A thermodynamic potential that measures the maximum useful work obtainable from a system at constant pressure and temperature.

Gibbs Free Energy

Gibbs free energy (G), named after physicist Josiah Willard Gibbs, is a fundamental thermodynamic quantity that determines whether a process will occur spontaneously under constant temperature and pressure conditions. It combines the system's enthalpy (H) and entropy (S) according to the equation:

G = H - TS

where T is the absolute temperature.

Significance in Chemical Systems

The change in Gibbs free energy (ΔG) serves as a crucial indicator:

ΔG < 0: Spontaneous process
ΔG = 0: System at equilibrium
ΔG > 0: Non-spontaneous process

This makes Gibbs free energy particularly valuable in understanding:

Applications

Chemical Reactions

In chemical reactions, Gibbs free energy helps predict:

Reaction spontaneity
Equilibrium constants
Maximum work obtainable
Direction of chemical processes

Materials Science

The concept is essential in:

Relationship to Other Thermodynamic Quantities

Gibbs free energy integrates several fundamental thermodynamic concepts:

The relationship can be expressed through the fundamental equation: G = U + PV - TS

Historical Development

The development of Gibbs free energy marked a significant advancement in Classical thermodynamics. It provided scientists with a powerful tool for predicting chemical and physical processes without needing to measure the complete energy changes in a system.

Modern Applications

Contemporary uses include:

The concept continues to be central in understanding and designing:

Industrial chemical processes
Environmental systems
Biological reactions
Materials synthesis

Mathematical Formulation

For a system with multiple components, the total Gibbs free energy can be expressed as:

G = ∑μᵢnᵢ

where:

μᵢ represents the Chemical potential of component i
nᵢ represents the number of moles of component i

This formulation is particularly useful in studying Multi-component systems and Phase equilibria.