For each pair of substances, choose the one that you expect...

For each pair of substances, choose the one that you expect to have the higher standard molar entropy $\left(S^{\circ}\right)$ at $25^{\circ} \mathrm{C}$. Explain the reasons for your choices. a. $\mathrm{NaNO}_{3}(s) ; \mathrm{NaNO}_{3}(a q)$ b. $\mathrm{CH}_{4}(\mathrm{~g}) ; \mathrm{CH}_{3} \mathrm{CH}_{3}(g)$ c. $\mathrm{Br}_{2}(l) ; \mathrm{Br}_{2}(g)$ d. $\mathrm{Br}_{2}(g) ; \mathrm{F}_{2}(g)$ e. $\mathrm{PCl}_{3}(g) ; \mathrm{PCl}_{5}(g)$ f. $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) ; \mathrm{SO}_{2}(g)$

For each pair of substances, choose the one that you expect to have the higher standard molar entropy $\left(S^{\circ}\right)$ at $25^{\circ} \mathrm{C}$. Explain the reasons for your choices.
a. $\mathrm{NaNO}_{3}(s) ; \mathrm{NaNO}_{3}(a q)$
b. $\mathrm{CH}_{4}(\mathrm{~g}) ; \mathrm{CH}_{3} \mathrm{CH}_{3}(g)$
c. $\mathrm{Br}_{2}(l) ; \mathrm{Br}_{2}(g)$
d. $\mathrm{Br}_{2}(g) ; \mathrm{F}_{2}(g)$
e. $\mathrm{PCl}_{3}(g) ; \mathrm{PCl}_{5}(g)$
f. $\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) ; \mathrm{SO}_{2}(g)$

Key Concepts

Molecular Size, Symmetry, and Entropy

The size and symmetry of a molecule affect its overall entropy. Larger molecules generally have more atoms and more complex motions which increase entropy, while higher symmetry usually decreases the number of unique configurations. Thus, when comparing molecules, those with greater molecular size and more degrees of unsymmetrical motion tend to exhibit higher standard molar entropies.

Intermolecular Interactions and Hydration Effects

Intermolecular interactions, such as hydrogen bonding, dipole-dipole interactions, and dispersion forces, influence the entropy of a system. In aqueous solutions, for example, solute ions can structure surrounding water molecules into organized hydration shells, thereby reducing the overall entropy compared to a less organized phase. This concept explains why an ion in a solvent may have lower entropy relative to its pure solid form.

Phase of Matter and its Effect on Entropy

The phase of matter plays a critical role in determining entropy. Gases, with their free-moving molecules, generally have much higher entropy compared to liquids and solids because the molecules in gases have greater translational freedom. In contrast, the ordered structure of solids and the semi-ordered nature of liquids reduce the number of accessible microstates, lowering their entropy.

Standard Molar Entropy

Standard molar entropy is a measure of the number of microstates or the degree of randomness available to a substance at a given temperature, typically 25°C. It reflects the inherent disorder present in different phases and molecular arrangements and is influenced by both the physical state and the molecular structure of the substance.

Molecular Complexity and Degrees of Freedom

Molecular complexity, which includes the number of atoms in a molecule as well as the types of bonds and motion available, directly affects entropy. Larger or more complex molecules typically have higher entropy because they can vibrate, rotate, and translate in more ways, leading to a greater number of accessible energy states.

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