Why is it more convenient to predict the direction of a reaction in terms of \(\Delta G_{\text {sys }}\) instead of \(\Delta S_{\text {univ }}\) ? Under what conditions can \(\Delta G_{\text {sys }}\) be used to predict the spontaneity of a reaction?

When we consider whether a chemical reaction can occur on its own, without any extra energy input, we are discussing its spontaneity. A key factor in determining this is the Gibbs free energy, denoted as \( \Delta G_{\text{sys}} \). If \( \Delta G_{\text{sys}} \) is negative, the reaction is said to be spontaneous because it indicates that the system is releasing energy. Conversely, if \( \Delta G_{\text{sys}} \) is positive, the reaction requires energy input to proceed, rendering it non-spontaneous.

Spontaneity does not imply that a reaction will happen quickly; rather, it means that the direction of the process is favorable energetically. Furthermore, the temperature can play a significant role in spontaneity. For instance, some reactions are spontaneous only at higher temperatures where thermal energy contributes to the process, making the prediction of spontaneity quite complex without considering \( \Delta G_{\text{sys}} \).

Entropy, symbolized by \( S \), is a measure of disorder or randomness within a system. The fundamental principle of thermodynamics is that the total entropy, or \( \Delta S_{\text{univ}} \), which includes the entropy of the system and its surroundings, always increases for a spontaneous process. This aligns with the concept that the universe tends toward disorder.

Although \( \Delta S_{\text{univ}} \) is fundamental in determining the direction of a reaction, it is challenging to measure directly. Hence, \( \Delta G_{\text{sys}} \) is often used as it incorporates entropy changes within the system, thus providing a more practical way to assess the trivial process of change in entropy in the universe.

Enthalpy, denoted by \( \Delta H \), is the total heat content in a system at constant pressure. It is a reflection of energy changes, particularly heat absorbed or released during a reaction. If a reaction releases heat (exothermic), \( \Delta H \) is negative, often aiding spontaneity, since it may increase entropy by distributing energy to the surroundings.

The relationship between enthalpy and Gibbs free energy is captured in the equation \( \Delta G_{\text{sys}} = \Delta H - T\Delta S \), where \( T \) is the absolute temperature. This equation indicates that spontaneity is not determined by enthalpy alone, but also by entropy and temperature. Thus, a deep understanding of enthalpy is crucial in evaluating a reaction's potential to occur without external influences.

Chemical equilibrium is the state in which the rates of the forward and reverse reactions are equal, leading to no net change in the concentrations of reactants and products over time. At equilibrium, the Gibbs free energy of a system is at its minimum, and \( \Delta G_{\text{sys}} \) equals zero.

Being at equilibrium does not mean the reactants and products are present in equal amounts, but rather their ratio will remain constant. Understanding how conditions such as pressure and temperature influence this balance is critical when predicting and manipulating reactions, especially in industrial chemical processes. By adjusting these conditions, chemists can shift the equilibrium to favor the formation of desired products, optimizing yield and efficiency.