Problem 18 - Chemistry The Molecular Nature of Matter

Question

Will the entropy change for each of the following be positive or negative? (a) Moisture condenses on the outside of a cold glass. (b) Raindrops form in a cloud. (c) Gasoline vaporizes in the carburetor of an automobile engine. (d) Air is pumped into a tire. (e) Frost forms on the windshield of your car. (f) Sugar dissolves in coffee.

Step-by-Step Solution

Answer

(a) Negative, (b) Negative, (c) Positive, (d) Negligible, (e) Negative, (f) Positive. The entropy changes are determined by the increased or decreased disorder in the system due to phase changes or mixing processes.

Step 1: Understanding entropy and phase changes

Entropy is a measure of the disorder or randomness in a system. Generally, a phase change from a gas to a liquid or a solid, which represents increased order, corresponds to negative entropy change. Conversely, a change from solid or liquid to gas, which represents increased disorder, corresponds to a positive entropy change.

Step 2: Analyzing moisture condensation

Moisture condensation on the outside of a cold glass is a phase change from gas to liquid. This represents a decrease in entropy because the molecules in the liquid state are more ordered than in the gaseous state.

Step 3: Examining raindrop formation

Raindrops forming in a cloud is a transition from water vapor (gas) to liquid water. Similar to condensation, it corresponds to decreased entropy, indicating a negative entropy change.

Step 4: Considering gasoline vaporization

When gasoline vaporizes in the carburetor of an automobile engine, it goes from a liquid to a gas. This transition to a more disordered state suggests an increase in entropy, implying a positive entropy change.

Step 5: Air being pumped into a tire

Pumping air into a tire increases the pressure and decreases the volume available to the air molecules, which slightly increases the order. However, as there's no phase change, it can be said that this is more of an increase in energy than a significant change in entropy. For simplicity, we assume near negligible entropy change.

Step 6: Frost formation on a windshield

Frost formation on a windshield is a transition from water vapor (gas) directly to a solid form (frost). This process, known as deposition, involves a decrease in disorder indicating a negative entropy change.

Step 7: Dissolving sugar in coffee

When sugar dissolves in coffee, the solid sugar breaks into individual particles that become distributed randomly in the liquid. This process results in an increased disorder within the system, which corresponds to a positive entropy change.

Key Concepts

Phase Transition

Understanding the intricacies of phase transitions is crucial when exploring the concept of entropy. In essence, a phase transition occurs when a substance changes from one state of matter to another, such as solid, liquid, or gas. This can happen via various processes, each accompanied by energy exchange.

For instance, when ice melts, it absorbs heat and transitions from a solid to a liquid state. Similarly, when water boils, it changes from a liquid to a gas. It's important to note that these changes are not just physical but also have implications for the molecular order within the substance, and this is where entropy comes into play.

Condensation

Condensation is a specific type of phase transition in which a substance moves from a gaseous to a liquid state. For students learning about thermodynamics, it's helpful to visualize this process on a molecular level. Think about water vapor in the air. When it condenses onto a cold glass, it loses energy and the molecules come closer together, forming into a liquid.

Now, why does this mean a decrease in entropy? Simply put, the molecules in liquid water are more ordered – they have less freedom to move around than they do in the gaseous state. This is a classic case where we would see a negative entropy change.

Vaporization

Vaporization, conversely, is the process where a liquid turns into a gas – as seen when gasoline vaporizes in a car's carburetor. Here, liquid molecules gain enough energy to overcome the attractive forces keeping them together, spreading out with increased movement and creating a state of greater disorder.

As order decreases and randomness increases, entropy rises. Therefore, in the context of vaporization, there is a positive entropy change. This concept is fundamental to understanding how energy transfer can affect the disorder within a system.

Entropy and Disorder

The relationship between entropy and disorder is at the heart of thermodynamics. Entropy is not just a term to throw around – it quantifies the level of disorder or randomness in a system. The more ways the components of a system can be arranged without changing the overall nature of the system, the higher the entropy. This ties back to the phase transitions: gases have higher entropy than liquids, which have higher entropy than solids, all because of the freedom of molecular movement in each respective state.

When teaching this concept, it's important to focus on the idea that increased disorder implies increased entropy, and understanding this relationship helps predict the outcome of chemical and physical processes.

Entropy in Chemical Processes

In chemical processes, entropy plays a critical role in determining the direction and feasibility of reactions. Dissolving sugar in coffee is an excellent example of how entropy increases in a chemical process. Initially, sugar crystals - highly ordered structures - break down into their component molecules. These molecules then disperse randomly within the liquid, increasing the system's disorder.

This dispersal results in higher entropy, which is characteristic of spontaneous processes. Understanding this phenomenon helps us appreciate why certain reactions occur naturally while others require the input of energy.