Comprehensive Study Guide to Alkanes and Cycloalkanes

Alkanes and Cycloalkanes: Definitions and Classification

• Functional group: An atom or a group of atoms within a molecule that has characteristic physical properties and is the site of chemical reactivity.
• Hydrocarbon: A compound composed entirely of carbon and hydrogen atoms.
• Saturated Hydrocarbon: A hydrocarbon containing only single bonds between carbon atoms, meaning it is saturated with the maximum possible number of hydrogen atoms.
• Unsaturated Hydrocarbon: A hydrocarbon containing one or more carbon-carbon double or triple bonds, or aromatic rings.
• Alkane: An open-chain saturated hydrocarbon with the general formula $C_nH_{2n+2}$.
• Cycloalkane: A saturated hydrocarbon in which the carbon atoms form a ring, also known as alicyclic compounds.

Hydrocarbon Classes and Examples

• Alkanes:
  • Bonding: Only carbon-carbon single bonds.
  • Example: Ethane ($H-C-C-H$ with hydrogens, or $CH_3CH_3$).
  • General Formula: $C_nH_{2n+2}$.
• Alkenes:
  • Bonding: One or more carbon-carbon double bonds ($C=C$).
  • Example: Ethene (Ethylene).
• Alkynes:
  • Bonding: One or more carbon-carbon triple bonds ($C\equiv C$).
  • Example: Ethyne (Acetylene).
• Arenes:
  • Bonding: One or more benzene-like rings.
  • Example: Benzene.

Structure and Properties of Alkanes

• Definition: Open-chain saturated hydrocarbons consisting only of $C-C$ single bonds and $C-H$ bonds.
• Functional Groups: Alkanes have no functional groups.
• Molecular Size: Connecting carbons can lead to either large or small molecules.
• Formula: For alkanes with no rings, the integer $n$ in $C_nH_{2n+2}$ can be (1, 2, 3, 4, …).
• Shape: The geometry is tetrahedral about each carbon atom.
• Bond Angles: All bond angles are approximately $109.5^\circ$.
• Representations:
  • Extended structures: Showing every bond.
  • Condensed structures: Groups like $CH_3$ or $CH_2$ are written together.
  • Line-angle formulas: An abbreviated method where each vertex and line ending represents a carbon atom; hydrogens are implied.

Alkane Isomers and Classification

• Isomers: Compounds that share the same molecular formula but differ in their structure.
• Constitutional Isomers: Isomers that differ specifically in the connectivity of their atoms. For example, while Methane ($CH_4$), Ethane ($C_2H_6$), and Propane ($C_3H_8$) have only one structure, larger alkanes have multiple:
  • Butane ($C_4H_{10}$): butane and isobutane.
  • Pentane ($C_5H_{12}$): pentane, 2-methylbutane, and 2,2-dimethylpropane.
• Straight-chain (Normal) Alkanes: Alkanes where carbons are connected to no more than two other carbons.
• Branched-chain Alkanes: Alkanes with one or more carbons connected to three or four other carbons.
• Classification of Carbons (C) and Hydrogens (H):
  • Primary ($1^\circ$) C: A carbon bonded to one other carbon. A hydrogen bonded to it is a $1^\circ$ H.
  • Secondary ($2^\circ$) C: A carbon bonded to two other carbons. A hydrogen bonded to it is a $2^\circ$ H.
  • Tertiary ($3^\circ$) C: A carbon bonded to three other carbons. A hydrogen bonded to it is a $3^\circ$ H.
  • Quaternary ($4^\circ$) C: A carbon bonded to four other carbons.

IUPAC Nomenclature for Alkanes

• General Format: prefix-infix-suffix.
  • Prefix: Indicates the number of carbon atoms in the parent chain.
  • Infix: Tells the nature of the carbon-carbon bonds (e.g., -an- for single bonds).
  • Suffix: Tells the class of the compound (e.g., -e for hydrocarbons).
• Prefixes for Carbon Count:
  • 1: meth-
  • 2: eth-
  • 3: prop-
  • 4: but-
  • 5: pent-
  • 6: hex-
  • 7: hept-
  • 8: oct-
  • 9: non-
  • 10: dec-
  • 11: undec-
  • 12: dodec-
  • 13: tridec-
  • 14: tetradec-
  • 15: pentadec-
  • 16: hexadec-
  • 17: heptadec-
  • 18: octadec-
  • 19: nonadec-
  • 20: eicos-
• Common Alkyl Groups ($R$): Formed by removing one hydrogen from an alkane.
  • Methyl (Me): $-CH_3$
  • Ethyl (Et): $-CH_2CH_3$
  • Propyl (Pr): $-CH_2CH_2CH_3$
  • Isopropyl (iPr or 1-methylethyl): $-CH(CH_3)_2$
  • Butyl (Bu): $-CH_2CH_2CH_2CH_3$
  • Isobutyl (iBu): $-CH_2CH(CH_3)_2$
  • sec-butyl (s-Bu or 1-methylpropyl): $-CH(CH_3)CH_2CH_3$
  • tert-butyl (t-Bu or 1,1-dimethylethyl): $-C(CH_3)_3$
• Rules for Naming:
  1. Find the parent chain (the longest continuous carbon chain). If two chains have the same length, choose the one with more substituents.
  2. Number the chain from the end closer to the first substituent to give it the lowest possible number.
  3. List substituents in alphabetical order. Prefixes like di-, tri-, tetra-, sec-, and tert- are ignored for alphabetization, but "iso" and "neo" are included.
  4. Use commas to separate numbers and hyphens to separate numbers from names.

