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In Huckel's rule (4n+2), based on what do we choose the number that replaces "n" ?

This is one of the beauties of math and science.  In this case, essentially, you pick.

In organic chemistry, Huckel's rule pertains to aromatic molecules, meaning:
- it must be cyclic
- it must be conjugated (all atoms much be able to have a pi-bond)
- it must be flat


Also, it must have a certain number of pi-electrons.  That what Huckel's Rule gives, those number of pi-electrons in aromatic molecules.  Given the structures of aromatic molecules, the number of pi-electrons has to be 2, 6, 10, 14, 18, 22, etc.  That series of numbers pertains to a mathematical sequence 4n+2.  So, the "n" only pertains to whichever number of pi-electrons you are looking at.



For instance, if n = 0, 4*0+2 = 2, so 2 pi-electrons
If n = 1, 4*1+2 = 6 pi-electrons
If n = 2, 4*2+2 = 10 pi-electrons
And so on.


So, n has essentially nothing to do with anything specific.  It is simply a whole number (0, 1, 2, 3, 4, etc.)

So, a sample problem could be, "Can an aromatic molecule have 12 pi-electrons?"  You would either need to remember the sequence 2, 6, 10, 14, 22, etc.  Or, you remember 4n+2 and start to plug in the numbers like above.  When 12 doesn't show up, the answer is "no".

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