Bond Strengths, Thermodynamics, and Free Radical Reactions in General Chemistry

Bond Strengths and Energetics

Bond Strengths

Bond strength refers to the amount of energy required to break a chemical bond. In general, longer bonds are weaker and easier to break, while shorter bonds are stronger and more stable.

• Bond Dissociation Energy (BDE): The energy required to break a specific bond in a molecule in the gas phase, producing radicals.

• Trends: As atomic size increases (down a group), bond strength generally decreases (except for F2).

• Example: The H–H bond has a BDE of 104 kcal/mol, while the I–I bond has a BDE of 36 kcal/mol.

Enthalpy and Entropy

Enthalpy (ΔH) and entropy (ΔS) are key thermodynamic quantities that determine the favorability of chemical reactions.

• ΔH (Enthalpy Change): The heat absorbed or released during a reaction. Negative ΔH indicates an exothermic reaction (releases heat), while positive ΔH indicates an endothermic reaction (absorbs heat).

• ΔS (Entropy Change): The change in disorder or randomness. Positive ΔS means increased disorder; negative ΔS means decreased disorder.

• Gibbs Free Energy (ΔG): Determines spontaneity of a reaction: $\Delta G = \Delta H - T\Delta S$ A negative ΔG indicates a spontaneous reaction.

• In gas-phase reactions without solvent, ΔS is often negligible, so ΔG ≈ ΔH.

Bond Cleavage

Bond cleavage is the process of breaking chemical bonds, which can occur in two main ways:

• Heterolytic Cleavage: Both electrons from the bond go to one atom, forming ions. Occurs in solution and is stabilized by solvent.

• Homolytic Cleavage: Each atom takes one electron, forming radicals. Occurs in the gas phase and produces neutral species.

Type	Products	Environment
Heterolytic	Ions (A+, B-)	Solution
Homolytic	Radicals (A•, B•)	Gas phase

Thermodynamics and Reaction Favorability

Equilibrium and Free Energy

At equilibrium, the ratio of products to reactants is constant and related to the free energy change:

• Equilibrium Constant (Keq): $K_{eq} = \frac{[B]}{[A]}$ where [B] and [A] are equilibrium concentrations of products and reactants, respectively.

• Relationship to Free Energy: $\Delta G^\circ = -2.3RT \log K_{eq}$ where R is the gas constant and T is temperature in Kelvin.

• A negative ΔGo means products are favored at equilibrium.

Predicting Reaction Outcome

• A large negative ΔHo (exothermic) can overcome a small negative ΔSo (decreased disorder).

• A large positive ΔSo (increased disorder) can overcome a small positive ΔHo (endothermic).

• To predict ΔGo, consider both bond energies and changes in disorder.

Entropy and Disorder

• More molecules = more disorder (higher entropy).

• Reactions that increase the number of molecules (A → B + C) have positive ΔSo.

• Reactions that decrease the number of molecules (A + B → C) have negative ΔSo.

• If the number of molecules does not change, ΔSo ≈ 0.

Free Radical Reactions

Formation of Radicals

Radicals are species with unpaired electrons, formed by homolytic bond cleavage. Radical formation requires energy input (heat or light):

• Initiation: Breaking a bond to form two radicals (e.g., Cl2 → 2 Cl•).

• Propagation: Radicals react with stable molecules to form new radicals (chain reaction).

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

Mechanisms and Electron Flow

• Use curved arrows to show electron movement in mechanisms:

  • Double-headed arrow: movement of an electron pair.

  • Single-headed ("fishhook") arrow: movement of a single electron.

• Arrow tail: where electrons start (reactant); arrow head: where electrons go (product).

Example: Halogenation of Methane

Chlorination of methane is a classic example of a free radical chain reaction:

1. Initiation: Cl2 → 2 Cl• (by heat or light)

2. Propagation:

   • Cl• + CH4 → HCl + CH3•

   • CH3• + Cl2 → CH3Cl + Cl•

3. Termination: Two radicals combine (e.g., Cl• + Cl• → Cl2).

This process can lead to multiple products (e.g., CH2Cl2, CHCl3, CCl4) if not controlled.

Bond Dissociation Energies (BDE) Table

The following table summarizes BDEs for selected bonds in the gas phase:

Bond	BDE (kcal/mol)
H–H	104
F–F	38
Cl–Cl	58
Br–Br	46
I–I	36
H–F	136
H–Cl	103
H–Br	88
H–I	71

Additional info: Larger atoms have lower BDEs due to longer, weaker bonds.

Radical Stability and Selectivity

• Radical stability: Tertiary (3°) > Secondary (2°) > Primary (1°) > Methyl.

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

• In halogenation, selectivity can be achieved by controlling reaction conditions and using excess alkane or limiting halogen.

Thermodynamics of Radical Reactions

• Overall enthalpy change (ΔHo) for a reaction can be estimated by summing the BDEs of bonds broken and subtracting the BDEs of bonds formed:

$\Delta H^\circ = \sum \text{(BDEs of bonds broken)} - \sum \text{(BDEs of bonds formed)}$

• For gas-phase halogenation, ΔS ≈ 0, so ΔG ≈ ΔH.

• Example: For CH4 + Cl2 → CH3Cl + HCl, ΔHo ≈ -25 kcal/mol.

Kinetics: Reaction Rates

• Rate Law: The rate of a reaction depends on the concentration of reactants and must be determined experimentally.

• General form: $\text{Rate} = k[A]^m[B]^n$ where k is the rate constant, and m and n are the reaction orders.

• Increasing temperature increases the rate by increasing the number of effective collisions.

• Activation energy (Ea): The minimum energy required for a reaction to occur.

Summary Table: Types of Bond Cleavage

Cleavage Type	Products	Example
Heterolytic	Ions (A+, B-)	SN1 reactions
Homolytic	Radicals (A•, B•)	Free radical halogenation

Key Definitions

• Radical: A species with an unpaired electron.

• Bond Dissociation Energy (BDE): The energy required to break a bond homolytically.

• Enthalpy (ΔH): Heat change at constant pressure.

• Entropy (ΔS): Measure of disorder in a system.

• Gibbs Free Energy (ΔG): Determines spontaneity of a reaction.

• Initiation, Propagation, Termination: Steps in a free radical chain reaction.

Example Problem

Calculate ΔHo for the reaction: CH4 + Cl2 → CH3Cl + HCl

• Bonds broken: CH4 (C–H, 104 kcal/mol), Cl2 (Cl–Cl, 58 kcal/mol)

• Bonds formed: CH3Cl (C–Cl, 84 kcal/mol), HCl (H–Cl, 103 kcal/mol)

• ΔHo = (104 + 58) – (84 + 103) = 162 – 187 = –25 kcal/mol

Applications

• Understanding bond strengths and thermodynamics is essential for predicting reaction outcomes and designing chemical syntheses.

• Free radical halogenation is widely used in organic synthesis for introducing halogen atoms into alkanes.

Additional info: These notes are based on general chemistry principles and are suitable for exam preparation on thermodynamics, kinetics, and free radical mechanisms.