Question

Predict the sign of \(\Delta S_{\text {sys }}\) for each process: (a) A piece of wax melts. (b) Silver chloride precipitates from solution. (c) Dew forms on a lawn in the morning.

Short answer

(a) Positive \(\text{\Delta S}_{\text{sys}}\), (b) Negative \(\text{\Delta S}_{\text{sys}}\), (c) Negative \(\text{\Delta S}_{\text{sys}}\).

Step-by-step solution

- Understand Entropy (\textstyle \text{\bold{S}})

Entropy, denoted by \(\text{S}\), is a measure of disorder or randomness in a system. An increase in disorder means a positive \(\text{S}\), while a decrease in disorder means a negative \(\text{S}\).

- Analyze Process (a): Wax Melting

Melting wax changes from a solid (more ordered) to a liquid (less ordered). Since the disorder increases, \(\text{\Delta S}_{\text{sys}}\) is positive.

- Analyze Process (b): Silver Chloride Precipitation

When silver chloride precipitates from solution, it forms a solid from ions in solution (less ordered to more ordered). Hence, \(\text{\Delta S}_{\text{sys}}\) is negative.

- Analyze Process (c): Dew Formation

Dew forms from water vapor (gas; more disorder) to liquid water (less disorder). Thus, the entropy decreases, making \(\text{\Delta S}_{\text{sys}}\) negative.

Key concepts

melting entropy change

Let's explore how entropy changes during the melting of a substance. When a piece of wax melts, it transitions from a solid to a liquid state. In a solid, molecules are tightly packed in an ordered structure. However, in a liquid, molecules are more spread out and can move around more freely. This increase in molecular motion means there is greater disorder or higher entropy. Therefore, the entropy change, \(\Delta S\_{\text{sys}}\), for melting wax is positive because the system's disorder increases.

Simply put:

• Solid wax (ordered) 👉 Liquid wax (disordered)
• Increase in disorder means \(\Delta S\_{\text{sys}}\) is positive

precipitation entropy change

Next, let's discuss the entropy change when silver chloride precipitates from a solution. Precipitation involves forming a solid from ions in a solution. In a solution, ions are dispersed and move freely, resulting in a higher level of disorder. When these ions come together to form a solid, they arrange in a more structured and ordered lattice.

Here’s a simple breakdown:

• Ions in solution (disordered) 👉 Solid silver chloride (ordered)
• Decrease in disorder means \(\Delta S\_{\text{sys}}\) is negative

Therefore, the entropy change, \(\Delta S\_{\text{sys}}\), for the precipitation of silver chloride is negative because the system's disorder decreases.

dew formation entropy change

Lastly, consider the formation of dew on a lawn. Dew forms when water vapor in the air (a gas) condenses into liquid water. In the gas state, water molecules are far apart and move randomly, resulting in high disorder. When these molecules condense into liquid, they become closer together and their motion is more restricted, leading to lower disorder.

Breaking it down:

• Water vapor (gas; disordered) 👉 Liquid water (less disordered)
• Decrease in disorder means \(\Delta S\_{\text{sys}}\) is negative

Thus, the entropy change, \(\Delta S\_{\text{sys}}\), for dew formation is negative because the system’s disorder decreases.