In-Depth Notes on Spontaneous and Non-Spontaneous Reactions, Entropy, and Gibbs Free Energy

Spontaneous Reactions

• Definition: Reactions that occur without external energy input.
• Characteristics:
  • Often (but not always) exothermic.
  • Thermodynamics is used to predict if reactions can occur.
• Entropy: A crucial factor for determining spontaneity.
  • Entropy (S): Measure of randomness in a system.
  • High entropy: Highly disordered system.
  • Low entropy: Organized system.
  • Change in entropy, labeled as ΔS, indicates the difference between the entropy of products and reactants.

Examples of Entropy:

• Crystals:
  • Form regular atomic arrays, indicating low entropy (high order).
• Gas Molecules:
  • Move randomly and disorganized, indicating high entropy (low order).

Chaos and Entropy

• Randomness: Absence of regular patterns.
• ΔS of Reaction (ΔSo):
  • ΔSo = S(products) - S(reactants).
  • Positive ΔSo: Increase in disorder.
  • Negative ΔSo: Decrease in disorder.

Redefining Spontaneous Reactions

• In a spontaneous reaction, order decreases:
  • ΔHo < 0 (exothermic) and ΔSo > 0 → Spontaneous.
• Nonspontaneous reaction:
  • ΔHo > 0 (endothermic) and ΔSo < 0 → Nonspontaneous.
• For other cases, spontaneity depends on relative sizes of ΔHo and ΔSo.

Thermodynamics Principles and Entropy

• Entropy (S):

  • Key factor in determining spontaneity.
  • Changes depend on arrangements of particles.

• Ludwig Boltzmann's Formula (1877):

  • S = k ln W
  • Where:
    • S = entropy
    • W = number of arrangements
    • k = Boltzmann's constant (related to gas constant R and Avogadro’s number N_A).

• Systems with:

  • Few arrangements → low entropy (less disorder).
  • Many arrangements → high entropy (more disorder).

• Second Law of Thermodynamics:

  • Total entropy of the universe (ΔSuniverse) = ΔSsystem + ΔSsurroundings > 0.

Changes in Entropy with Phase and State

1. Temperature Changes:
   • Higher temperature → increased entropy.
2. Phase Changes:
   • More ordered to less ordered (e.g. solid to liquid).
3. Dissolution:
   • Dissolved solids or liquids usually have greater entropy than their pure forms.
4. Atomic Size/Molecular Complexity:
   • Larger or more complex structures result in increased entropy.

Gibbs Free Energy

• Gibbs Free Energy (G):

  • ΔG = ΔH - TΔS
  • Indicates spontaneity of processes:
  • ΔG < 0 → Spontaneous.
  • ΔG > 0 → Nonspontaneous.
  • ΔG = 0 → Equilibrium.

• Work and Free Energy:

  • For spontaneous processes:
  • ΔG = maximum work obtainable.
  • For nonspontaneous processes:
  • ΔG = maximum work needed.

Reaction Spontaneity Summary (Table 20.1)

Equilibrium and Reaction Direction

• Reaction Quotient (Q) vs Equilibrium Constant (K):
  • If Q/K < 1 → ln Q/K < 0 → Reaction proceeds right (ΔG < 0).
  • If Q/K > 1 → ln Q/K > 0 → Reaction proceeds left (ΔG > 0).
  • If Q/K = 1 → ln Q/K = 0 → Reaction at equilibrium (ΔG = 0).

Key Equations:

• ΔG = RT ln Q/K = RT ln Q - RT ln K
• Under standard conditions (1 M concentrations, 1 atm for gases):
  • Q = 1 and ln Q = 0 so ΔG° = -RT ln K.

Summary of Gibbs Free Energy vs Equilibrium Constant (Table 20.2)

Summary

• Entropy and Gibbs Free Energy are fundamental to understanding reaction spontaneity and predicting the direction of chemical processes. Spontaneity is influenced by temperature, phase changes, and the characteristics of reactants. Understanding these principles allows for better insight into chemical thermodynamics.