Comprehensive Study Notes on Alkanes, Alkenes, and Conjugated Dienes

Concepts and Principles of Hybridization

• Definition: Hybridization describes the process where atomic orbitals mix to create new hybrid orbitals. These new orbitals facilitate covalent bonding in organic chemistry.
• General Principles:
  • Hybridization involves the intermixing of atomic orbitals to form a new set of equivalent orbitals.
  • The total number of electrons held by the new hybrid orbitals remains equal to the number of electrons in the original orbitals.
  • The energy and properties of the hybridized orbitals represent an "average" of the original unhybridized orbitals.

Types of Carbon Hybridization

• sp3 Hybridization:
  • Atomic Orbitals Used: One s-orbital and three p-orbitals ($s, p, p, p$).
  • Resulting Orbitals: 4 equivalent $sp^3$ orbitals; no remaining p-orbitals.
  • Geometry: Tetrahedral.
  • Ideal Bond Angle: $109.5^∘$.
  • Bonds: Single bonds.
  • Example: Methane ($CH_4$) and Ethane ($C_2H_6$).
• sp2 Hybridization:
  • Atomic Orbitals Used: One s-orbital and two p-orbitals ($s, p, p$).
  • Resulting Orbitals: 3 $sp^2$ orbitals and 1 unhybridized p-orbital.
  • Geometry: Flat triangular (trigonal planar).
  • Ideal Bond Angle: $120^∘$.
  • Bonds: Double bonds.
  • Example: Ethene ($C_2H_4$).
• sp Hybridization:
  • Atomic Orbitals Used: One s-orbital and one p-orbital ($s, p$).
  • Resulting Orbitals: 2 $sp$ orbitals and 2 unhybridized p-orbitals.
  • Geometry: Linear.
  • Ideal Bond Angle: $180^∘$.
  • Bonds: Triple bonds.
  • Example: Ethyne ($C_2H_2$).

Comparative Bond Parameters of Hydrocarbons

• Ethane ($CH_3-CH_3$):
  • Hybridization: $sp^3$.
  • Bond Angle: $109.5^∘$.
  • C-C Bond Length: 1.54\,& (1.53\,& specifically noted for ethane).
  • C-C Bond Strength: $90\,kcal/mol$ ($377\,kJ/mol$).
  • C-H Bond Length: 1.10\,& (1.09\,& for methane).
  • C-H Bond Strength: $101\,kcal/mol$ ($423\,kJ/mol$).
• Ethene ($CH_2=CH_2$):
  • Hybridization: $sp^2$.
  • Bond Angle: $120^∘$.
  • C-C Bond Length: 1.33\,&.
  • C-C Bond Strength: $174\,kcal/mol$ ($720\,kJ/mol$).
  • C-H Bond Length: 1.08\,&.
  • C-H Bond Strength: $111\,kcal/mol$ ($466\,kJ/mol$).
• Ethyne ($H-C\equiv C-H$):
  • Hybridization: $sp$.
  • Bond Angle: $180^∘$.
  • C-C Bond Length: 1.20\,&.
  • C-C Bond Strength: $231\,kcal/mol$ ($967\,kJ/mol$).
  • C-H Bond Length: 1.06\,&.
  • C-H Bond Strength: $131\,kcal/mol$ ($548\,kJ/mol$).

Factors Affecting Bond Lengths

• Atomic Size: Primarily determines the base bond length.
• Bond Order: Bond length follows the order: Single > Double > Triple.
• Hybridization Effect: C-H and C-C bonds shorten as the "s character" of the carbon atom increases (e.g., $sp^3$ to $sp$).

Types of Carbon-Carbon Sigma (σ) Bonds

1. $sp^3-sp^3$: Found in Ethane ($H_3C-CH_3$).
2. $sp^3-sp$: Found in Propyne ($H_3C-C\equiv C-H$).
3. $sp-sp^2$: Found in specific vinyl-acetylene compounds ($H-C\equiv C-CH=CH_2$).
4. $sp^3-sp^2$: Found in Propene ($H_3C-CH=CH_2$).
5. $sp^2-sp^2$: Found in Ethene bonds ($H_2C=CH_2$).
6. $sp-sp$: Found in Butadiyne ($H-C\equiv C-C\equiv C-H$).

Detailed Structure of Methane ($CH_4$)

• Process: Intermixing of one 2s orbital and three 2p orbitals to form four equivalent hybrid orbitals.
• Experimental Observations: All four C-H bonds have a length of 1.09\,& and bond angles of $109.5^∘$.
• Electronic Configuration:
  • Ground State: Two unpaired electrons in 2p orbitals.
  • Excited State: One 2s electron promoted to the 2p orbital.
• Key Characteristics:
  • $25\%$ s-character and $75\%$ p-character.
  • Hybrids point toward the corners of a regular tetrahedron to minimize electronic repulsion.
  • The hybrid orbitals are more directional and effective at overlapping compared to pure atomic orbitals.

