Well then that one can leave, and Meritxell will teach the ones who don't object to her teaching style.

That's fucking cold.  Even most of the crueler teachers don't do that.

The rest of the new kids will listen attentively.

PL-timestamp:  Day 20 (16)

Actual chemistry lecture this morning!  The newcomers should probably at least try to attend; it's not relying on math from Keltham's earlier lectures.

This is the Periodic Table of Elements.  It's ordered by protons, and organized by the arrangement of electrons as they fill up the least energetic orbital positions.

Keltham will spend much longer, this time, describing the electron orbitals; and how covalent bonds allow shared electrons to fill more of their shells; and how this lower-potential-energy state, where more electrons are closer to stronger attractive charges of protons, makes molecules tightly bound together in a way that takes heat to pry apart.

When you could-in-principle rearrange all the atoms in a reaction into a lower-energy state at the end, releasing heat along the way, it implies a potential more stable state the system might get into, and stay in afterwards.  To get there, you need a high temperature, so that the vibrations of heat will break apart some of the original molecules and let them randomly recombine, sometimes into the lower-energy state.  Ideally, you pick a reaction temperature that easily breaks apart the feed molecules, but doesn't so easily break apart the more tightly bound final forms.

The reaction they're trying for with sulfuric acid is:

Stage 1: burn sulfur to sulfur dioxide, this is exothermic but requires a high starting temperature

S + O2 => SO2

Stage 1.5: purify the sulfur dioxide?? Keltham doesn't actually remember how to do this, unfortunately

Stage 2: catalyze sulfur dioxide to sulfur trioxide, in the presence of oxygen, using Element-23 oxide as a catalyst

SO2 + V2O5 => SO3 + V2O4 (probably)
maybe SO2 + V2O4 => SO3 + V2O3 and then V2O3 + O2 = V2O5??

Stage 3: cool and dissolve the sulfur trioxide in sulfuric acid to form oleum

H2SO4 + SO3 => H2S2O7

Stage 4: react oleum with water to form concentrated sulfuric acid, twice as much as previously existed

H2S2O7 + H2O => 2 H2SO4

He's not really sure about the details, in the case of the sulfuric-acid synthesis pathway.  But a reason the vanadium catalyst might help in the first place - is if it's relatively hard to tear apart an O2 molecule, for example, and the exoergic reaction of a single SO2 to SO3 isn't enough pull to tear apart a single O2 molecule - it could happen with two SO2 molecules at once, cooperating to tear apart an O2 molecule that's already heated and vibrating, but then it's less likely for all those molecules to be in the right positions.  But V2O5 could resist the tug more weakly, giving up an O molecule to a demanding SO2 molecule; and then giving up another O molecule and turning into V2O3; and then swallowing down a whole O2 molecule to go back to V2O5 again.  Possibly.  For example.

The main point of this process, as Keltham understands it, is that it's liable to produce relatively high-purity sulfuric acid at scale.

It will also - he suspects - be much easier to do, much much easier to do reliably, if they can learn to really use Prestidigitation.

Prestidigitation can alter color, taste, stickiness.  Keltham has now verified that Prestidigitation can modify acidity and basicness in order to modify the reaction of vinegar with wood ash (lye).  He's previously verified that Prestidigitation can produce temporary magnetism but only for so long as Keltham is concentrating, and even that he can get a material to reject a magnetic field using Prestidigitation.

All of this is of a kind with the shapes of the electron orbitals, the potential energy surfaces that determine possible reactions and reaction rates.

Prestidigitation should definitely be a sort of thing that can break the rules of chemistry.  They can maybe make Element-20 'calcium' behave like Element-23 'vanadium' for purposes of turning it into something that behaves like vanadium oxide, without Keltham needing to somehow figure out which Golarion metal is 'vanadium'.  Though vanadium oxide is donating oxygen molecules within the chemical reaction, so the oxygen part ought to be real.

