Alkanes, Cycloalkanes, and Free Radical Reactions: Structure, Nomenclature, and Mechanisms

Alkanes and Cycloalkanes: Structure and Nomenclature

General Formulas and Parent Names

Alkanes and cycloalkanes are fundamental classes of hydrocarbons in organic chemistry. Understanding their structure and nomenclature is essential for further study.

• Alkanes have the general formula: $C_nH_{2n+2}$

• Cycloalkanes have the general formula: $C_nH_{2n}$

• The first ten unbranched (linear) alkanes are:

  • Methane (CH4)

  • Ethane (C2H6)

  • Propane (C3H8)

  • Butane (C4H10)

  • Pentane (C5H12)

  • Hexane (C6H14)

  • Heptane (C7H16)

  • Octane (C8H18)

  • Nonane (C9H20)

  • Decane (C10H22)

Naming Alkyl Groups and Branched Alkanes (IUPAC Rules)

• Alkyl groups are derived from alkanes by removing one hydrogen atom. Common groups include methyl, ethyl, propyl, isopropyl, isobutyl, sec-butyl, and tert-butyl.

• IUPAC Naming Rules for Alkanes:

  • Identify the longest continuous carbon chain (parent chain).

  • Number the chain to give the lowest possible numbers to substituents.

  • Name and number substituents (alkyl groups).

  • List substituents alphabetically, using prefixes (di-, tri-, etc.) for multiples.

  • Combine the names: [number]-[substituent][parent alkane].

• Naming Cycloalkanes: Use the prefix 'cyclo-' before the parent name. Number the ring to give substituents the lowest possible numbers.

• Bicyclic Systems: Name as bicyclo[x.y.z]alkane, where x, y, z are the number of carbons in each bridge (excluding the bridgehead carbons).

Drawing Structures

• Given a name, draw the corresponding line-angle or wedge-dash structure for alkanes and cycloalkanes.

• Be able to convert between different representations (e.g., condensed, line-angle, Newman projection).

Physical Properties and Trends

• Alkanes and cycloalkanes are nonpolar, hydrophobic, and have low boiling and melting points compared to compounds with similar molecular weights but with polar functional groups.

• Boiling point increases with molecular weight and surface area; branching lowers boiling point.

• Cycloalkanes generally have higher boiling points than their open-chain counterparts due to increased surface area.

Conformational Analysis of Alkanes and Cycloalkanes

Newman Projections and Conformations

Newman projections are used to visualize the spatial arrangement of atoms around a carbon-carbon single bond.

• Conformations:

  • Anti: Largest groups are 180° apart (most stable).

  • Gauche: Largest groups are 60° apart (less stable than anti).

  • Eclipsed: Groups are aligned (higher energy).

  • Totally Eclipsed: Largest groups are directly aligned (highest energy).

• Stability Ranking: Anti > Gauche > Eclipsed > Totally Eclipsed

Stability of Cycloalkanes

• Strain Types:

  • Torsional Strain: Due to eclipsing interactions.

  • Angle Strain: Deviation from ideal bond angles (109.5° for sp3 carbon).

  • Ring Strain: Combination of torsional and angle strain.

• Stability Ranking of Cycloalkanes: Cyclohexane (least strain) > Cyclopentane > Cyclobutane > Cyclopropane (most strain)

• Cyclohexane Conformers:

  • Chair (most stable) > Twist-boat > Boat > Half-chair (least stable)

Cis and Trans Isomerism in Cycloalkanes

• Cis: Substituents on the same side of the ring.

• Trans: Substituents on opposite sides of the ring.

• Draw chair conformations for cis and trans isomers, and determine the most stable conformation (bulky groups prefer equatorial positions).

Bond Cleavage and Thermodynamics

Homolytic vs. Heterolytic Cleavage

• Homolytic Cleavage: Each atom retains one electron from the bond, forming radicals.

• Heterolytic Cleavage: Both electrons go to one atom, forming ions (carbocation and carbanion).

