Question

Predict the sign of \(\Delta S_{\text {surr }}\) for the following processes. a. \(\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g)\) b. \(\mathrm{I}_{2}(g) \longrightarrow \mathrm{I}_{2}(s)\)

Short answer

For the given processes: a. H2O(l) → H2O(g): ΔSsurroundings is negative, as it's an endothermic process, removing heat from the surroundings. b. I2(g) → I2(s): ΔSsurroundings is positive, as it's an exothermic process, adding heat to the surroundings.

Step-by-step solution

Process a: H2O(l) → H2O(g)

This process depicts the phase change from liquid water to water vapor. During this process, energy is absorbed by water molecules in the form of heat, causing them to gain enough kinetic energy to enter the gas phase. Since energy is absorbed from the surroundings, the heat transfer is endothermic. An endothermic process removes heat from the surroundings, leading to a decrease in the entropy of the surroundings. Therefore, for this process, ΔSsurroundings will be negative.

Process b: I2(g) → I2(s)

This process represents the phase change from gaseous iodine to solid iodine. During this process, energy is released by the iodine molecules in the form of heat, causing them to lose kinetic energy and form a solid. Since energy is released into the surroundings, the heat transfer is exothermic. An exothermic process adds heat to the surroundings, resulting in an increase in the entropy of the surroundings. Therefore, for this process, ΔSsurroundings will be positive.

Key concepts

Endothermic Process

An endothermic process is one where a system absorbs energy from its surroundings, typically in the form of heat. This energy absorption is fundamental during phase changes, such as when water transitions from a liquid to a vapor state. The absorbed heat increases the kinetic energy of the molecules, allowing them to break free from their liquid state and enter the gaseous phase.

• During this transition, the system requires energy input.
• As a result, the surroundings lose heat, which decreases their entropy.

In the example of water turning into vapor, the surroundings experience a drop in entropy, marked by a negative change in \( \Delta S_{\text{surr}} \). This is because energy—specifically in the form of heat—is taken from the surroundings to facilitate the transformation of water into steam.

Exothermic Process

An exothermic process occurs when energy is released from the system to the surroundings. This is commonly observed when substances release heat, such as when iodine gas turns into iodine solid. During this transition:

• The system loses energy, which the surroundings gain.
• The release of heat increases the surroundings' energy and count of possible arrangements, thus increasing their entropy.

In chemical reactions, exothermic processes result in a positive change in \( \Delta S_{\text{surr}} \), as the surroundings become more disordered due to the added energy. The transformation of gaseous iodine to solid iodine demonstrates this concept, where the process of solidification releases heat, boosting the disorder in the surrounding environment.

Phase Change

Phase change refers to the transition of a substance from one state of matter to another, for example from liquid to gas or gas to solid. These transformations are critical in understanding concepts like endothermic and exothermic processes.

• When water turns into vapor, it is an example of an endothermic phase change that requires heat absorption (liquid to gas).
• Conversely, when iodine gas becomes solid iodine, it represents an exothermic phase change that releases heat (gas to solid).

For both types of phase changes, the direction of heat flow (into or out of the system) determines whether the change is endothermic or exothermic. Understanding phase changes is key to mastering thermodynamics, as they illustrate how energy is transferred and transformed between a system and its surroundings.