Chapter 4 Thermodynamics and Kinetics in Organic Chemistry: Radical Reactions, Equilibrium, and Reaction Rates

Radical Chain Reactions

Steps or Phases of a Radical Chain Reaction

Radical chain reactions are a fundamental class of organic reactions, often involved in halogenation and combustion processes. These reactions proceed through three main phases:

• Initiation: The process that generates two radicals from a non-radical species, typically via homolytic bond cleavage. For example, the splitting of a chlorine molecule (Cl2) into two chlorine radicals.

• Propagation: Steps where a radical reacts with a stable molecule to produce a new radical and a new product. This phase sustains the chain reaction.

• Termination: Two radicals combine to form a stable molecule, thus ending the chain reaction.

Example: Chlorination of methane proceeds via radical chain mechanism.

Additional info: Radical reactions are important in polymerization and atmospheric chemistry.

Thermodynamics of Chemical Reactions

Equilibrium and the Equilibrium Constant (Keq)

Chemical equilibrium is the state where the concentrations of reactants and products remain constant over time. The equilibrium constant quantifies the ratio of products to reactants at equilibrium.

• General Reaction: $aA + bB \rightleftharpoons cC + dD$

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

• "Products over reactants" is a common mnemonic for the equilibrium expression.

• If $K_{eq} \gg 1$, the reaction favors products and is said to go to completion.

Example: If $[CH_4] \gg [CO_2]$, the reaction has gone to completion.

Gibbs Free Energy (ΔG) and Reaction Favorability

The change in Gibbs free energy determines whether a reaction is thermodynamically favorable.

• Relationship to Equilibrium: $\Delta G = -RT \ln K_{eq}$

• Interpretation: If $\Delta G < 0$, the reaction is spontaneous (favorable).

• Standard Free Energy Change: $\Delta G^\circ = \Delta G_{products} - \Delta G_{reactants}$

• Temperature and Pressure: Standard conditions are 25°C and 1 atm.

Example: A negative $\Delta G$ indicates a reaction will proceed spontaneously.

Enthalpy (ΔH) and Entropy (ΔS)

Gibbs free energy is determined by both enthalpy and entropy changes:

• Equation: $\Delta G = \Delta H - T\Delta S$

• Enthalpy (ΔH): Heat evolved or consumed during a reaction. $\Delta H = H_{products} - H_{reactants}$

• Entropy (ΔS): Measure of disorder or randomness. $\Delta S = S_{products} - S_{reactants}$

• Favorability: $\Delta S > 0$ is favorable; reactions that increase disorder are favored.

Example: Cracking of hydrocarbons increases entropy.

Additional info: At room temperature, the entropy term is often smaller than the enthalpy term and may be neglected in introductory calculations.

Bond Dissociation Enthalpy (BDE) and Homolytic vs. Heterolytic Cleavage

BDE is the energy required to break a bond homolytically, forming two radicals. It is used to estimate reaction enthalpy.

• Homolytic Cleavage: Each atom takes one electron, forming radicals.

• Heterolytic Cleavage: One atom takes both electrons, forming ions; depends on solvation for charge stabilization.

• Estimating ΔH: $\Delta H_{rxn} = \text{Bonds broken} - \text{Bonds formed}$

Example: Breaking a C-H bond ($\Delta H = 57$ kcal/mol) and forming an O-H bond ($\Delta H = 105$ kcal/mol).

Additional info: BDE values are tabulated and used for quick estimation of reaction energetics.

Kinetics: Reaction Rates and Rate Laws

Reaction Rate and Rate Law

Kinetics studies how fast reactions occur and what factors influence their rates.

• Rate Law: $\text{Rate} = k [A]^x [B]^y$

• Rate Constant (k): Unique to each reaction, depends on temperature.

• Reaction Order: The exponents x and y are determined experimentally and indicate the dependence of rate on reactant concentrations.

• First Order: Rate depends linearly on one reactant.

• Second Order: Rate depends on two reactants or the square of one.

• Overall Order: Sum of individual orders.

Example: For $CH_3Br + NaOH \rightarrow CH_3OH + NaBr$, rate law is $\text{Rate} = k [CH_3Br][NaOH]$ (second order overall).

Arrhenius Equation and Activation Energy

The Arrhenius equation relates the rate constant to temperature and activation energy:

• Equation: $k = A e^{-E_a/(RT)}$

• Activation Energy (Ea): Minimum energy required for a reaction to occur.

• Frequency Factor (A): Represents the frequency of correctly oriented collisions.

• Temperature (T): Higher temperature increases the fraction of molecules with sufficient energy.

Example: Increasing temperature from 300 K to 373 K increases reaction rate.

Additional info: The fraction of molecules with energy greater than $E_a$ determines the rate.

Reaction Coordinate and Intermediates

The reaction coordinate diagram illustrates the energy changes during a reaction.

• Intermediate: A local minimum on the reaction coordinate; may have a lifetime from nanoseconds to years.

• Transition State: Highest energy point; determines activation energy.

Example: Carbocation intermediates in SN1 reactions.

Bond Dissociation Enthalpy Table

BDE values are used to estimate reaction enthalpy. Below is a sample table:

Bond	BDE (kcal/mol)
C-H	57
O-H	105
O-O	84
C-C	83
H-F	136
H-Cl	103
H-Br	87
H-I	71
Additional info: Values inferred from standard tables.

Summary Table: Thermodynamics vs. Kinetics

Aspect	Thermodynamics	Kinetics
Definition	Study of energy changes and equilibrium	Study of reaction rates
Key Parameter	ΔG, ΔH, ΔS, Keq	Rate constant (k), Activation energy (Ea)
Determines	If reaction is favorable	How fast reaction occurs
Example	Combustion of glucose	SN2 reaction rate

Key Takeaways

• Radical chain reactions proceed via initiation, propagation, and termination.

• Thermodynamics determines if a reaction is favorable; kinetics determines how fast it occurs.

• Equilibrium constant ($K_{eq}$) and Gibbs free energy ($\Delta G$) are central to understanding reaction spontaneity.

• Bond dissociation enthalpy (BDE) is used to estimate reaction enthalpy.

• Rate laws and the Arrhenius equation describe how concentration and temperature affect reaction rates.

• Intermediates and transition states are key concepts in reaction mechanisms.