What is the equation that relates free energy, enthalpy, and entropy?

The relationship between free energy, enthalpy, and entropy is described by the equation:

[

\Delta G = \Delta H - T \Delta S

]

In this equation, (\Delta G) represents the change in Gibbs free energy, (\Delta H) indicates the change in enthalpy, (T) is the temperature in Kelvin, and (\Delta S) is the change in entropy. This equation establishes a fundamental principle in thermodynamics regarding the spontaneity of processes.

When assessing spontaneity, the Gibbs free energy ((\Delta G)) must be negative for a process to occur spontaneously at constant temperature and pressure. The term (T \Delta S) accounts for the entropy change, which contributes positively to the free energy change when the system increases in entropy. By subtracting this term from the enthalpy change, the equation effectively captures the trade-off between the energy content of a system (represented by enthalpy) and the degree of disorder or energy dispersal (represented by entropy).

As temperature increases or the entropy change becomes more favorable (positive), the term (T \Delta S) can significantly influence the overall value of (\Delta G), thereby determining