Final answer:
The entropy increase from iodine (solid) to bromine (liquid) to chlorine (gas) is due to the physical states of the halogens at room temperature, with gases inherently having more entropy than liquids and solids
Step-by-step explanation:
The trend in the entropy of the halogens at room temperature is explained primarily by their physical states. Iodine (I₂) is a solid, bromine (Br₂) is a liquid, and chlorine (Cl₂) is a gas. Generally, gases have higher entropy than liquids, and liquids have higher entropy than solids because the particles in a gas are more spread out and have more random motion than in liquids or solids. The entropy of a substance increases as it goes from being a solid to a liquid to a gas because the amount of possible microscopic configurations (microstates) increases, which allows for more disorder or randomness in the system.
This observed trend is counterintuitive because we might initially think that heavier molecules like iodine would have higher entropy due to greater molecular complexity and more microstates. However, the physical state of the substance at room temperature overrules this because it has a more significant effect on the relative entropy values. Dispersion forces are stronger in larger and heavier atoms and leading to iodine being a solid and thus having lower entropy at room temperature compared to bromine and chlorine.