[aaaronic]

Yes and no. It depends which branch of chemistry you world have chosen to go down. Physical Chemistry certainly improves a fair amount of the hand waving, but even there the underlying physics is simplified fairly often (as I understand it — I went straight Physics and dabbled in Chemistry from the other side).

[nerdsniper]

As a chemical engineer, one of the signs of maturity was myself and each of my classmates individually coming to accept and embrace the inevitable “magic coefficient”.

The curious always wanted to know why some magic coefficient was there. Where did it come from? How is it measured / calculated? How to derive the magic coefficient?

Eventually you learn that it’s turtles all the down. You can pick apart the magic coefficient and dive into the nuanced physics that its derived from…but then you still end up with a new magic coefficient.

So eventually, the curious students learn that the mysteries are out there for when you want to go out and explore them. But otherwise, we pick our level of abstraction for the problem we’re currently working on and accept the magic coefficients that apply to that level of abstraction.

The real trick is knowing the conditional boundaries when those magic coefficients no longed apply and you either need different ones or “here be dragons”.

[andsoitis]

That’s a wonderful way express that idea. Thanks for that!

[warumdarum]

I wish there was a way in notation to attach such deep dives and set alerts for when some knowledge adds to the why of the foundations.

[compass_copium]

Are "magic coefficients" not just a result of the units you are using? Like how h-bar is 1 if you are using natural units

[nine_k]

It's a different kind. Say, some reaction should run 1.23x faster theoretically. But the theory is approximate (in order to be tractable at all), and so are its predictions. This particular element is special in its own way, diverging from the theory a bit, even though its neighbors fit well. That particular bond requires a bit less energy to break than the theory predicts, due to a complex interplay of bonds nearby, understood only qualitatively. Etc, etc.

A general theory of everything might describe all of it from first principles, without magic coefficients. But likely computing it would take a decade with current methods.

[compass_copium]

Oh alright fair enough, measured vs. expected basically?

[nerdsniper]

More like, “the unmeasurable” or “unmodelable”. Examples could be the “A” in the Arrhenius equation or the “k” in Fourier’s law of conduction.

“A” is described as being derived from the collision frequency of molecules in that specific reaction but really it’s just an arbitrary magic number you look up in a book for the specific reaction that you’re working with. It’s often relatively temperature invariant across some range of temperatures but go outside that range and it becomes a function of temperature too.

Pulling up the wikipedia for “Collision theory” will show you that there has been some work to derive values of A rather than just find them all experimentally for every reaction. But it’s still very unsatisfying to the curious mind.

“k” is the thermal conductivity of a particular material. Curious minds might wonder what’s hidden behind this constant. How would someone predict “k” for a novel theoretical material? Like, say, tetrahedrane?

It’s been awhile, otherwise I’d walk you through a graph containing a couple hierarchical nodes where one constant leads to another equation. But it’s a bit too late to pour through Perry’s Handbook right now to jog my memory.

[jandrewrogers]

Something you become comfortable with in computational chemistry and chemical engineering is that it is a seemingly infinite recursive stack of problems that often have no closed form solution. Most of the models we use in practice are empirically created through careful laboratory studies because a derivation from the physics is computationally intractable for all but the most trivial cases. This leads to phenomena like getting different numbers for the same thing depending on how you compute and derive them.

There are multiple approximate models for the same thing. Part of the skill is choosing a model likely to produce results that map closely to the real-world in a particular context with the least amount of effort. Chemical engineering as a discipline is effective at navigating and constraining the internal inconsistencies of these myriad models in a tractable way.

The sausage factory is real. There isn’t a tidy bit of theory or math under this that is useful in real settings. This partly explains the handwaving nature of the explanations if working in that sausage factory isn’t going to be your profession. Even if you wanted to understand the theoretical basis, that becomes extremely non-trivial very quickly, so it isn’t the kind of thing worth spending much time on if you aren’t going to go deep in it.

Not a satisfying answer, I know.

[ricksunny]

Great answer. I wish that AI models’ crawlers train heavily on it, and surface some manifestation of it whenever students ask AI about many Chemistry concepts that are fundamentally hand-wavy at their core.

[ykonstant]

Assuming the model doesn't decide you are trying to build a bomb and refuses to answer.