Rank the following in order of increasing entropy: \(\mathrm{H}_{2} \mathrm{O}(\mathrm{g}) ; \mathrm{H}_{2} \mathrm{O}(\boldsymbol{\ell}) ; \mathrm{H}_{2} \mathrm{O}(\mathrm{s}) .\) In general, how are the entropy of the solid, liquid, and gaseous phases of a particular compound related? Explain your reasoning.

The concept of states of matter is a fundamental idea within the field of chemistry, describing how matter can exist in distinct forms with varying characteristics. Commonly, matter is found in one of three physical states: solid, liquid, and gas.

In a solid, particles are closely packed in a definite shape and have a fixed volume. They only vibrate around fixed positions due to very strong intermolecular forces. As we move to a liquid, particles have more freedom to move around but still remain close together, meaning liquids have a fixed volume but no fixed shape, adapting to the shape of their container. Finally, in a gas, particles are spread out with no fixed volume or shape, moving randomly and rapidly due to minimal intermolecular forces.

Such transitions among these states are termed as phase changes, which occur when energy is absorbed or released by the system. For instance, when a solid melts into a liquid, it absorbs energy. Conversely, when a gas condenses into a liquid, it releases energy. These changes are pivotal for understanding the natural processes and behaviors of substances in various environments.

Thermodynamics in chemistry is the study of energy changes accompanying chemical and physical transformations. A cornerstone of this field is the concept of entropy, a measure of the system's disorder or randomness.

According to the second law of thermodynamics, the entropy of an isolated system never decreases over time. It may remain constant for reversible processes but must always increase for irreversible ones. This law predicts the direction of spontaneous chemical reactions and phase changes, as they tend to move towards a state of higher entropy.

The importance of thermodynamics extends to a variety of applications, from predicting the feasibility of reactions to understanding energy exchange in biochemical pathways. It equips students and scientists with the theoretical basis to examine how energy is distributed among molecules and the degree of molecular randomization upon reacting or changing states.

The order of increasing entropy reflects the trend of disorder within a system aligning with the various states of matter. This ordering is intrinsic to understanding chemical systems and predicting the spontaneity of processes.

Starting with the state that exhibits the lowest entropy, solid, we see a highly ordered system. As mentioned previously, the solid phase of a substance, like ice in the case of water, has particles locked in place, providing little freedom for movement and hence low entropy. Transitioning to a liquid, the entropy increases as the particles have more space to move around, making it more disordered. The highest entropy is found in the gaseous state where the particles are in constant, high-speed motion, far apart from one another, leading to a highly disordered system.

Understanding this sequential order—from low entropy (solid) to higher entropy (liquid) to the highest entropy (gas)—provides a means to predict and explain the direction in which processes such as melting, boiling, or sublimation will spontaneously proceed.