Determining stereochemistry of carbon in a cycloalkane

[Chem_Mod]

Question: In cyclooctane with 2 substituents exactly opposite one another, how do we find the other two groups (going from one stereocenter)? Basically where does each one end (do they overlap)?.

[Chem_Mod]

Answer: When trying to determine the stereochemistry of a carbon in a cycloalkane, the 4 attachments include the 2 substituents and the cyclo group counted in both the clockwise and counterclockwise directions. By examining a 1,5 disubstituted cyclooctane, you see that going around the ring in one direction is exactly the same as the other direction. Neither C1 nor C5 is asymmetric. Looking closely, you can also see a mirror plane which cuts through C1 and C5.