Chapter 7 - Alkenes: Structure and Reactivity

Overview and Industrial Significance of Alkenes

• Definition and General Features of Alkenes:

  • An alkene is a hydrocarbon containing at least one carbon–carbon double bond ($C=C$).
  • Alkenes are historically and synonymously referred to as olefins.
  • Because their carbon atoms possess fewer hydrogen atoms than the corresponding alkanes, alkenes are classified as unsaturated hydrocarbons.
  • Naturally occurring examples include:
    • $\alpha$-Pinene: A bicyclic monoterpene found extensively in pine trees and turpentine.
    • $\beta$-Carotene: An extensive conjugated polyene responsible for the orange pigment in carrots and serving as a dietary precursor to vitamin A.
    • Ethylene ($H_2C=CH_2$): The simplest possible alkene, functioning plant hormonally as a fruit-ripening agent.

• Industrial Importance of Low-Molecular-Weight Alkenes:

  • Ethylene (ethene) and propylene (propene) are the simplest alkenes and represent the highest-volume organic chemicals manufactured globally.
  • They serve as foundational petrochemical feedstocks converted into a wide array of industrial polymers, solvents, and bulk chemicals:
    • Key Derivatives of Ethylene ($H_2C=CH_2$):
      • Ethanol ($CH_3CH_2OH$): Industrial alcohol and fuel additive synthesized by the hydration of ethylene.
      • Ethylene glycol ($HOCH_2CH_2OH$): Primary constituent of automotive engine antifreeze and a monomer for polyester manufacturing.
      • Ethylene dichloride ($ClCH_2CH_2Cl$): Chlorinated intermediate utilized almost exclusively in the synthesis of vinyl chloride.
      • Acetaldehyde ($CH_3CHO$): Versatile precursor to acetic acid, pyridine bases, and peracetic acid.
      • Acetic acid ($CH_3COOH$): Bulk commodity chemical for solvent, ester, and cellulose acetate production.
      • Ethylene oxide: Reactive cyclic oxirane used in non-ionic surfactant and glycol manufacture.
      • Vinyl acetate ($H_2C=CHOCOCH_3$): Monomer for poly(vinyl acetate) used in latex paints and adhesives.
      • Polyethylene ($(-CH_2CH_2-)_n$): World's most prevalent packaging plastic.
      • Vinyl chloride ($H_2C=CHCl$): Monomer for poly(vinyl chloride) (PVC) construction materials.
    • Key Derivatives of Propylene ($CH_3CH=CH_2$):
      • Isopropyl alcohol ($CH_3CH(OH)CH_3$): Rubbing alcohol, industrial cleaning solvent, and chemical intermediate.
      • Propylene oxide: Oxirane used primarily in the production of polyether polyols for polyurethane plastics.
      • Polypropylene ($(-CH_2CH(CH_3)-)_n$): Thermoplastic polymer employed in fibers, packaging, automotive parts, and containers.
      • Cumene (isopropylbenzene): Intermediate produced via alkylation of benzene, processed commercially into phenol and acetone.

• Thermal Cracking (Steam Cracking):
  • On a commercial scale, ethylene, propylene, and butene are synthesized via the steam cracking (thermal cracking) of light alkanes ($C_2-C_4$ hydrocarbons such as ethane, propane, and butane from natural gas or petroleum refining):
    • The process occurs non-catalytically at elevated temperatures approaching $900\,^\circ\text{C}$.
    • Under extreme heat, homolytic carbon–carbon bond fission occurs to generate short-lived alkyl radical intermediates.
    • Subsequent $\beta$-scission and disproportionation reactions yield alkenes and diatomic hydrogen ($H_2$):             $CH_3CH_2CH_2CH_3 \xrightarrow{900\,^\circ\text{C}} 2\,[\cdot CH_2CH_3] \rightarrow 2\,H_2C=CH_2 + H_2$

Degree of Unsaturation

• Fundamental Principles:

  • A saturated open-chain (acyclic) alkane possesses the general molecular formula $C_n H_{2n+2}$.
  • Every structural feature that removes hydrogen atoms relative to an open-chain saturated alkane introduces unsaturation:
    • A double bond reduces the hydrogen count by $2\,\text{H}$.
    • A ring reduces the hydrogen count by $2\,\text{H}$.
    • A triple bond reduces the hydrogen count by $4\,\text{H}$ (equivalent to two degrees of unsaturation).
  • The degree of unsaturation (also called the index of hydrogen deficiency, IHD) corresponds to the combined total number of rings and multiple bonds in a molecule.
  • For a pure hydrocarbon with formula $C_n H_m$:         $\text{Degree of Unsaturation} = \frac{(2n + 2) - m}{2}$
  • Comparison Example: Ethane ($C_2H_6$) is saturated ($2n+2 = 2(2)+2 = 6$). Ethylene ($C_2H_4$) contains fewer hydrogens ($6 - 4 = 2\,\text{H}$ missing), establishing a degree of unsaturation equal to $1$.
  • Multifunctional Isomer Example ($C_6H_{10}$):
    • The saturated alkane with $6$ carbons is hexane ($C_6H_{14}$).
    • $C_6H_{10}$ possesses a deficit of $14 - 10 = 4\,\text{H}$, indicating a degree of unsaturation equal to $2$.
    • Constitutional isomers of $C_6H_{10}$ illustrate different structural combinations contributing to an unsaturation value of $2$:
      • 4-Methyl-1,3-pentadiene: Two double bonds ($1 + 1 = 2$).
      • Cyclohexene: One ring plus one double bond ($1 + 1 = 2$).
      • Bicyclo[3.1.0]hexane: Two fused rings ($1 + 1 = 2$).
      • 4-Methyl-2-pentyne: One triple bond ($2$).

