Problem 35 - Chemistry The Central Science

Question

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

Step-by-Step Solution

Answer

(a) For a reaction where two moles of gaseous reactants are converted to three moles of gaseous products, the change in entropy (ΔS) is expected to be positive, as there is an increase in disorder due to the increase in the number of gas molecules: ΔS > 0 (b) We cannot provide specific details about the processes in Exercise 19.11, but you can identify processes with increasing entropy by looking for scenarios where the number of moles of gas increases, the system undergoes a phase change from solid to liquid or liquid to gas, the temperature of the system increases, or energy is transferred to the system as heat.

Step 1: Part (a) - Analyzing the given reaction and predicting the sign of ΔS

For a reaction where two moles of gaseous reactants are converted to three moles of gaseous products, we expect an increase in disorder (or randomness) because we are going from a smaller number of gas molecules to a larger number of gas molecules. Therefore, in this case, the change in entropy, ΔS should be greater than zero (i.e. positive). This can be represented mathematically as: ΔS > 0

Step 2: Part (b) - Identifying the processes in Exercise 19.11 with increasing entropy

Unfortunately, we do not have access to Exercise 19.11. However, if you can provide the information about the processes mentioned in Exercise 19.11, we can help you find which ones experience an increase in entropy. In general, the entropy of a system increases in the following scenarios: 1. When the number of moles of gas increases. 2. When the system undergoes a phase change from solid to liquid or liquid to gas. 3. When the temperature of the system increases. 4. When energy is transferred to the system as heat. Consider these guidelines and analyze the processes mentioned in Exercise 19.11 to determine which ones experience an increase in entropy.

Key Concepts

Change in Entropy

Entropy is a measure of the disorder or randomness in a system, and in chemistry, it's essential to understanding chemical reactions. When a reaction occurs, the entropy, denoted by the symbol \( S \), can change. The change in entropy, \( \Delta S \), is the difference in entropy between the final state and the initial state of the reaction.

In a chemical reaction, an increase in the number of gaseous molecules typically leads to an increase in disorder, as the gas molecules can move more freely and occupy a larger volume compared to liquids or solids. This results in a positive \( \Delta S \), indicating that the system has become more disordered. Conversely, if a reaction results in fewer gas molecules, the entropy tends to decrease, leading to a negative \( \Delta S \). Recognizing that entropy is a function of the state of a system helps in predicting whether its value will increase or decrease in a given chemical reaction.

Moles of Gaseous Reactants

The moles of gaseous reactants in a chemical reaction represent the quantity of gaseous substances present before the reaction takes place. Since gases have high entropy due to their considerable molecular movement and space occupation, the amount of gas in a reaction is directly linked to the system's entropy.

When predicting the change in entropy for a reaction, counting the moles of gaseous reactants provides crucial insight. For instance, a reaction that involves a decrease in the number of gas moles tends to consolidate energy and decrease system disorder, leading to a negative \( \Delta S \). It's this relationship between the moles of gaseous reactants and the resulting entropy that lays the groundwork for understanding how chemical reactions proceed energetically.

Moles of Gaseous Products

After a chemical reaction, the moles of gaseous products are the measure of gaseous substances produced. This ties directly into the concept of entropy; a higher number of gas moles as products usually indicates an increase in disorder, positively affecting entropy (\( \Delta S > 0 \) ).

In the case where a reaction yields more gaseous products than the reactants it started with, the reaction is moving toward a more disordered state, which intrinsically means increased entropy. This understanding is essential in not only predicting the direction of \( \Delta S \) but also in comprehending the energetic favorability of reactions and how energy is distributed in a system.