Question

Does the entropy of the system increase or decrease for each of the following? Explain. a. the evaporation of alcohol b. the freezing of water c. dissolving \(\mathrm{NaCl}\) in water

Short answer

a. The evaporation of alcohol leads to an increase in entropy, as alcohol molecules become more randomized in the vapor state compared to the ordered liquid state. b. The freezing of water causes a decrease in entropy, as water molecules become more ordered and structured in the solid state compared to the more randomized liquid state. c. The dissolving of \(\mathrm{NaCl}\) in water results in an increase in entropy, as the ions become dispersed throughout the solution, leading to increased randomness of both solute and solvent particles.

Step-by-step solution

Identify the initial and final states of the process

In this process, alcohol in the liquid state is evaporating and turning into alcohol vapor.

Analyze the entropy change

In the initial state, alcohol molecules are in the liquid state where they are more ordered and packed together. In the final state, alcohol molecules are in the vapor state where they are freely moving, and the system becomes more randomized. Therefore, the entropy of the system increases during the evaporation of alcohol. #b. the freezing of water#

Identify the initial and final states of the process

In this process, water in the liquid state is freezing and turning into solid ice.

Analyze the entropy change

In the initial state, water molecules are moving more freely in the liquid state, and the system is more randomized. In the final state, water molecules are in the solid state, where they form a more ordered and structured lattice. Therefore, the entropy of the system decreases during the freezing of water. #c. dissolving \(\mathrm{NaCl}\) in water#

Identify the initial and final states of the process

In this process, the initial state is solid \(\mathrm{NaCl}\) and liquid water, and the final state is an aqueous solution of \(\mathrm{NaCl}\).

Analyze the entropy change

In the initial state, \(\mathrm{NaCl}\) ions are arranged in an ordered crystal lattice, and water molecules are more freely moving. When \(\mathrm{NaCl}\) is dissolved in water, the ions become dispersed throughout the solution. This causes an increase in the randomness of both the solute and solvent particles. Therefore, the entropy of the system increases during the dissolution of \(\mathrm{NaCl}\) in water.

Key concepts

Understanding Entropy Changes During the Evaporation of Alcohol

When alcohol evaporates, it undergoes a phase change from liquid to gas, a process where the entropy of the system experiences a notable increase. To understand this, let's think about what happens on the molecular level. In the liquid state, alcohol molecules are relatively close to each other and move with limited freedom. As the liquid evaporates, these molecules spread out into the gas phase where they can move more randomly and independently, thus occupying a greater volume with higher unpredictability in their positions and velocities.

This dispersal of molecules leads to a greater number of possible microstates that the system can assume, which directly corresponds to an increase in entropy. Entropy, in essence, measures the level of disorder or randomness in a system; hence, the process of evaporation, in which a substance changes from a more structured liquid state to a less structured gaseous state, always leads to an increase in entropy. This concept is crucial in understanding physical changes and is a fundamental part of the second law of thermodynamics, which highlights that entropy within an isolated system tends to increase over time.

Entropy Decrease in the Freezing of Water

Freezing water is an example of a process that results in a decrease of entropy within the system. During freezing, molecules of water, which are in a disordered liquid state where they move freely and randomly, begin to slow down as the temperature decreases. At the freezing point, they arrange themselves into a crystal lattice, creating solid ice.

In this structured lattice, each water molecule maintains a fixed position, relative to its neighboring molecules, resulting in a decrease in the randomness of the system. Fewer microstates are possible since the positions and movements of the molecules become highly predictable. This reduced number of configurations corresponds to a decrease in entropy, aligning with the definition that entropy is a measure of disorder. The concept of freezing can serve as a valuable illustration of entropy changes in chemical processes and provides insight into the energy transformations that take place during phase changes.

Entropy Increase When Dissolving NaCl in Water

Dissolving sodium chloride (NaCl) in water is another physical process that illustrates an increase in entropy. Initially, NaCl is in a crystalline form, where the ions are tightly bound in an orderly and repeating pattern. Upon dissolving in water, this arrangement breaks down as the individual Na+ and Cl- ions dissociate and disperse throughout the solvent.

This dispersion leads to a higher degree of randomness, as the ions move more freely and independently in the aqueous solution compared to their fixed positions in the solid crystal. Consequently, the system shifts from a state of lower entropy (ordered solid) to one of higher entropy (disordered solution). This process provides an excellent example of how dissolution can lead to an increase in entropy and reinforces the principle that entropy tends to increase in spontaneous processes, particularly when a substance transitions from a more ordered to a more disordered state.