Problem 2 - Chemistry: Introducing Inorganic, Organic and Physical Chemistry

Question

Predict the sign of the change in entropy in the system for the following processes (Section \(14.1)\) (a) Steam condensing on a cold window (b) A cloud forming in the atmosphere (c) Inflating a bicycle tyre with air (d) Dissolving sugar in hot coffee (e) \(P C l_{3}(g)+C l_{2}(g) \rightarrow P C l_{5}(g)\) (f) \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g})+\mathrm{CaSO}_{4}(\mathrm{s}) \rightarrow \mathrm{CaSO}_{4} \cdot \mathrm{H}_{2} \mathrm{O}(\mathrm{s})\) (g) \(\mathrm{SO}_{3}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}() \rightarrow \mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{aq})\) (h) \(2 \mathrm{KCl}(\mathrm{s})+\mathrm{H}_{2} \mathrm{SO}_{4}(\mathrm{I}) \rightarrow \mathrm{K}_{2} \mathrm{SO}_{4}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{g})\) \((i) \quad \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}()\)

Step-by-Step Solution

Answer

Entropy decreases in processes (a), (b), (e), (f), (g), and (i), while it increases in (c), (d), and (h).

Step 1: Analyze Phase Changes

When steam condenses (process a), water loses its gaseous phase and becomes liquid. A gas-to-liquid transition leads to decreased entropy as gas particles are more disordered than liquid particles. Similarly, when clouds form (process b), water vapor condenses into tiny droplets, reducing entropy for the same reason.

Step 2: Assess Gas Volume and Moles Changes

For inflating a bicycle tyre (process c), adding air increases the total number of gas particles inside the tyre, increasing disorder and thus increasing entropy. Additionally, dissolving sugar in hot coffee (process d) results in increased disorder as sugar molecules disperse within the coffee, also signifying an increase in entropy.

Step 3: Evaluate Chemical Reactions

For the reaction in process (e), 1 eq: PCl_{5}(g) is less disordered than the separately existing PCl_{3}(g) and Cl_{2}(g), thus, entropy decreases. In process (f), the formation of a solid hydrate from a gaseous and solid reactant reduces disorder, decreasing entropy. Process (g) converts gas reactants to an aqueous solution, indicating a decrease in entropy due to increased order. Conversely, process (h) forms more gas molecules than solid ones, indicating an increase in entropy.

Step 4: Consider Specific Molecular Structure

The reaction in process (i) consumes gas molecules to form a less disordered liquid alcohol, resulting in decreased entropy as the final product is more structured.

Key Concepts

Phase Changes

Phase changes are physical transformations where a substance shifts from one state of matter to another, such as from gas to liquid. In the context of entropy, which is a measure of disorder or randomness in a system, the type of phase change significantly affects this property.
When steam condenses on a cold window, a gas-to-liquid phase change occurs. This transition results in a decrease in entropy because gases are typically more disordered than liquids due to their high-energy, widely-spaced molecules. In contrast, liquid molecules are more closely packed and orderly. Similarly, when clouds form through the condensation of water vapor into liquid droplets, the system becomes less disordered, resulting in a decrease in entropy. Such changes are crucial in understanding natural phenomena and industrial processes where control of entropy is desired for efficiency.

Gas Volume

The concept of gas volume involves understanding how changes in the amount of gas in a system influence entropy. When inflating a bicycle tire, we introduce more air molecules into the confined space of the tire, which increases the disorder of the system due to increased particle movement and the larger volume occupied. This results in an increase in entropy.
It's important to acknowledge that the volume occupied by gas correlates with the number of particles present. More particles generally equate to more randomness within the system. Hence, anytime we add more gas molecules, as in inflating the bike tire or even dissolving a solute like sugar into a solvent like hot coffee, entropy tends to increase because the molecule's positions become more randomized. Understanding this can be beneficial in fields like thermodynamics and engineering, where gas dynamics play a crucial role.

Chemical Reactions

Chemical reactions often involve changes in the arrangement and types of molecules, affecting the system's entropy. The reaction between phosphorus trichloride and chlorine to produce phosphorus pentachloride illustrates how combining separate gas molecules into one product leads to decreased entropy. This is due to the reaction forming a more ordered structure from the initial disordered gases.
Consider also other reactions like the formation of a solid hydrate in the presence of a gaseous and solid reactant. Such transformations typically lead to decreased entropy since solids represent a more ordered state than the gases or liquids from which they form. Conversely, reactions that generate more gas molecules, like producing hydrochloric acid gas from solid reactants, usually increase entropy by creating greater disorder. The evaluation of these reactions is paramount in understanding energy exchange and predictability in chemical processes.

Molecular Structure

Molecular structure significantly impacts how substances behave and their entropy levels. When molecules change from a more disordered form, such as gas, to an ordered molecular structure in liquids or solids, the entropy decreases. During the conversion of ethene and water into ethanol, gas molecules rearrange into a liquid alcohol, which implies a more structured state with fewer possible arrangements, thus lowering entropy.
Understanding molecular structure allows scientists and engineers to predict how changes at the molecular level affect the system as a whole. For instance, in chemical manufacturing or materials science, knowing how molecular changes affect entropy can lead to better control over product consistency and process efficiency. Each molecular rearrangement impacts the overall system's disorder, and understanding this helps in optimizing reactions and designing systems.