Gibbs Free Energy-

Gibbs Free Energy (G) is a thermodynamic potential used to predict whether a process will occur spontaneously under constant temperature and pressure. It combines enthalpy, entropy, and temperature into a single value.

1. Basic Definition

The Gibbs Free Energy of a system is defined as- G= H−TS

Where:

  • G: Gibbs free energy (Joules or kJ/mol)
  • H: Enthalpy of the system (total heat content, J or kJ/mol)
  • T: Absolute temperature (Kelvin, K)
  • S: Entropy of the system (measure of disorder, J/K or kJ/K)

2. Importance of Gibbs Free Energy

  • Spontaneity: Determines whether a reaction/process occurs without external intervention:
    • ΔG<0: Spontaneous process.
    • ΔG=0: System at equilibrium.
    • ΔG>0: Non-spontaneous process.
  • Used extensively in chemical thermodynamics, biochemistry, and engineering.

3. Gibbs Free Energy Change (ΔG)

ΔG=ΔH−TΔS

Where:

  • ΔH: Change in enthalpy (heat exchange at constant pressure).
  • ΔS: Change in entropy.
  • T: Temperature in Kelvin.

4. Conditions for Spontaneity

  • If ΔG<0: The reaction is thermodynamically favorable.
  • If ΔG>0: The reaction is not favorable and requires energy input.
  • If ΔG=0: The system is in equilibrium.

5. Standard Gibbs Free Energy (ΔG∘)

The standard Gibbs free energy change is measured under standard conditions:

  • Pressure: 1 atm.
  • Concentration: 1 M for solutions.
  • Temperature: Typically 298 k (25°C).

Formula: ΔG∘=ΔH∘−TΔS∘

Where ΔH∘ and ΔS∘ are standard enthalpy and entropy changes.

6. Relation to Equilibrium Constant (K)

Gibbs free energy is related to the equilibrium constant of a reaction: ΔG∘=−RT ln⁡ K

Where:

  • R: Universal gas constant (8.314 J/mol K).
  • T: Absolute temperature (K).
  • K: Equilibrium constant.
  • For reactions:
    • If K>1: ΔG∘<0 (favors products).
    • If K=1: ΔG∘=0 (equilibrium).
    • If K<1: ΔG∘>0 (favors reactants).

7. Temperature Dependence

The spontaneity of a reaction depends on T (temperature):

  • At high T: TΔS dominates; entropy-driven processes are favored.
  • At low T: ΔH dominates; enthalpy-driven processes are favored.

8. Applications

  1. Chemical Reactions: Predicts reaction spontaneity and equilibrium.
  2. Phase Changes:
    • During melting or boiling, ΔG=0 as the system is in equilibrium.
    • Helps determine melting/boiling points.
  3. Biochemistry: Determines whether biochemical reactions (e.g., ATP hydrolysis) are energy-favorable.
  4. Electrochemistry: ΔG∘=−nFE∘ Where:
    • n: Number of moles of electrons transferred.
    • F: Faraday constant (96485 C/mol).
    • E∘: Standard electrode potential.

9. Advanced Insights

  1. Non-Standard Conditions: Under non-standard conditions, Gibbs free energy is expressed as: ΔG=ΔG∘+RT ln ⁡Q, Where Q is the reaction quotient.
  2. Gibbs-Helmholtz Equation: Relates ΔG with ΔH and temperature: ΔGT=ΔHT−ΔS
  3. Partial Molar Gibbs Energy: Used in mixtures to describe the Gibbs energy contribution of individual components.
  4. Chemical Potential (μ): The change in Gibbs energy with respect to the change in the number of particles: μ = (∂G / ∂n)T,P​