Cycloalkanes

• General Formula: $(CH_2)_n$ or $C_nH_{2n}$.
• Naming: Add the prefix "cyclo-" to the alkane name.
• Substituent Numbering:
  • One substituent: No number needed.
  • Two substituents: Number starting from the substituent with lower alphabetical priority.
  • Three or more: Number to provide the lowest set of numbers, then alphabetize.

Conformations of Alkanes

• Conformation: Any 3-D arrangement resulting from rotation around a $C-C$ single bond.
• Staggered Conformation: Atoms/groups are as far apart as possible. Interactions are minimized, making it energetically favorable.
• Eclipsed Conformation: Atoms/groups are as close as possible. This creates steric and torsional strain and is energetically unfavorable.
• Newman Projection: A viewing method looking directly down a $C-C$ bond axis.
• Dihedral Angle ($\theta$): The angle between two intersecting planes.
  • Eclipsed: $\theta = 0^\circ$
  • Staggered: $\theta = 60^\circ$
• Ethane Energetics: The energy difference between staggered and eclipsed ethane is $12.6\,kJ/mol$ ($3.0\,kcal/mol$).
• Butane Conformations (viewed along C2-C3):
  • Anti: Methyl groups are $180^\circ$ apart (staggered, most stable).
  • Gauche: Methyl groups are $60^\circ$ apart (staggered, $3.8\,kJ/mol$ higher than anti due to steric strain).
  • Eclipsing interactions (Methyl-H or Methyl-Methyl) increase energy significantly; Methyl-Methyl eclipsed ($0^\circ$) is the least stable ($21\,kJ/mol$).

Intramolecular Strain

• Torsional Strain: Also called eclipsed-interaction strain; arises when nonbonded atoms separated by three bonds are forced into an eclipsed conformation. In ethane, this is $12.6\,kJ/mol$.
• Steric Strain: Arises when nonbonded atoms separated by four or more bonds are forced closer together than their atomic radii allow.
• Angle Strain: Arises when bond angles deviate from the ideal tetrahedral value of $109.5^\circ$.
• Stability Trends: Low energy corresponds to low reactivity and high stability. High energy corresponds to high reactivity and low stability.

Cycloalkane Conformations and Strain

• Cyclopropane: Planar. High angle strain (compressed to $60^\circ$) and high torsional strain (6 sets of eclipsed hydrogens). Total strain: $116\,kJ/mol$.
• Cyclobutane: Puckered (nonplanar) to reduce torsional strain. Bond angles are approximately $88^\circ$. Total strain: $110\,kJ/mol$.
• Cyclopentane: Adopts an "envelope" conformation. Angles are approximately $105^\circ$. Total strain: $27\,kJ/mol$.
• Cyclohexane:
  • Chair Conformation: The most stable. Bond angles are $110.9^\circ$. All bonds are staggered, resulting in zero torsional strain.
  • Axial positions: Six hydrogens perpendicular to the ring.
  • Equatorial positions: Six hydrogens near the plane of the ring.
  • Ring-Flip: Rapid interconversion between two equivalent chair forms where axial positions become equatorial and vice versa.
  • Boat Conformation: Less stable than chair by $27\,kJ/mol$ due to four eclipsed pair interactions and "flagpole" steric strain.
  • Twist-Boat Conformation: Slightly more stable than the boat ($6.3\,kJ/mol$ better) but significantly less stable than the chair ($41.8\,kJ/mol$ worse).

Substituted Cyclohexanes and Isomerism

• Monosubstituted Cyclohexanes: Substituents prefer the equatorial position to avoid 1,3-diaxial interactions (a form of steric strain). For methylcyclohexane, the equatorial form is more stable by $7.6\,kJ/mol$.
• Bulky Groups: Groups like tert-butyl ($tBu$) or isopropyl ($iPr$) must always be equatorial.
• Stereoisomers: Compounds with the same formula and connectivity but different spatial orientations.
• Cis-Trans Isomerism:
  • Cis: Substituents on the same side of the ring.
  • Trans: Substituents on opposite sides of the ring.
  • In 1,4-dimethylcyclohexane, the trans isomer is most stable in the diequatorial conformation.

Physical Properties

• Polarity: Alkanes are nonpolar because $C-H$ bonds are nonpolar covalent.
• Intermolecular Forces: Weak induced dipole-induced dipole (van der Waals) forces.
• Boiling/Melting Points: Increase as the number of carbons increases.
  • $C_1 - C_4$: Gases.
  • Pentane to Decane (Gasoline/Kerosene): Liquids.
  • Paraffin wax: Semisolid/Solid.
• Branching: Branched isomers have lower boiling points than straight-chain isomers because they are more compact, with less surface area for van der Waals interactions.

Reactions of Alkanes

• Oxidation (Combustion): Alkanes react with $O_2$ to produce $CO_2$, $H_2O$, and heat.
• Halogenation: Reaction with $Cl_2$ or $Br_2$ in the presence of heat or light.
  • Type: Substitution reaction.
  • Mechanism: Free radical mechanism.
    • Initiation: Homolytic cleavage of the halogen bond ($X-X \rightarrow 2X\cdot$).
    • Propagation: A repeating cycle where a radical reacts with a molecule to form a new radical (e.g., $CH_4 + Cl\cdot \rightarrow CH_3\cdot + HCl$).
    • Termination: Two radicals combine to form a stable molecule.
  • Radical Stability: $allyl > 3^\circ > 2^\circ > 1^\circ > methyl > vinyl$.
  • Regioselectivity: The reaction favors replacing hydrogen at the most highly substituted carbon. Bromination is significantly more regioselective than chlorination.