Thermodynamics, Kinetics, and Radical Halogenation of Organo Halides

Bond Dissociation Energy and Reaction Thermodynamics

• The study of reaction energy often begins with the assumption that the free energy change ($\Delta G$) is approximately equal to the enthalpy change ($\Delta H$), which can be calculated using experimental data.

• Bond Dissociation Energy (BDE): This is defined as the energy required to break a specific chemical bond homolytically to form radicals.

• Reaction Enthalpy Calculation:

  • To calculate $\Delta H$ for a reaction like $AB + CD \rightarrow AC + BD$:

  • First, break the reactant bonds ($A-B$ and $C-D$). This requires an input of energy (positive BDE values).

  • Second, form the product bonds ($A-C$ and $B-D$). Bond formation releases energy, represented as the negative value of the respective BDEs.

  • The total energy change is the sum of the energy put in to break bonds and the energy released by forming bonds.

• Exergonic vs. Endergonic:

  • If more energy is released by forming bonds than is consumed by breaking them, the reaction is exergonic (\Delta G < 0) and product-favored.

  • If more energy is required to break bonds than is released by forming them, the reaction is endergonic (\Delta G > 0) and reactant-favored.

• Benzene Chlorination Example:

  • Reactants: Benzene and Chlorine ($Cl_2$).

  • Products: Chlorobenzene and $HCl$.

  • Bond Energies provided in transcript: $438$, $589$, $234$, and $298$.

  • Result: $\Delta H = +57$.

  • Conclusion: Because the value is positive (\Delta H > 0), the reaction is reactant-favorable and will not proceed spontaneously in the indicated direction without assistance.

Reaction Kinetics and Energy Profiles

• Thermodynamics vs. Kinetics: Thermodynamics tells us if a reaction is feasible (product-favored), but it does not dictate how fast the reaction will occur. For example, the chlorination of benzene is thermodynamically feasible but extremely slow without a catalyst.

• Transition State ($\ddagger$):

  • The maximum energy point on a reaction coordinate diagram.

  • It represents a structure where bonds are in the process of breaking or forming (or both).

  • Transition states are fleeting and cannot be isolated.

  • It is denoted with a double dagger symbol ($\ddagger$) and often enclosed in square brackets.

• Activation Energy ($E_a$):

  • The minimum energy required to reach the transition state from the reactants.

  • The transcript notes: "The higher the activation energy, the faster the rate," though it immediately clarifies with visual aids that a smaller activation energy leads to a faster reaction, while a larger activation energy leads to a slower reaction.

• Multistep Reactions:

  • Reactions involving multiple steps have multiple transition states and intermediates (energy minima between peaks).

  • Rate-Limiting Step: The slowest step in a sequence, which determines the overall rate of the reaction. It is characterized by having the largest activation energy hump.

• Example: Alkene Reaction with $HBr$:

  • Step one: Alkene reacts with the hydrogen of $HBr$ to form a carbocation intermediate. This is the rate-limiting step with a large $E_a$.

  • Step two: Bromide ($Br^-$) attacks the positive carbon to form the product. This step has a much smaller $E_a$ and is fast due to the strong attraction between opposite full charges.

Properties of Organo Halides

• Bond Lengths: As you move down the halogen group (Fluorine to Iodine), the size of the halogen atom increases, leading to longer carbon-halogen ($C-X$) bonds.

  • Order from shortest to longest: C-F < C-Cl < C-Br < C-I.

• Bond Strengths: Bond strength is inversely proportional to length.

  • $C-F$ is the strongest bond and very stable.

  • $C-I$ is the longest and weakest bond.

• Reactivity: Due to the strength of the $C-F$ bond, organofluorines are relatively unreactive. Most organic reactions focus on the more reactive $C-Cl$, $C-Br$, and $C-I$ bonds.

Radical Monochlorination and Isomer Yields

• Constitutional Isomers: When chlorinating a hydrocarbon, multiple isomers can form depending on which hydrogen is replaced. For example, propane yields two isomers, while more complex rings or chains can yield many more.

• Relative Reactivity Rates: Different types of hydrogens react at different rates during radical chlorination:

  • Primary ($1^\circ$): $1.0$ (baseline).

  • Secondary ($2^\circ$): $3.5$.

  • Tertiary ($3^\circ$): $5.0$.

• Calculating Product Yields:

  • To predict the major product, multiply the number of equivalent hydrogens of a certain type by their relative reactivity rate.

  • Example: Butane monochlorination:

  • $6$ primary hydrogens: $6 \times 1.0 = 6.0$.

  • $4$ secondary hydrogens: $4 \times 3.5 = 14.0$.

  • The secondary product (2-chlorobutane) is the major product because 14.0 > 6.0.

• The Carbon Radical Intermediate: The reactivity order (3^\circ > 2^\circ > 1^\circ) is explained by the stability of the resulting radical.

  • Tertiary radicals are the most stable and have the lowest activation energy for formation.

  • Carbon radicals are planar structures ($sp^2$ hybridized) with the single electron residing in an unhybridized $p$ orbital.

Stereochemistry in Radical Reactions

• When calculating the total number of products, one must account for stereoisomers (enantiomers and diastereomers).

• Chiral Centers: If chlorination creates a chiral center, a racemic mixture of two enantiomers ($R$ and $S$) will be formed.

• Example: Butane monochlorination:

  • 1-chlorobutane: Achiral (1 product).

  • 2-chlorobutane: Contains a chiral center, resulting in two enantiomers (2 products).

  • Total products including stereoisomers: $3$.

Allylic Bromination

• Allylic Carbon: The carbon atom directly attached to a carbon-carbon double bond (e.g., in propene, the methyl carbon is allylic).

• Allylic Hydrogen: A hydrogen atom attached to an allylic carbon.

• Reagents: Typically uses Bromine ($Br_2$) in the presence of UV light or $N$-Bromosuccinimide (NBS).

• Mechanism:

  • Initiation: Homolytic cleavage of $Br-Br$ into Bromine radicals.

  • Propagation: The Bromine radical abstracts an allylic hydrogen to form an allylic radical.

  • Resonance Stabilization: The allylic radical is resonance-stabilized (the unpaired electron is delocalized across the pi-system).

• Bond Dissociation Energies: Allylic bonds are significantly weaker than alkyl or vinylic ($C=C-H$) bonds because the resulting radical is stabilized by resonance.

• Product Formation: Because of resonance, the Bromine can attack at different positions within the radical system, potentially leading to multiple constitutional isomers in non-symmetrical alkenes.