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

Comparing the formulas or states for each pair of substances, tell which you would expect to have 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, tell which you would expect to have 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

Entropy (Measure of Disorder)

Entropy is a thermodynamic quantity that measures the number of ways a system can be arranged at the molecular level. Essentially, it quantifies the disorder or randomness of a system. Higher entropy corresponds to a greater number of accessible microstates, and factors such as particle motion, energy dispersion, and molecular configuration all contribute to the overall entropy.

Phase Effects on Entropy

The phase of a substance has a substantial impact on its entropy. Gases generally exhibit much higher entropy than solids because their particles move freely and occupy large volumes, offering many more possible positional and energetic configurations. In contrast, solids have well-ordered, fixed structures which limit the number of accessible microstates. Aqueous solutions generally have an entropy between that of a pure solid and a gas, as the solute ions or molecules are freer than in a crystal lattice but may still induce some order in the surrounding solvent molecules.

Molecular Complexity and Degrees of Freedom

The complexity of a molecule, including the number of atoms it contains and its structural arrangement, affects its internal degrees of freedom (translational, rotational, and vibrational motions). More complex molecules have additional vibrational and rotational modes that enhance the number of ways energy can be distributed within the molecule, typically resulting in a higher entropy.

Ionic Interactions and Lattice Energy in Solids

Ionic compounds in the solid state are held together by strong electrostatic forces, which create a highly ordered, rigid crystal lattice. The strength of these ionic bonds (reflected in the lattice energy) limits the movement and vibrational freedom of the ions. Consequently, ionic solids with stronger interionic attractions tend to have lower entropy compared to those with weaker attractions, due to a reduced number of accessible microstates.

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