Thursday, July 9, 2009

Where Does the Wealth Of Variety In Chemistry Come From? Math!

Physical properties of substances have to do with the relocation of electrons. Of stacking electron orbitals.


neon starts of with 8 electrons and none in the outer shell. neon is a quiet inert atom. it doesn't engage in much chemistry. Add one electron to that outer shell however and you get sodium a highly reactive metal that wants to give up that lone electron. So Sodium cations swim in a sea of shiny malleable wandering valence electrons.

Add yet another electron to the mix and we have 2 electrons in the outer shell. anothe slightly less reactive metal, magnesium. Add another electron to the outer shell and now we have a total new orbital and we get aluminum, less reactive and the transition from MgO a soluble opaqe soft crystal to Al2O3 a nonsoluble transparent very hard crystal: ruby.

Add yet another electron and we get another orbital, silicon. A softer metal again but it's oxide SiO4 now can form dozens of varieties of chains and rings and matrixes which give us our vast variety of minerals on Earth: quartz, feldspar, mica..

Add yet another electron and we get a third orbital, phosphorus, a very reactive P4, nonmetalic spongy stuff, and PO4 cannot form stable chains at all, no vast variety of minerals, it forms instead, an acid.

Add another electron, no new orbital, start filling in the old ones and we get Sulfur, S8 a harder nonreactive solid, and S02 is now a gas. Add another electron and we get chlorine, Cl2 a highly reactive gas, and ClO is i don't know what.

Add another electron and all the orbitals are full again and once again we have argon, an inert element who engages in no chemistry at all.

To what do we owe this INTERESTING wealth of variety? The variety of chemistry is fascinating yet not totally chaotic. It all comes eventually from mathematics, Which is one of the recurring themes of complexity lab.

The relationships between these electron orbitals are determined by their energy level, their arrangement in space. Which are ultimately determined by the properties of solutions to a complex set of shrodinger's partial differential equations. Solutions that make different structures in 3 dimensional space. It would take us too far afield to explain these solutions (a few years of calcullus actually...), so we will present a simpler example: numbers.

What could be simpler than the numbers: 1, 2, 3, 4...

Lets see what happens to them every time we add one to the previous number to get the next. Just like we added one electron at a time to our elements.

1 is a unique number. 2 is the first prime number and peculiar because it is even. 3 is the first odd prime number. 4 all of a sudden is composite 2X2. 5 is prime again. 6 is now composite with TWO DIFFERENT factors 2X3. 7 is prime again. 8 is very composite 2X2X2 if we like we can consider it 3 dimensional. The next number? a prime again? NO, it's composite also; 9; 3X3. The next is composite also 10; 2X5. 8 seems to stand out as a lonely 3 dimensional number here. 11 is prime. 12 is the first example of a number with 2 different factorizations 2X6 or 3X4. Or you can call it also, 3 dimensional 2X2X3. 13 is prime again.

You get the drift. by simply adding 1 to the number we change the MULTIPLICITIVE (or geometric) properties of the numbers in unpredictable interesting ways. This is one of the simplest examples of how mathematics can give us the spice of life, the variety in the world that we see around us.


Adam said...

This is why I had such a hard time with chemistry. All the damn math.

barry goldman said...

but i gave you really easy math... Well, i'll keep trying.