Problem 29 - Chemistry The Molecular Science

Question

Without consulting a table of standard molar entropies, predict whether \(\Delta_{\mathrm{r}} S_{\text {system }}^{\circ}\) is positive or negative for each of these reactions. (a) \(2 \mathrm{CO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{CO}_{2}(\mathrm{~g})\) (b) \(2 \mathrm{H}_{2}(\mathrm{~g})+\mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(\ell)\) (c) \(2 \mathrm{O}_{3}(\mathrm{~g}) \longrightarrow 3 \mathrm{O}_{2}(\mathrm{~g})\)

Step-by-Step Solution

Answer

(a) Negative, (b) Negative, (c) Positive.

Step 1: Understanding the concept of entropy change

Entropy, denoted as \( S \), is a measure of randomness or disorder in a system. In chemical reactions, we assess the change in entropy, \( \Delta_{\text{r}} S^{\circ}_{\text{system}} \), which indicates if the system becomes more disorderly or orderly. A positive value implies increased disorder, while a negative value indicates decreased disorder.

Step 1: Analyze reaction (a)

For the reaction \( 2\, \mathrm{CO(g)} + \mathrm{O_{2}(g)} \rightarrow 2\, \mathrm{CO_{2}(g)} \), both reactants and products are gases. We visualize whether there's an increase or decrease in the number of gas molecules. Originally there are 3 moles of gas on the reactant side and 2 on the product side. Fewer gas molecules generally mean less disorder; hence, \( \Delta_{\text{r}} S^{\circ}_{\text{system}} \) is likely negative.

Step 2: Analyze reaction (b)

In the reaction \( 2\, \mathrm{H_{2}(g)} + \mathrm{O_{2}(g)} \rightarrow 2\, \mathrm{H_{2}O(\ell)} \), we start with 3 moles of gas and end up with a liquid. The transition from gas to liquid significantly reduces the disorder, as liquids are more orderly than gases. Therefore, \( \Delta_{\text{r}} S^{\circ}_{\text{system}} \) for this reaction is negative.

Step 3: Analyze reaction (c)

The reaction \( 2\, \mathrm{O_{3}(g)} \rightarrow 3\, \mathrm{O_{2}(g)} \) sees an increase in the number of gas molecules from 2 to 3. More gas molecules typically equate to more disorder, implying \( \Delta_{\text{r}} S^{\circ}_{\text{system}} \) is positive.

Key Concepts

Entropy Change

Entropy change is a fundamental concept in chemistry often symbolized by \( \Delta S \). It describes the alteration in disorder or randomness between the reactants and products during a chemical reaction. When we say that the entropy change, \( \Delta_{\text{r}} S^{\circ}_{\text{system}} \), is positive, it means the system has become more disorderly. Conversely, a negative entropy change indicates the system has become more orderly.
Understanding how to predict entropy change involves considering the states and amounts of substances before and after the reaction.

• Gas to liquid: Significant decrease in entropy (more order)
• Increase in gas moles: Increase in entropy (more disorder)

By analyzing reactions, we often compare the number of moles of gases on either side of the equation, as they play a major role in the disorder of the system.

Gaseous Reactions

Gaseous reactions involve substances that are in the gas phase during the course of the chemical change. Because gases have higher entropy than liquids or solids, changes in the number of gas moles can heavily influence the reaction's overall entropy change.
For instance, consider the reaction \(2 \mathrm{CO} (\mathrm{g}) + \mathrm{O}_2 (\mathrm{g}) \rightarrow 2 \mathrm{CO}_2 (\mathrm{g})\). Initially, there are 3 moles of gas, which reduces to 2 moles on the product side. A reduction in the number of gaseous moles leads to less disorder and suggests a negative entropy change.
Similarly, for the reaction from gases to liquid, such as \(2 \mathrm{H}_2 (\mathrm{g}) + \mathrm{O}_2 (\mathrm{g}) \rightarrow 2 \mathrm{H}_2O (\ell)\), the change is even more drastic. Gases turning into liquid profoundly lower the entropy, leading to a negative \(\Delta_{\text{r}} S^{\circ}_{\text{system}}\).
In contrast, when gases increase, such as in \(2 \mathrm{O}_3 (\mathrm{g}) \rightarrow 3 \mathrm{O}_2 (\mathrm{g})\), more moles of gas mean more randomness and a positive entropy change.

Disorder in Chemistry

Disorder, or randomness, in chemistry is quantified by the concept of entropy. This is crucial to understanding how substances behave during chemical reactions. An increase in disorder is usually associated with an increase in entropy, leading to a positive \( \Delta\) in entropy.
Entropy serves as a measure of unpredictability or chaos. In reactions involving gases, more moles of gases on the product side usually lead to more disorder. This is because gases have particles that move freely, enhancing randomness.

• A decrease in gaseous molecules typically signifies a reduction in disorder and a negative entropy change.
• An increase in the gaseous molecules correlates with increased disorder and a positive entropy change.

Considering these aspects helps us understand and predict whether a reaction will lead to an increase or decrease in disorder, influencing the reaction's energetic favorability.