The Gibbs free energy of a reaction plays a critical role in determining its spontaneity, with negative values indicating that a reaction can occur spontaneously.

Gibbs free energy, denoted as $G$, quantifies a reaction’s potential to perform work. It is calculated using the equation:

In this equation, $\Delta G$ represents the change in Gibbs free energy, $\Delta H$ is the change in enthalpy, $T$ is the temperature in Kelvin, and $\Delta S$ is the change in entropy. A negative value for $\Delta G$ indicates that the reaction is spontaneous, meaning it can proceed without the need for external energy. In contrast, a positive value for $\Delta G$ signifies that the reaction is non-spontaneous and will require an input of external energy to occur.

The spontaneity of a reaction is determined by comparing the Gibbs free energy of the products and the reactants. If the Gibbs free energy of the products is lower than that of the reactants, the reaction is spontaneous. This is because the products possess lower potential energy than the reactants, allowing the reaction to release energy as it progresses.

It is also essential to consider the magnitude of the Gibbs free energy change, as it affects the spontaneity of the reaction. A reaction with a small negative $\Delta G$ may still need a considerable amount of energy to overcome the activation energy barrier before it can proceed. Conversely, a reaction characterized by a large negative $\Delta G$ will typically occur quickly and spontaneously.

In summary, the Gibbs free energy of a reaction is a vital factor in determining its spontaneity, where negative values indicate that a reaction can occur spontaneously. However, the magnitude of the Gibbs free energy change also influences how easily a reaction can take place.