Problem 20 - Chemistry The Molecular Science

Question

For each process, tell whether the entropy change of the system is positive or negative. (a) Water boils. (b) A teaspoon of sugar dissolves in a cup of coffee. (The system consists of both sugar and coffee.) (c) Calcium carbonate precipitates out of water in a cave to form stalactites and stalagmites. (Consider only the calcium carbonate to be the system.)

Step-by-Step Solution

Answer

(a) Positive, (b) Positive, (c) Negative.

Step 1: Understanding Entropy

Entropy is a measure of the disorder or randomness in a system. When the molecules in a system become more disordered, the entropy increases.

Step 2: Analyzing Water Boiling

When water boils, it changes from a liquid to a gaseous state. In the gaseous state, water molecules are more disordered because they have more freedom of movement compared to the liquid state.

Step 3: Entropy Change of Boiling Water

Since the boiling process increases the disorder of water molecules, the entropy of the system increases.

Step 4: Analyzing Sugar Dissolving

When sugar dissolves in coffee, sugar molecules disperse throughout the liquid, increasing the randomness and disorder in the system.

Step 5: Entropy Change of Dissolving Sugar

The dissolution process increases the disorder of the sugar molecules in the coffee, leading to an increase in the system's entropy.

Step 6: Analyzing Calcium Carbonate Precipitation

When calcium carbonate precipitates from a solution, it forms solid formations like stalactites and stalagmites, reducing the disorder since molecules are becoming more ordered in a solid form.

Step 7: Entropy Change of Calcium Carbonate Precipitation

The formation of solid structures like stalactites and stalagmites decreases the disorder of calcium carbonate molecules, resulting in a decrease in the system's entropy.

Key Concepts

Entropy change

Entropy change refers to the measure of how much the disorder or randomness of a system changes during a process. When a system undergoes a change, its entropy can either increase or decrease.

• The entropy increases when the disorder or randomness within a system increases.
• Conversely, the entropy decreases when the system becomes more ordered.

Understanding entropy change helps explain why certain processes occur spontaneously and provides insights into the energy flow within systems. For example, when water boils, the entropy increases because the water molecules gain more freedom in the gaseous phase. On the other hand, when calcium carbonate precipitates, the process reduces entropy as the molecules arrange into a more ordered solid form.

Disorder in a system

Disorder in a system is a fundamental concept related to entropy, representing how dispersed or randomized the components are within a system.

• High disorder indicates that the particles are randomly arranged and not tightly packed.
• Low disorder means that particles are more organized and structured.

For instance, when sugar dissolves in coffee, the sugar molecules scatter evenly throughout the liquid, increasing disorder. The increase in disorder or randomness generally leads to a rise in the system's entropy. In contrast, when a system transitions from a more disordered state to a more ordered one, such as during precipitation, entropy decreases.

Phase transitions

Phase transitions involve changes from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. Each transition affects the entropy of a system due to changes in molecular arrangement and movement.

• From solid to liquid to gas: Entropy increases because molecules have more freedom and become less ordered.
• From gas to liquid to solid: Entropy decreases as molecules settle into more structured and constrained states.

Boiling is a prime example of a phase transition where water changes from a liquid to a gas. This transition greatly increases the entropy of the system as water molecules move more freely in the gaseous state.

Dissolution

Dissolution is the process where a solute (like sugar) disperses in a solvent (such as coffee) to form a homogeneous mixture. This process significantly affects entropy due to the increase in disorder.

• During dissolution, solute molecules spread throughout the solvent.
• This increase in molecular dispersion results in higher disorder and therefore an increase in entropy.

Because the molecules are less restricted in movement and more dispersed, the entropy rises. This spontaneous increase in entropy is why substances often dissolve more readily than they precipitate.

Precipitation

Precipitation involves the solidification of a substance from a solution, leading to a decrease in system entropy. During this process, dissolved ions or molecules come together to form a solid structure.

• This results in a more ordered state as molecules or ions occupying a solution organize into a structured solid form.
• Because of the reduced randomness, the entropy of the system typically decreases.

An example of this is calcium carbonate forming stalactites and stalagmites. As the ions in the solution precipitate, they create orderly solid structures, reflecting the decrease in entropy associated with precipitation.