Gibbs free energy

Gibbs Free Energy: Definition, Characteristics & Gibbs-Helmholtz Equation

Definition of Gibbs Free Energy

Gibbs Free Energy (G) is a thermodynamic function that represents the maximum amount of useful work obtainable from a system at constant temperature and pressure. It brings together enthalpy (H), entropy (S), and temperature (T) into one expression used to determine whether a process will occur spontaneously.

It is defined as:

G = H - T·S

where:
G = Gibbs free energy
H = Enthalpy
T = Absolute temperature measured in kelvin
S = Entropy

Change in Gibbs Free Energy (ΔG)

The change in Gibbs free energy, denoted by ΔG, determines whether a reaction is spontaneous or not under constant temperature and pressure.

ΔG = ΔH - T·ΔS

- If ΔG < 0 → the process is spontaneous (favorable).
- If ΔG = 0 → the system is at a stable equilibrium point.
- If ΔG > 0 → the process is non-spontaneous (not favorable).

Characteristics of Gibbs Free Energy

• State Function: Gibbs free energy depends only on the current state of the system, not on how the system reached that state.
• Predicts Spontaneity: A negative ΔG indicates a spontaneous process, while a positive value indicates a non-spontaneous one.
• Extensive Property: It depends on the quantity of matter present.
• Equilibrium Condition: At equilibrium, the free energy of the system is at a minimum and ΔG = 0.
• Helpful in Determining Work: It indicates the greatest quantity of useful work, excluding expansion work, that a system can perform.

Gibbs-Helmholtz Equation

The Gibbs-Helmholtz equation connects the variation of free energy change with temperature by incorporating enthalpy and entropy. It helps explain how ΔG changes as temperature changes.

ΔG = ΔH - T·ΔS

Taking temperature dependence into account, the equation can also be written as:

\(\Big(\frac{\partial (\triangle G/T)}{\partial T}\Big)_{p}=\frac{\triangle H}{T^{2}}\)

This form helps in studying how ΔG/T changes with temperature under constant pressure.

Gibbs free energy is an essential concept in chemical thermodynamics that helps determine the direction in which chemical reactions proceed. By analyzing ΔG, students can determine whether a reaction will occur spontaneously and understand how temperature and entropy affect chemical processes. The Gibbs-Helmholtz equation further provides insights into temperature-dependent behavior of reactions, making it an essential tool for JEE aspirants.