Free Energy


By the end of this section, you will be able to:

  • Define Gibbs free energy, and describe its relation to spontaneity
  • Calculate free energy change for a process using free energies of formation for its reactants and products
  • Calculate free energy change for a process using enthalpies of formation and the entropies for its reactants and products
  • Explain how temperature affects the spontaneity of some processes
  • Relate standard free energy changes to equilibrium constants

One of the challenges of using the second law of thermodynamics to determine if a process is spontaneous is that it requires measurements of the entropy change for the system and the entropy change for the surroundings. An alternative approach involving a new thermodynamic property defined in terms of system properties only was introduced in the late nineteenth century by American mathematician Josiah Willard Gibbs. This new property is called the Gibbs free energy (G) (or simply the free energy), and it is defined in terms of a system’s enthalpy and entropy as the following:


Free energy is a state function, and at constant temperature and pressure, the free energy change (ΔG) may be expressed as the following:


(For simplicity’s sake, the subscript “sys” will be omitted henceforth.)

The relationship between this system property and the spontaneity of a process may be understood by recalling the previously derived second law expression:


The first law requires that qsurr = −qsys, and at constant pressure qsys = ΔH, so this expression may be rewritten as:


Multiplying both sides of this equation by −T, and rearranging yields the following:


Comparing this equation to the previous one for free energy change shows the following relation:


The free energy change is therefore a reliable indicator of the spontaneity of a process, being directly related to the previously identified spontaneity indicator, ΔSuniv. [link] summarizes the relation between the spontaneity of a process and the arithmetic signs of these indicators.

Relation between Process Spontaneity and Signs of Thermodynamic Properties
ΔSuniv > 0ΔG < 0spontaneous
ΔSuniv < 0ΔG > 0nonspontaneous
ΔSuniv = 0ΔG = 0at equilibrium