Calculate the \(\Delta S_{\text {soln }}^{\circ}\) for the following processes: (a) \(\mathrm{NH}_{4} \mathrm{NO}_{3}(s) \longrightarrow \mathrm{NH}_{4}^{+}(a q)+\mathrm{NO}_{3}^{-}(a q)\) and (b) \(\mathrm{FeCl}_{3}(s) \longrightarrow \mathrm{Fe}^{3+}(a q)+3 \mathrm{Cl}^{-}(a q) .\) Give a qualitative explanation for the signs.

Thermodynamics is a branch of chemistry that deals with the energy changes involved in chemical reactions and physical transformations. The first law of thermodynamics, also known as the law of energy conservation, states that energy can neither be created nor destroyed, only transformed from one form to another. In chemistry, this often involves the conversion of potential energy stored in chemical bonds to kinetic energy or thermal energy.

When studying chemical reactions, one essential concept is the change in enthalpy, denoted as \( \Delta H \), which reflects the heat absorbed or released. However, this only tells part of the story. That's where entropy (\( S \)) and the second law of thermodynamics come into play. The second law introduces the idea of disorder or randomness in a system, suggesting that processes occur in a direction that increases the total entropy of the universe.

From dissolving a salt in water to the rusting of iron, thermodynamics provides the framework to predict whether a process will occur spontaneously based on enthalpy and entropy changes. Calculating these changes, as in the exercise above, allows chemists to gain profound insights into the driving forces behind chemical phenomena.

Entropy is a measure of the randomness or disorder of a system and is a fundamental concept in thermodynamics. Represented by the symbol \( S \), entropy quantifies the number of ways particles can be arranged, where higher entropy signifies greater disorder and a larger number of microstates.

At the microscopic level, molecules are in constant motion, and this motion contributes to the entropy of a system. For example, gases have higher entropy than liquids, and liquids have higher entropy than solids, because particles in a gas can move more freely and have more accessible microstates.

The tendency of entropy to increase in isolated systems explains many natural processes—it’s why perfume diffuses throughout a room and why ice melts into water. For the dissolution processes in the given exercise, the entropy change (\( \Delta S \)) reflects the disorder change when a solid solute dissolves into its constituent ions in solution, generally leading to an increase in entropy.

The chemical dissolution process involves the breaking down of a substance into its ions or molecules in the presence of a solvent. This process is significant in chemistry because it affects the behavior and reactivity of substances. Dissolution can be endothermic, requiring energy to overcome intermolecular forces, or exothermic, releasing energy when new interactions are formed.

In the exercise, the dissolution of \( \mathrm{NH}_{4}\mathrm{NO}_{3} \) and \( \mathrm{FeCl}_{3} \) into their constituent ions in water is evaluated in terms of entropy change. As a general rule, the dissolution process tends to increase the entropy of the system. The solid lattice structure is broken into freely moving ions or molecules that can interact with the solvent, leading to a higher level of randomness in the solution than in the solid state.

By calculating the standard molar entropy changes, \( \Delta S_{\text{soln}}^{\circ} \) for these processes using the given steps, we can confirm this principle. A positive value of \( \Delta S_{\text{soln}}^{\circ} \) indicates that the resulting solution is more disordered than the original solid, which is usually the case when a solid dissolves in a solvent.