There are three different substituted benzene compounds with the formula \(\mathrm{C}_{6} \mathrm{H}_{4} \mathrm{~F}_{2}\). (a) Draw the structures of the three compounds. (b) Assume that the benzene rings pack similarly into their crystal lattices. If the positions of the \(\mathrm{H}\) and \(\mathrm{F}\) atoms are statistically disordered in the solid state, which isomer will have the least residual molar entropy?

In organic chemistry, understanding the layout of atoms on a benzene ring is crucial for identifying compounds, predicting reactivity, and discussing properties. The terms ortho, meta, and para describe the relative positions of substituent atoms or groups on the benzene ring.

When two substituents are attached to adjacent carbons, they are in the ortho position. If there is a one-carbon gap between the two, they are said to be in the meta position. Lastly, when the substituents lie across from each other on the benzene ring, this is the para position. These positional notations are not only helpful in naming molecules but also indicate how different isomers of a substance might react or interact in various chemical environments.

Isomers are molecules with the same molecular formula but different structural arrangements, which often lead to different chemical properties. For the substituted benzene compound with the formula \( \mathrm{C}_{6} \mathrm{H}_{4} \mathrm{~F}_{2} \), the isomers are differentiated by the positions of the two fluorine atoms on the ring.

Drawing the isomeric structures involves visualizing how each unique position—ortho, meta, and para—alters the molecule. These structural variations can greatly influence the physical properties, such as boiling points, and the chemical reactivity, like how the compound might participate in reactions. Being able to sketch these structures is fundamental in organic chemistry for understanding and predicting the behavior of different isomers.

Entropy is a measure of the statistical disorder or randomness in a system, and it plays a vital role in thermodynamics and chemistry. For a crystal lattice of a solid, residual molar entropy refers to the entropy remaining at absolute zero—where theoretically all motion stops, but some degree of disorder may remain.

In the context of different benzene isomers, the residual molar entropy depends on how the atoms are arranged. Symmetrical isomers, like the para-difluorobenzene, provide fewer orientational possibilities compared to their less symmetrical ortho and meta counterparts, thus leading to a lower residual molar entropy. This concept links the microscopic arrangement of atoms to macroscopic thermodynamic properties.

The idea of statistical disordering describes the randomness in the positions of atoms or molecules within a solid. In a perfectly ordered crystal, every atom is in a fixed and predictable location. However, real solids often show some degree of disorder due to the presence of defects, impurities, or, as mentioned earlier, the presence of isomers with various substituent positions.

For the substituted benzene cases, the disordered arrangement of hydrogen and fluorine atoms contributes to the solid's residual molar entropy. The different amounts of residual molar entropy among the benzene isomers reflect the differing levels of statistical disorder. Such disorder can affect the entropy-related properties of a material, including its melting point and solubility.