# D20.3 Gibbs Free Energy

A new thermodynamic property was introduced in the late 19th century by American mathematician Josiah Willard Gibbs. The property is called the Gibbs free energy (G) (or simply the free energy), and is defined in terms of a system’s enthalpy, entropy, and temperature:

Gsys = Hsys − TSsys

The change in Gibbs free energy (ΔG) at constant temperature may be expressed as:

ΔGsys = ΔHsys − TΔSsys

ΔG is related to whether a process is spontaneous. This relationship can be seen by comparing to the second law of thermodynamics:

ΔSuniv = ΔSsys + ΔSsurr
ΔSuniv = ΔSsys

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

TΔSuniv = ΔHsys – TΔSsys

which can be compared to the equation:

ΔGsys = ΔHsys − TΔSsys

Hence:

ΔGsys = −TΔSuniv

For a process that is spontaneous, ΔSuniv must be positive. Because thermodynamic temperature is always positive (values are in kelvins), ΔG must be negative for a process that proceeds forward of its own accord.

 ΔSuniv > 0 ΔGsys < 0 spontaneous (takes place of its own accord) ΔSuniv < 0 ΔGsys > 0 not spontaneous (reverse reaction would occur) ΔSuniv = 0 ΔGsys = 0 at equilibrium