Problem 41 - Chemistry The Central Science In Si Units

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

Step 1: Analyze Reaction (a)

For the reaction \( \mathrm{CO}(g) + \mathrm{H}_2(g) \rightarrow C(s) + \mathrm{H}_2\mathrm{O}(g) \), notice that the reaction starts with two moles of gas and produces one solid and one gas. Solids have lower entropy compared to gases. Initially, there are two gaseous molecules, but the final gases have only one gaseous molecule, indicating a decrease in the total entropy of the system. Thus, the entropy change is negative.

Step 2: Analyze Reaction (b)

The reaction is \( 2 \mathrm{O}_2(g) + \mathrm{N}_2(g) \rightarrow 2 \mathrm{NO}_2(g) \). Starting with three moles of gas to form two moles of gas, the total number of moles of gas decreases. A decrease in the number of gas molecules generally leads to a decrease in entropy. Therefore, the entropy change is negative.

Step 3: Analyze Reaction (c)

In the reaction \( \mathrm{NH}_4 \mathrm{Cl}(s) \rightarrow \mathrm{HCl}(g) + \mathrm{NH}_3(g) \), you start with a solid and end with two gases. This transformation significantly increases entropy due to the higher entropy of gases compared to solids. Thus, the entropy change is positive.

Step 4: Analyze Reaction (d)

The reaction \( 2 \mathrm{C}_2 \mathrm{H}_4(g) + \mathrm{O}_2(g) \rightarrow 2 \mathrm{C}_2 \mathrm{H}_4 \mathrm{O}(g) \) involves three moles of gaseous reactants and results in two moles of gaseous products. There is a decrease in the number of gas molecules, which typically indicates a decrease in entropy. Therefore, the entropy change is negative.

Key Concepts

Entropy

Entropy is a fundamental concept in thermodynamics that measures the degree of disorder or randomness in a system. It is often denoted as "S." When we talk about entropy change in a chemical reaction, we are referring to the difference in entropy between the reactants and the products.

• If the products are more disordered than the reactants, the entropy change (9S) is positive.
• Conversely, if the products are less disordered, the entropy change is negative.

Understanding entropy helps predict the spontaneity of a process. Reactions tend to favor an increase in entropy because the universe prefers to move towards disorder. This concept is pivotal in chemical reactions and transformations.

Chemical Reactions

In chemical reactions, atoms and molecules interact to form new substances. These reactions involve changes in energy and matter. Entropy plays a crucial role in determining the direction and feasibility of these reactions. During a reaction, if products are in a more disordered state than the reactants, the reaction is likely to occur spontaneously. For instance, when a solid decomposes into gases, like in reaction (c) where solid NH4Cl transforms into gaseous HCl and NH3, the resulting increase in entropy promotes spontaneity. Chemical reactions can be classified based on several criteria, such as change in entropy, energy changes, and conservation laws, giving us invaluable predictive power in chemistry.

Gaseous Reactions

Gaseous reactions often involve noticeable changes in entropy because gases inherently possess high entropy due to their free movement and randomness. The more particles or moles of gas you have in a system, the higher the entropy. When the reaction involves a change in the number of gaseous molecules, the entropy change is affected significantly:

• If more gas molecules form or if gas is produced from a non-gaseous reactant, the entropy increases.
• Conversely, if gas molecules combine to form fewer gas molecules or if gases turn into solids or liquids, the entropy decreases.

For example, in reaction (b), the reduction of three moles of gas to two illustrates a decrease in entropy.

Phase Change

Phase changes involve transitions between different states of matter: solid, liquid, and gas. These changes are key examples of entropy alterations.

• When a substance transitions from a solid to a liquid, or from a liquid to a gas, its entropy increases. This is because molecules have more freedom to move around.
• On the other hand, when a gas condenses to a liquid or a liquid freezes to a solid, entropy decreases.

For example, in reaction (a), the formation of a solid from gases suggests a decrease in entropy, as solid structures are more ordered compared to gases. This type of understanding is essential to predicting and analyzing many natural and industrial processes.

Molecular Entropy

Molecular entropy considers how the arrangement and movement of molecules contribute to the overall entropy of a system. Different molecules have distinct levels of entropy influenced by their structure and complexity.

• More complex molecules tend to have higher entropy because they can vibrate and rotate in more ways, contributing to greater disorder.
• Molecules in gases, given their high energy state and freedom to move, typically have the highest entropy compared to solids and liquids.

Understanding molecular entropy is crucial for predicting the outcome of reactions at the molecular level. It involves considering each molecule's contribution to the total disorder of the system. Such insights are incredibly useful for chemists trying to manipulate or predict chemical processes.