Free Radicals

• Definition: An atom or group of atoms containing an unpaired electron.
• Formation: Produced via the homolytic fission of a covalent bond.
• Properties: Highly reactive with a strong tendency to pair their unpaired electron; they exist as short-lived reaction intermediates.
• Example: Production of chlorine free radicals ($Cl^\bullet$) from $Cl_2$ in the presence of UV light.
• Classification:
  • Primary: One carbon atom attached to the radical carbon.
  • Secondary: Two carbon atoms attached.
  • Tertiary: Three carbon atoms attached.
• Structure: Alkyl free radicals involve $sp^2$ hybridization. The geometry is planar with three hybrid orbitals forming σ-bonds; the unpaired electron resides in an unhybridized p-orbital.

Halogenation of Alkanes (Free Radical Substitution)

• Reaction Summary: Treated with $Br_2$ or $Cl_2$ in the presence of UV light or heat to produce haloalkanes ($R-X$) and $HX$.
• Reactivity Orders:
  • Alkanes: Tertiary > Secondary > Primary > Methyl.
  • Halogens: $F_2 > Cl_2 > Br_2 > I_2$.
• Selectivity: Bromination is highly selective for the most stable radical (tertiary), whereas chlorination is less selective.
• Mechanism (Radical Chain):
  • Initiation Step: $X-X \xrightarrow{UV} 2X^\bullet$.
  • Propagation Steps:
    • $R-H + X^\bullet \rightarrow R^\bullet + HX$
    • $R^\bullet + X_2 \rightarrow R-X + X^\bullet$
  • Termination Steps:
    • $X^\bullet + X^\bullet \rightarrow X_2$
    • $R^\bullet + X^\bullet \rightarrow R-X$
    • $R^\bullet + R^\bullet \rightarrow R-R$
• Inhibitors: Substances like Oxygen ($O_2$) break the propagation cycle, slowing or stopping the reaction during an "inhibition period."

Thermodynamics of Halogenation

• Fluorination: Extremely exothermic ($\Delta H^∘ = -431\,kJ/mol$). One initiation can trigger thousands of reactions, potentially leading to explosions. It is controlled by diluting products with inert gas or using copper granulate to absorb heat.
• Chlorination: Less exothermic ($\Delta H^∘ = -115\,kJ/mol$) and has higher activation energy in initiation than fluorination, making it easier to control.
• Bromination: Initiation activation energy is lower than chlorination, but propagation is far less exothermic. The first propagation step is strongly endothermic ($+75\,kJ/mol$ compared to chlorine's $+8\,kJ/mol$), making the reaction very slow even at $300^∘C$.
• Iodination: Although initiation activation energy is lower than fluorination, the complete chain propagation is endothermic ($+54\,kJ/mol$), with the first step being very endothermic ($+142\,kJ/mol$). Radical iodination does not take place.

Factors Affecting Free Radical Stability

1. Electron Density: Radicals are electron-deficient. Stabilization occurs via electron density donation from neighbor atoms (Methyl < Primary < Secondary < Tertiary). Neighboring atoms with lone pairs (O, N) also stabilize radicals.
2. Delocalization/Resonance: Spread of the radical over multiple carbons stabilizes the species.
3. Hybridization: Stability decreases as s-character increases ($sp^3 > sp^2 > sp$) because the orbital is closer to the nucleus.
4. Electronegativity: In a periodic row, stability decreases as electronegativity increases.
5. Periodic Column: Stability increases going down a column because the electron-deficient orbital is spread over a larger volume ($F^\bullet < Cl^\bullet < Br^\bullet < I^\bullet$).

Paraffin Properties and Applications

• General Formula: $C_nH_{2n+2}$.
• Physical States:
  • $1-4$ Carbons: Gas.
  • $5-15$ Carbons: Liquid.
  • $16+$ Carbons: Solid (Waxes).
• Paraffin wax: White solid obtained from petrol or coal ($C_{16}-C_{40}$).
• Medicinal Liquid Paraffin (Paraffinum Liquidum): Highly refined mineral oil.
  • Laxative: Passes through the intestinal tract without absorption, easing constipation.
  • Skin Care: Used in creams, lotions, lip balms, and eczema ointments (emollient/lubricant).
  • Therapeutic Baths: Hot wax baths for rheumatism and joint pain to soothe muscles.
  • Barrier Cream: Prevents water evaporation from the skin surface.

