy gain in the system exceeds the rate at which the system maintains energetic equilibrium with the surrounding environment. That's the point where we would macroscopically observe the reaction to "proceed". There's no discrete point at which that actually happens, of course, it's more of a continuum along a "reaction time" axis. Supposing you had infinite computing power, I guess you could model reaction dynamics of large systems at a quantum level by balancing kinetic energy gains from individual reaction events against rates of energy transfer (in all its potential forms) between nearby molecules against rates of loss to the surroundings. But what we observe experimentally is just the average effects. And speaking of quantum processes as those they are discrete events is probably wrong, in any case.

Any way, that's the way I view it. 

[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 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

[Enthalpy]

Energy barriers to reactions:

The reactants are almost always molecules, not atoms. Lone atoms are energetically so unfavorable, except for rare gases, that they form molecules under normal conditions.

Take H₂+Cl₂ 2HCl: the weaker bond, Cl-Cl, is already 243kJ/mol strong, so at 2478J/mol=298K the probability of one being broken is around e^-98 = 10^-43, so again even Avogadro's N gives no significant chance. H-H is stronger: 436kJ/mol, very close to H-Cl: 432kJ/mol.

But then, reactions must go against the reactant molecules, which is more difficult, and heat doesn't suffice for that. They happen thanks to reaction mechanisms that often involve more exotic species that are very far from thermal equilibrium, must be created somehow, and have a limited lifespan. For HCl synthesis, classical steps are:
Cl+H₂ HCl+H  and  H+Cl₂ HCl+Cl
which together make the global reaction as a chain reaction and need more reasonable chance to proceed.

Something must start each chain. For instance light can dissociate Cl₂. Later in the reaction, strong heat can suffice, or some impurity, catalyst... As long as Cl or H meet only Cl₂ or H₂, either the chain propagates or nothing happens, but if they meet Cl or H or something else, the chain stops by creating only a complete molecule. Consider 100 or 10000 events in a chain - it varies even more than that. So some mechanism must create new lone atoms often enough. If it's heat, you need an initial zone big and rich enough that the newly produced heat isn't lost immediately: you need a minimum energy, say from a spark.

Such process involving extremely rare species explain why reactions take ms or h or eons to proceed despite a molecule bumps an other every ns (gas) or ps (liquid). More so if one step demands energy rarely available from the local temperature: in the example, the "limiting step" is the one that breaks H₂.

Much of the science of chemical synthesis seeks intermediate reactions able to proceed, and even better, that produce mostly the desired compound and no other. This involves solvents, catalysts, varied intermediate reactants...

[Enthalpy]

@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

Thanks Corribus!