• Rules for Incorporating Heteroatoms ($X, O, N$):

  • Organohalogens ($C, H, X$, where $X = F, Cl, Br, I$):
    • Halogens are monovalent and effectively substitute directly for hydrogen in a hydrocarbon framework.
    • Calculation procedure: Treat each halogen atom as equivalent to one hydrogen atom (add the count of halogen atoms to the count of hydrogen atoms).
    • Example: For $1,4$-dibromo-2-butene ($BrCH_2CH=CHCH_2Br$, empirical formula $C_4H_6Br_2$):             $\text{Equivalent hydrocarbon formula} = ``C_4H_{6+2}" = ``C_4H_8"$$\text{Degree of unsaturation} = \frac{(2 \times 4 + 2) - 8}{2} = 1 \quad (\text{one double bond})$
  • Organooxygen Compounds ($C, H, O$):
    • Divalent oxygen forms two covalent single bonds (or one double bond), essentially inserting between a carbon atom and a hydrogen atom or between two carbons without altering the hydrogen-to-carbon ratio of the carbon skeleton.
    • Calculation procedure: Oxygen atoms are completely ignored when determining the degree of unsaturation.
    • Example: For penta-2,4-dien-1-ol ($H_2C=CHCH=CHCH_2OH$, formula $C_5H_8O$):             $\text{Equivalent hydrocarbon formula} = ``C_5H_8"$$\text{Degree of unsaturation} = \frac{(2 \times 5 + 2) - 8}{2} = 2 \quad (\text{two double bonds})$
  • Organonitrogen Compounds ($C, H, N$):
    • Trivalent nitrogen forms three covalent single bonds, thereby introducing an additional hydrogen into the skeleton compared to a standard alkane framework.
    • Calculation procedure: Subtract the number of nitrogen atoms from the total hydrogen count to determine the equivalent hydrocarbon formula.
    • Example: For a cyclic allylic amine ($C_5H_9N$):             $\text{Equivalent hydrocarbon formula} = ``C_5H_{9-1}" = ``C_5H_8"$$\text{Degree of unsaturation} = \frac{(2 \times 5 + 2) - 8}{2} = 2 \quad (\text{one ring and one double bond})$

• Worked Examples on Calculating Degree of Unsaturation and Isomers:

  • Case A: Formula $C_4H_8$
    • Calculation: Fully saturated acyclic 4-carbon alkane is $C_4H_{10}$. Difference = $10 - 8 = 2\,\text{H}$. Degree of unsaturation = $1$.
    • Constitutional/Stereoisomeric structures include:
      • 1-Butene ($CH_3CH_2CH=CH_2$)
      • cis-2-Butene ($CH_3CH=CHCH_3$, Z)
      • trans-2-Butene ($CH_3CH=CHCH_3$, E)
      • 2-Methylpropene ($(CH_3)_2C=CH_2$)
      • Cyclobutane
      • Methylcyclopropane
  • Case B: Formula $C_4H_6$
    • Calculation: Saturated 4-carbon alkane is $C_4H_{10}$. Difference = $10 - 6 = 4\,\text{H}$. Degree of unsaturation = $2$.
    • Constitutional/ring structures include:
      • 1,3-Butadiene ($H_2C=CH-CH=CH_2$)
      • 1,2-Butadiene ($CH_3-CH=C=CH_2$, an allene)
      • 1-Butyne ($CH_3CH_2C\equiv CH$)
      • 2-Butyne ($CH_3C\equiv CCH_3$)
      • Cyclobutene
      • Bicyclo[1.1.0]butane
      • 1-Methylcyclopropene
      • 3-Methylcyclopropene
      • Methylenecyclopropane
  • Case C: Formula $C_3H_4$
    • Calculation: Saturated 3-carbon alkane is $C_3H_8$. Difference = $8 - 4 = 4\,\text{H}$. Degree of unsaturation = $2$.
    • Constitutional structures include:
      • Propadiene (allene, $H_2C=C=CH_2$)
      • Propyne ($CH_3C\equiv CH$)
      • Cyclopropene

Systematic Nomenclature of Alkenes (IUPAC Rules)

