Problem 41 - Chemistry: The Central Science

Question

Predict the sign of the entropy change of the system for each of the following reactions: (a) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)\) (b) \(\mathrm{Ba}(\mathrm{OH})_{2}(s) \stackrel{\mathrm{L}}{\longrightarrow} \mathrm{BaO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (c) \(\mathrm{CO}(\mathrm{g})+2 \mathrm{H}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\) (d) \(\mathrm{FeCl}_{2}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+2 \mathrm{HCl}(g)\)

Step-by-Step Solution

Answer

(a) The sign of the entropy change is negative. (b) The sign of the entropy change is positive. (c) The sign of the entropy change is negative. (d) The sign of the entropy change is positive.

Step 1: Analyze molecular complexity and phase change

In this reaction, there is no phase change, as both reactants and products are in gaseous state. The reaction involves 3 gas molecules combining to form 2 gas molecules. As there are fewer gas molecules in the products than the reactants, the molecular complexity and randomness of the system is decreasing.

Step 2: Determine the sign of entropy change

Since the molecular complexity and randomness of the system decreases, the entropy change must be negative. So, the sign of the entropy change of this reaction is negative. (b) Reaction: \(\mathrm{Ba}(\mathrm{OH})_{2}(s) \stackrel{\mathrm{L}}{\longrightarrow} \mathrm{BaO}(s)+\mathrm{H}_{2} \mathrm{O}(g)\)

Step 1: Analyze molecular complexity and phase change

In this reaction, there is a phase change from a solid reactant to a solid and a gaseous product. The system undergoes an increase in randomness by releasing a gas molecule.

Step 2: Determine the sign of entropy change

The entropy change in this reaction is positive because the phase change and release of a gas molecule increase the randomness of the system. (c) Reaction: \(\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l)\)

Step 1: Analyze molecular complexity and phase change

In this reaction, there is a phase change from gaseous reactants to a liquid product. Also, 3 gas molecules combine to form 1 liquid molecule. Both the molecular complexity and phase change indicate a decrease in randomness.

Step 2: Determine the sign of entropy change

The entropy change in this reaction is negative because the phase change from gas to liquid and combination of molecules decrease the randomness of the system. (d) Reaction: \(\mathrm{FeCl}_{2}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+2 \mathrm{HCl}(g)\)

Step 1: Analyze molecular complexity and phase change

In this reaction, there is no phase change for the solid reactant and product, however, one gas molecule reacts to form two gas molecules. This increase in the number of gas molecules increases the randomness of the system.

Step 2: Determine the sign of entropy change

Since the molecular complexity and randomness of the system increases, the entropy change must be positive. So, the sign of the entropy change of this reaction is positive.

Key Concepts

Molecular Complexity

Molecular complexity refers to the number of atoms or structural features within a molecule. In terms of entropy, more complex molecules generally have higher entropy due to a greater number of ways to arrange their atoms. When a reaction involves a change in molecular complexity, it often impacts the system's entropy.

• For instance, if simpler molecules transform into more complex ones, this typically leads to an increase in entropy.
• If the opposite occurs—complex molecules simplify into less complex ones—entropy might decrease.

Consider the reaction of \ \(2 \, \mathrm{SO}_{2}(g)+ \mathrm{O}_{2}(g) \stackrel{L}{\longrightarrow} 2 \, \mathrm{SO}_{3}(g), \) consisting initially of three gas molecules. Here, two are \( \mathrm{SO}_{2}, \) and one is oxygen. They combine to form two \( \mathrm{SO}_{3} \) gas molecules. The reduction in the number of molecules indicates a decrease in molecular complexity. This typically corresponds to a negative entropy change, reflecting less randomness.

Phase Change

In chemistry, phase changes are transitions between different states of matter: solids, liquids, and gases. Phase changes can dramatically impact entropy changes.

• When a substance moves from a solid to a liquid or from a liquid to a gas, the entropy generally increases because the particles in these states are less ordered.
• Conversely, phase changes from gas to liquid or liquid to solid usually result in a decrease in entropy.

Let's explore the reaction \( \mathrm{CO}(g)+2 \, \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(l). \) Here, the transition from gaseous reactants to a liquid product highlights a significant decrease in entropy. The liquid \( \mathrm{CH}_{3} \mathrm{OH} \) has more structured, less random movements compared to the gaseous \( \mathrm{CO} \) and \( \mathrm{H}_{2} \) reactants. This phase change results in a negative entropy change, indicating decreased randomness.

Gaseous State

The gaseous state is unique among the phases of matter for its high degree of randomness and freedom of molecular movement. Because gas molecules can move freely and occupy more space, reactions that produce gases tend to increase the system's entropy.

• When reactions generate more gas molecules than they consume, entropy usually increases, reflecting greater randomness and disorder.
• On the contrary, if the number of gas molecules decreases, entropy may decrease.

In the reaction \( \mathrm{FeCl}_{2}(s)+ \mathrm{H}_{2}(g) \longrightarrow \mathrm{Fe}(s)+2 \, \mathrm{HCl}(g), \) the product side yields two \( \mathrm{HCl} \) gas molecules from just one gaseous \( \mathrm{H}_{2} \) molecule. This increase in gas molecules results in a positive entropy change, indicating heightened disorder and randomness in the system.

Randomness

Randomness, in the context of entropy, represents the degree of disorder or unpredictability within a system. Reactions that lead to an increase in disorder will generally result in a positive entropy change.

• System randomness tends to increase when more gas molecules are formed or when solids and liquids transition to gas.
• Decreased randomness occurs if the system transitions from gas to liquid or solid, or if the number of gas molecules is reduced.

Consider the reaction \( \mathrm{Ba}(\mathrm{OH})_{2}(s) \longrightarrow \mathrm{BaO}(s)+ \mathrm{H}_{2} \mathrm{O}(g). \) Upon breaking down, it releases \( \mathrm{H}_{2} \mathrm{O}(g), \) introducing additional randomness and increasing entropy. It's seen as a positive change in entropy due to gas formation, even though it involves a solid phase initially. This concept is crucial in understanding reactions and their impact on the system's entropy.