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

Introduction to Chemical Reactions

Overview of Reaction Analysis

Chemical reactions in organic chemistry are analyzed by considering the transformation of reactants into products. To fully understand a reaction, chemists study both the energy changes (thermodynamics) and the rates at which reactions occur (kinetics). The mechanism describes the step-by-step process by which reactants are converted to products.

• Thermodynamics: Study of energy changes during chemical and physical transformations.

• Kinetics: Study of reaction rates and factors affecting them.

• Mechanism: Detailed sequence of steps describing how a reaction proceeds.

Chlorination of Methane: A Case Study

Reaction and Initiation

The chlorination of methane is a classic example of a free-radical chain reaction. The overall reaction is:

$\ce{CH4 + Cl2 -> CH3Cl + HCl}$

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

• One photon can initiate a chain reaction, producing many product molecules.

Mechanism: Free-Radical Chain Reaction

• Initiation: Generates a radical intermediate (e.g., splitting Cl2 into two Cl radicals).

• Propagation: Radical reacts with a stable molecule to produce another radical and a product.

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

Initiation Step Example

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

Chlorine molecule splits homolytically into two chlorine atoms (free radicals).

Lewis Structures of Free Radicals

• Free radicals are species with an odd number of electrons.

• Halogen atoms (e.g., Cl, Br) have seven valence electrons, one of which is unpaired in the radical.

Propagation Steps

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

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

The chlorine radical abstracts a hydrogen from methane, forming a methyl radical and HCl. The methyl radical then reacts with Cl2 to regenerate the chlorine radical and produce methyl chloride.

Termination Steps

• Any two radicals combine to form a non-radical product (e.g., $\ce{CH3\cdot + Cl\cdot -> CH3Cl}$).

• Radicals can also be removed by collision with contaminants or the reaction vessel wall.

Thermodynamics of Reactions

Equilibrium Constant ($K_{eq}$)

The equilibrium constant expresses the ratio of product to reactant concentrations at equilibrium:

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

For methane chlorination:

$K_{eq} = \frac{[CH_3Cl][HCl]}{[CH_4][Cl_2]} = 1.1 \times 10^{19}$

Free Energy Change ($\Delta G^\circ$)

• $\Delta G^\circ =$ (energy of products) $-$ (energy of reactants)

• Negative $\Delta G^\circ$ indicates a spontaneous, favorable reaction.

• $\Delta G^\circ = -RT \ln K_{eq} = -2.303RT \log_{10} K_{eq}$

• Where $R = 8.314$ J/K·mol and $T$ is temperature in kelvins.

Factors Determining $\Delta G^\circ$

• $\Delta H^\circ$ (enthalpy change): Heat released or absorbed.

• $\Delta S^\circ$ (entropy change): Change in disorder or randomness.

• $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$

Enthalpy ($\Delta H^\circ$)

• Exothermic ($-\Delta H$): Heat released; products have lower enthalpy.

• Endothermic ($+\Delta H$): Heat absorbed; products have higher enthalpy.

• Reactions favor products with the lowest enthalpy (strongest bonds).

Entropy ($\Delta S^\circ$)

• Increase in heat, volume, or number of particles increases entropy.

• Spontaneous reactions maximize disorder and minimize enthalpy.

• In $\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ$, the entropy term is often small.

Bond-Dissociation Enthalpies (BDE)

• Energy required to break a bond homolytically (+BDE).

• Energy released when a bond forms (–BDE).

• BDEs are used to estimate $\Delta H$ for reactions.

• Homolytic cleavage: Each atom gets one electron.

• Heterolytic cleavage: More electronegative atom gets both electrons.

Kinetics of Organic Reactions

Reaction Rate and Rate Law

• Rate: Change in concentration of products or reactants over time.

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

• $k$ = rate constant; $a$, $b$ = reaction orders (determined experimentally).

• Overall order = $a + b$.

Activation Energy ($E_a$)

• Minimum kinetic energy required for reaction.

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

• Higher $E_a$ means slower reaction; higher temperature increases rate.

Energy Diagrams

• Vertical axis: Potential energy.

• Transition state (‡): Highest energy point; $E_a$ is the energy difference between reactants and transition state.

• Multistep reactions: Highest $E_a$ step is rate-limiting.

Mechanistic Details and Selectivity

Primary, Secondary, and Tertiary Hydrogens

• Hydrogens are classified by the type of carbon they are attached to (1°, 2°, 3°).

• Tertiary hydrogens react faster with Cl• than primary hydrogens due to more stable radical intermediates.

Stability of Free Radicals

• Order of stability: methyl < 1° < 2° < 3°

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

Hammond Postulate

• Transition state structure resembles the closest stable species in energy.

• Endothermic reactions: TS resembles product.

• Exothermic reactions: TS resembles reactant.

Tables

Product Composition as a Function of $\Delta G^\circ$ at 25°C

$\Delta G^\circ$ (kJ/mol)	$\Delta G^\circ$ (kcal/mol)	$K$	Conversion to Products (%)
+4.0	(+1.0)	0.20	17%
+2.0	(+0.5)	0.37	27%
0.0	(0.0)	1.0	50%
-2.0	(-0.5)	5.0	83%
-4.0	(-1.0)	25	96%
-6.0	(-1.5)	130	99%
-8.0	(-1.9)	700	99.9%
-12.0	(-2.9)	3,300	99.97%
-20.0	(-4.8)	320,000	99.999%

Bond Dissociation Energies for Homolytic Cleavage (Selected)

Bond	D (kJ/mol)	D (kcal/mol)
H–H	436	104
Cl–Cl	242	58
CH3–H	439	105
CH3–CH2	423	101
CH3–CH	413	99
(CH3)3C–H	403	96

Summary

• Organic reactions are governed by both thermodynamic and kinetic factors.

• Free-radical mechanisms involve initiation, propagation, and termination steps.

• Stability of intermediates (radicals, carbocations) influences reaction rates and selectivity.

• Energy diagrams and the Hammond postulate help visualize and predict reaction pathways.