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 rotation around single bonds in organic molecules, 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 exists in anti (no strain) and gauche (strain) conformations. The anti conformation is lower in energy due to less steric strain.

• Strain Energy: The energy difference between anti and gauche conformations is approximately 0.9 kcal/mol, attributed to steric strain in the gauche form.

• Example: For butane, the anti conformation is favored over gauche due to lower strain energy.

Gibbs Free Energy and Reaction Favorability

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

• $G = H - TS$

• H: Enthalpy (heat content)

• S: Entropy (disorder)

• ΔG: Change in Gibbs Free Energy indicates spontaneity and favorability of a reaction.

• Standard State: When reactants and products are in their standard states, use $\Delta G^\circ$ to predict reaction direction.

Relationship Between ΔG° and Equilibrium Constant (Keq)

The standard change in Gibbs Free Energy ($\Delta G^\circ$) is quantitatively related to the equilibrium constant ($K_{eq}$):

• $\Delta G^\circ = -RT \ln K_{eq}$

• R: Universal gas constant (1.987 cal/(mol·K))

• T: Absolute temperature in Kelvin (assume 298 K if not specified)

• Interpretation:

  • If $\Delta G^\circ < 0$, reaction favors products ($K_{eq} > 1$)

  • If $\Delta G^\circ > 0$, reaction favors reactants ($K_{eq} < 1$)

  • If $\Delta G^\circ = 0$, equilibrium ($K_{eq} = 1$)

• Example: For butane, more molecules are in the anti conformation (more stable), so $K_{eq} < 1$ for gauche to anti equilibrium.

Assessment 5.7: Predicting Equilibrium Constants

Given $\Delta G^\circ$ values for equilibrium processes, determine if $K_{eq}$ is greater than, equal to, or less than 1 and justify:

Process	$\Delta G^\circ$	Expected $K_{eq}$	Justification
A → B	+8.8 kcal/mol	< 1	Positive $\Delta G^\circ$ favors reactants
anti → gauche	+0.9 kcal/mol	< 1	Anti is more stable, equilibrium favors anti

Thermodynamic Factors: Enthalpy and Entropy

The standard change in Gibbs Free Energy ($\Delta G^\circ$) is related to enthalpy and entropy:

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

• ΔH° (Enthalpy): Negative $\Delta H^\circ$ (exothermic) favors reaction; positive $\Delta H^\circ$ (endothermic) disfavors.

• ΔS° (Entropy): Positive $\Delta S^\circ$ (increased disorder) favors reaction.

• Example: Bond formation releases energy ($\Delta H^\circ < 0$); bond breaking requires energy ($\Delta H^\circ > 0$).

Strain Energy and Molecular Stability

Strain in molecules affects enthalpy and stability:

• Increased Strain: Decreases stability, increases $\Delta H^\circ$

• Decreased Strain: Increases stability, decreases $\Delta H^\circ$

• Example: Gauche butane has 0.9 kcal/mol strain energy compared to anti.

Assessment 5.16: Strain Energy in Conformations

Identify which conformation in each pair has the least strain energy:

• Chair conformation of cyclohexane is less strained than boat.

• Staggered conformation of alkanes is less strained than eclipsed.

Entropy Changes in Conformational Equilibria

Rotation around a single bond is generally entropically neutral:

• Entropy (ΔS°): Measure of disorder; positive $\Delta S^\circ$ favors processes that increase the number of molecules.

• Conformational Change: Anti to gauche (or vice versa) involves no change in number of molecules, so $\Delta S^\circ \approx 0$.

Kinetics: Activation Energy and Reaction Rates

Kinetics describes the rate at which reactions occur, determined by activation energy and transition state:

• Transition State: Highest energy point along the reaction coordinate.

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

• Equation: $E_a = E_{\text{TS}} - E_{\text{reactant}}$

• Low Ea: Fast reaction; High Ea: Slow reaction.

• Conformational Interconversion: Anti to gauche is slower than gauche to anti due to stability differences.

Rotation Around Double Bonds

Rotation around double bonds is energetically unfavorable due to the nature of π bonds:

• π Bond: Formed by overlapping p orbitals; rotation disrupts this overlap.

• Activation Energy: Much higher for double bonds (e.g., $+85$ kcal/mol for 90° rotation).

• Result: Double bonds are rigid; rotation does not occur under normal conditions.

5.3 Chemical Reaction Analysis: Halogenation of Alkanes

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

• Type: Substitution reaction

• Application: Used in organic synthesis to introduce halogen atoms into alkanes.

• Example: Methane reacts with chlorine to form chloromethane and HCl.