Comparing the formulas or states for each pair of...

Comparing the formulas or states for each pair of substances, predict which has the higher entropy per mole at the same temperature, and explain why. (a) $\mathrm{NaCl}(\mathrm{s})$ or $\mathrm{CaO}(\mathrm{s})$ (b) $\mathrm{Cl}_{2}(\mathrm{~g})$ or $\mathrm{P}_{4}(\mathrm{~g})$ (c) $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s})$ or $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{aq})$

Comparing the formulas or states for each pair of substances, predict which has the higher entropy per mole at the same temperature, and explain why.
(a) $\mathrm{NaCl}(\mathrm{s})$ or $\mathrm{CaO}(\mathrm{s})$
(b) $\mathrm{Cl}_{2}(\mathrm{~g})$ or $\mathrm{P}_{4}(\mathrm{~g})$
(c) $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{~s})$ or $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{aq})$

Key Concepts

Thermodynamic Entropy

Entropy is a measure of the number of microscopic configurations – or the degree of disorder – that are available to a system. In thermodynamics, it quantifies the randomness or randomness spread among the particles, which increases with the number of accessible microstates at a given temperature.

Phase States and Entropy

The entropy of a substance is strongly influenced by its physical state. Generally, gases have significantly higher entropy than liquids, and liquids have higher entropy than solids, because the particles in a gas have more freedom of movement and access to a larger number of microstates compared to those in more ordered phases.

Molecular Complexity and Degrees of Freedom

More complex molecules or larger aggregates have a greater number of vibrational, rotational, and translational degrees of freedom. This multiplicity of possible motions and configurations increases the number of accessible microstates, leading to a higher entropy per mole.

Intermolecular and Ionic Interactions

The strength and type of interactions among particles—such as ionic bonds in crystalline solids or ion-dipole interactions in solutions—affect the number of accessible microstates. Strong interactions tend to create highly ordered structures with fewer available configurations, which decreases entropy, whereas weaker interactions allow for more randomness and higher entropy.

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