When liquid water is converted into solid ice cubes in an ordinary freezer, how does the entropy of the water itself change during this freezing process?

Introduction / Context:
Entropy is a central concept in thermodynamics and physical chemistry. It is often described as a measure of disorder, randomness, or the number of microscopic arrangements available to a system. This question asks what happens to the entropy of water when it freezes into ice cubes. Understanding this change is important for interpreting phase changes, spontaneity of processes, and the behaviour of systems at different temperatures.

Given Data / Assumptions:
- The substance is pure water that starts in the liquid state.
- The water is cooled in a freezer until it becomes solid ice cubes.
- Pressure is assumed to be approximately constant at around one atmosphere.
- We are asked specifically about the entropy of the water system, not the entropy of the entire universe.

Concept / Approach:
In the liquid state, water molecules have considerable freedom to move, rotate, and vibrate, and they can arrange themselves in many different microscopic configurations. In the solid state, ice has a rigid crystalline structure in which each water molecule occupies a more ordered position with restricted motion. Entropy is lower in more ordered states and higher in more disordered states. When water freezes, energy is released to the surroundings and the system becomes more ordered. Therefore the entropy of the water decreases during freezing, even though the total entropy of the system plus surroundings can still increase, which makes the process compatible with the second law of thermodynamics.

Step-by-Step Solution:
Step 1: Recall that entropy, usually denoted by S, is larger for states with more microscopic disorder and smaller for states with more order. Step 2: Compare molecular motion in liquid water and solid ice. Liquid water has molecules that move freely past one another, whereas solid ice has molecules fixed in a regular lattice. Step 3: Recognise that freezing is a phase transition from a more disordered state to a more ordered state, because the molecules line up in a crystalline arrangement. Step 4: Use the rule that a change from liquid to solid at constant pressure and temperature leads to a decrease in entropy of the substance undergoing the change. Step 5: Among the given options, the statement that the entropy of the water decreases as it freezes matches the thermodynamic description of a liquid to solid transition.

Verification / Alternative check:
Another way to think about this is to consider the direction of heat flow. When water freezes, it releases latent heat to the surroundings. The water loses energy and becomes more ordered, which corresponds to a negative entropy change for the water. The surroundings gain energy and experience a positive entropy change. For a spontaneous freezing process at a given temperature, the positive entropy gained by the surroundings must outweigh the negative entropy change of the water. This perspective again shows that the entropy of the water itself decreases, confirming that the correct option is the one that states that entropy decreases during freezing.

Why Other Options Are Wrong:
No change in entropy: A phase change from liquid to solid involves a clear change in molecular order, so entropy cannot stay constant.
Entropy increases: This would correspond to a transition to a more disordered state, which is not true when a liquid becomes a crystal.
May increase or decrease depending on process: For a given substance at specified temperature and pressure, the direction of entropy change for liquid to solid is fixed and does not depend on the particular freezer used.

Common Pitfalls:
Many learners confuse the entropy of the system with the entropy of the universe. They know that the total entropy must increase for a spontaneous process and may wrongly assume that every part of the system must show increased entropy. In reality, entropy can decrease in one part, such as the water, while increasing more in the surroundings. Another common mistake is to equate lower temperature directly with lower entropy without considering phase, or to rely too heavily on the idea that freezing is a spontaneous process in a freezer and therefore must involve an entropy increase for the water. Keeping the system and surroundings clearly separated avoids these errors.

Final Answer:
When liquid water is converted into ice cubes, the entropy of the water system decreases as it freezes because the molecules become more ordered in the solid state.