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 your choices. \begin{equation}\begin{array}{ll}{\text { a. } \mathrm{CO}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { b. } \mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)} \\ {\text { c. } \operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { d. } \mathrm{CH}_{4}(g) ; \operatorname{siH}_{4}(g)} \\ {\text { e. } \mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) \quad \text { f. } \operatorname{NaBr}(s) ; \mathrm{NaBr}(a q)}\end{array}\end{equation}

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 your choices.
\begin{equation}\begin{array}{ll}{\text { a. } \mathrm{CO}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { b. } \mathrm{CH}_{3} \mathrm{OH}(l) ; \mathrm{CH}_{3} \mathrm{OH}(g)} \\ {\text { c. } \operatorname{Ar}(g) ; \mathrm{CO}_{2}(g)} \quad \quad \quad \quad \quad {\text { d. } \mathrm{CH}_{4}(g) ; \operatorname{siH}_{4}(g)} \\ {\text { e. } \mathrm{NO}_{2}(g) ; \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{3}(g) \quad \text { f. } \operatorname{NaBr}(s) ; \mathrm{NaBr}(a q)}\end{array}\end{equation}

Key Concepts

Standard Molar Entropy

This concept refers to the entropy content per mole of a substance, usually measured under a standard set of conditions (1 bar pressure and a specified temperature, typically 25°C). It is a thermodynamic property that quantifies the degree of randomness or disorder in a system and serves as a benchmark for comparing the intrinsic disorder in different substances.

Effect of Phase on Entropy

The phase of a substance plays a critical role in determining its entropy. Gases generally have higher entropy than liquids, and liquids have higher entropy than solids because the particles in gases move freely with high translational motion, resulting in greater dispersal of energy compared to the more constrained motion in liquids and solids.

Molecular Complexity and Degrees of Freedom

A molecule’s complexity, including its size and the number of atoms, contributes to its entropy by providing additional degrees of freedom. These degrees of freedom encompass translational, rotational, and vibrational motions, each of which increases the number of accessible microstates and thus the overall entropy of the substance.

Intermolecular Forces and Solvation Effects

Intermolecular forces, such as hydrogen bonding or ionic interactions, and solvation effects in solutions can significantly influence entropy. In solutions, solvation tends to order the solvent molecules around solute ions or molecules, reducing the system's overall entropy compared to a similar substance in the gas phase where such ordering is absent.