• Four-Step Systematic Naming Methodology:

  • Step 1: Identify and name the parent hydrocarbon chain:
    • Locate the longest continuous carbon chain that must contain the carbon–carbon double bond.
    • Replace the alkane suffix -ane with the alkene suffix -ene.
    • Critical rule: If a longer carbon chain exists that fails to include the double bond, it cannot be designated as the parent chain. For instance, a six-carbon aliphatic chain lacking the alkene functionality is bypassed in favor of a five-carbon chain incorporating the double bond, designating the compound as a pentene, not a hexene.
  • Step 2: Number the carbon atoms in the parent chain:
    • Number from the chain terminus nearer the double bond.
    • This ensures that the two carbons of the double bond receive the lowest possible locants.
    • If the double bond is equidistant from both termini, number from the terminus that yields the lower locants for substituents at the first point of difference.
  • Step 3: Assemble the complete name:
    • Indicate the position of the double bond by prefixing the parent name with the lower-numbered double-bond carbon (or directly before the "-ene" suffix in modern IUPAC notation, e.g., hex-2-ene).
    • Designate the position of all substituents according to their numerical locant on the parent chain.
    • List substituents in alphabetical order (ignoring multiplying prefixes like di-, tri-, tetra-, except iso- and cyclo-).
    • If multiple double bonds are present, use multiplying suffixes: -diene (two double bonds), -triene (three double bonds), etc.
  • Step 4: Cycloalkene Nomenclature:
    • In rings containing a double bond, prefix the ring size with cyclo-.
    • The double-bond carbons are universally assigned positions C1 and C2.
    • Numbering must traverse through the double bond around the ring in the direction that delivers the lowest possible locant to the first substituent.

• IUPAC vs. Common Nomenclature of Selected Alkenes:

• Representative IUPAC Nomenclature Examples:

  • $CH_3CH_2CH_2CH=CHCH_3$: Numbering from the right places the double bond at carbon 2. 2-Hexene (or hex-2-ene).
  • $CH_3CH(CH_3)CH=CHCH_2CH_3$: Numbering from the left gives the double bond locant 3 and the methyl substituent locant 2 (numbering from the right would give double bond locant 3, but methyl locant 5). 2-Methyl-3-hexene.
  • $H_2C=C(CH_2CH_3)CH_2CH_2CH_3$: Longest chain including the double bond contains 5 carbons; the ethyl group is at carbon 2. 2-Ethyl-1-pentene.
  • $H_2C=C(CH_3)CH=CH_2$: A four-carbon diene with double bonds at C1 and C3, and a methyl group at C2. 2-Methyl-1,3-butadiene.
  • Cycloalkene examples:
    • Cyclohexene with a methyl at C1: 1-Methylcyclohexene.
    • Cyclohexadiene with double bonds starting at C1 and C4: 1,4-Cyclohexadiene (or cyclohexa-1,4-diene).
    • Cyclopentene with methyl groups at C1 and C5: Numbering through the double bond from C1 to C2 places the second substituent at C5. 1,5-Dimethylcyclopentene.

• Detailed Worked Solutions to Nomenclature Problems:

  • Problem 1: Name $H_2C=CH-CH(CH_3)-C(CH_3)_3$
    • Identify parent chain: Longest carbon chain containing the double bond has 5 carbons (pentene).
    • Number the chain: Begin at the double bond terminus ($C1 = H_2C=$; $C2 = =CH-$; $C3 = -CH(CH_3)-$; $C4 = -C(CH_3)_3$; $C5 = -CH_3$).
    • Locate substituents: Three methyl groups exist: one attached to C3 and two attached to C4.
    • Prefix with tri-: Assemble as 3,4,4-Trimethyl-1-pentene.
  • Problem 2: Name $CH_3CH_2CH=C(CH_3)CH_2CH_3$
    • Identify parent chain: Longest chain contains 6 carbons (hexene).
    • Number the chain: The double bond begins at C3 whether numbered from left or right. Numbering from the right assigns the methyl branch to C3 (whereas numbering from the left assigns it to C4). Hence, numbering starts from the right.
    • Assemble name: 3-Methyl-3-hexene.
  • Problem 3: Name 6-membered cycloalkene with methyl groups at each double-bond carbon.
    • Ring is cyclohexene; double-bond carbons are C1 and C2.
    • Both C1 and C2 bear methyl substituents.
    • Assemble name: 1,2-Dimethylcyclohexene.
  • Problem 4: Name 7-membered cycloalkene with two methyl groups at one carbon.
    • Ring is cycloheptene; double-bond carbons are C1 and C2.
    • Numbering through the double bond toward the substitution site assigns locant 4 to the geminal dimethyl position (assigning C1 away would yield locant 5).
    • Assemble name: 4,4-Dimethylcycloheptene.

