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. $\mathrm{I}_{2}(g) ; \mathrm{F}_{2}(g) ; \mathrm{Br}_{2}(g) ; \mathrm{Cl}_{2}(g)$ b. $\mathrm{H}_{2} \mathrm{O}(g) ; \mathrm{H}_{2} \mathrm{O}_{2}(g) ; \mathrm{H}_{2} \mathrm{~S}(g)$ c. $\mathrm{C}(s$, graphite $) ; \mathrm{C}(s$, diamond $) ; \mathrm{C}(s$, amorphous $)$

Rank each set of substances in order of increasing standard molar entropy $\left(S^{\circ}\right)$. Explain your reasoning.
a. $\mathrm{I}_{2}(g) ; \mathrm{F}_{2}(g) ; \mathrm{Br}_{2}(g) ; \mathrm{Cl}_{2}(g)$
b. $\mathrm{H}_{2} \mathrm{O}(g) ; \mathrm{H}_{2} \mathrm{O}_{2}(g) ; \mathrm{H}_{2} \mathrm{~S}(g)$
c. $\mathrm{C}(s$, graphite $) ; \mathrm{C}(s$, diamond $) ; \mathrm{C}(s$, amorphous $)$

Key Concepts

Structural Order and Allotropy in Solids

Different forms of a pure elemental solid, known as allotropes, can have differing entropies because of variations in their crystal structures and the associated disorder. More ordered crystalline structures tend to have lower entropy compared to less ordered or amorphous forms. This is important when comparing allotropes like graphite, diamond, and amorphous carbon, where structural disorder directly influences the level of entropy.

Molecular Complexity and Degrees of Freedom

The complexity of a molecule—including its molecular weight, the number of atoms, and the types of bonds—affects its entropy. More complex molecules have more vibrational modes and possible configurations, resulting in higher entropy. This concept is essential for comparing substances with different molecular makeups, such as different chemical gases.

Standard Molar Entropy

Standard molar entropy is a thermodynamic quantity that represents the amount of randomness or disorder per mole of a substance under standard conditions. It is influenced by factors like temperature, phase, and molecular structure, and is a measure of the energy dispersal in a system which increases with increased probability of microstates.

Phase Effects and Intermolecular Motion

The phase of a substance greatly affects its entropy because gases typically have higher entropy than liquids or solids due to the greater freedom of molecular motion. In ranking substances, gaseous forms will usually have higher entropy than their solid or liquid equivalents because the particles in gases possess considerable translational, rotational, and vibrational degrees of freedom.

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