Chapter 4: The Study of Chemical Reactions – Mechanisms, Thermodynamics, and Kinetics

Chlorination of Methane

Overview of the Reaction

The chlorination of methane is a classic example of a free-radical substitution reaction, where a hydrogen atom in methane is replaced by a chlorine atom to form chloromethane and hydrogen chloride. This reaction is initiated by heat or light and proceeds via a chain mechanism.

• Substitution Reaction: One atom or group in a molecule is replaced by another atom or group.

• Initiation: Requires heat or light (especially blue light, which is absorbed by chlorine gas).

• Chain Reaction: Many product molecules are formed from the absorption of a single photon.

Equation:

$\ce{CH4 + Cl2 ->[\text{heat or light}] CH3Cl + HCl}$

The Free-Radical Chain Reaction

Mechanism Steps

The mechanism involves three fundamental steps:

• Chain Initiation: Generates free radical intermediates.

• Chain Propagation: Free radicals react with stable molecules to produce new free radicals and products.

• Chain Termination: Two free radicals combine to form a stable, non-radical product, ending the chain process.

Initiation Step: Formation of Chlorine Atom

• A chlorine molecule absorbs a photon ($h\nu$) and splits homolytically into two chlorine atoms (free radicals):

$\ce{Cl2 + h\nu -> 2Cl\cdot}$

• Free radicals are highly reactive species with unpaired electrons.

Propagation Steps: Formation of Products

• First Propagation: Chlorine radical abstracts a hydrogen atom from methane, forming HCl and a methyl radical.

$\ce{CH4 + Cl\cdot -> CH3\cdot + HCl}$

• Second Propagation: Methyl radical reacts with another chlorine molecule, forming chloromethane and regenerating a chlorine radical.

$\ce{CH3\cdot + Cl2 -> CH3Cl + Cl\cdot}$

• Overall: One hydrogen atom in methane is replaced by chlorine.

Termination Steps

Termination occurs when two free radicals combine, removing radicals from the reaction mixture and forming stable products.

• Examples:

• $\ce{Cl\cdot + Cl\cdot -> Cl2}$

• $\ce{CH3\cdot + Cl\cdot -> CH3Cl}$

• $\ce{CH3\cdot + CH3\cdot -> C2H6}$

• Radicals can also be terminated by colliding with the reaction vessel wall or contaminants.

Equilibrium and Thermodynamics

Equilibrium Constant ($K_{eq}$)

The equilibrium constant quantifies the ratio of products to reactants at equilibrium for a given reaction:

$aA + bB \rightleftharpoons cC + dD$

$K_{eq} = \frac{[C]^c[D]^d}{[A]^a[B]^b}$

• Large $K_{eq}$ means products are favored.

Example: $\ce{CH4 + Cl2 <=> CH3Cl + HCl}$, $K_{eq} = 1.1 \times 10^{19}$

Free Energy Change ($\Delta G$)

Free energy change determines the spontaneity of a reaction:

$\Delta G = \Delta H - T\Delta S$

• $\Delta H$ = enthalpy change (heat)

• $T$ = temperature (Kelvin)

• $\Delta S$ = entropy change (disorder)

Relationship to equilibrium:

$\Delta G^\circ = -RT \ln K_{eq}$

• Negative $\Delta G$ indicates a spontaneous reaction.

Enthalpy ($\Delta H$)

• Exothermic: $\Delta H < 0$ (heat released)

• Endothermic: $\Delta H > 0$ (heat absorbed)

• Reactions favor products with lower enthalpy (stronger bonds).

Entropy ($\Delta S$)

• Measures randomness or disorder.

• Increases with heat, volume, or number of particles.

• Spontaneous reactions maximize disorder and minimize enthalpy.

Bond-Dissociation Enthalpies (BDE)

BDE is the energy required to break a bond homolytically:

• Bond breaking: $+\text{BDE}$ (energy absorbed)

• Bond formation: $-\text{BDE}$ (energy released)

BDE can be used to estimate $\Delta H$ for a reaction:

$\Delta H = \sum \text{BDE}_{\text{bonds broken}} - \sum \text{BDE}_{\text{bonds formed}}$

Reaction Mechanisms and Kinetics

Homolytic vs. Heterolytic Cleavage

• Homolytic cleavage: Each atom gets one electron (forms radicals).