Cis-Trans Isomerism and Double-Bond Geometry

• Orbital Structure and Rotational Restriction:
  • Both carbon atoms involved in an alkene double bond are $sp^2$-hybridized.
  • Each carbon forms three planar $\sigma$ bonds utilizing its three $sp^2$ hybrid orbitals arranged with approximately $120^\circ$ bond angles.
  • The remaining unhybridized $2p$ orbital on each carbon lies strictly perpendicular to the molecular $\sigma$-bonding plane.
  • Parallel, side-by-side overlap of these unhybridized $p$ orbitals forms a bonding $\pi$ molecular orbital (accompanied by an unfilled higher-energy antibonding $\pi^*$ orbital).
  • Free rotation around the carbon–carbon double bond is impossible at ambient temperatures because rotation by $90^\circ$ disrupts the parallel alignment of the $p$ orbitals, breaking the $\pi$ bond completely.
  • The energetic barrier to rotation around a carbon–carbon double bond is approximately $350\,\text{kJ/mol}$ ($\approx 84\,\text{kcal/mol}$), corresponding to the homolytic strength of the $\pi$ bond.

• Prerequisites for Cis-Trans Isomerism:

  • Cis-trans stereoisomerism exists in alkenes if and only if both carbons of the double bond are attached to two distinct chemical groups.
  • General representation: For an alkene written as $AB\,C=C\,DE$:
    • If $A \neq B$ and $D \neq E$, stereoisomers exist.
    • If either carbon possesses two identical groups ($A = B$ or $D = E$), cis-trans isomerism is impossible because swapping the identical groups creates an indistinguishable molecule.
  • Isomers of 2-Butene: 2-Butene ($CH_3CH=CHCH_3$) fulfills this condition (each carbon is bonded to $-H$ and $-CH_3$):
    • cis-2-Butene: Both methyl groups reside on the identical side of the double bond axis.
    • trans-2-Butene: Methyl groups reside on opposite sides of the double bond axis.
  • Because they cannot spontaneously interconvert at room temperature, cis- and trans-2-butene are distinct chemical substances possessing unique boiling points, melting points, and thermodynamic stabilities.

• Structural Application Problem (cis-9-Tricosene):

  • cis-9-Tricosene (muscalure) functions as the sex pheromone of the common housefly (Musca domestica).
  • "Tricosane" denotes a 23-carbon straight chain.
  • The prefix "9-tricosene" signifies an unsaturation between C9 and C10.
  • The cis configuration establishes that both alkyl chains—the 8-carbon octyl tail at C9 and the 13-carbon tridecyl chain at C10—extend toward the identical side of the double bond plane, introducing a characteristic bend into the extended aliphatic hydrocarbon skeleton.

Alkene Stereochemistry: The E,Z System (Cahn–Ingold–Prelog Rules)

• Limitations of Cis-Trans Terminology:

  • Cis-trans nomenclature becomes ambiguous when applied to tri- or tetra-substituted alkenes (e.g., distinguishing relative geometry when three or four distinct halogens/alkyl groups are present).
  • The IUPAC standard adopts the generalized $E,Z$ system, utilizing the sequence priority rules formulated by R. S. Cahn, C. Ingold, and V. Prelog (the CIP rules).

• The Cahn–Ingold–Prelog (CIP) Sequence Rules:

  • Rule 1: Direct Atomic Number Priority:
    • Examine the two atoms attached directly to a specific double-bond carbon.
    • Assign higher priority to the substituent atom having the higher atomic number ($Z$).
    • Common hierarchy: $-I > -Br > -Cl > -S > -P > -F > -O > -N > -C > -H$.
    • In cases of isotopic substitution, higher mass number takes precedence (e.g., $^2H$ [deuterium] $>\, ^1H$ [protium]).
  • Rule 2: Point of Difference Along Chains:
    • If the directly attached atoms on a double-bond carbon are identical, compare the atoms bonded to each of them in order of decreasing atomic number.
    • Proceed along each chain one connection point at a time until the first point of difference is identified.
    • Examples:
      • $-CH_2CH_3$ (carbon attached to $C, H, H$) takes priority over $-CH_3$ (carbon attached to $H, H, H$).
      • $-OCH_3$ (oxygen attached to $C$) takes priority over $-OH$ (oxygen attached to $H$).
      • $-CH(CH_3)_2$ (carbon attached to $C, C, H$) takes priority over $-CH_2CH_3$ (carbon attached to $C, H, H$).
      • $-CH_2Cl$ (carbon attached to $Cl, H, H$) takes priority over $-CH_2NH_2$ (carbon attached to $N, H, H$).
  • Rule 3: Treatment of Multiple Bonds:
    • Multiply-bonded atoms are conceptually duplicated or triplicated, equivalent to an identical number of single-bonded atoms.
    • Aldehyde ($-CH=O$): The carbonyl carbon is treated as bonded to $(O, O, H)$, and the carbonyl oxygen is treated as bonded to $(C, C)$.
    • Carboxylic ester ($-CO_2R$): The carbonyl carbon is bonded to $(O, O, O)$.
    • Vinyl ($-CH=CH_2$): The terminal carbon has a double bond to carbon; the internal carbon is treated as bonded to $(C, C, H)$.
    • Nitrile ($-C\equiv N$): The carbon is treated as bonded to $(N, N, N)$.

