Problem 106 - Chemistry: The Central Science in SI Units, Global Edition

Question

The following processes were all discussed in Chapter 18 , "Chemistry of the Environment." Estimate whether the entropy of the system increases or decreases during each process: (a) photodissociation of \(\mathrm{O}_{2}(g),(\mathbf{b})\) formation of ozone from oxygen molecules and oxygen atoms, (c) diffusion of CFCs into the stratosphere, (d) desalination of water by reverse osmosis.

Step-by-Step Solution

Answer

(a) The entropy of the system increases during the photodissociation of O₂(g), as the number of particles and possible configurations increase. (b) Entropy decreases during the formation of ozone, as the total number of particles decreases and the system becomes more ordered. (c) Entropy increases in the diffusion of CFCs into the stratosphere, as the particles become more dispersed and the number of possible configurations increases. (d) In the desalination of water by reverse osmosis, entropy decreases as the system becomes more ordered and the number of possible configurations decreases.

Step 1: Process (a): Photodissociation of O₂(g)

When O₂(g) undergoes photodissociation, it breaks down into two individual oxygen atoms. This process results in an increase in the number of particles, leading to an increase in the number of possible configurations or microstates of the system. As a result, the entropy of the system increases.

Step 2: Process (b): Formation of ozone from oxygen molecules and oxygen atoms

In this process, we have a reaction between an oxygen molecule (O₂) and an oxygen atom (O) to form ozone (O₃). The total number of particles in the system decreases, as three particles combine to form one particle. As the number of particles decreases, the number of possible configurations or microstates also decreases, leading to a decrease in the system's entropy.

Step 3: Process (c): Diffusion of CFCs into the stratosphere

During the diffusion process, CFCs move from a region of higher concentration to a region of lower concentration. As the CFCs spread out, the number of possible configurations or microstates of the system increases because the particles are more dispersed. Therefore, the entropy of the system increases in this process.

Step 4: Process (d): Desalination of water by reverse osmosis

In reverse osmosis, water is forced through a semipermeable membrane, separating the water from dissolved salts. As a result, the system becomes more ordered as the separated water has a lower concentration of dissolved salts. The number of possible configurations or microstates decreases because the particles are not as dispersed as they were before the process. Therefore, the entropy of the system decreases during desalination by reverse osmosis.

Key Concepts

Photodissociation

Photodissociation is a process where molecules absorb light and break apart into smaller fragments or atoms. When oxygen gas ( O₂(g) ) undergoes photodissociation, it absorbs ultraviolet light causing the molecule to break into two separate oxygen atoms. This process increases the entropy of the system. Here's why:

• The number of particles increases from one ( O₂ ) to two ( O and O )
• The increased number of particles means more possible arrangements or microstates
• More microstates mean higher entropy because the system is now more disordered

Overall, the breaking apart of molecules into simpler atoms results in an increase of entropy, representing a transition to a more disordered state.

Diffusion Processes

Diffusion is a natural process where particles move from an area of higher concentration to an area of lower concentration. This spread is due to the random motion of particles, which naturally want to achieve a state of equilibrium. For example, when Chlorofluorocarbons (CFCs) diffuse from the ground level into the stratosphere, their entropy increases. Here's a breakdown of why this happens:

• Initially, CFCs are densely packed at a higher concentration
• They diffuse, moving to an area where they are less concentrated, or more spread out
• This results in a greater number of possible configurations or microstates
• Increased spread and more microstates mean higher entropy

The key concept in diffusion is the spreading out or distribution of particles, which increases disorder and therefore raises entropy over time.

Reverse Osmosis

Reverse osmosis is a method used to purify water by removing dissolved solids. Unlike osmosis, where water naturally moves through a membrane from low to high solute concentration, reverse osmosis uses external pressure to achieve the opposite. In the context of entropy, here's how reverse osmosis affects it:

• Water is forced through a semipermeable membrane, separating it from salts and other impurities
• The separation process results in purified water on one side, which is more ordered
• Since order is increased, the number of possible configurations or microstates decreases
• Lower microstates translate to a decrease in entropy

In essence, reverse osmosis reduces the disorder in the system by creating a more uniform, less mixed state—resulting in decreased entropy.

Ozone Formation

Ozone formation is a fascinating natural process involving the reaction between oxygen molecules ( O₂ ) and oxygen atoms ( O ) to form ozone ( O₃ ). This process is crucial for protecting life on Earth as ozone absorbs harmful ultraviolet radiation. When looking at entropy, the formation of ozone affects it in the following way:

• Oxygen molecules and atoms bond to form ozone, reducing the number of individual particles
• This reduction in particle count means fewer possible configurations or microstates
• Fewer microstates mean the system is more orderly
• An increase in order corresponds to a decrease in entropy

Thus, while ozone formation is critical for blocking UV rays, it represents a more structured state, leading to decreased entropy in the environment where this reaction occurs.