There could maybe be a way to directly Prestidigitate sulfur dioxide to quickly react with oxygen at high temperatures, and turn into sulfur trioxide without need of a vanadium catalyst, if they really knew what they were doing.  There may be, conceptually speaking, something sulfur dioxide could taste like, which would make it react more easily with oxygen and slide down the exothermic gradient to sulfur trioxide.

Keltham is guessing that energy is probably conserved, even in the presence of Prestidigitation, which means that they probably can't do very much work of a form 'make this very tight binding loose' because it should properly take energy to shake loose of a binding like that.  But even small changes at the potential energy surfaces can do a lot to eliminate reaction barriers.

...though there's already hints that you need to be able to... sort of understand that stuff, or visualize it, on some level, to get Prestidigitation to know what it is you want it to do?

How are people doing on that.

Uh, how should they be visualizing 'electrons' and 'orbitals'? Are these...tiny beads on strings?

Keltham's not sure how far they're going to have to go into Law to get Prestidigitation working for them.

Layer one:  There's tiny little pointlike particles called 'electrons' with 'LEFT' charge being pulled towards nuclei with 'RIGHT' charge.  Identical electrons can't be in the same place at the same time, so there's only so much room for electrons to crowd around each other, as they get closer to a nucleus.  Actually electrons can only be at certain exact distances from nuclei for, uh, reasons, so there's only so many 'orbitals' for them to live in.  The lowest distance can only contain 2 electrons.

Atoms with more protons, like Element-8 'oxygen', are strongly electron-stealing or 'electronegative' and tend to tear away electrons from weaker nuclei like Element-4 'beryllium'; the electrons are still shared, still orbiting around everywhere, but you'll find more of them around the oxygen nucleus and less around the beryllium nucleus.  Which in turn will make the oxygen side of beryllium oxide more LEFT-charged, since it's got fewer protons than electrons, since the electrons are crowding around the part with more protons to attract them; and the beryllium side more RIGHT-charged.  This means that beryllium oxide is liable to go forming crystals in which the beryllium RIGHT sides of one molecule can get closer to the LEFT oxygen parts of another molecule, and the crystal structure will have its own strength - though not as strong as the underlying molecules, which is why it's easier to break substances with a hammer than transmute them.

If knowing layer one is enough to get Prestidigitation working, everyone's lives will be a lot simpler.

Layer two is about why two electrons can fit into the lowest orbital; it's because they need to have different ????-states and there's only two possible ????-states.  Similarly, the next shell out, that can contain up to eight electrons, is actually two possible states of one kind of orbit, and six different possible kinds of another orbit.

The electrons have magnetism going on, and there's a way that electric charges and magnetic fields have a nature that fits together.  A wave that propagates through the coupled electric and magnetic fields is a photon; when you have a lot of photons together, that's light.

Layer three is that the electrons aren't actually pointlike particles moving around, they're clouds of complex numbers with an equation that propagates the cloud, and the reason electrons can only orbit in certain distances and patterns is that their waves would interfere and cancel each other out otherwise.  This is the point at which you could start to calculate where the orbitals go, though that's rapidly going to get harder for anything beyond one electron orbiting one proton.

Layer four is learning what the clouds are made of, and starts to get into underlying 'realityfluids'.  And 'anthropics'.

......hopefully that doesn't turn out to be necessary for Prestidigitation.

(Actually she kind of hopes that it does. Then they'd know what anthropics are.)

We can hope!  Hope is cheap since it doesn't affect actual outcomes!

Keltham hung a Silent Image earlier today!  Here's what sulfuric acid actually looks like.  You can see how those dangling hydrogen atoms on the end could potentially be ripped loose from the electrons holding them in, repelled by the positive charges at the center, and go off as positively charged protons to mess around with other chemical bonds and break them and dissolve them, which is what makes an acid acidic.

Here's what electron orbitals actually look like.