• Assigning E and Z Stereoisomers:

  • Rank the two substituents on double-bond carbon 1 as High or Low priority.
  • Rank the two substituents on double-bond carbon 2 as High or Low priority.
  • Z Geometry (zusammen = together): Both higher-priority groups reside on the same side of the double bond reference axis.
  • E Geometry (entgegen = opposite): Higher-priority groups reside on opposite sides of the double bond reference axis.

• Complex Assignment Example:

  • Consider an alkene containing:
    • Carbon 1: Attached to a vinyl group ($-CH=CH_2$) and an isopropyl group ($-CH(CH_3)_2$).
      • Comparing atoms: Both groups attach via carbon. The vinyl carbon is double-bonded to carbon, counting as bonded to $(C, C, H)$. The isopropyl methine carbon is bonded to two methyl carbons, counting as $(C, C, H)$.
      • Advancing to next atoms: Vinyl's second carbon is bonded to $(C, H, H)$, whereas the isopropyl methyl carbons are bonded only to $(H, H, H)$.
      • Result: $-CH=CH_2$ ranks High; $-CH(CH_3)_2$ ranks Low.
    • Carbon 2: Attached to a methyl ester ($-CO_2CH_3$) and a hydroxymethyl group ($-CH_2OH$).
      • Comparing atoms: The ester carbonyl carbon is bonded to three oxygens $(O, O, O)$. The hydroxymethyl carbon is bonded to one oxygen and two hydrogens $(O, H, H)$.
      • Result: $-CO_2CH_3$ ranks High; $-CH_2OH$ ranks Low.
    • Geometry: Since the High-priority vinyl group and the High-priority ester group are situated on the same spatial side of the double bond, the alkene configuration is $Z$.

Alkene Stability and Thermodynamics

• Cis versus Trans Relative Stability:

  • In disubstituted alkenes, trans isomers are uniformly more stable than their corresponding cis isomers.
  • Cause: Steric strain occurs in cis isomers due to non-bonding van der Waals repulsion between substituent electron clouds crowded onto the same side of the double bond. In trans isomers, substituents are oriented $180^\circ$ apart across the double bond, completely relieving steric interference.
  • Chemical Equilibrium Evidence: Acid-catalyzed equilibration of 2-butene produces a thermodynamic mixture consisting of $76\%$ trans-2-butene and $24\%$ cis-2-butene, demonstrating directly that the trans isomer is lower in free energy.

• Heats of Hydrogenation ($\Delta H^\circ_\text{hydrog}$):

  • Hydrogenation involves the catalytic addition of $H_2$ across a double bond to produce the corresponding saturated alkane:         $\text{Alkene} + H_2 \xrightarrow{\text{Pt or Pd}} \text{Alkane} + \text{Heat}$
  • Because the alkane hydrogenation products are identical for isomeric alkenes, measuring the enthalpy change ($\Delta H^\circ_\text{hydrog}$) allows direct determination of the relative thermodynamic ground-state energy levels.
  • Because the reaction is exothermic, a more stable alkene sits at a lower initial ground-state energy, and thus releases less heat (less negative $\Delta H^\circ_\text{hydrog}$).
  • A less stable alkene sits higher in potential energy, releasing more heat (more negative $\Delta H^\circ_\text{hydrog}$).

• Experimental Heats of Hydrogenation Data:

• General Stability Ranking Based on Substitution:$\text{Tetrasubstituted} > \text{Trisubstituted} > \text{Disubstituted} > \text{Monosubstituted} > \text{Ethylene}$

• Electronic Basis of Alkyl Stabilization (Hyperconjugation):

  • Hyperconjugation: A stabilizing electronic interaction involving the overlap of a filled $\sigma$ bond orbital (specifically an adjacent $C-H$ or $C-C$ bond orbital of an alkyl group) with an adjacent vacant antibonding $\pi^*$ molecular orbital of the double bond.
  • This electron donation from the neighboring $\sigma$ orbital delocalizes electron density into the $\pi$ framework, lowering the overall net energy of the molecule.
  • The greater the number of alkyl substituents attached to the double-bond carbons, the greater the opportunities for hyperconjugative orbital overlap, yielding increased thermodynamic stability.
  • Additionally, carbon atoms in double bonds are $sp^2$-hybridized and possess greater $s$-character ($33\%\,s$) than $sp^3$-hybridized carbons ($25\%\,s$). An $sp^3-sp^2$ carbon–carbon bond is shorter, stronger, and more thermodynamically favorable than an $sp^3-sp^3$ carbon–carbon single bond.

