For a system in equilibrium, \(\Delta G=0\) under conditions of constant (a) temperature and pressure (b) temperature and volume (c) pressure and volume (d) energy and volume

Understanding chemical equilibrium is crucial for interpreting various chemical reactions and processes. It is the state at which the concentrations of reactants and products do not change over time, signifying a balance has been reached in a reversible reaction.

At equilibrium, the rate of the forward reaction equals the rate of the backward reaction, resulting in no net change. This concept is vital for predicting the behavior of chemical systems under different conditions. For example, predicting how changes in temperature or pressure can shift the equilibrium to favor either the reactants or the products.

Navigating the principles of thermodynamics is essential to understand energy conversion and the feasibility of reactions. It encompasses the study of relationships between heat, work, temperature, and energy. The first law of thermodynamics insists on the conservation of energy, meaning energy can neither be created nor destroyed, only transformed.

The second law introduces the concept of entropy, dictating the direction of spontaneous processes and highlighting that the total entropy of an isolated system can never decrease over time. In practical terms, thermodynamics helps us apprehend how energy changes impact chemical systems, including reactions at chemical equilibrium.

Diving into entropy, we delve into the measure of disorder or randomness in a system. Represented by the symbol \(S\), entropy is a cornerstone of the second law of thermodynamics. The increase in entropy is a natural tendency in the universe, describing the direction toward which processes naturally proceed.

When interpreting the solution in our exercise, the term \(T\Delta S\) in the Gibbs free energy equation represents the energy dispersal due to entropy changes. Entropy can be influenced by several factors, such as temperature; typically, as temperature increases, so does entropy. It's the entropic factor that often determines whether or not a reaction will proceed spontaneously.

Enthalpy, symbolized by \(H\), is a measure of the total heat content in a thermodynamic system, reflecting the energy required to create a system and the energy required to allow the system to expand against the atmospheric pressure. It's an extensive property, meaning it depends on the amount of substance in a system.

In the context of our exercise, the change in enthalpy, \(\Delta H\), represents the heat absorbed or released during a process at constant pressure. If \(\Delta H\) is negative, the reaction is exothermic (releases heat); if positive, it is endothermic (absorbs heat). Enthalpy plays a key role in determining whether reactions are energetically favorable under certain conditions.