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

a. For the process \(H_2O(l) \rightarrow H_2O(g)\), the sign of \(ΔS_{surr}\) is positive: \(ΔS_{surr}(a) > 0\). b. For the process \(I_2(g) \rightarrow I_2(s)\), the sign of \(ΔS_{surr}\) is negative: \(ΔS_{surr}(b) < 0\).

Step-by-step solution

Case (a): Conversion of liquid water to water vapor

When liquid water is converted into water vapor, the molecules gain kinetic energy and occupy a larger volume. This increase in volume means that there is more positional freedom for the water molecules, creating more disorder. Since this process increases the disorder, it means that the change in entropy of the surroundings will be positive. So the sign of \(ΔS_{surr}\) for the process \(H_2O(l) \rightarrow H_2O(g)\) is: \(ΔS_{surr}(a) > 0\)

Case (b): Conversion of iodine gas to solid iodine

When iodine gas is converted into solid iodine, the molecules lose kinetic energy and become more ordered, as they are now in a solid-state with a fixed arrangement. Since the process leads to a more ordered state, it means that the change in entropy of the surroundings will be negative. So the sign of \(ΔS_{surr}\) for the process \(I_2(g) \rightarrow I_2(s)\) is: \(ΔS_{surr}(b) < 0\) In summary, the signs of \(ΔS_{surr}\) for the given processes are: a. \(ΔS_{surr}(a) > 0\) for \(H_2O(l) \rightarrow H_2O(g)\) b. \(ΔS_{surr}(b) < 0\) for \(I_2(g) \rightarrow I_2(s)\)

Key concepts

Thermodynamics

Thermodynamics is a branch of physics that deals with the relationships between heat, work, temperature, and energy. It analyzes the energy transformations that occur in a system. In any process, energy can be transferred between the system and its surroundings, leading to changes in the system's thermodynamic properties. An essential concept in thermodynamics is entropy, symbolized as \( S \), which measures the degree of disorder or randomness in a system. Entropy is central to predicting the spontaneity of a process. In general, the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. The system evolves toward a state of maximum entropy.

• Systems naturally progress towards higher entropy states.
• Understanding energy exchange helps predict reaction behavior.

In the original exercise, considering entropy changes helps us predict whether the surroundings release or absorb energy, and whether entropy increases or decreases. This is particularly crucial in phase change processes.

Phase Change

A phase change refers to a transformation in the state of matter: from solid to liquid, liquid to gas, or vice versa. Every phase change involves a rearrangement of molecules, often leading to changes in energy and entropy. A common example is the evaporation of water, which is an endothermic process. When water converts from liquid to gas

• it absorbs energy to overcome intermolecular forces,
• leading to an increase in volume and entropy due to greater molecular freedom.

Conversely, when a gas transitions to a solid, as seen with iodine gas forming solid iodine, the entropy decreases. This transition is accompanied by the release of energy, and the molecules become more ordered. Phase changes not only highlight various states of matter but also underscore how energy and entropy changes are interlinked.

Disorder

In the realm of thermodynamics, disorder refers to randomness in the arrangement of particles within a system. Entropy quantifies this disorder. A system with higher entropy has greater disorder. As molecules spread out during a phase change, such as liquid to gas, the system's disorder increases, enhancing the entropy. For example:

• During the transition from water to steam, the molecules are more dispersed and move freely, representing increased disorder.
• In contrast, gases transitioning into a solid state, like iodine gas turning solid, see a substantial decrease in disorder.

Understanding how a system's disorder correlates with its entropy is crucial because it helps predict the spontaneity and direction of a process.

Enthalpy

Enthalpy, denoted as \( H \), is the total heat content of a system. It represents the sum of the internal energy along with the product of pressure and volume. Enthalpy helps us understand heat changes at constant pressure, particularly during phase transitions.When analyzing phase changes:

• An endothermic process, like liquid water transforming into vapor, requires heat absorption, indicating a positive change in enthalpy.
• On the contrary, an exothermic process, such as gas turning into a solid, releases heat, which results in a negative change in enthalpy.

Thus, enthalpy and entropy together will predict whether the external surroundings become cooler or warmer and whether these processes are spontaneous. By exploring enthalpy variations during phase changes, we gain insights into the energy dynamics of reactions and processes.