Gibbs Free Energy and Spontaneity of a Reaction

Gibbs Free Energy Overview

• Gibbs Free Energy (G) predicts the spontaneity of a chemical reaction by focusing on system changes.
• Defined as G = H – TS, where H is enthalpy, T is temperature, and S is entropy.
• All components (H, S, G) are state functions with energy units.

Spontaneity and ΔG

• A change is spontaneous when ΔG is negative.
• If the entropy of the universe increases, the ΔG for the system will decrease.
• Positive ΔSuniv correlates with negative ΔG for the system, indicating a spontaneous process.

Calculating ΔG

• For constant temperature, ΔG = ΔH – TΔS.
• At standard conditions: ΔG⁰ = ΔH⁰ – TΔS⁰.
• Free energy (ΔG) represents the energy available to perform work in the system.
• Standard measurements typically reference a temperature of 25°C (298 K).

Example Calculation: Mg Reaction

• Reaction: Mg + ½ O2 → MgO
• Standard entropy values:
  • S°(Mg) = 32.7 J/K·mol
  • S°(O2) = 205.0 J/K·mol
  • S°(MgO) = 26.9 J/K·mol
• Standard enthalpy values:
  • ΔH°f(Mg) = 0
  • ΔH°f(O2) = 0
  • ΔH°f(MgO) = -601.2 kJ/mol

Steps for Determining ΔG

• Step 1: Calculate ΔS°

  • ΔS° = S°(MgO) – [S°(Mg) + ½ S°(O2)]
  • ΔS° = 26.9 - (32.7 + 0.5 × 205.0) = -108.3 J/K·mol

• Step 2: Calculate ΔH°

  • ΔH° = Σ nΔHf° (products) – Σ mΔHf° (reactants)
  • ΔH° = [-601.2] – [0 + 0] = -601.2 kJ

Understanding ΔSuniv and ΔG Relationship

• The direction of spontaneous change is indicated by negative ΔG.
• Conditions for spontaneity:
  • ΔSuniv increases → spontaneous change (ΔG < 0)
  • No change at equilibrium: ΔSuniv = 0, ΔG = 0
  • ΔSuniv decreases → not spontaneous (ΔG > 0)

Implications of Gibbs Free Energy

• ΔG is essential for predicting whether a chemical reaction can occur under specified conditions.
• The spontaneity is directly tied to the free energy change, aiding in analyses of various chemical processes and reactions.