Oxygen can be made in the laboratory by reacting sodium peroxide and water. $$ \begin{gathered} 2 \mathrm{Na}_{2} \mathrm{O}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 4 \mathrm{NaOH}(s)+\mathrm{O}_{2}(g) \\ \Delta H^{\circ}=-109.0 \mathrm{~kJ} ; \Delta G^{\circ}=-148.4 \mathrm{~kJ} \text { at } 25^{\circ} \mathrm{C} \end{gathered} $$ (a) Calculate \(\Delta S^{\circ}\). Is the sign reasonable? (b) Calculate \(S^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\). (c) Calculate \(\Delta H_{f}^{\circ}\) for \(\mathrm{Na}_{2} \mathrm{O}_{2}(s)\).

Gibbs free energy, represented as \( G \), plays a pivotal role in thermodynamics within chemistry; primarily, it helps predict whether a chemical reaction will occur spontaneously under constant pressure and temperature. A reaction is considered spontaneous if it leads to a decrease in the system's free energy (\(\Delta G^\circ < 0\)). The concept revolves around energy conservation and conversions between different forms, such as heat and work.When discussing Gibbs free energy in the context of chemical reactions, the Gibbs-Helmholtz equation is often utilized:\[\Delta G^\circ = \Delta H^\circ - T\Delta S^\circ\]This equation links the change in Gibbs free energy (\(\Delta G^\circ\)) to the change in enthalpy (\(\Delta H^\circ\)) and change in entropy (\(\Delta S^\circ\)) at a constant temperature (\(T\)). In essence, it's a balance between the energy given off or absorbed (in the form of heat) and the degree of freedom at the molecular level—an interplay of enthalpy and entropy. The temperature, measured in Kelvin, scales the impact of entropy change on the free energy change.In our exercise, the given reaction is spontaneous as the calculated Gibbs free energy change is negative (\(\Delta G^\circ = -148.4 \text{kJ}\)), indicating the process can proceed without external energy input. This forms the groundwork for many predictions and designs in chemical processes, such as reaction feasibility and the direction of equilibria.

Standard enthalpy change, represented as \( \Delta H^\circ \), signifies the heat absorbed or released during a chemical reaction at standard conditions (1 atm pressure and, usually, 25°C or 298K). It is intrinsic to the types of bonds formed and broken in the reaction, with endothermic reactions absorbing heat (\(\Delta H^\circ > 0\)) and exothermic reactions releasing heat (\(\Delta H^\circ < 0\)).

Chemists use this concept to assess the thermal aspect of reactions and how much energy is involved in breaking and forming chemical bonds. It’s also handy in calculating how heat changes affect the surroundings and the overall energy efficiency of chemical processes.

In the exercise, the reaction exhibits a negative standard enthalpy change (\(\Delta H^\circ = -109.0 \text{kJ}\)), classifying it as exothermic. Thus, it releases heat to its surroundings. The standard enthalpy change is also pivotal in calculating other thermodynamic properties, such as Gibbs free energy.

Standard entropy change, indicated as \( \Delta S^\circ \), quantifies the change in disorder or randomness in a system during a chemical process. Entropy is a fundamental concept in thermodynamics embodying the distribution of energy within a system, and by extension, the possible microstates a system can occupy. Increases in entropy (\(\Delta S^\circ > 0\)) suggest a transition towards more disorder, while decreases imply the opposite.

In chemical reactions, entropy considers molecular complexity, phase changes, and changes in the number of particles. Reactions that produce gases typically show a significant increase in entropy because gases have more random movement and higher disorder than solids or liquids.

Our exercise explores the entropy change in a reaction forming a gas, oxygen, from solid and liquid reactants. The expectation is a positive entropy change, supported by the computation using the Gibbs-Helmholtz equation. Analyzing the entropy change offers insight into the 'driving force' behind reaction spontaneity; it's not just about the energy exchanges but also how the system’s order is affected.