Chapter 5 – Chemical Reaction Analysis: Thermodynamics & Kinetics

Chapter 5 – Chemical Reaction Analysis: Thermodynamics & Kinetics

5.1 Chemical Reaction Analysis: Rotation Around a Single Bond

This section explores the thermodynamic and kinetic principles governing the rotation around single bonds, with a focus on butane conformations and their energy differences.

• Energy Change (ΔE): The change in energy for a process is calculated as the difference between the energy of the product and the reactant. $\Delta E = E_{\text{product}} - E_{\text{reactant}}$

• Butane Conformations: Butane can exist in anti (no strain) and gauche (strain) conformations. The anti conformation is lower in energy and more stable than the gauche conformation.

• Strain Energy: The energy difference between anti and gauche conformations is due to strain energy, typically about 0.9 kcal/mol for butane.

• Example: The anti conformation of butane has 0 kcal/mol strain energy, while the gauche conformation has 0.9 kcal/mol strain energy.

Gibbs Free Energy and Reaction Favorability

Gibbs Free Energy (G) is the energy available to do work in a system. It is defined as:

• $G = H - TS$ where H is enthalpy, T is absolute temperature (K), and S is entropy.

• Change in Gibbs Free Energy (ΔG): Indicates the spontaneity of a process. A negative ΔG means the process is spontaneous.

• Standard Change in Gibbs Free Energy (ΔG°): Used when reactants and products are in their standard states.

Relationship Between ΔG° and Equilibrium Constant (Keq)

ΔG° and the equilibrium constant are quantitatively related:

• $\Delta G^\circ = -RT \ln K_{eq}$ where R = 1.987 cal/(mol·K), T = absolute temperature in K.

• If temperature is not specified, assume 298 K (standard conditions).

Equilibrium and Stability of Conformations

• Keq: Ratio of products to reactants. Equilibrium favors the more stable species.

• For butane, anti conformation is favored, so $K_{eq} < 1$ (more anti than gauche).

• ΔG° and Direction of Reaction:

  • ΔG° < 0: Reaction to the right favored, $K_{eq} > 1$

  • ΔG° > 0: Reaction to the left favored, $K_{eq} < 1$

  • ΔG° = 0: Neither side favored, $K_{eq} = 1$

• Example Table:

ΔG°	Keq	Reaction Direction
< 0	> 1	Right (products favored)
> 0	< 1	Left (reactants favored)
= 0	= 1	Neither side favored

ΔG° in Terms of Enthalpy and Entropy

ΔG° is determined by both enthalpy and entropy:

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

• A negative ΔH° (exothermic) and a positive ΔS° (increase in disorder) both favor spontaneity.

Enthalpy Changes and Molecular Strain

• Bond Formation: Releases energy, ΔH° < 0 (favorable).

• Bond Breaking: Requires energy, ΔH° > 0 (unfavorable).

• Molecular Strain: Increased strain decreases stability and increases ΔH°; decreased strain increases stability and decreases ΔH°.

• Example: Anti conformation of butane has no strain, gauche has 0.9 kcal/mol strain energy.

Entropy Changes in Conformational Equilibria

• Entropy (ΔS°): Measure of disorder or randomness.

• ΔS° is approximately zero when one molecule becomes one molecule (e.g., anti to gauche).

• A positive ΔS° (more molecules formed) favors spontaneity.

Kinetics: Activation Energy and Reaction Rates

• Transition State: Highest energy state during a reaction.

• Activation Energy (Ea): Energy difference between reactants and transition state.

• High Ea = slow reaction; low Ea = fast reaction.

• Rotation around single bonds is fast; rotation around double bonds is slow due to higher activation energy.

• Example: Rotation around a C–C double bond requires breaking π bond (overlapping p orbitals), with Ea ≈ +85 kcal/mol.

Assessment Examples

• Assessment 5.7: Given ΔG° for equilibrium processes, predict whether Keq is >1, <1, or =1 and justify.

• Assessment 5.16: Identify which conformation in a pair has the least strain energy.

5.3 Chemical Reaction Analysis: Halogenation of Alkanes

Halogenation of alkanes is a substitution reaction where an alkyl hydrogen is replaced by a halogen (typically chlorine or bromine).

• Definition: Halogenation is a key synthetic technique in organic chemistry.

• Application: Used to introduce functional groups and modify molecular properties.

Summary Table: Key Thermodynamic and Kinetic Concepts

Term	Definition	Effect on Reaction
ΔG°	Standard Gibbs Free Energy Change	Determines spontaneity and equilibrium position
ΔH°	Standard Enthalpy Change	Negative favors reaction, positive disfavors
ΔS°	Standard Entropy Change	Positive favors reaction, negative disfavors
Ea	Activation Energy	High slows reaction, low speeds reaction
Keq	Equilibrium Constant	>1 favors products, <1 favors reactants

Additional info: These notes expand on the original slides by providing definitions, equations, and context for thermodynamic and kinetic principles relevant to chemical reaction analysis, especially conformational equilibria and halogenation reactions.