Chapter 6: Chemical Reactivity and Mechanisms – Thermodynamics, Kinetics, and Reaction Mechanisms in Organic Chemistry

Chapter 6: Chemical Reactivity and Mechanisms

6.1 Enthalpy (ΔH)

Enthalpy is a measure of heat energy exchange between a chemical reaction and its surroundings. It is a key concept in understanding the energy changes that occur during chemical reactions, especially in organic chemistry.

• Bond Breaking: Requires absorption of energy by the system; electrons must gain kinetic energy to overcome bond stability.

• Bond Dissociation Energy (BDE): The energy required to break a bond homolytically (each atom takes one electron). BDE values are used to estimate enthalpy changes.

• Exothermic Reaction: Energy released by forming new bonds exceeds energy required to break bonds. Products are more stable than reactants. ΔH is negative.

• Endothermic Reaction: Energy required to break bonds exceeds energy released by forming new bonds. Products are less stable than reactants. ΔH is positive.

Energy Diagram: The y-axis represents potential energy (PE), and the x-axis represents reaction progress. Exothermic reactions have products lower in energy than reactants; endothermic reactions have products higher in energy.

• Equation for Enthalpy Change:

$\Delta H = \text{BDE (bonds broken)} - \text{BDE (bonds formed)}$

• Example Calculation:

Bonds broken: C–H (397 kJ/mol), Br–Br (193 kJ/mol) Bonds formed: C–Br (285 kJ/mol), H–Br (368 kJ/mol)

$\Delta H = (397 + 193) - (285 + 368) = -63\ \text{kJ/mol}$

Negative ΔH indicates an exothermic reaction.

6.2 Entropy (ΔS)

Entropy is a measure of molecular disorder, randomness, or freedom. Both enthalpy and entropy must be considered to predict whether a reaction will occur spontaneously.

• Definition: Entropy quantifies the number of vibrational, rotational, and translational states available to a system.

• Visualization: Gases expand to fill available volume, increasing entropy as the number of accessible states increases.

• Total Entropy Change: The spontaneity of a process depends on the total entropy change:

$\Delta S_{\text{tot}} = \Delta S_{\text{sys}} + \Delta S_{\text{surr}}$

• If ΔStot is positive, the process is spontaneous.

• ΔSsys increases when:

  • There are more moles of product than reactant.

  • A cyclic compound becomes acyclic.

6.3 Gibbs Free Energy (ΔG)

Gibbs free energy combines enthalpy and entropy to predict spontaneity. A negative ΔG indicates a spontaneous process.

• Definition: ΔG is the maximum amount of work a system can perform at constant temperature and pressure.

• Equation:

$\Delta G = \Delta H - T\Delta S$

• If ΔG < 0, the reaction is spontaneous (exergonic).

• If ΔG > 0, the reaction is nonspontaneous (endergonic).

• In energy diagrams, free energy (G) is plotted instead of enthalpy (H).

Example: If entropy decreases (ΔS negative), ΔH must be sufficiently negative for ΔG to be negative and the reaction to be spontaneous.

6.4 Equilibria and the Relationship to ΔG

Thermodynamics determines the position of equilibrium, not the rate of reaction. The equilibrium constant (Keq) quantifies the extent to which products or reactants are favored.

• Relationship:

$\Delta G = -RT \ln K_{eq}$

• Where R is the gas constant and T is temperature in Kelvin.

• A more negative ΔG means a larger Keq (more products at equilibrium).

• Thermodynamic terms (Keq, ΔG, ΔH, ΔS) describe stability, not reaction rate.

Table: Sample Values of ΔG and Keq

ΔG (kJ/mol)	Keq
0	1
-6	10
-12	100
-18	1000
+6	0.1
+12	0.01
+18	0.001

Additional info: Table values inferred from standard thermodynamic relationships.

6.5 Kinetics

Kinetics describes the rate at which a reaction proceeds, independent of thermodynamic favorability (ΔG).

• Five Factors Affecting Rate:

  • Concentration of reactants

  • Activation energy (Ea)

  • Temperature

  • Geometry and steric effects

  • Presence of a catalyst

• Rate Law: Expresses the dependence of rate on reactant concentrations.

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

• Order of Reaction: The exponents x and y indicate the order with respect to each reactant.

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

• Temperature: Higher temperature increases kinetic energy, leading to more frequent and energetic collisions.

• Steric Effects: Proper orientation is required for effective collisions; steric hindrance can slow reactions.

• Catalysts: Lower activation energy and provide alternative pathways without being consumed. Enzymes are biological catalysts.

