For chemical systems, the value of ΔS was not always possible to determine. As a result, a new thermodynamic function was needed to predict the direction of spontaneity. J. Gibbs introduced a new function known as Gibbs' free energy. Denoted by the letter G, it is mathematically defined by

G = H - TS

Where,

H= Enthalpy of the system

T= Absolute temperature (Kelvin scale)

S= Entropy of a system

Let us consider an isothermal change at temperature T from initial state 1 to final state 2.

Then for the initial state,

G₁= H₁ - TS₁

And, for final state,

G₂=H₂-TS₂

The change of free energy ΔG is given by

ΔG =G₂-G₁

      =H₂-TS₂-(H₁-TS₁)

      =(H₂-H₁)-T(S2-S₁)

  Thus,

      ΔG=ΔH-TΔS 

This equation is also known as Gibbs Helmholtz Equation.