Problem 41 - Chemistry: The Central Science in SI Units, Global Edition

Question

Predict the sign of the entropy change of the system for each of the following reactions: (a) \(\mathrm{CO}(g)+\mathrm{H}_{2}(g) \longrightarrow C(s)+\mathrm{H}_{2} \mathrm{O}(g)\) (b) \(2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)\) (c) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow \mathrm{HCl}(g)+\mathrm{NH}_{3}(g)\) (d) \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)\)

Step-by-Step Solution

Answer

(a) \(\Delta S < 0\) (negative entropy change) (b) \(\Delta S < 0\) (negative entropy change) (c) \(\Delta S > 0\) (positive entropy change) (d) \(\Delta S < 0\) (negative entropy change)

Step 1: Identify the change in the number of gas particles

In this reaction, we have 2 moles of gas as reactants (CO and H2) and 1 mole of gas as the product (H2O). The product also includes C(s), a solid.

Step 2: Determine the entropy change

The reaction involves a decrease in the number of gas particles and the appearance of a solid. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative. (b) \(2 \mathrm{O}_{2}(g)+\mathrm{N}_{2}(g) \longrightarrow 2\mathrm{NO}_{2}(g)\)

Step 3: Identify the change in the number of gas particles

In this reaction, we have 3 moles of gas as reactants (2 moles O2 and 1 mole N2) and 2 moles of gas as products (2 moles NO2).

Step 4: Determine the entropy change

The reaction involves a decrease in the number of gas particles. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative. (c) \(\mathrm{NH}_{4} \mathrm{Cl}(s) \longrightarrow\mathrm{HCl}(g)+\mathrm{NH}_{3}(g)\)

Step 5: Identify the change in the number of gas particles

In this reaction, we have no moles of gas as reactants (only solid NH4Cl) and 2 moles of gas as products (HCl and NH3).

Step 6: Determine the entropy change

The reaction involves an increase in the number of gas particles. This means the disorder of the system increases. Therefore, the entropy change for this reaction will be positive. (d) \(2 \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{O}_{2}(g) \longrightarrow 2\mathrm{C}_{2} \mathrm{H}_{4} \mathrm{O}(g)\)

Step 7: Identify the change in the number of gas particles

In this reaction, we have 3 moles of gas as reactants (2 moles C2H4 and 1 mole O2) and 2 moles of gas as products (2 moles C2H4O).

Step 8: Determine the entropy change

The reaction involves a decrease in the number of gas particles. This means the disorder of the system decreases. Therefore, the entropy change for this reaction will be negative.

Key Concepts

Gas Particles

Gas particles are tiny, fast-moving molecules constantly in motion. They play a crucial role when predicting changes in entropy, often indicated by the phrase "number of gas particles." It's essential to understand that gas particles have more freedom to move compared to liquids and solids. This freedom leads to higher entropy, as the particles can occupy more space and positions. As a rule of thumb, an increase in the number of gas particles during a reaction usually leads to an increase in entropy. For instance, if a chemical reaction converts a solid to a gas, or simply increases the number of gas molecules, the system becomes more disordered. This increased disorder typically signifies an increase in entropy. On the other hand, if gas particles decrease, the system generally becomes more ordered, leading to a decrease in entropy. Understanding these dynamics is fundamental when analyzing chemical reactions and predicting entropy changes.

Reactions

Chemical reactions can significantly alter the number of gas particles, influencing entropy change. Each reaction is unique and brings a specific alteration in particle count and state, affecting the system's overall disorder. Consider a reaction where gaseous reactants form fewer gaseous products, like the conversion of oxygen and nitrogen to nitrogen dioxide \[ 2 \mathrm{O}_{2}(g) + \mathrm{N}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g) \] This example shows a decrease in gas particles, often hinting at a decrease in entropy. Conversely, reactions that increase gas particles, such as \[ \mathrm{NH}_{4}\mathrm{Cl}(s) \rightarrow \mathrm{HCl}(g) + \mathrm{NH}_{3}(g) \] where a solid decomposes to form gases, tend to increase system entropy.Predicting entropy largely focuses on evaluating gas particles before and after reactions, offering insights into the spontaneous nature of chemical changes.

System Disorder

Entropy is often described as a measure of disorder within a system. When predicting how a reaction affects system disorder, understanding these changes can illuminate whether entropy increases or decreases. This measure directly ties to the freedom and arrangement of particles, especially gases. When a system's particles become more randomly organized, its disorder increases, resulting in higher entropy. Consider a scenario where solids or liquids convert to gases—their increased movement freedom raises disorder, thus boosting entropy. Conversely, when gas particles decrease or convert into a more organized state, disorder diminishes, signaling a drop in entropy. Such reactions generally anchor towards forming more organized structures, reducing randomness. Recognizing the union between particle organization and system disorder provides crucial clues for predicting how entropy changes through chemical transformations.

Entropy Prediction

Predicting entropy change aids in understanding reaction direction and system spontaneity. It is rooted in observing shifts in particle states and quantities, especially for gases. A pivotal prediction tool is evaluating whether gas particles increase or decrease through the chemical transformation process. Generally, systemic entropy rises if there is a transformation from solids or liquids into gases, or if more gas molecules result from a reaction. Important points to consider include:

• An increase in gas particles typically indicates an increase in entropy.
• A decrease in gas particles leans towards lowered entropy.
• Reactions leading to higher disorder in the system show positive entropy change.
• A decrease in system disorder usually signals a negative entropy change.

By assessing these factors, one can effectively predict whether a reaction will potentially progress spontaneously or if it needs energy input, a crucial aspect of studying thermodynamics.