Gibbs (Free) Energy

Learning Objectives

• Understand Gibbs energy and its applications in chemistry
• Comprehend Gibbs energy's role in reaction properties, equilibria, and electrochemical properties

Introduction to Gibbs Free Energy

• Gibbs Free Energy (G) combines enthalpy (H) and entropy (S) into a single value.
• Change in free energy (ΔG) = Enthalpy change + (Temperature x Entropy change)
• Predicts reaction direction under constant temperature and pressure:
  • ΔG > 0: Nonspontaneous reaction (requires external energy)
  • ΔG < 0: Spontaneous reaction (occurs without external energy)

Historical Context

• Developed by Josiah Willard Gibbs in the 1870s
• Originally termed "available energy"
• Key publication: "Graphical Methods in the Thermodynamics of Fluids" (1873)

Gibbs Energy Equations

1. Simple Formula: G = H - TS
2. Complete Formula: G = U + PV - TS
   • U: Internal energy (joules)
   • P: Pressure (pascals)
   • V: Volume (cubic meters)
   • T: Temperature (kelvin)
   • S: Entropy (joules/kelvin)
   • H: Enthalpy (joules)

Gibbs Energy in Reactions

• Spontaneous Reaction: Occurs naturally without external energy.
• Non-Spontaneous Reaction: Requires continuous external energy.
• Calculating ΔG:
  • ΔG = ΔH - TΔS

Example Calculation

• Reaction: 2NO(g) + O2(g) → 2NO2(g)
  • Given: ΔH = -120 kJ, ΔS = -150 J/K
  • Convert S: 150 J/K to 0.15 kJ/K
  • ΔG = -120 kJ + 0.15 kJ/K * 290 K = -77 kJ*

Factors Affecting ΔG

• Depends on difference in free energy of products and reactants
• Independent of reaction path and mechanism
• Cannot predict reaction rate

Standard Gibbs Energy Change (ΔG°)

• Reaction: aA + bB → cC + dD
• ΔG° = ΣΔG°f(products) - ΣΔG°f(reactants)
• Conditions: 1 bar pressure, concentrations of 1 M, at 298 K
• Enthalpy-driven: |ΔH| >> |TΔS|
• Entropy-driven: ΔH << TΔS

Example: NH4NO3 Dissolution

• Calculate ΔG° to determine spontaneity
• At 298 K, ΔG° = 4.4 kJ → Spontaneous

Gibbs Energy in Equilibria

• Equation: G = G° + RT ln(Q)
  • At equilibrium, G = 0, Q = K
  • ΔG° = RT ln(K)
  • Keq > 1: Favors products

Gibbs Energy in Electrochemistry

• Nernst Equation relates cell potentials:
  • E = E° - (RT/nF) ln(Q)
• Relationship with Gibbs Energy:
  • ΔG = -nFE
  • ΔG° = -nFE°

Remarks on Gibbs "Free" Energy

• Not 'free': Represents maximum useful work energy
• Not real energy: Not conserved like enthalpy or entropy
• Not a real property: More of a useful calculation construct

References

• Chang, R. (2005). Physical Chemistry for the Biosciences.
• Atkins, P., de Paula, J. (2006). Physical Chemistry for the Life Sciences.
• Stryer, L. (1988). Biochemistry.