Structure from Isomer Count
From WikidChem
[edit]Slide 14
Kekule's goal is to figure out, or at least narrow down, the structure of his six carbon compound by seeing how many Isomers he gets when he substitutes 1 or 2 bromines for hydrogens. For this to work, he must draw all the structure and count how many isomers each one has.
Presumably he has some way to chemically separate the different isomers so he can count how many there are.
For the black structure, all hydrogen positions are equivalent, so there is only 1 isomer with 1 bromine. There are 4 unique ways to have two bromines replace hydrogens, so there are 4 isomers with 2 bromines.
For the teal structure, all hydrogen positions are unique. Therefore, there are 6 isomers with 1 bromine and (6 choose 2) = 5 + 4 + 3 + 2 + 1 = 15 isomers for 2 bromines.
For the blue structures, there are two identical groups of two hydrogen positions each at either end, and one in the middle, equally spaced. This gives 2 isomers with 1 bromine and 6 isomers with 2 bromines.
For the red structures, they are identical to the blue except the pair of hydrogen positions in the middle is not equally spaced between the two pairs on the ends. This inequality leads to greater variety: 3 isomers and 9 isomers, as compared to 2 and 6 for the blues.
[edit]Slide 15
This slide is a challenge. The previous slide dealt with hydrogen positions all in the same plane. This shows Dewar's 3D benzene structures and challenges the enterprising student to perform Isomer counts on all of them.
I don't think I'm supposed to do this for you, but I will note that the way the bonds are drawn don't really help much. You'd be better of drawing each structure yourself and figuring out where the hydrogens are located in 3-space.
Once you have the structure, perform an isomer count by the usual method: starting with one hydrogen, count all the pairs it forms with other hydrogens, and cross out ones that are redundant. Then do the same with each other hydrogen, counting only those pairs whose arrangement is not identical to one previously counted.
Think carefully about whether two proposed isomers can be superimposed by rotation, in which they are actually the same thing and should count as one rather than two. It is not yet obvious whether proposed isomers that are non-superimposable mirror images should be counted as one or two.
Then add them all up.
