Concise Summary of Entropy and Gibbs Free Energy Concepts

Prayers

Entropy Changes in Surroundings

  • Change in entropy of surroundings is proportional to enthalpy of the system:

    • ΔSsurroundings ∝ -ΔHsystem

    • Exothermic process increases entropy in surroundings.

  • Change in entropy inversely proportional to temperature:

    • ΔS_surroundings ∝ 1/T

Spontaneity of Reactions

  • Reaction spontaneous if: ΔSuniverse = ΔSsystem + ΔS_surroundings > 0

  • Example reaction:

    • ΔS_system = -187.5 J/K·mol, ΔH = -35.8 kJ/mol

    • Calculate ΔS_surroundings = +120.0 J/K·mol

    • ΔS_univ = -187.5 + 120.0 < 0 (non-spontaneous)

Third Law of Thermodynamics

  • Entropy of perfect crystalline substance is zero at absolute zero.

  • Allows for calculation of absolute entropies for substances.

Gibbs Free Energy

  • Equation: ΔG = ΔH - TΔS

  • If ΔG < 0: reaction is spontaneous.

  • If ΔG = 0: reaction at equilibrium.

  • If ΔG > 0: reaction is non-spontaneous.

Predicting Sign of ΔG

  • Table for predicting ΔG sign based on ΔH and ΔS.

  • Important cases:

    • Negative ΔH & Positive ΔS: Spontaneous

    • Positive ΔH & Negative ΔS: Non-spontaneous

Temperature Predictions

  • Set ΔG = 0 for equilibrium: 0 = ΔH - TΔS

  • Rearranging gives temperature for spontaneous reactions.

  • Example: T = 385 K for a reaction with ΔH = 125 kJ/mol and ΔS = 325 J/K·mol.

Standard Free Energy Changes

  • Can be calculated from standard values.

  • Example calculation:

    • 2KClO3 → 2KCl + 3O2 results in ΔG°_rxn = -236.8 kJ/mol (spontaneous).

Free Energy and Chemical Equilibrium

  • ΔG = ΔG° + RT ln Q

  • Relationship between free energy change and equilibrium constant.

Key Equations

  • ΔS = k ln W

  • ΔSuniv = ΔSsys + ΔS_surr > 0 (spontaneous process).

  • ΔG = ΔH - TΔS (Gibbs free energy).

  • ΔG = ΔG° + RT ln Q (free-energy change at constant temperature).

Thermodynamics in Living Systems

  • Coupled reactions: favorable reactions drive unfavorable ones.

  • Example: ATP conversion driving protein synthesis.

Key Points

  • Understand spontaneous vs nonspontaneous reactions.

  • Relate enthalpy, entropy, and free energy.

  • Calculate changes based on standard values or Gibbs equation.