Conformations of Cyclohexane and Substituted Cyclohexanes

Chair Conformations

The chair conformation is the most stable form of cyclohexane due to minimized torsional and steric strain. Substituents on cyclohexane rings can occupy either axial or equatorial positions, which affects their stability and reactivity.

• Axial Position: Substituents point parallel to the ring axis (up or down), leading to 1,3-diaxial interactions and increased steric strain.

• Equatorial Position: Substituents extend outward from the ring, minimizing steric interactions and generally being more stable.

• Energy Difference: The chair conformation with bulky groups in equatorial positions is lower in energy than when they are axial.

• Example: In cis-1,3-dimethylcyclohexane, the lowest energy chair conformation places both methyl groups in equatorial positions.

Formula:

$\text{Stability} \propto \text{Number of bulky groups in equatorial positions}$

Counting Axial and Equatorial Hydrogens

Each carbon in cyclohexane has one axial and one equatorial hydrogen. Substituents replace hydrogens, so the number of remaining axial hydrogens depends on the number and position of substituents.

• Key Point: For substituted cyclohexanes, count the number of hydrogens in axial positions by considering which carbons have substituents and their orientation.

• Example: In the lowest energy chair of cis-1,3-dimethylcyclohexane, there are 4 axial hydrogens.

Stereochemistry: Isomers and Configurations

Types of Isomers

Organic molecules can exist as different isomers, which are compounds with the same molecular formula but different arrangements of atoms.

• Constitutional Isomers: Same formula, different connectivity.

• Stereoisomers: Same connectivity, different spatial arrangement.

• Enantiomers: Non-superimposable mirror images.

• Diastereomers: Stereoisomers that are not mirror images.

• Example: (2R,3S)-2,3-dichloroheptane and (2S,3R)-2,3-dichloroheptane are diastereomers.

Assigning Stereochemistry (R/S)

The Cahn-Ingold-Prelog rules are used to assign absolute configuration to chiral centers.

• Step 1: Assign priorities to substituents based on atomic number.

• Step 2: Orient the molecule so the lowest priority group is away from you.

• Step 3: Determine if the sequence 1-2-3 is clockwise (R) or counterclockwise (S).

• Example: D-Threonine (2R,3S) configuration.

Optical Activity

Chiral molecules rotate plane-polarized light. The specific rotation ($[\alpha]$) is a characteristic property.

• Formula:

$[\alpha] = \frac{\alpha_{\text{obs}}}{l \cdot c}$

• $\alpha_{\text{obs}}$ = observed rotation (degrees)

• $l$ = path length (dm)

• $c$ = concentration (g/mL)

• Example: If $[\alpha] = +52.8^\circ$, $l = 1.0$ dm, $\alpha_{\text{obs}} = +15.8^\circ$, then $c = 0.299$ g/mL.

Radical Reactions and Halogenation

Free Radical Chlorination

Halogenation of alkanes proceeds via a free radical mechanism, which includes initiation, propagation, and termination steps.

• Initiation: Formation of radicals, often by homolytic cleavage (e.g., $Cl_2 \xrightarrow{hv} 2Cl\cdot$).

• Propagation: Radicals react with stable molecules to form new radicals (e.g., $Cl\cdot + CH_4 \rightarrow CH_3\cdot + HCl$).

• Termination: Two radicals combine to form a stable molecule.

• Energetics: Initiation step typically has $\Delta H > 0$ and $\Delta S > 0$.

Stability of Alkyl Radicals

Radical stability increases with the degree of alkyl substitution due to hyperconjugation and inductive effects.

• Order of Stability: $CH_3\cdot < CH_2=CHCH_2\cdot < (CH_3)_2CH\cdot < (CH_3)_3C\cdot$

• Example: Tertiary radicals are more stable than secondary, which are more stable than primary.

Regioselectivity in Halogenation

Halogenation can produce multiple products depending on which hydrogen is replaced. The major product is typically formed via the most stable radical intermediate.

• Example: Chlorination of 3,4-dimethylhexane yields several monochlorinated products; the major product results from substitution at the tertiary carbon.

Bond Dissociation Energies

Bond dissociation energy (BDE) is the energy required to break a bond homolytically. Lower BDE indicates a weaker bond.

• Example Table:

Key Point: The carbon-bromine bond is weakest (lowest BDE) in tertiary alkyl bromides.

Reactivity and Mechanisms of Alkyl Halides

SN2 Reactivity

SN2 reactions are bimolecular nucleophilic substitutions, proceeding with inversion of configuration at the reactive center.

• Rate Law:

$\text{Rate} = k[\text{Alkyl Halide}][\text{Nucleophile}]$

• Key Point: Primary alkyl halides react fastest; tertiary are slowest due to steric hindrance.

• Example: 1-iodobutane reacts faster than 1-fluorobutane in SN2 reactions.

Nucleophilicity

Nucleophilicity refers to the ability of a species to donate an electron pair to an electrophile. It is influenced by charge, solvent, and steric factors.

• Order: $CN^- > HO^- > I^- > BF_3$ (BF3 is not a nucleophile)

Carbocation Stabilization

Allyl substituents stabilize carbocations via resonance and inductive effects.

• Resonance: Delocalization of positive charge over multiple atoms.

• Inductive Effect: Electron donation through sigma bonds.

Halides: Classification and Reactivity

Types of Alkyl Halides

Alkyl halides are classified as primary, secondary, or tertiary based on the carbon to which the halogen is attached.

• Primary: Halogen attached to a carbon bonded to one other carbon.

• Secondary: Halogen attached to a carbon bonded to two other carbons.

• Tertiary: Halogen attached to a carbon bonded to three other carbons.

• Example: CH3CHBrCH3 is a secondary halide.

Practice Problems and Applications

Drawing Products and Assigning Stereochemistry

• Monochlorination: Draw all possible products for chlorination of 3,4-dimethylhexane and identify the major product.

• Major Organic Product: Predict the product for reactions such as alkyl halide substitution with NaCN.

• Radical Bromination: Use NBS and light to brominate allylic positions in cyclohexene.

• Assigning Diastereomers: Identify diastereomers from given structures.

• Structure Drawing: Draw the structure of (2R,3R)-2,3-dibromo-3-chloropentane.

Summary Table: Types of Isomers

Additional info:

• Some questions require drawing explicit chair conformations and indicating axial/equatorial hydrogens for cyclohexane derivatives.

• Students should be able to use the periodic table for atomic number and element identification.

• Knowledge of bond dissociation energies and their implications for radical stability is essential.

• Understanding the difference between propagation and initiation steps in radical halogenation is critical for mechanism questions.