Chapter 4: The Study of Chemical Reactions

Overview

This chapter explores the fundamental principles underlying organic chemical reactions, focusing on free-radical halogenation of alkanes, thermodynamics, kinetics, activation energy, transition states, and the stability of free radicals. Understanding these concepts is essential for predicting reaction outcomes and mechanisms in organic chemistry.

Free-Radical Halogenation of Alkanes

Reaction Mechanism

Free-radical halogenation is a chain reaction in which a halogen atom replaces a hydrogen atom in an alkane. The process is initiated by heat or light (often blue light, ), which provides the energy required to break the halogen bond and generate radicals.

• Mechanism: A step-by-step description of which bonds break and form, and in what order, to give the observed products.

• Radical (Free Radical): A species with unpaired electrons, highly reactive.

The mechanism is divided into three major steps:

1. Initiation: Generation of radicals, usually by homolytic cleavage of a halogen molecule (e.g., ).

2. Propagation: Radicals react with alkanes to form new radicals and products (e.g., ).

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

Example: Chlorination of methane:

• Initiation:

• Propagation:

• Termination:

Similar mechanisms apply to other alkanes and halogens (e.g., bromination of cyclohexane).

Review of Thermodynamics

Thermodynamics examines the energy changes that accompany chemical and physical transformations. It helps predict whether a reaction is energetically favorable and the position of equilibrium.

• Equilibrium Constant ():

• Change in Free Energy (): (free energy of products) (free energy of reactants)

• If , the reaction favors products; if , the reaction favors reactants.

• If , the reaction is energetically favored; if , it is not favored.

The relationship between and :

Two factors contribute to :

• Enthalpy (): Heat evolved or consumed. Exothermic (), endothermic ().

• Entropy (): Measure of disorder or number of microstates.

In most organic reactions, is small, so .

Bond Dissociation Enthalpy

Bond dissociation energy (BDE) is the amount of energy required to break a bond homolytically (each atom retains one electron).

• Homolytic cleavage:

• Heterolytic cleavage: (varies with solvent)

• Energy is released when bonds are formed and consumed when bonds are broken.

The overall enthalpy change for a reaction:

Example: Chlorination of methane:

• Using values: kJ/mol (exothermic)

Review of Kinetics and Rate Equation

Kinetics is the study of reaction rates, which depend on the concentrations of reactants. The rate law shows the relationship between reactant concentrations and the observed rate.

• General form:

• and are the orders with respect to A and B; is the rate constant.

• The overall order is .

• Orders must be determined experimentally, not from stoichiometry.

Examples:

• (first order in each reactant, second order overall)

• (first order overall)

Activation Energy and Transition State

Activation energy () is the minimum kinetic energy required for molecules to react, overcoming electron cloud repulsions. The transition state is the highest-energy state along the reaction path.

• Transition State: Cannot be isolated; represents the point of maximum energy.

• Exothermic Reaction: Transition state is closer in energy and structure to reactants.

• Endothermic Reaction: Transition state is closer in energy and structure to products.

• Catalyst: Lowers and stabilizes the transition state, increasing reaction rate without affecting or .

Equations:

• Energy diagram: Reactants (transition state) Products

Multistep Reactions: Intermediates and Rate-Determining Step

Many reactions proceed via multiple steps, each with its own transition state and intermediate. The slowest step is the rate-determining step.

• Intermediate: Species that exists for a finite time between steps; not present in the final product mixture.

• The highest point on the energy diagram is the transition state for the rate-determining step.

Example: Two-step halogenation of methane, with energy diagram showing two transition states and an intermediate.

Stability of Free Radicals

The stability of free radicals increases with the degree of substitution at the radical center:

• Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl

Explanation: More substituted radicals require less energy to form (lower bond dissociation enthalpy), making them more stable.

• Methyl radical: kJ/mol

• Primary radical: kJ/mol

• Secondary radical: kJ/mol

• Tertiary radical: kJ/mol

Therefore: The more substituted the radical, the more stable it is.

Predicting Product Ratio and Major Product in Free-Radical Halogenation

In halogenation of alkanes, the type and number of hydrogens determine the product distribution. For methane and ethane, all hydrogens are equivalent, so only one mono-halogenated product forms.

• General mechanism for free-radical halogenation:

  • Initiation:

  • Propagation:

• For higher alkanes, the ratio of products depends on the number and reactivity of different types of hydrogens (primary, secondary, tertiary).

Summary Table: Stability of Free Radicals

Key Equations and Relationships

• Rate law:

Additional info:

• Transition state theory and the Hammond postulate are important for understanding the structure and energy of transition states in organic reactions.

• Reactive intermediates such as carbocations, carbanions, and carbenes are also important in other types of organic reactions (not detailed here).