**Gibbs Free Energy and Spontaneity**

**Context**:

Historically, the study of thermodynamics was central to understanding why certain reactions occurred spontaneously while others did not. In the late 19th century, Josiah Willard Gibbs, an American scientist, proposed the concept of free energy, a combination of enthalpy and entropy, to explain the spontaneity of processes. His work has since become foundational in the realm of physical chemistry and plays a critical role in predicting whether a given reaction will be spontaneous under certain conditions.

**Detailed Content**:

**1. Defining Gibbs Free Energy (G)**:

- Gibbs Free Energy (often denoted as G) is a thermodynamic potential that measures the maximum reversible work that can be performed by a system at constant temperature and pressure.

**2. Gibbs Free Energy Change (ΔG)**:

- ΔG is the change in Gibbs Free Energy as a process or reaction occurs. It provides crucial information about the spontaneity of the reaction:a. If ΔG < 0: The process is spontaneous in the forward direction.
b. If ΔG > 0: The process is non-spontaneous in the forward direction (but spontaneous in the reverse).

c. If ΔG = 0: The system is at equilibrium, and no net change will occur.

**3. Relationship with Enthalpy (H) and Entropy (S)**:

- The Gibbs Free Energy is related to enthalpy and entropy by the equation: $ΔG=ΔH−TΔS$Where ΔH is the change in enthalpy, ΔS is the change in entropy, and T is the absolute temperature (in Kelvin).

**4. Interpretation of the Relationship**:

- For a process to be spontaneous at all temperatures, it should be exothermic (ΔH < 0) and have an increase in entropy (ΔS > 0).
- However, even if one of the conditions isn’t met, a reaction can still be spontaneous under certain temperatures. For instance, an endothermic reaction (ΔH > 0) with ΔS > 0 can still be spontaneous at high temperatures.

**Patterns and Trends**:

**Temperature Dependence**: The spontaneity of reactions can be dependent on temperature due to the TΔS term in the Gibbs equation. Some reactions might be spontaneous only at high or low temperatures.

**Influential Figures or Works**:

**Josiah Willard Gibbs**: The foundational figure behind the concept of free energy, his work in the late 19th century set the stage for modern physical chemistry and thermodynamics.

**Relevance in the Broader Framework**:

**Predicting Reaction Favorability**: By calculating or estimating ΔG, chemists can predict whether a certain reaction will proceed under the given conditions. This has profound implications in fields ranging from biochemistry, where the spontaneity of metabolic reactions is of interest, to industries aiming to synthesize specific compounds.**Understanding Energy Harnessing**: In biological systems, processes that have a negative ΔG release energy that can be harnessed for work. For instance, the hydrolysis of ATP, a central energy currency in cells, is exergonic (ΔG < 0) and powers various cellular activities.

**Conclusion**:

Gibbs Free Energy offers a unified view of the thermodynamic favorability of processes, combining the effects of enthalpy and entropy. Understanding this concept is key to predicting the behavior of systems and has been instrumental in advances in both the natural sciences and industries.