Protons are heavy and RIGHT-charged and clumped together by more powerful forces into nuclei despite the repulsion of similar charges; electrons are LEFT lighter and cloudlike, attracted to protons, self-repelling, and no two of them can be in the same place at the same time with the same ????.  The heavy protonic nuclei settle into a configuration of least energy, taking into account the attractive electron charges and that the protonic nuclei repel each other insofar as not electron-neutralized; the heavy protonic nuclei act as a sort of backbone for the light electron cloud.

It's actually less complicated than the weird twisted interactions found in hanging spells, in some ways?  There's a lot fewer interactions, really?  It's just that these are different interactions, and the math is a tad deeper than any individual force described in second-circle wizard textbooks.

Also they can't just manually manipulate the forces, they've got to subtly influence them with Prestidigitation to make bulk chemical interactions go differently.

Also also nobody's ever done anything like this before, so far as Keltham knows.  So they're gonna have to try a lot of stuff, and it's not actually clear which level of understanding is gonna be required to do what.

After lunch it'll be time for more experimentation using various things Keltham requested, using cheap materials he could identify, that will chemically react in ways that Keltham knows about!

Can they, for example, alter various substances, so that, when plunged into a hot fire, they burn with a different color of flame?  Not alter the flame's color directly, Prestidigitate the material so that it burns with a different color when lit?  That's a fairly direct test of their ability to mess with orbitals and potentials; it's electrons moving between orbitals that emit light of a particular energy and hence color.

Are they ready to get a lot of identical NO answers to 'Did that work?' while carefully observing for signs that anything observable went even slightly differently?

That is actually the kind of thing Chelish wizard education prepares you for unusually well.

A fair number of people are now trying incredibly hard to be the fastest to figure it out.

Well so is Keltham.  It doesn't matter how unfair the competition is, he's still competing.

...and yes, Keltham is first to Prestidigitate materials to burn with different colors of light.  Yay?  If he was feeling competitive about that?

Feeling competitive is beneath Lady Avaricia, but winning is not. 

She's studied under an alchemist; her education has generally been more varied than that of the other students. And none of what Keltham said was that complicated, if you're not overawed by him, which she isn't.

Can she imagine this flame burns like salt, even though it didn't? More complicated than that? Can she imagine it tastes like salt? Can she imagine what's going on in salt, what its electrons are doing, and -

- she doesn't get it as fast as Keltham, but she gets it.

Well, now he's actually interested in this 'county's heiress'-type person.

Everyone pause.  Does Eulalia have any guesses for what she knows that the other students might not know?

"I know all kinds of things they don't know, since they're peasants. Relevantly I was thinking about how salt burns in different colors. Prestidigitation can be used to make food salty. That was insufficient."

"What sufficed for you, if thinking about saltiness didn't do it?"

"I kept thinking about saltiness, but in more detail - about what structures salts form, what alchemical properties they have, how different salts make different colors, what specific salt I was pretending to burn."

"Do you remember the last thing you thought before it worked?"

"That green would go better with my nails today so I should burn copper."

He doesn't really get this person, but that's fine on a level where Keltham hardly even notices it.  Dath ilan has lots of weirdos.

"Huh.  All right, time to slow down in at least that section and do slightly less maniacal experimentation.  Let's have you peel off somebody and try to teach them to do what you do, but note down what you're trying to teach them in what order.  Any tier-1s want to volunteer for that?"

"Sure." Otherwise she'll be worrying about Lady Avaricia/Asmodia or Lady Avaricia/Ione explosions. 

Willa had been trying to influence her Prestidigitation with complicated math in her head in the hopes it might be enough like real chemistry. Maybe unsurprisingly, it wasn't getting anywhere. A little while after Eulàlia's comment though, she decides it's time to escape her solution space.

She gets out a copper and licks it. And now she has some green flames too, how about that!

She immediately starts licking her other coins to try to branch out, but it seems to be harder going getting anything but green.

All right, somebody else should definitely just try that.