List the following substances in order of increasing molar entropy at \(298 \mathrm{~K}: \mathrm{H}_{2} \mathrm{O}(\mathrm{l}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{s}), \mathrm{C}\) (s, diamond). Explain your reasoning.

Entropy measures the degree of randomness or disorder within a system and is a fundamental concept in thermodynamics. When comparing the entropy between different states of matter for a given substance, it is essential to understand that entropy is inherently related to how organized or dispersed the particles are.

In the solid state, particles are tightly packed in a well-defined, orderly arrangement, resulting in lower entropy. As a substance transitions to a liquid, the particles have more freedom to move around, creating greater disorder and hence, higher entropy. In the gaseous state, particles are free to move in all directions and occupy the entire volume available to them, leading to the highest entropy among the three states of matter.

A practical application for understanding entropy state comparison is in predicting the direction of chemical processes or determining the feasibility of a reaction proceeding under certain conditions.

The states of matter—solids, liquids, and gases—are determined by the energy and arrangement of particles within a substance.

• Solids: Particles are closely packed in a fixed, ordered structure. This arrangement allows solids to maintain a definite shape and volume.
• Liquids: The particles are less tightly bound and can move more freely than in solids, though they're still attracted to one another. Liquids have a definite volume but take the shape of their container.
• Gases: Particles move rapidly and are widely spaced, with negligible attraction to one another. Gases assume both the shape and volume of their containers.

Understanding how the states of matter correlate with energy and temperature is critical for grasping a wide range of physical phenomena, such as phase transitions and the behavior of substances under differing pressure and temperature conditions.

Entropy is often associated with the concept of disorder in a system. As a substance's temperature increases, its particles absorb energy, move more vigorously, and become more disordered, thereby increasing entropy.

For example, the structure of a crystalline solid like diamond is extremely orderly, which corresponds to low entropy. In contrast, gases exhibit high entropy due to the high degree of disorder, as their particles are spread out and move independently. Entropy is a measure of the number of ways a system can be arranged, often described as the number of microscopic configurations that correspond to a thermodynamic system's macroscopic state. Educational exercises often involve predicting the change in entropy during phase changes or chemical reactions, reinforcing the link between microscopic behavior and observable phenomena.