Alkene Structure and Stability

• Ethane/Ethene sp2 Structure: Trigonal planar arrangement ($120^∘$). Each carbon has three planers $sp^2$ orbitals forming σ-bonds and a pure unhybridized p-orbital forming a π-bond via sideways overlapping.
• Alkene Hydrogenation: Alkenes react with $H_2$ via a carbocation intermediate. Metal catalysts (Pt, Pd, Ni) reduce activation energy and facilitate "syn-addition" (adding hydrogens to the same side).
• Heats of Hydrogenation: Approximately $-30\,kcal/mol$. Lower heat release indicates higher stability. Substituents increase stability via hyperconjugation.

Structure of Ethyne (Acetylene)

• Hybridization: $sp$.
• Bonding: One $sp-sp$ overlap (C-C σ-bond) and two $sp-s$ overlaps (C-H σ-bonds). Two pairs of pure p-orbitals overlap to form two π-bonds.
• Parameters: Bond angle $180^∘$, C-C length 1.20\,&, C-H length 1.06\,&.

Elimination Reactions

• Definition: Removal of two substituents from a molecule to increase unsaturation (forming a double bond).
• Key Events: Removal of a proton, formation of the CC π-bond, and breaking of the bond to the leaving group.
• E1 Reaction (Unimolecular):
  • Steps: Two steps with a carbocation intermediate.
  • Kinetics: First order, Rate = $k[R-LG]$.
  • Reactivity: Tertiary > Secondary > Primary.
  • Conditions: Favored by good leaving groups, weak bases ($H_2O, ROH$), and polar protic solvents.
  • Regioselectivity: Follows Zaitsev (Saytseff) Rule.
• E2 Reaction (Bimolecular):
  • Steps: Single step (concerted).
  • Kinetics: Second order, Rate = $k[Base][Substrate]$.
  • Stereochemistry: Stereospecific; requires anti-periplanar geometry (staggered conformation).
  • Conditions: Favored by strong bases and polar aprotic solvents.
  • Reactivity: Tertiary > Secondary > Primary ($R_3CX > R_2CHX > RCH_2X$).

Carbocations and Rearrangements

• Structure: Trigonal planar, $sp^2$ hybridized carbon with a vacant p-orbital and a "sextet" (six valence electrons).
• Classification: Primary, Secondary, Tertiary, Allylic (adjacent to C=C), Benzylic (adjacent to benzene), Vinylic (part of C=C), and Aryl (part of benzene ring).
• Formation Mechanism:
  1. Ionization: Breaking of a C-LG bond (curved arrow pointing to LG).
  2. Electrophilic Addition: Electrophile attacks a π-bond.
• Rearrangements: 1,2-hydride shifts, 1,2-alkyl shifts, or ring expansions (e.g., five-membered to six-membered) to form more stable carbocations.

Prediction Rules for Addition and Elimination

• Saytzeff's (Zaitsev) Rule: In elimination, hydrogen is preferentially removed from the carbon atom with fewer hydrogens, leading to the more highly substituted alkene (thermodynamic control).
• Markownikoff's Rule: In electrophilic addition of $HX$, hydrogen attaches to the carbon with more hydrogen substituents, and the halide ($X$) attaches to the carbon with more alkyl substituents (explained by carbocation stability and the Alkyl Inductive Effect).
• Anti-Markownikoff's Rule (Peroxide Effect): Occurs only with $H-Br$ in the presence of peroxides. Hydrogen bonds to the carbon with fewer hydrogens. It follows a free radical mechanism involving homolytic cleavage.

Ozonolysis

• Reaction: Cleavage of unsaturated bonds ($C=C, C\equiv C$) using ozone to form carbonyl groups.
• Reagents: Ozone followed by a reducing work-up ($Zn$/acetic acid or $(CH_3)_2S$) or an oxidizing work-up ($H_2O_2$ for carboxylic acids).
• Mechanism:
  1. Addition of ozone to form unstable molozonide.
  2. Breakdown into carbonyl and carbonyl oxide (zwitterion).
  3. Rearrangement into a stable ozonide intermediate.
  4. Workup to final carbonyl products.

Dienes and Specialized Reactions

• Classification of Dienes:
  1. Cumulated: Double bonds share a common atom (allenes, non-planar, central carbon is $sp$ hybridized).
  2. Conjugated: Double bonds separated by one single bond. Two conformations: s-cis and s-trans (s-trans is $12\,kJ/mol$ more stable).
  3. Isolated (Unconjugated): Double bonds separated by two or more single bonds.
• Diels-Alder Reaction: Concerted conversion of a diene and a "dienophile" into a six-membered ring. It is stereospecific (cis-dienophile yields cis-substituents).
• Addition to Conjugated Dienes: Can result in 1,2-product (kinetic product, lower activation energy) or 1,4-product (thermodynamic product, more stable).
• Allylic Rearrangement: Migration of a functional group and double bond, often observed in $S_N1$ or $S_N2$ reactions due to resonance stability of the allylic intermediate.