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Molecular complexity refers to the degree of intricate structures within a molecule. It involves considering how many atoms are present in a molecule and how they are bonded together. More atoms and diverse types of bonds introduce more rotational and vibrational motions.
\( \text{CH}_3 \text{OH} \) and \( \text{CH}_3 \text{OD} \) are examples of more complex molecules due to the hydroxyl group \((\text{-OH})\). This group introduces additional vibrational modes, contributing to higher entropy. In contrast, simpler molecules like \( \text{CH}_4 \) have fewer vibrational modes due to fewer atoms and bonds.
Higher molecular complexity generally leads to an increase in molar entropy, as more structures within the molecule allow more ways to distribute energy among the available degrees of freedom.

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole \(\left( \text{g/mol} \right)\). It is calculated by adding the atomic masses of all atoms in the molecule.
Molecules with a higher molar mass, such as \( \text{CH}_3 \text{OH} \) and \( \text{CH}_3 \text{OD} \), typically have higher molar entropy. This is because heavier molecules tend to have more atoms and bonds, contributing to a greater number of possible microstates and configurations.
As you compare the given molecules, note how \( \text{CH}_4 \), being much lighter, possesses a lower molar entropy compared to the heavier methanol molecules.

Molecular symmetry refers to the balanced distribution of a molecule's shape. Symmetric molecules can have certain axes of rotation or planes of symmetry. This symmetry can reduce entropy because it limits the number of distinct ways energy can be dispersed.
For instance, \( \text{NH}_3 \) and \( \text{CH}_4 \) are symmetric due to their geometric structures, leading them to possess lower entropy. Contrarily, asymmetric molecules such as \( \text{H}_2 \text{O} \) or those with asymmetrical groups like the \( \text{-OH} \) group in \( \text{CH}_3 \text{OH} \), tend to have higher entropy.
Understanding symmetry helps in assessing entropy as less symmetrical molecules allow for a bigger variety of energy configurations.

Molecular structure encompasses the spatial arrangement of atoms in a molecule, which ultimately determines its chemical properties, including entropy.
The presence of specific functional groups or the type of bonds in the molecule significantly influences its entropy level. For example, the hydroxyl group \(\text{-OH}\) present in \(\text{CH}_3\text{OH}\) affects the molecular structure by introducing additional bonds, which increases the molecule's ability to vibrate and rotate, hence raising its entropy.
Comparing molecules like \(\text{CH}_4\), a simple structure, with \(\text{CH}_3\text{OH}\), which includes the hydroxyl group, illustrates how variations in molecular structure can lead to differences in molar entropy.