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. \(I_{2}(g) \longrightarrow I_{2}(s)\)

Short answer

a. For the process \(H_2O(l) \longrightarrow H_2O(g)\), \(\Delta S_{\text{surr}} < 0\). b. For the process \(I_2(g) \longrightarrow I_2(s)\), \(\Delta S_{\text{surr}} > 0\).

Step-by-step solution

Process a: \(H_2O(l) \longrightarrow H_2O(g)\)

This process involves the conversion of water from liquid state to gaseous state. When water evaporates, it absorbs heat from the surroundings, causing the surroundings to cool down. As heat flows out of the surroundings, the entropy of the surroundings decreases. Therefore, for this process, \(\Delta S_{\text{surr}}\) is negative.

Process b: \(I_2(g) \longrightarrow I_2(s)\)

This process involves the conversion of iodine from gaseous state to solid state. When iodine undergoes this change, it releases heat to the surroundings, causing the surroundings to warm up. As heat flows into the surroundings, the entropy of the surroundings increases. Therefore, for this process, \(\Delta S_{\text{surr}}\) is positive. To summarize: a. \(\Delta S_{\text{surr}} < 0\) for the process \(H_2O(l) \longrightarrow H_2O(g)\) b. \(\Delta S_{\text{surr}} > 0\) for the process \(I_2(g) \longrightarrow I_2(s)\)

Key concepts

Phase Change

A phase change occurs when a substance transitions between different states of matter, such as solid, liquid, and gas. During a phase change, the temperature of the substance remains constant, as all the energy provided or released is used to alter the state, not the temperature.
For instance, when water evaporates from liquid to gas, the process requires energy input, known as the heat of vaporization. This energy is absorbed from the surroundings, resulting in a cooling effect. Conversely, when a substance like iodine transitions from gas to solid, it releases energy, which warms the surroundings. These transformations impact the energy exchange and play a significant role in determining the changes in entropy of the surroundings.

Thermodynamics

Thermodynamics is the branch of science concerned with heat, work, and the forms of energy involved in processes. It provides the foundational principles to understand the behavior of energy during chemical reactions and physical transformations.
The second law of thermodynamics is vital here, as it introduces the concept of entropy. This law states that the total entropy of an isolated system can never decrease over time. It governs the directional flow of heat and predicts the feasibility of a process. During a phase change, such as water evaporating, thermodynamics dictates that energy is absorbed from the surroundings, often leading to a decrease in the surrounding's entropy. Alternatively, when iodine solidifies, the heat released increases the surroundings’ entropy.

Surroundings Entropy

Surroundings entropy refers to the change in the disorder of the environment due to a particular process. When a process occurs, like a phase change, energy exchanges happen with the surroundings, intriguingly affecting its entropy.
Several factors determine the sign of the change in surroundings entropy (\(\Delta S_{\text{surr}}\)):

• If a process absorbs heat from the surroundings, as in the case of water evaporation (\(H_2O(l) \longrightarrow H_2O(g)\)), the surrounding's entropy decreases (\(\Delta S_{\text{surr}} < 0\)).
• Conversely, if a process releases heat to the surroundings, like when iodine solidifies (\(I_2(g) \longrightarrow I_2(s)\)), the surrounding's entropy increases (\(\Delta S_{\text{surr}} > 0\)).

Understanding how these processes impact surrounding entropy can help predict the feasibility and spontaneity of chemical reactions in environmental systems.