Electrophilic Addition Reactions of Alkenes

• General Reaction Nature:

  • Alkene reactivity is dominated by electrophilic additions.
  • The carbon–carbon double bond is electron-rich; its loosely held $\pi$ electrons reside above and below the molecular plane, rendering the double bond nucleophilic.
  • Consequently, alkenes react vigorously with strong electrophiles ($E^+$ or polarized reagents like $H-X$).

• Two-Step Mechanism of Hydrohalogenation ($HX$ Addition):

  • Step 1: Proton Transfer and Carbocation Formation (Rate-Determining Step):
    • The nucleophilic $\pi$ electrons attack the electrophilic proton ($H^+$) of the hydrogen halide ($H-X$).
    • A pair of electrons forms a new covalent $C-H$ $\sigma$ bond with one of the double-bond carbons.
    • Simultaneously, the two electrons in the $H-X$ covalent bond depart entirely onto the halogen atom, generating a free halide anion ($X^-$).
    • The other carbon atom of the original double bond is deprived of its electron pair, converting it into a trivalent carbocation intermediate possessing a positive formal charge and a vacant $2p$ orbital.
    • This step is slow and endergonic, possessing a high activation energy ($\Delta G^\ddagger_1$).
  • Step 2: Nucleophilic Attack of Halide Ion (Fast Step):
    • The nucleophilic halide ion ($:X^-$) rapidly donates an unshared electron pair into the vacant $2p$ orbital of the strongly electrophilic carbocation intermediate.
    • A new covalent $C-X$ $\sigma$ bond is formed, yielding the neutral alkyl halide addition product.
    • This step is fast and highly exergonic, characterized by a minimal activation barrier ($\Delta G^\ddagger_2$).

• Reagents for Alkene Electrophilic Additions:

  • $HCl$: Reacts readily in solvents such as diethyl ether.
  • $HBr$: Highly reactive, standard bench reagent for hydrohalogenations.
  • $HI$: Typically generated in situ using a mixture of potassium iodide ($KI$) and phosphoric acid ($H_3PO_4$):         $KI + H_3PO_4 \rightarrow HI + KH_2PO_4$
  • Water ($H_2O$): In the presence of an acid catalyst (e.g., $H_3O^+$ or dilute aqueous $H_2SO_4$), water adds electrophilically across alkenes to yield alcohols.

Orientation of Electrophilic Additions: Markovnikov’s Rule

• Regiospecificity:

  • Electrophilic additions to unsymmetrically substituted alkenes are regiospecific: when an unsymmetrical reagent adds to an unsymmetrical alkene, one constitutional isomer is formed exclusively or in heavy preference over the alternative regioisomer.

• Classical Markovnikov’s Rule (Empirical Formulation):

  • Formulated by Russian chemist Vladimir Markovnikov in 1869:
  • In the electrophilic addition of $HX$ to an unsymmetrical alkene, the hydrogen atom ($H$) bonds to the double-bond carbon possessing fewer alkyl substituents (more hydrogens), and the halogen atom ($X$) bonds to the double-bond carbon possessing more alkyl substituents (fewer hydrogens).

• Modern Markovnikov’s Rule (Mechanistic Formulation):

  • In the electrophilic addition of $HX$ to an alkene, the reaction proceeds through the pathway that forms the more highly substituted (more stable) carbocation intermediate rather than the less substituted one.
  • Protonation occurs at the less substituted carbon atom specifically because doing so places the resulting positive charge on the more substituted carbon atom.

• Illustrative Examples:

  • Addition of $HCl$ to 2-Methylpropene:
    • Protonation of the terminal $=CH_2$ carbon generates a stable tertiary ($3^\circ$) tert-butyl carbocation ($(CH_3)_3C^+$).
    • Alternative protonation of the internal carbon would generate an unstable primary ($1^\circ$) isobutyl carbocation ($(CH_3)_2CHCH_2^+$), which does not form.
    • Chloride attacks the tert-butyl carbocation, generating 2-chloro-2-methylpropane in $94\%$ yield as the sole product. 1-Chloro-2-methylpropane is not observed.
  • Addition of $HBr$ to 1-Methylcyclohexene:
    • Protonation directed to the C2 methine position ($-CH=$) produces a tertiary ($3^\circ$) carbocation at C1.
    • Protonation at C1 would yield a secondary ($2^\circ$) carbocation.
    • Bromide addition occurs exclusively at C1 to give 1-bromo-1-methylcyclohexane.
  • Non-Regiospecific Alkene Addition:
    • If both double-bond carbons share identical degrees of alkyl substitution, Markovnikov's rule cannot discriminate between the carbons.
    • For example, reaction of 2-pentene ($CH_3CH_2CH=CHCH_3$) with $HBr$: both C2 and C3 are disubstituted (each possesses one hydrogen and one alkyl chain). Protonation at either site generates a secondary ($2^\circ$) carbocation of comparable stability, yielding an equimolar mixture of 2-bromopentane and 3-bromopentane.

