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

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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. 

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