6.6 Reading Energy Diagrams

Energy diagrams illustrate the energy changes during a reaction, distinguishing between kinetic and thermodynamic control.

• Kinetic Control: Product forms faster (lower Ea), but may not be the most stable.

• Thermodynamic Control: Product is more stable (lower energy), but may form more slowly.

Transition States: High-energy, non-isolable points (energy maxima) on the reaction coordinate.

Intermediates: Observable species (energy minima) that exist between steps in a reaction mechanism.

The Hammond Postulate: The structure of a transition state resembles the species (reactant or product) to which it is closer in energy.

• Exothermic reaction: Transition state resembles reactants.

• Endothermic reaction: Transition state resembles products.

6.7 Nucleophiles and Electrophiles

Polar reactions involve the interaction of electron-rich (nucleophilic) and electron-deficient (electrophilic) species.

• Nucleophile: Electron-rich species that donates a pair of electrons (Lewis base). More polarizable nucleophiles are stronger.

• Electrophile: Electron-deficient species that accepts a pair of electrons (Lewis acid). Carbocations and partially positive atoms are common electrophiles.

Table: Summary of Nucleophiles and Electrophiles

Nucleophiles	Electrophiles
OH−, RO−, NH3, Halide ions (Cl−, Br−, I−), Alkenes, Alkynes	Carbocations, Carbonyl carbons, Alkyl halides, Protonated alcohols, Alkyl sulfonates

Additional info: Table entries inferred from common organic chemistry examples.

6.8 Mechanisms and Arrow Pushing

Curved arrows are used to depict the movement of electrons during chemical reactions. There are four main patterns in polar mechanisms:

1. Nucleophilic Attack: Nucleophile donates electrons to an electrophile. Arrow starts at electron pair and ends at electrophilic atom.

2. Loss of a Leaving Group: Heterolytic bond cleavage; leaving group takes electron pair. May require multiple arrows.

3. Proton Transfers (Acid/Base): Proton is transferred between species, often requiring two arrows.

4. Rearrangements: Carbocation rearrangements (hydride or methyl shifts) to form more stable carbocations.

Pi bonds can act as nucleophiles in nucleophilic attacks. Multiple arrows may be needed for complex mechanisms.

6.9 Combining Patterns of Arrow Pushing

Multistep mechanisms combine the four basic arrow-pushing patterns. Sometimes, two patterns occur in a single step (e.g., nucleophilic attack and loss of a leaving group simultaneously).

6.10 Drawing Curved Arrows

Proper arrow notation is essential for accurately depicting mechanisms.

• Arrow starts at a pair of electrons (bond or lone pair).

• Arrow ends at an atom, showing bond formation or lone pair creation.

• Arrows must not violate the octet rule or depict impossible electron flows.

6.11 Carbocation Rearrangements

Carbocations can rearrange via hydride or methyl shifts to form more stable carbocations. Rearrangement occurs only if a more stable carbocation results.

• Identify neighboring hydrogens or methyl groups that can shift.

• Tertiary carbocations are generally most stable and do not rearrange unless resonance stabilization is possible (e.g., allylic carbocation).

6.12 Reversible and Irreversible Reaction Arrows

Some reactions are reversible (equilibrium), while others are essentially irreversible. The reversibility depends on the nature of the nucleophile, leaving group, and reaction conditions.

• Reversible: If the attacking nucleophile is a good leaving group, or if the leaving group can act as a nucleophile, the reaction is reversible.

• Irreversible: If the nucleophile is a poor leaving group, the reaction is essentially irreversible.

• Proton Transfers: Generally reversible, unless the pKa difference is 10 units or more.

• Carbocation Rearrangements: Generally irreversible; more stable carbocations do not rearrange to less stable ones.

• Le Châtelier’s Principle: Removal of a product (e.g., as a gas) can drive a reaction to completion, making it effectively irreversible.

Summary Table: Key Thermodynamic and Kinetic Terms

Term	Definition	Equation
Enthalpy (ΔH)	Heat energy change at constant pressure	$\Delta H = \text{BDE (bonds broken)} - \text{BDE (bonds formed)}$
Entropy (ΔS)	Measure of disorder/randomness	—
Gibbs Free Energy (ΔG)	Predicts spontaneity	$\Delta G = \Delta H - T\Delta S$
Equilibrium Constant (Keq)	Extent of reaction at equilibrium	$\Delta G = -RT \ln K_{eq}$
Activation Energy (Ea)	Minimum energy for reaction	—