• Synthetic Planning / Retrosynthetic Analysis:

  • Target: Synthesize 1-iodo-1-ethylcyclohexane.
  • Analysis: Iodine is bonded to a tertiary ring carbon bearing an ethyl substituent.
  • Feasible Alkene Precursors: Using Markovnikov addition of $HI$ ($KI / H_3PO_4$):
    1. 1-Ethylcyclohexene: An endocyclic trisubstituted alkene where protonation at C2 produces the tertiary C1 carbocation.
    2. Ethylidenecyclohexane: An exocyclic alkene where protonation at the ethylidene carbon produces the tertiary C1 ring carbocation.

Carbocation Structure and Stability

• Geometric and Electronic Configuration:

  • Carbocations are trivalent carbon cations possessing six valence electrons ($C^+$).
  • The central positively charged carbon is $sp^2$-hybridized.
  • The three hybrid orbitals form a trigonal planar geometry with $120^\circ$ bond angles.
  • The remaining unhybridized $2p$ orbital extends perpendicularly above and below the trigonal plane and is completely vacant.

• Carbocation Stability Hierarchy:$\text{Tertiary } (3^\circ) > \text{Secondary } (2^\circ) > \text{Primary } (1^\circ) > \text{Methyl}$

• Thermodynamic Dissociation Enthalpies:

  • Heterolytic carbon–chlorine bond dissociation enthalpies in the gas phase ($R-Cl \rightarrow R^+ + Cl^-$) directly corroborate the stability ranking:
    • Methyl ($CH_3Cl$): Dissociation enthalpy $\approx 950\,\text{kJ/mol}$.
    • Primary ($CH_3CH_2Cl$): Dissociation enthalpy $\approx 810\,\text{kJ/mol}$.
    • Secondary ($(CH_3)_2CHCl$): Dissociation enthalpy $\approx 730\,\text{kJ/mol}$.
    • Tertiary ($(CH_3)_3CCl$): Dissociation enthalpy $\approx 660\,\text{kJ/mol}$ ($157\,\text{kcal/mol}$).
  • The significantly lower enthalpy required to dissociate a tertiary chloride shows that the tertiary carbocation is heavily stabilized relative to less substituted analogs.

• Factors Governing Carbocation Stabilization:

  • 1. Inductive Effects:
    • Alkyl groups are polarizable and electron-donating relative to hydrogen.
    • The positively charged carbon induces a shift in electron density from adjacent $\sigma$ bonds of alkyl substituents toward itself, dispersing the localized positive charge over a larger atomic volume.
  • 2. Hyperconjugation:
    • Stabilizing overlap takes place between the vacant $2p$ orbital of the positively charged carbon and neighboring filled $C-H$ (or $C-C$) $\sigma$ bonding orbitals.
    • Delocalization of electrons into the empty $p$ orbital disperses positive charge into the surrounding bonds.
    • A tertiary carbocation has nine available neighboring $C-H$ $\sigma$ bonds for hyperconjugative delocalization, secondary has six, primary has three, and methyl has zero.

The Hammond Postulate

• Conceptual Rationale:

  • According to transition state theory, reaction rates depend on activation energies ($\Delta G^\ddagger$) associated with transition states.
  • However, transition states represent transient energetic maxima with lifetimes on the order of femtoseconds ($10^{-15}\,\text{s}$); their structures cannot be isolated or directly analyzed experimentally.
  • The Hammond Postulate provides a direct relationship bridging observable thermodynamics and unobservable transition state geometries:
    • The structure of a transition state resembles the structure of the stable chemical species (reactant, intermediate, or product) to which it is closest in free energy.

• Application to Endergonic and Exergonic Reaction Steps:

  • Endergonic Step ($\Delta G^\circ > 0$):
    • The transition state is closer in free energy to the product (or reactive intermediate) of that step than to the starting reactant.
    • Conclusion: The transition state is late and structurally resembles the product/intermediate.
  • Exergonic Step ($\Delta G^\circ < 0$):
    • The transition state is closer in free energy to the starting material of that step.
    • Conclusion: The transition state is early and structurally resembles the reactant.

• Explaining Markovnikov’s Rule via the Hammond Postulate:

  • Step 1 of electrophilic addition (alkene protonation to yield a carbocation) is strongly endergonic.
  • By the Hammond Postulate, the transition state for this rate-limiting step strongly resembles the resulting carbocation intermediate in both structure and electronic distribution.
  • Consequently, factors that stabilize carbocations (hyperconjugation and inductive donation from alkyl groups) also directly stabilize the transition state leading to them.
  • Because a tertiary carbocation is significantly more stable than a primary or secondary carbocation, the transition state leading to the tertiary carbocation is much lower in free energy ($\Delta G^\ddagger_\text{tert} \ll \Delta G^\ddagger_\text{prim}$).
  • The lower activation energy causes the tertiary intermediate to form substantially faster, dictating the observed Markovnikov regioselectivity.

