What is the relationship between ΔGand$∆G\stackrel{+}{+}$?

For example, Gibbs free energy is the total amount of energy available in the system to carry out useful work, for example, the chemical reaction. It is mathematically calculated by taking the difference between the enthalpy and energy of a system that maintains its entropy.

The change in Gibbs free energy$∆G$is the change in the enthalpy of the reaction minus the product of temperature and entropy of the reaction and is represented as follows:
$∆G=∆H-T∆S$

The change in free energy of activation is the change in the enthalpy of activation minus the product of temperature and entropy of the activation and is represented as follows:

$∆G=∆H\stackrel{+}{+}-T∆S\stackrel{+}{+}$

In both the free energies (Gibbs free energy and free energy of activation), if less than zero or minus, the reaction proceeds spontaneously from reactant to product, and if they are more than zero or positive, the reaction becomes non-spontaneous. This is represented as follows:

$$\begin{gathered} ∆G\stackrel{+}{+},∆G<0\to \left(\text{Spontaneous}\text{Reaction}\right) \\ ∆G\stackrel{+}{+},∆G>0\to \left(\text{Non - spontaneous}\text{Reaction}\right) \end{gathered}$$