Why is \(\Delta S_{\mathrm{ac}}^{\circ}\) of \(\mathrm{N}(\mathrm{g})=0\) ?

Entropy is a foundational concept in thermodynamics, often symbolized as 'S'. It measures the disorder or randomness within a system. From a microscopic perspective, it is related to the number of possible microstates that a system can have. An increase in entropy corresponds to increased disorder and energy dispersion.

In chemical processes, when a substance is formed from its elements, the amount of energy distribution can change, and with it, the entropy. The standard entropy change of formation, \(\Delta S_{\mathrm{ac}}^{\circ}\), indicates how the entropy of a substance changes from its reference state when formed under standard conditions.

Thermodynamics is the study of energy, heat, work, and how they interact with each other in physical systems. It encompasses several laws that govern energy transformations and equilibrium. In terms of chemical reactions, thermodynamics focuses on how energy is transferred, the directionality of reactions based on energy states, and the concept of spontaneity, which is often linked with the concept of entropy.

In fact, the Second Law of Thermodynamics states that for a spontaneous process, the total entropy of a system and its surroundings always increases. Therefore, understanding the changes in entropy, including the standard entropy change of formation, is vital to determining the feasibility and direction of a chemical reaction.

Chemical stability refers to the propensity of a chemical compound to maintain its original structure and not react or decompose under normal storage conditions. Stability can be influenced by factors such as temperature, pressure, and the presence of catalysts or other chemicals.

In thermodynamic terms, more stable compounds generally have lower energy states. With entropy being a key factor in determining the spontaneity of reactions, the standard entropy change of formation can provide insights into a compound's stability. A zero \(\Delta S_{\mathrm{ac}}^{\circ}\) means the substance is already in its most stable form and thus doesn't change its entropy when it 'forms' from itself, as in the case of elemental nitrogen gas.

The reference state serves as a baseline or standard condition from which changes in thermodynamic quantities can be measured. In thermodynamics, it is essential to define a reference point to assess relative changes. For entropy, the reference state for pure substances is their most stable form at 1 bar of pressure and a specified temperature, usually 25°C (298 K).

This convention simplifies calculations for chemical reactions and makes tabulation of data feasible, as seen with standard entropy changes of formation. When the textbook says that \(\Delta S_{\mathrm{ac}}^{\circ}\) of \(\mathrm{N}(\mathrm{g})=0\), it reflects that nitrogen gas, \(\mathrm{N}_{2}\), in its most stable state, represents the reference state for nitrogen, and thus there is no entropy change when it is formed from itself.