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Free Energy and Equilibrium

The concept of free energy, specifically Gibbs free energy (G), is essential in predicting the spontaneity of chemical reactions and understanding chemical equilibrium.

Gibbs Free Energy​

Gibbs free energy combines enthalpy (H), entropy (S), and temperature (T) into a single term:

[ \Delta G = \Delta H - T \Delta S ]

  • ΔG < 0 → reaction is spontaneous
  • ΔG > 0 → reaction is non-spontaneous
  • ΔG = 0 → reaction is at equilibrium

Free Energy and the Equilibrium Constant​

The relationship between free energy and the equilibrium constant (K) is:

[ \Delta G^\circ = -RT \ln K ]

Where:

  • ΔG° = standard Gibbs free energy change

  • R = gas constant (8.314 J/mol·K)

  • T = temperature (K)

  • K = equilibrium constant

  • K >> 1 → products favored at equilibrium

  • K << 1 → reactants favored at equilibrium

  • K ≈ 1 → significant amounts of both reactants and products

Key Points​

  • Free energy predicts the direction and extent of a reaction.
  • ΔG links thermodynamics and equilibrium quantitatively.
  • Changes in temperature, pressure, or concentration affect ΔG and equilibrium.

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