Define Gibbs free energy in your own words.

In the context of understanding Gibbs free energy, it's crucial to first grasp what we mean by a thermodynamic system. A thermodynamic system refers to a specific portion of the universe that is under study. It could be as simple as a container of gas or as complex as a living organism. The rest of the universe outside this system is known as the surroundings. A thermodynamic system can exchange energy and matter with its surroundings in several ways — through the walls of the container holding the gas, for example.

Systems are classified based on how they interact with their surroundings. There are isolated systems, which do not exchange energy or matter with the environment; closed systems, which exchange energy but not matter; and open systems, which can exchange both energy and matter. Understanding which type of system you're dealing with is fundamental when discussing thermodynamic properties like pressure, volume, temperature, and in particular, Gibbs free energy.

The concept of reversible work is a theoretical ideal that involves a system undergoing a process where it can be returned to its original state without any change in itself or the surroundings. In other words, reversible processes are idealized processes that are infinitesimally close to equilibrium at all stages. When we discuss reversible work in the context of Gibbs free energy, we're referring to the work that can be theoretically obtained as a system undergoes a change in such a perfectly efficient manner.

Understanding reversible work is essential when analyzing thermodynamic cycles, engines, or any system where efficiency plays a critical role. Although no real process can be perfectly reversible due to natural irreversibilities (like friction and heat loss), the concept sets an upper limit to how efficient a process can be. Reversible work is connected to the maximum work that a system can do, underlining why Gibbs free energy is so important, particularly because it gives us the upper bound of useful work obtainable from a chemical reaction at constant temperature and pressure.

A spontaneous process is a physical or chemical change that occurs by itself without needing an external force or energy once it has been initiated. In thermodynamics, we're often interested in predicting whether a reaction or phase change will occur spontaneously. This is where Gibbs free energy becomes an invaluable tool. If the change in Gibbs free energy (\( \boldsymbol{\bigtriangleup G} \) for a process) is negative, this implies that the process can proceed without external energy input — it's spontaneous.

However, it's critical to note that a negative Gibbs free energy does not tell us anything about the rate of the process — it only indicates the potential for spontaneity. Fast processes like explosions and slow processes like the rusting of iron can both be spontaneous, yet their kinetics (rates) are vastly different. This is a crucial distinction that can sometimes confuse students but is essential for a complete understanding of spontaneous processes in thermodynamics.