Rank each set of substances in order of increasing standard...

Rank each set of substances in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain your reasoning. a. $\mathrm{NH}_{3}(g) ; \mathrm{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \mathrm{He}(g)$ b. $\mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(l) ; \mathrm{H}_{2} \mathrm{O}(g)$ c. $\mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)$

Rank each set of substances in order of increasing standard molar entropy $\left(S^{\circ}\right) .$ Explain your reasoning.
a. $\mathrm{NH}_{3}(g) ; \mathrm{Ne}(g) ; \mathrm{SO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}(g) ; \mathrm{He}(g)$
b. $\mathrm{H}_{2} \mathrm{O}(s) ; \mathrm{H}_{2} \mathrm{O}(l) ; \mathrm{H}_{2} \mathrm{O}(g)$
c. $\mathrm{CH}_{4}(g) ; \mathrm{CF}_{4}(g) ; \mathrm{CCl}_{4}(g)$

Key Concepts

Intermolecular Interactions and Molecular Weight

Intermolecular forces and the mass of the molecules influence entropy through their impact on molecular motion and the number of accessible energy states. Substances with strong intermolecular attractions tend to have restricted molecular motion, leading to lower entropy, while heavier molecules often have more vibrational modes available, contributing to an increase in entropy.

Molecular Complexity and Degrees of Freedom

The complexity of a molecule, including factors like its size, shape, and number of atoms, affects its entropy. More complex molecules possess more internal degrees of freedom—translational, rotational, and vibrational—resulting in a larger number of possible microstates and thereby a higher standard molar entropy.

Standard Molar Entropy

Standard molar entropy is a fundamental thermodynamic quantity that measures the degree of molecular disorder or randomness in one mole of a substance at a specified temperature and pressure. It provides insights into the energy dispersion within a system and is typically reported in joules per mole-kelvin (J/(mol·K)).

Physical State Effects on Entropy

The physical state of a substance (solid, liquid, or gas) greatly influences its entropy. Gaseous substances exhibit much higher entropy than liquids, which in turn are higher than solids, due to the increasing freedom of movement and number of accessible microstates as one moves from ordered solids to disordered gases.

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