• Heterolytic cleavage: One atom gets both electrons (forms ions).

Kinetics and Rate Laws

• Kinetics studies the rate at which reactions occur.

• Rate law: $\text{rate} = k[A]^a[B]^b$

• Order of reaction is determined experimentally and reflects the number of molecules involved in the rate-determining step.

Activation Energy ($E_a$)

• The minimum energy required for a reaction to occur.

• Arrhenius equation: $k = Ae^{-E_a/RT}$

• Lower $E_a$ means a faster reaction; higher temperature increases rate.

Energy Diagrams

• Show the energy changes during a reaction.

• Transition state: highest energy point.

• Intermediates: local minima between transition states.

• Rate-limiting step: step with the highest $E_a$.

Reactivity and Selectivity in Halogenation

Primary, Secondary, and Tertiary Hydrogens

• Hydrogens attached to different types of carbons (1°, 2°, 3°) have different reactivities toward halogenation.

• Tertiary hydrogens are most reactive, followed by secondary, then primary.

Chlorination and Bromination of Alkanes

• Chlorination is less selective but faster; bromination is more selective but slower.

• Product distribution depends on both the number of hydrogens and their reactivity.

Example Table: Relative Reactivity of Hydrogens in Propane

Hydrogen Type	Number in Propane	Relative Reactivity (Cl)	Product Distribution (%)
Primary (1°)	6	1.0	40%
Secondary (2°)	2	4.5	60%

Additional info: The 2° hydrogens are 4.5 times as reactive as the 1° hydrogens.

Bond Dissociation Energies for Free Radical Formation

Radical Type	Bond Dissociation Enthalpy (kJ/mol)	BDE (kcal/mol)
Methyl	439	105
Primary	423	101
Secondary	413	99
Tertiary	403	96

Additional info: Tertiary free radicals form more readily than secondary, which form more readily than primary.

Stability of Free Radicals

• Order of stability: methyl < primary < secondary < tertiary

• Highly substituted radicals are more stable due to hyperconjugation and inductive effects.

Hammond Postulate

• Transition state structure resembles the species (reactant or product) to which it is closer in energy.

• Endothermic reaction: transition state resembles the product.

• Exothermic reaction: transition state resembles the reactant.

Reactive Intermediates

Carbocations

• Positively charged carbon species (e.g., $\ce{CH3^+}$).

• sp2 hybridized, planar structure, vacant p orbital.

• Stability: tertiary > secondary > primary > methyl.

• Stabilized by resonance if adjacent to a double bond.

Free Radicals

• sp2 hybridized carbon with one unpaired electron in a p orbital.

• Stability order: tertiary > secondary > primary > methyl.

• Resonance stabilization possible if adjacent to a double bond.

Carbanions

• Negatively charged carbon species with a lone pair.

• sp3 hybridized, tetrahedral geometry.

• Stability: methyl > primary > secondary > tertiary (opposite of carbocations/radicals).

• Very strong bases and nucleophiles.

Carbenes

• Neutral carbon species with two nonbonded electrons (one lone pair, one vacant p orbital).

• sp2 hybridized, can act as both electrophile and nucleophile.

• Commonly generated from diazomethane or by reaction of haloforms with base.

• React with alkenes to form cyclopropanes.

Practice Problems and Applications

• Identify products and mechanisms for free radical halogenation reactions.

• Calculate $\Delta G^\circ$ from equilibrium data or vice versa.

• Predict major products based on radical stability and hydrogen reactivity.

• Draw and interpret reaction energy diagrams, identifying transition states, intermediates, and rate-limiting steps.

Summary Table: Key Concepts

Concept	Definition/Key Point
Initiation	Formation of radicals (usually by homolytic cleavage)
Propagation	Radicals react to form products and new radicals
Termination	Two radicals combine to form a stable molecule
Activation Energy ($E_a$)	Minimum energy required for reaction
Enthalpy ($\Delta H$)	Heat change at constant pressure
Entropy ($\Delta S$)	Change in disorder/randomness
Free Energy ($\Delta G$)	Determines spontaneity of reaction
Radical Stability	Tertiary > Secondary > Primary > Methyl