Gibbs free energy is fundamentally influenced by the interaction between enthalpy and entropy changes within a system.

The change in Gibbs free energy, denoted as $\Delta G$, is a measure of the maximum reversible work that a system can perform while maintaining constant temperature and pressure. It is calculated using the equation

where $\Delta H$ represents the change in enthalpy, $T$ is the absolute temperature, and $\Delta S$ signifies the change in entropy.

Enthalpy, denoted as $H$, quantifies the total energy of a system. This includes both the internal energy of the system—which is the energy required to create the system—and the energy needed to accommodate the system by displacing its surroundings. A negative change in enthalpy ($\Delta H < 0$) indicates an exothermic reaction, where heat is released, whereas a positive change in enthalpy ($\Delta H > 0$) signifies an endothermic reaction, where heat is absorbed.

Conversely, entropy, represented as $S$, measures the disorder or randomness within a system. An increase in entropy ($\Delta S > 0$) signifies greater disorder, while a decrease in entropy ($\Delta S < 0$) indicates reduced disorder.

The relationship between enthalpy and entropy changes is crucial in determining the Gibbs free energy change, which subsequently influences the spontaneity of a reaction. If $\Delta G$ is negative, the reaction is spontaneous; if $\Delta G$ is positive, the reaction is non-spontaneous; and if $\Delta G$ equals zero, the system is at equilibrium.

For instance, consider an exothermic reaction characterized by a negative $\Delta H$ that also leads to an increase in disorder (positive $\Delta S$). In this case, the Gibbs free energy change will be negative, indicating that the reaction is spontaneous. Conversely, if the reaction is endothermic (positive $\Delta H$) and results in decreased disorder (negative $\Delta S$), the Gibbs free energy change will be positive, suggesting that the reaction is non-spontaneous.

In conclusion, the interaction between changes in enthalpy and entropy is essential for determining the Gibbs free energy change and the spontaneity of a reaction. A thorough understanding of this interplay is vital for predicting the behavior of chemical systems.