Question

(a) What do you expect for the sign of \(\Delta S\) in a chemical reaction in which 3 mol of gaseous reactants are converted to 2 mol of gaseous products? (b) For which of the processes in Exercise 19.11 does the entropy of the system increase?

Short answer

(a) Since the number of moles of gaseous reactants (3 mol) is higher than the number of moles of gaseous products (2 mol), the randomness of the system decreases during the reaction. Therefore, the entropy change, \(\Delta S\), will be negative: \[ \Delta S < 0 \] (b) We cannot provide specific processes from Exercise 19.11, but to identify which processes increase the entropy of the system, look for processes that increase the number of moles of gases, the randomness of the system, or where the system moves from a more ordered state to a less ordered state.

Step-by-step solution

Part (a)

To determine the sign of the entropy change, \(\Delta S\), we can consider the number of moles of gaseous reactants and the number of moles of gaseous products. The entropy change for a chemical reaction can be given as: \[ \Delta S = S_\text{products} - S_\text{reactants} \] In general, the entropy of a gas is directly proportional to its number of moles, so having more moles of gas results in greater randomness and higher entropy. In the given reaction, we have 3 mol of gaseous reactants and 2 mol of gaseous products. Since the number of moles of reactants is higher than the number of moles of products, the randomness of the system is expected to decrease during the reaction. Therefore, the entropy change will be negative, which means: \[ \Delta S < 0 \]

Part (b)

Unfortunately, we don't have Exercise 19.11 available to address this part of the exercise. However, we can still provide general guidance on how to solve this part when Exercise 19.11 is available: 1. Write down the processes given in Exercise 19.11. 2. For each process, check if it increases the number of moles of gases, the randomness of the system, or whether it's a process where the system moves from a more ordered state to a less ordered state. 3. Identify the processes that fulfill any of these conditions, as these are the ones that lead to an increase in the entropy of the system. 4. Write down the selected processes as the answer to part (b) of the exercise.

Key concepts

Chemical Reactions and Entropy Change

In chemical reactions, the transformation of reactants to products often involves changes in the number of moles of gases and, consequently, in entropy. Entropy, denoted by \( \Delta S \), is a measure of the disorder or randomness of a system. In reactions involving gases, an increase in the number of gaseous particles usually signifies an increase in entropy.

When analyzing chemical reactions, if the number of moles of gaseous products is less than that of the reactants, the system becomes more ordered. This decrease in entropy is typical when gaseous molecules are rearranged into fewer products. Conversely, if more moles of gas are produced than consumed, entropy increases due to greater randomness.

Therefore, the sign of \( \Delta S \) is closely related to the change in the number of gas moles during the reaction. An understanding of this concept helps predict whether a reaction will have a positive or negative entropy change, giving insights into the spontaneity of the process.

Moles of Gas in a Reaction

The concept of moles is central to understanding chemical reactions. Moles represent the amount of substance containing as many entities (atoms, molecules, etc.) as there are atoms in 12 grams of carbon-12. In gaseous reactions, the number of moles not only dictates the quantities of reactants and products but also influences entropy changes.

Gases have high entropy due to their freedom to move and occupy a larger volume. When evaluating a reaction such as the conversion of 3 moles of gases into 2, it indicates that the system undergoes a reduction in gas quantity. This reduction leads to decreased disorder and a negative change in entropy (\( \Delta S < 0 \)).

To determine the overall entropy change, one needs to compare the total moles of gaseous reactants with those of the products. If the product moles are fewer, expect an entropy decrease; if they're greater, anticipate an increase. This simple comparison allows for quick assessment of how the molecular rearrangements will affect the perceived randomness of the system.

Entropy of Gaseous Systems

Entropy is a crucial concept in understanding gaseous systems, as gases possess inherently high entropy compared to liquids and solids. This is because gas particles move freely and occupy most of the available space, resulting in more possible arrangements and higher disorder.

In the context of gaseous systems, entropy changes (\( \Delta S \)) are greatly affected by molecular interactions and reactions. For example, in a closed system where a reaction turns gaseous reactants into fewer gaseous products, the disorder decreases, leading to a negative entropy change. This is contrary to reactions where more gas forms, promoting disorder and increasing entropy.

Understanding entropy in gaseous reactions is essential as it helps predict the feasibility and spontaneity of a chemical process. Reactions that result in increased entropy are generally more spontaneous under constant temperature and pressure conditions. Thus, analyzing changes in gaseous moles is vital for predicting the direction and likelihood of chemical reactions.