Question

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

Short answer

(a) In the given chemical reaction, 2 moles of gaseous reactants are converted to 3 moles of gaseous products, resulting in an increase in the number of moles of gas particles. This leads to an increase in disorder in the system, and the entropy (∆S) increases. Therefore, the sign of ∆S is positive. (b) From Exercise 19.11, the entropy of the system increases for the following processes: 1. Melting of 1 mole of ice at 0°C 3. Vaporization of 1 mole of boiling water at 100°C 4. Sublimation of 1 mole of ice at -15°C under low pressure

Step-by-step solution

Understand the concept of entropy

Entropy is a measure of randomness or disorder in a system. When a system becomes more random or disordered, its entropy increases.

Identify the number of moles before and after the reaction

The given reaction has 2 moles of gaseous reactants converting to 3 moles of gaseous products. This means the number of moles of gas particles increases during the reaction.

Relate the change in the number of moles to the change in entropy

As we have an increase in the number of moles of gas particles, the system becomes more disordered (i.e., more random). This increased disorder in the system means that the entropy of the system (ΔS) increases. Consequently, the sign of ΔS is positive. So, the sign of ΔS for the given chemical reaction is positive. #b) Processes in which entropy of the system increases#

Refer to Exercise 19.11

In Exercise 19.11, there are four processes. We need to analyze each of these processes to see if the entropy of the system increases for any of them: 1. Melting of 1 mole of ice at 0°C. 2. Freezing of 1 mole of water at 0°C. 3. Vaporization of 1 mole of boiling water at 100°C. 4. Sublimation of 1 mole of ice at -15°C under low pressure.

Analyze the processes

1. Melting of 1 mole of ice at 0°C: In this process, ice (a solid) is converted to water (a liquid). The molecules in a liquid are more disordered than in a solid, so the entropy of the system increases in this process. 2. Freezing of 1 mole of water at 0°C: In this process, water (a liquid) is converted to ice (a solid). The molecules in a solid are more ordered than in a liquid, so the entropy of the system decreases in this process. 3. Vaporization of 1 mole of boiling water at 100°C: In this process, water (a liquid) is converted to steam (a gas). The molecules in a gas are more disordered than in a liquid, so the entropy of the system increases in this process. 4. Sublimation of 1 mole of ice at -15°C under low pressure: In this process, ice (a solid) is directly converted to water vapor (a gas) without passing through the liquid state. The molecules in a gas are more disordered than in a solid, so the entropy of the system increases in this process.

Identify the processes with an increase in entropy

Based on the analysis of the processes in Exercise 19.11, the entropy of the system increases for the following processes: 1. Melting of 1 mole of ice at 0°C 3. Vaporization of 1 mole of boiling water at 100°C 4. Sublimation of 1 mole of ice at -15°C under low pressure

Key concepts

Entropy Change

When we talk about entropy change in chemical reactions, we are referring to how the disorder or randomness of a system changes as a reaction proceeds. Entropy, denoted by the symbol \(S\), is a thermodynamic property that quantifies the amount of disorder within a system. In a reaction where the number of gaseous molecules increases, like from 2 mol to 3 mol, the system becomes more chaotic. This change in moles indicates an increase in disorder because there are more ways the gas molecules can be arranged. Entropy change, \(\Delta S\), is positive when the system becomes more disordered. Understanding this helps in predicting the spontaneity and feasibility of reactions, as reactions that lead to increased entropy are often spontaneous under the right conditions.

Chemical Reactants and Products

Chemical reactions involve the transformation of reactants into products. During this process, it's important to observe changes in the state and arrangement of molecules, as this significantly affects entropy. In reactions where gaseous reactants are converted into an even greater number of gaseous products, the increase in the number of gas particles often results in higher entropy. For example, if you start with 2 mol of reactants turning into 3 mol of products, the system now has more particles to spread energy and disorder. This change indicates that the reaction leads to a greater number of possible configurations, increasing the disorder of the system.

Disorder in Systems

The concept of disorder is central to understanding entropy in systems. Disorder, or randomness, refers to the unpredictability in the arrangement and movement of particles in a substance. When a system undergoes a process that increases its entropy, it means the molecules are less structured and more dispersed in comparison to their original state. Processes that increase disorder typically result in an increase in entropy.

• Adding heat to a system often increases entropy as particles move more vigorously, becoming less ordered.
• Breaking chemical bonds usually results in increased entropy since the pieces the bond breaks into are less ordered.
• Mixing substances can lead to higher entropy, as mixed substances have more random arrangements compared to when they are separate.

Entropy in Phase Changes

Phase changes in substances are excellent illustrations of entropy changes. During phase transitions, like melting, vaporization, or sublimation, the degree of molecular disorder changes. For instance, when ice melts into water, the rigid structure of the solid breaks down into a fluid structure, increasing entropy as molecules move more freely. Similarly, when water vaporizes into steam, the liquid's orderly molecular arrangement spreads further apart in the gaseous state, further increasing the entropy. Therefore, any phase change from solid to liquid, liquid to gas, or solid to gas signifies an increase in disorder, and hence, an increase in entropy.

• Melting and vaporization both lead to greater molecular movement and dispersion.
• Sublimation skips the liquid phase, showing a direct and significant increase in disorder from solid to gas.

Understanding these changes helps explain how energy and matter interactions facilitate greater disorder in thermodynamic processes.