Predict the sign of the entropy change for the following processes. Give a reason for your prediction. (a) \(\mathrm{Pb}^{2+}(a q)+\mathrm{S}^{2-}(a q) \longrightarrow \mathrm{PbS}(s)\) (b) \(2 \mathrm{Fe}(s)+\frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_{2} \mathrm{O}_{2}(s)\) (c) \(2 \mathrm{C}_{6} \mathrm{H}_{14}(l)+19 \mathrm{O}_{2}(g) \longrightarrow 14 \mathrm{H}_{2} \mathrm{O}(g)+12 \mathrm{CO}_{2}(g)\)

When studying Chemical Reactions, the concept of entropy provides crucial insight into the spontaneity and feasibility of reactions. Entropy, symbolized as \( \Delta S \), measures the disorder or randomness within a chemical system.

For instance, in the reaction \( \mathrm{Pb}^{2+}(aq) + \mathrm{S}^{2-}(aq) \longrightarrow \mathrm{PbS}(s) \) from the exercise, two ions in a solution (which have high entropy due to their movement and dispersion in water) combine to form a solid compound. Solids have lower entropy compared to solutions because the particles are in a fixed position and have less freedom to move. This combination signifies a decrease in entropy, leading to a negative entropy change.

In chemistry, tracking such entropy changes helps in predicting the direction of the reaction. If a process leads to increased disorder, the entropy change is positive, indicating the reaction may favor the products; conversely, a decrease in entropy suggests a less favorable reaction towards the product formation.

The field of Thermodynamics in Chemistry is pivotal in understanding how energy exchange and transformation govern chemical processes. Thermodynamics deals with several state functions, including temperature, pressure, enthalpy, and entropy. Specifically, the Second Law of Thermodynamics tells us that the total entropy of the universe always increases for a spontaneous process.

When analyzing the reaction \(2 \mathrm{Fe}(s) + \frac{3}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Fe}_2\mathrm{O}_3(s)\), the role of thermodynamics is clear. The reaction involves the transformation from gas to solid, representing a move towards a more ordered state, thus a negative change in entropy. Despite this, such a reaction can still occur spontaneously if it releases enough energy (exothermic), which can contribute to an overall increase in the universe's entropy, aligning with thermodynamic principles.

Physical and Chemical Changes are two types of processes that alter the state or composition of a substance. Physical changes concern the state of a substance, like melting or boiling, which do not result in new substances, whereas chemical changes involve the making or breaking of bonds to form new substances.

For example, in the provided exercise, the combustion reaction \(2 \mathrm{C}_6 \mathrm{H}_{14}(l) + 19 \mathrm{O}_{2}(g) \longrightarrow 14 \mathrm{H}_2\mathrm{O}(g) + 12 \mathrm{CO}_2(g)\) showcases a chemical change. This transformation produces gas molecules from a liquid and a gas, reflecting an increase in disorder and positive entropy change.

It is important to realize that chemical changes are often accompanied by physical changes. An increase in the volume occupied by gas molecules is a physical change, while the formation of new gaseous compounds is a chemical change. Together, these changes illustrate how entropy can increase or decrease depending on the nature of the process, and why differentiating between the two types of changes is essential in the study of thermodynamics and chemical reactions.