Predict the sign of \(\Delta S_{\text { sys }}\) for each of the following processes: (a) Molten gold solidifies. (b) Gaseous \(C l_{2}\) dissociates in the stratosphere to form gaseous Cl atoms. (c) Gaseous CO reacts with gaseous \(\mathrm{H}_{2}\) to form liquid methanol, \(\mathrm{CH}_{3} \mathrm{OH} .(\mathbf{d})\) Calcium phosphate precipitates upon mixing \(\mathrm{Ca}\left(\mathrm{NO}_{3}\right)_{2}(a q)\) and \(\left(\mathrm{NH}_{4}\right)_{3} \mathrm{PO}_{4}(a q)\)

Thermodynamics is a fundamental branch of physical chemistry that deals with the relationships between energy, heat, work, and the changes these cause in the chemical composition of substances. One of the core concepts of thermodynamics is entropy, symbolized as 'S', which is a measure of the disorder or randomness in a system. The second law of thermodynamics states that entropy in an isolated system will tend to increase over time.

In the context of chemistry, this law helps predict the direction in which a chemical process will naturally proceed. A chemical reaction or physical change will favor the direction that increases the system's overall entropy, making entropy an essential indicator of reaction spontaneity.

Phase changes, such as melting, freezing, vaporization, condensation, and sublimation, are physical changes that involve a transition between different states of matter. During a phase change, the entropy of a system changes significantly because the molecular arrangement and degree of movement change drastically.

When a substance melts or vaporizes, it goes from an ordered phase (solid or liquid) to a more disordered phase (liquid or gas), resulting in an increase in entropy (\texttt{\(\Delta S_{sys}>0\)}). Conversely, when a substance freezes or condenses, the disorder decreases as the molecules become more ordered and fixed, which leads to a decrease in entropy (\texttt{\(\Delta S_{sys}<0\)}). These changes are predictable through the concept of entropy.

The principle of entropy applies not only to phase changes but also to chemical reactions. Chemical reactions involve the breaking and forming of chemical bonds, leading to changes in the molecular structure and, consequently, the entropy of the system. A reaction resulting in more complex molecules from simpler ones, or in molecules with more motion possibilities like gases, will generally increase the entropy.

It's also noteworthy that reactions that produce more moles of gas from fewer moles of gas or from liquids or solids usually lead to an increase in entropy. This links back to the notion that gases have more freedom of movement than liquids and solids, contributing to a more disordered system.

The change in entropy, denoted as \texttt{\(\Delta S_{sys}\)}, is a key parameter to determine when discussing chemical reactions. When we predict the sign of \texttt{\(\Delta S_{sys}\)} for a given process, we consider whether the process induces more disorder or less within the system.

For example, reactions that result in a solid from either a liquid or a gaseous state will typically lead to a decrease in entropy (\texttt{\(\Delta S_{sys}<0\)}) due to the increased order and rigidity in the solid state. Similarly, reactions that create fewer or simpler molecules from many or more complex ones will also reduce the system's entropy. Understanding these entropy changes assists chemists in predicting the behavior of chemical reactions under various conditions.