Bond Dissociation Energies and Thermodynamic Calculations

• Calculate enthalpy change ($\Delta H^\circ$) using bond dissociation energies:

• $\Delta H^\circ = \sum \text{(BDE of bonds broken)} - \sum \text{(BDE of bonds formed)}$

• Calculate free energy change ($\Delta G^\circ$) from equilibrium concentrations:

• $\Delta G^\circ = -RT \ln K_{eq}$

• Where $R = 8.314$ J/mol·K and $T$ is temperature in Kelvin.

Free Radical Halogenation of Alkanes

Mechanism and Steps

• Initiation: Formation of radicals (e.g., $Cl_2 \rightarrow 2Cl\cdot$ via homolytic cleavage).

• Propagation: Radicals react with alkanes to form new radicals and products (chain reaction).

• Termination: Two radicals combine to form a stable molecule, ending the chain.

Hammond Postulate and Energy Diagrams

• Hammond Postulate: The transition state resembles the structure (reactants or products) to which it is closer in energy.

• Energy Diagrams: Show reactants, products, transition state ($\ddagger$), activation energy ($E_a$), and $\Delta H$.

• Identify the rate-determining step as the highest energy transition state.

Halogen Reactivity and Selectivity

• Halogen Activity Series: $F_2 > Cl_2 > Br_2 > I_2$ (in terms of reactivity).

• Higher reactivity correlates with lower selectivity and higher activation energy.

• Temperature increases reaction rate by providing more energy to overcome $E_a$.

Predicting Products and Isomer Distribution

• Product distribution depends on the stability of the intermediate radicals and the selectivity of the halogen.

• Calculate the percentage of each isomer formed based on the number and reactivity of different types of hydrogens (primary, secondary, tertiary).

• Example Calculation: For chlorination of propane:

  • Primary H: 6 hydrogens, reactivity = 1

  • Secondary H: 2 hydrogens, reactivity = 3.8

  • Relative % = (number of H) × (reactivity)

  • Calculate for each type, sum, and find the percentage for each product.

Inhibitors

• Inhibitors are substances that slow or stop free radical chain reactions by reacting with radicals to form non-radical products.

Reactive Intermediates and Reactivity Concepts

Carbocations, Carbanions, Carbon Radicals, and Carbenes

• Carbocation: Positively charged carbon atom (electron-deficient, sp2 hybridized).

• Carbanion: Negatively charged carbon atom (electron-rich, sp3 hybridized).

• Carbon Radical: Carbon atom with an unpaired electron (sp2 hybridized).

• Carbene: Neutral carbon with two nonbonded electrons (sp2 or sp hybridized).

• Stabilization: Resonance, hyperconjugation, and inductive effects stabilize these intermediates. Tertiary > Secondary > Primary for carbocations and radicals; the reverse for carbanions.

Electrophiles and Nucleophiles

• Electrophile: Electron-deficient species that seeks electrons (e.g., carbocations, positively polarized atoms).

• Nucleophile: Electron-rich species that donates electrons (e.g., anions, molecules with lone pairs).

Summary Table: Conformations and Stability

Conformation	Relative Stability	Energy
Anti (Newman)	Most stable	Lowest
Gauche (Newman)	Less stable	Higher
Eclipsed (Newman)	Unstable	High
Totally Eclipsed (Newman)	Least stable	Highest
Chair (Cyclohexane)	Most stable	Lowest
Boat (Cyclohexane)	Less stable	Higher
Twist-boat (Cyclohexane)	Intermediate	Intermediate
Half-chair (Cyclohexane)	Least stable	Highest

Key Equations

• Free energy change: $\Delta G^\circ = -RT \ln K_{eq}$

• Bond dissociation enthalpy: $\Delta H^\circ = \sum \text{(BDE of bonds broken)} - \sum \text{(BDE of bonds formed)}$

Example: Free Radical Halogenation of Propane

• Initiation: $Cl_2 \xrightarrow{hv} 2Cl\cdot$

• Propagation: $Cl\cdot + CH_3CH_2CH_3 \rightarrow HCl + CH_3CH_2CH_2\cdot$

• Termination: $Cl\cdot + CH_3CH_2CH_2\cdot \rightarrow CH_3CH_2CH_2Cl$

• Product distribution depends on the number and type of hydrogens abstracted.