For each pair, tell which would have the greater absolute...

For each pair, tell which would have the greater absolute entropy per mole (standard molar entropy) at the same temperature. Give the reasons for your choice. (a) $\mathrm{NaF}(\mathrm{s})$ or $\mathrm{MgO}(\mathrm{s})$ (b) $\mathrm{Au}(\mathrm{s})$ or $\mathrm{Hg}(\ell)$ (c) $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ or $\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})$ (d) $\mathrm{CH}_{3} \mathrm{OH}(\ell)$ or $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$ (e) $\mathrm{NaOH}(\mathrm{s})$ or $\mathrm{NaOH}(\mathrm{aq})$

For each pair, tell which would have the greater absolute entropy per mole (standard molar entropy) at the same temperature. Give the reasons for your choice.
(a) $\mathrm{NaF}(\mathrm{s})$ or $\mathrm{MgO}(\mathrm{s})$
(b) $\mathrm{Au}(\mathrm{s})$ or $\mathrm{Hg}(\ell)$
(c) $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ or $\mathrm{H}_{2} \mathrm{~S}(\mathrm{~g})$
(d) $\mathrm{CH}_{3} \mathrm{OH}(\ell)$ or $\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(\ell)$
(e) $\mathrm{NaOH}(\mathrm{s})$ or $\mathrm{NaOH}(\mathrm{aq})$

Key Concepts

Intermolecular Forces

The type and strength of intermolecular forces (such as hydrogen bonding, van der Waals interactions, and dipole–dipole interactions) play a crucial role in determining the entropy of liquids and solids. Strong intermolecular forces can lead to more ordered structures and reduce the number of accessible microstates, thereby lowering the entropy. Conversely, weaker intermolecular forces allow for greater molecular motion and higher entropy.

Solvation and Hydration Effects

When an ionic compound dissolves in water, it is separated into individual ions that become surrounded by solvent molecules in a process called hydration. This interaction can either increase or decrease the overall entropy of the system depending on how the structured solvation shell organizes the solvent molecules around the ions, often leading to a decrease in entropy relative to the free ions in the gas phase.

Ionic Lattice Energy and Structure

Ionic compounds, especially in the solid state, have structures determined by strong electrostatic interactions between oppositely charged ions that form a highly ordered lattice. High lattice energy typically corresponds to low entropy as the ions are tightly organized in a crystalline structure. This concept is essential when comparing the absolute entropies of different ionic solids.

Phase States and Disorder

The phase of a substance (solid, liquid, or gas) fundamentally influences its entropy. Generally, gases have higher entropy due to the greater freedom of motion and more available microstates, whereas liquids have moderate entropy, and solids exhibit the lowest entropy because of their fixed, highly ordered structure. Understanding phase states is key when comparing the disorder associated with different physical states.

Standard Molar Entropy

Standard molar entropy is a thermodynamic property that quantifies the degree of randomness or disorder per mole of a substance at a specified temperature and pressure. It reflects the number of available microstates that a system can access, and thus, a higher entropy indicates a more disordered state. This property is intrinsic to a substance and is used to compare different phases or forms of matter under similar conditions.

Molecular Size and Complexity

The complexity and size of a molecule affect its entropy because larger and more complex molecules possess more internal degrees of freedom, such as vibrations, rotations, and translations. These additional modes of motion allow for a greater number of microstates, thus increasing the overall entropy. This concept helps explain differences in entropy among various molecular compounds.

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