• Application to Step 2 of Hydrohalogenation:

  • Step 2 (combination of an electrophilic carbocation with a halide anion to yield the neutral haloalkane) is strongly exergonic.
  • According to the Hammond Postulate, the transition state of this second step must structurally resemble the reactant of that step—namely, the carbocation intermediate.
  • In this transition state, the carbon atom still retains considerable planar $sp^2$ character and positive charge, while the carbon–halogen bond has barely begun to form (extended, partial bond distance).

Carbocation Rearrangements in Electrophilic Additions

• Mechanism and Structural Driving Force:

  • When an electrophilic addition reaction generates a carbocation intermediate, structural rearrangements often occur prior to capture by a nucleophile.
  • Thermodynamic driving force: Conversion of an intrinsically less stable carbocation (e.g., secondary) into a thermodynamically more stable carbocation (e.g., tertiary) via intramolecular migration of a substituent with its bonding electron pair.

• Hydride Shifts (1,2-Hydride Shift):

  • A 1,2-hydride shift involves the migration of a hydrogen atom accompanied by its two bonding electrons (a hydride ion, $:H^-$) from an adjacent carbon atom to the positively charged carbon center.
  • Reaction Example (Addition of $HCl$ to 3-Methyl-1-butene):
    • Electrophilic protonation of 3-methyl-1-butene ($(CH_3)_2CHCH=CH_2$) places $H^+$ at the terminal carbon, producing a secondary ($2^\circ$) carbocation at C2:             $(CH_3)_2CH-\overset{+}{C}H-CH_3$
    • Direct nucleophilic attack by chloride yields the un-rearranged product, 2-chloro-3-methylbutane ($\approx 50\%$
    • Alternatively, a tertiary hydrogen at C3 shifts with its electron pair as a hydride ($:H^-$) to the C2 carbocation, generating an exceptionally stable tertiary ($3^\circ$) carbocation:             $(CH_3)_2\overset{+}{C}-CH_2-CH_3$
    • Capture of this tertiary intermediate by chloride yields the rearranged product, 2-chloro-2-methylbutane ($\approx 50\%$

• Alkyl Shifts (1,2-Methyl Shift):

  • When an unstable carbocation lacks a neighboring hydrogen atom on a highly substituted carbon, an alkyl group migrates with its bonding electron pair (e.g., a methide ion, $:CH_3^-$).
  • Reaction Example (Addition of $HCl$ to 3,3-Dimethyl-1-butene):
    • Initial protonation forms a secondary ($2^\circ$) carbocation at C2 adjacent to a quaternary carbon:             $(CH_3)_3C-\overset{+}{C}H-CH_3$
    • Because C3 bears no hydrogens, a methyl group undergoes a 1,2-methyl shift along with its electron pair, converting the secondary carbocation into a more stable tertiary ($3^\circ$) carbocation:             $(CH_3)_2\overset{+}{C}-CH(CH_3)-CH_3$
    • Chloride nucleophilic trapping yields both the unrearranged product, 3-chloro-2,2-dimethylbutane, and the predominant rearranged product, 2-chloro-2,3-dimethylbutane.

• Biological Hydride Shifts:

  • Carbocation rearrangements are fundamental in cellular biochemistry, particularly during the biosynthesis of cholesterol, steroid hormones, and cyclic terpenes.
  • During the cyclization of squalene epoxide to lanosterol (catalyzed by oxidosqualene cyclase), carbocation intermediates undergo a cascade of sequential 1,2-hydride and 1,2-methyl shifts across fused ring skeletons, transforming an initial tertiary carbocation into an isomeric tertiary carbocation before deprotonation.

• Ring-Expansion / Rearrangement Worked Example (Vinylcyclohexane + $HBr$):
  • Observation: Treatment of vinylcyclohexane with $HBr$ unexpectedly yields 1-bromo-1-ethylcyclohexane as the major addition product.
  • Step-by-Step Reaction Mechanism:
    • Step 1 (Electrophilic Addition): Nucleophilic attack of the exocyclic $\pi$ bond on the proton of $H-Br$ protonates the terminal vinyl carbon ($=CH_2$), producing an exocyclic secondary ($2^\circ$) carbocation:             $\text{Cyclohexyl}-\overset{+}{C}H-CH_3 + Br^-$
    • Step 2 (1,2-Hydride Shift): The adjacent ring carbon (C1 of the cyclohexane ring) is tertiary and bonded to a single hydrogen. A 1,2-hydride shift transfers this hydrogen with its electron pair from the ring carbon to the exocyclic carbocation carbon.
    • This relieves the positive charge from the side chain and establishes a significantly more stable tertiary ($3^\circ$) carbocation directly inside the cyclohexane ring at the C1 position:             $\text{1-Ethylcyclohexyl cation}$
    • Step 3 (Nucleophilic Attack): The bromide ion ($Br^-$) attacks the endocyclic tertiary carbocation center, completing the reaction to yield 1-bromo-1-ethylcyclohexane.