Organic Chemistry - Cyclohexanes, Isomers, and Chirality

Every carbon in a cyclohexane ring is tetrahedral; two bonds are in the ring, two are out.
Axial bonds: Straight up and down relative to the ring, alternate up/down around the ring.
Equatorial bonds: Extend outward from the ring at approximately \text{109.5^\circ}, away from the ring center.

A bond rotation that interconverts two chair conformations, not a molecular flip.
During a chair flip, axial substituents become equatorial, and equatorial substituents become axial.
The relative "up" or "down" orientation of a substituent on its carbon atom remains the same; only its axial/equatorial character changes.
Two chair conformations exist for every cyclohexane.

Equatorial positions are generally favored by substituents due to less steric hindrance.
Axial positions can lead to 1,3-diaxial strain (or axial strain) where axial substituents clash with other axial hydrogens on carbons three positions away.
Larger substituents have a stronger preference for the equatorial position (e.g., a t-butyl group is almost exclusively equatorial).

To determine stability: Draw one chair, perform a ring flip, then compare the two conformations.
Cis-1,2-dimethylcyclohexane: One methyl is axial, one is equatorial in both chair forms. Both chairs are equally stable; roughly a $50:50$ equilibrium.
Trans-1,2-dimethylcyclohexane: One chair has both methyls equatorial (more stable), the other has both methyls axial (less stable).
The most stable chair minimizes axial interactions, prioritizing larger groups in equatorial positions.

Decalin: Two fused cyclohexane rings (e.g., cis- or trans-decalin).
Trans-decalin is generally more stable than cis-decalin.
Bridged rings (e.g., Bicycloheptane/Norbornane): Highly rigid structures where a carbon chain forms a "bridge" across a ring, locking conformations.

Represent electron delocalization (e.g., pi bonds, lone pairs, charges).
Rules for drawing resonance structures:
- Do not break sigma bonds.
- Do not exceed the octet rule for second-row elements (especially carbon); draw in implicit hydrogens if unsure.
- Look for pi bonds, lone pairs, or charges separated by a single bond to identify potential resonance.

Constitutional Isomers: Same molecular formula, different connectivity of atoms. Different physical properties.
Conformational Isomers: Different spatial arrangements that can interconvert by bond rotation (e.g., cyclohexane chair forms). Properties are typically an average.
Stereoisomers: Same connectivity, different spatial arrangement:
- Cis/Trans Isomers: Groups on the same side (cis) or opposite sides (trans) of a ring or double bond. These are a type of diastereomer.
- Enantiomers: Non-superimposable mirror images of each other. A chiral molecule has only one enantiomer. All chiral centers invert configuration.
- Diastereomers: Stereoisomers that are not enantiomers (e.g., cis/trans isomers or molecules with multiple chiral centers where not all centers invert).

Chiral object: An object that is non-superimposable on its mirror image (e.g., human hands).
Chiral carbon (stereocenter): A tetrahedral carbon atom bonded to four different groups.
Drawing mirror images involves reflecting the groups: wedges remain wedges, dashes remain dashes.
Inverting the configuration of a chiral carbon can be achieved by swapping any two groups attached to it.