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 \(19.9\) does the entropy of the system increase?

Short answer

Answer to part (a): The sign of \(\Delta S\) in the given reaction is expected to be positive. Answer to part (b): Without the information from Exercise 19.9, it is impossible to answer this part.

Step-by-step solution

Recall the relationship of entropy to the number of microstates

Entropy, \(S\), is a measure of the number of possible microstates available for molecules in a system, such that a system with a higher entropy has more available microstates. Entropy change, \(\Delta S\), in a chemical reaction can be positive or negative depending on whether the number of microstates increases or decreases during the reaction. Generally, an increase in the number of gaseous molecules in the system results in increased entropy.

Determine the change in entropy for the given reaction

In the given reaction, the number of gaseous molecules increases from 2 moles of reactants to 3 moles of products. As the number of gaseous molecules in the system increases, the number of microstates available for the molecules also increases. Therefore, the entropy of the system increases, and the entropy change (\(\Delta S\)) will be positive. Answer to part (a): The sign of \(\Delta S\) in the given reaction is expected to be positive. Part (b) Without the information from Exercise 19.9, it is impossible to answer this part.

Key concepts

Entropy Change in Chemical Reactions

When tackling entropy change in chemical reactions, it's essential to understand that entropy, represented by the symbol S, is a measure of disorder or randomness in a system. This concept is thrilling because it allows us to predict how particles in a reaction will behave based purely on statistical probabilities.

During a chemical reaction, when the number of gas molecules increases, such as going from two moles of reactants to three moles of gaseous products, the entropy change (gg) is typically positive. This is because more gas particles mean more ways they can be arranged. Imagine throwing three dice instead of two – you’d have more possible outcomes, or microstates. In your textbook exercise, the transition from two to three moles of gaseous substances hints at a positive S, signifying a delightful increase in chaos and possibilities!

Microstates and Entropy

Diving into microstates and entropy, we uncover the microscopic secrets behind the apparent disorder. A microstate can be likened to a specific arrangement of particles in a system; the more microstates available, the higher the entropy. It’s like having more options for organizing books on a shelf.

In thermodynamics, the term 'microstate' paints a picture of the countless ways particles can be arranged, with each unique arrangement counting as one microstate. Since moves in entropy are all about going from fewer to more microstates, it helps to picture a party where guests represent molecules: a party with more guests has more potential group photos (microstates), thus indicating higher entropy.

Understanding how microstates contribute to entropy empowers students to not only follow the math but also to grasp the chaotic dance of particles within a reaction, making the concept much more intuitive and engaging.

Gaseous Reactants and Products

Looking at gaseous reactants and products offers an exciting avenue to explore entropy. Gases are like free-spirited travelers compared to the more settled down liquid and solid molecules. Imagine the gas molecules flying around the room, bouncing off walls, and each other. Each of these scenarios depicts a different microstate.

When chemical reactions turn solids or liquids into gases, or increase the number of gaseous molecules, they open up the room and invite more chaos to the party—this translates to a higher number of microstates. To visualize this, think of a single balloon filled with gas particles as opposed to multiple balloons; more balloons provide more ways the particles can spread out, symbolizing higher entropy.
Our textbook example, where two moles of gaseous reactants produce three moles of gaseous products, illustrates this beautifully. There's more room for the molecules to roam, more microstates, and hence, a significant positive bump in entropy.

Thermodynamics

Thermodynamics is the branch of physical science that deals with heat, work, and energy in the context of systems. It lays out the playground rules for how energy changes within those systems. Within this playground, entropy is one of the key players.

We learn from thermodynamics that energy likes to spread out, and this concept is tightly knit with entropy—it's the measure of that 'spread-out-ness'. This discipline shows us that, over time, systems prefer to move toward a state of equilibrium and maximum entropy, akin to a natural tendency for things to become more disordered.

When applying thermodynamic principles to chemical reactions, like in our textbook example, we're dealing with a spectacular showdown where entropy can either win or lose, depending on whether substances become more ordered or disordered, solidify or vaporize, combine or separate. It's a scientific saga of energy flow and transformation, ultimately determining the fate of reactions in our tangible world.