Study Notes: Chemical Reactions and Thermodynamics in Organic Chemistry

Chapter 4: The Study of Chemical Reactions

Introduction to Chemical Reactions

Chemical reactions involve the transformation of reactants into products. Understanding these processes requires knowledge of thermodynamics, kinetics, and mechanisms.

• Thermodynamics: Studies the energy changes accompanying chemical and physical transformations.

• Kinetics: Examines the rates at which reactions occur.

• Mechanism: Describes the step-by-step process by which reactants are converted to products.

Chlorination of Methane

Overview of the Reaction

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

• $\ce{CH4 + Cl2 \xrightarrow{\text{heat or light}} CH3Cl + HCl}$

• Requires heat or light for initiation; most effective wavelength is blue, absorbed by chlorine gas.

• Many molecules of product are formed from absorption of only one photon of light.

The Free-Radical Chain Reaction

Steps in the Chain Reaction

Free-radical chain reactions proceed through three main steps:

• Initiation: Generates a radical intermediate.

• Propagation: The intermediate reacts with a stable molecule to produce another reactive intermediate and a product molecule.

• Termination: Side reactions that destroy the reactive intermediate.

Initiation Step: Formation of Chlorine Atom

Chlorine molecules absorb energy (photon) and split homolytically into chlorine atoms (free radicals):

• $\ce{Cl2 + h\nu \rightarrow Cl^{\cdot} + Cl^{\cdot}}$

• Each chlorine atom has an unpaired electron, making it highly reactive.

Lewis Structures of Free Radicals

Free radicals are species with odd numbers of electrons. Halogens have seven valence electrons; one will be unpaired in the radical form.

• Examples:

• Chlorine atom: $\ce{Cl^{\cdot}}$

• Hydroxyl radical: $\ce{HO^{\cdot}}$

• Methyl radical: $\ce{CH3^{\cdot}}$

Propagation Steps

Propagation involves two main steps:

• Step 1: Chlorine atom abstracts a hydrogen from methane, forming methyl radical and HCl:

• $\ce{Cl^{\cdot} + CH4 \rightarrow CH3^{\cdot} + HCl}$

• Step 2: Methyl radical reacts with another chlorine molecule to form methyl chloride and regenerate a chlorine atom:

• $\ce{CH3^{\cdot} + Cl2 \rightarrow CH3Cl + Cl^{\cdot}}$

Overall Reaction

The overall process combines the propagation steps:

• $\ce{CH4 + Cl2 \rightarrow CH3Cl + HCl}$

Termination Steps

Termination occurs when two free radicals combine, removing them from the reaction cycle:

• $\ce{CH3^{\cdot} + Cl^{\cdot} \rightarrow CH3Cl}$

• Radicals may also collide with contaminants or the reaction vessel wall, ending the chain.

Thermodynamics of Chemical Reactions

Equilibrium Constant ($K_{eq}$)

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

• General form: $\ce{aA + bB <=> cC + dD}$

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

• For chlorination: $K_{eq} = \frac{[CH3Cl][HCl]}{[CH4][Cl2]} = 1.1 \times 10^{19}$

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

Free energy change determines reaction spontaneity:

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

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

Free energy change depends on:

• Enthalpy ($\Delta H^\circ$): $\Delta H^\circ = \text{enthalpy of products} - \text{enthalpy of reactants}$

• Entropy ($\Delta S^\circ$): $\Delta S^\circ = \text{entropy of products} - \text{entropy of reactants}$

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

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

This table shows how the value of $\Delta G^\circ$ affects the percentage of products formed at equilibrium.

$\Delta G^\circ$ (kJ/mol)	% Product at Equilibrium
0	50%
-5	99%
-10	99.99%
-15	99.9999%
-20	99.99999%

Enthalpy ($\Delta H^\circ$)

Enthalpy change reflects heat released or absorbed during a reaction:

• Exothermic ($-\Delta H^\circ$): Heat is released.

• Endothermic ($+\Delta H^\circ$): Heat is absorbed.

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

Entropy ($\Delta S^\circ$)

Entropy measures randomness, disorder, or freedom of movement:

• Increasing 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 value is often small.

Solved Problem 1: Calculating $\Delta G^\circ$

Example calculation for the chlorination of methane:

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

• Given $K_{eq} = 1.1 \times 10^{19}$, $R = 8.314$ J/K·mol, $T = 298$ K

• Calculation yields $\Delta G^\circ = -109$ kJ/mol

• This large negative value shows the reaction is highly favorable.

Bond-Dissociation Enthalpies (BDE)

Definition and Application

BDE is the energy required to break a bond in a molecule:

• Bond dissociation requires energy (+BDE); bond formation releases energy (-BDE).

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

• BDE for homolytic cleavage of bonds in a gaseous molecule.

Homolytic and Heterolytic Cleavages

• Homolytic cleavage: Each atom gets one electron; free radicals result.

• $\ce{A-B \rightarrow A^{\cdot} + B^{\cdot}}$

• Heterolytic cleavage: Most electronegative atom gets both electrons; ions result.

• $\ce{(CH3)2C-Cl \rightarrow (CH3)2C^+ + Cl^-}$

Enthalpy Changes in Chlorination

Calculation of enthalpy change for the overall reaction:

• Bond dissociation: $\ce{CH4 + Cl2 \rightarrow CH3Cl + HCl}$

• Sum of bond dissociation enthalpies for bonds broken and formed:

• Bonds broken: $\ce{CH-H}$ (435 kJ/mol), $\ce{Cl-Cl}$ (243 kJ/mol)

• Bonds formed: $\ce{CH3-Cl}$ (352 kJ/mol), $\ce{H-Cl}$ (428 kJ/mol)

• Total $\Delta H^\circ = 678 - 780 = -102$ kJ/mol

Additional info: These notes cover foundational concepts in chemical thermodynamics and kinetics, with a focus on free-radical mechanisms and energy changes in organic reactions, suitable for General Chemistry and introductory Organic Chemistry students.