(a) Which substance would you expect to have the highest molar entropy in the liquid phase, benzene, methanol \(\left(\mathrm{CH}_{3} \mathrm{OH}\right)\), or 1-propanol \(\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)\) ? (b) Would your answer be different if these substances were in the gas phase?

Intermolecular forces are the forces that mediate interaction between molecules, including attractions and repulsions. These forces significantly influence the physical properties of a compound, such as boiling point, melting point, and crucial for our discussion, molar entropy. There are several types of intermolecular forces, but the most relevant to consider in the context of molar entropy are London dispersion forces, dipole-dipole interactions, and hydrogen bonding.

London dispersion forces are weak and arise due to the momentary fluctuations in electron density within otherwise nonpolar molecules. Molecules with larger surface areas and higher molar masses typically exhibit stronger London dispersion forces. Dipole-dipole interactions occur between molecules that have a permanent dipole moment, which means that there is an uneven distribution of electron density within the molecule. Lastly, hydrogen bonding is a strong type of dipole-dipole interaction that occurs when hydrogen is bound to a highly electronegative atom like oxygen, nitrogen, or fluorine.

The strength of these intermolecular forces is inversely related to molar entropy. Stronger intermolecular forces, as seen in hydrogen bonding, tend to reduce molar entropy because the molecules are more ordered and have less freedom of movement. In contrast, weaker forces, like London dispersion forces, result in higher molar entropy due to increased disorder and a greater number of accessible microstates for the molecules.

In the liquid phase, the entropy of a substance is heavily influenced by intermolecular forces. Stronger intermolecular forces in liquids lead to more structured and ordered systems, which decreases the entropy. The ability of molecules to move relative to one another is restrained and energy distribution becomes more restricted compared to the gas phase.

For substances like benzene, methanol, and 1-propanol, this principle translates into varying entropy values based on their molecular interactions. Benzene, being nonpolar, has weaker London dispersion forces and therefore the highest entropy among the three because its molecules are comparatively less ordered. Methanol and 1-propanol can engage in hydrogen bonding due to their -OH groups, causing them to be more ordered and consequently possess lower entropy. As such, in a liquid state, any substance that can form hydrogen bonds is likely to have reduced entropy relative to a substance that cannot, given similar molecular sizes and complexities.

Impact of Molecular Size

Molecular size also plays a role in liquid phase entropy. Larger molecules have more ways in which their atoms can move or vibrate, which can increase entropy. However, if increased size also leads to stronger intermolecular forces, the net impact on entropy will depend on which factor is more dominant.

When considering the gas phase, the entropy difference among substances becomes more pronounced due to the increased freedom of movement of the molecules. In this phase, intermolecular forces are less of a concern because the distances between gas particles are much greater, and the attractions between them are significantly weaker than in liquids. Consequently, the intrinsic properties of the molecules themselves, such as molecular complexity and the number of atoms, become the primary factors influencing molar entropy.

A key point is that gas phase entropy increases with molecular complexity. This is because complex molecules have a greater number of vibrational modes and rotational freedoms, allowing for more microstates where energy can be distributed (i.e., more ways to achieve a particular energy level). Therefore, a molecule like 1-propanol, with its larger size and more complex structure compared to benzene and methanol, typically exhibits the highest molar entropy in the gas phase. Its increased number of atoms allows for more vibrational modes and possible microstates, which is directly related to higher entropy.

Relevance of Molecular Complexity

Understanding the concept of molecular complexity is valuable not only when comparing molar entropy between substances in a similar phase but also when trying to determine the entropy of a substance as it changes state. The transition from liquid to gas invariably results in a significant increase in entropy due to the liberation from intermolecular forces and the increase in accessible microstates for the substance.