Using the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{Cl}_{2}\), draw the structural formula of (a) a molecule that is polar, (b) a molecule that is nonpolar, and (c) a molecule that contains only \(\mathrm{C}-\mathrm{C}\) single bonds.

When it comes to understanding the intricacies of a molecule, the structural formula is your go-to visual aid. This representation doesn't just tell you what atoms are present, as a molecular formula does; it shows you where they are in relation to each other. Consider it the blueprint of a molecule's architecture, illustrating how each atom is bonded to its neighbors.

For instance, in the molecular formula \(\mathrm{C}_{4} \mathrm{H}_{6} \mathrm{Cl}_{2}\), the structural formula is key in revealing whether a molecule is polar or nonpolar. It does this by laying out the exact spatial arrangement of the atoms, making it clear how electron density is distributed throughout the molecule. When the atoms are arranged asymmetrically, differing electronegativity values between bonded atoms can lead to an uneven distribution of charge and, hence, polarity. As we illustrate the connections between atoms, like the single bonds in our exercise, the structural formula becomes an indispensable tool in predicting the molecule's properties.

Diving into the world of nonpolar molecules, you'll find that symmetry is a key player. Nonpolar molecules are characterized by an even distribution of electron density, meaning no one region of the molecule hoards more negative charge than another. This balance of charge is often the result of symmetrical structural arrangements, where polar bonds – bonds between atoms with different electronegativities – are distributed in such a way that they cancel each other out.

Take \(C_4H_6Cl_2\) as a prime example. When the \(C-Cl\) bonds are placed opposite each other, they effectively neutralize the molecule's polarity, rendering the molecule nonpolar despite having polar bonds. The structural formula shows us this balancing act in action. It's like a game of tug-of-war; if the teams on either side of the rope are equally strong, the rope won't move, and likewise, if the polar bonds in a molecule are arranged symmetrically, the molecule remains nonpolar.

Last but not least, let's look at single bonds, which are the simplest type of chemical bond. In a single bond, two atoms are held together by the sharing of one pair of electrons, one from each atom. These bonds are pivotal in molecular construction—they're the nuts and bolts holding the structure together.

In our case with \(C_4H_6Cl_2\), we observe that drawing a molecule that contains only \(C-C\) single bonds gives us a straight chain of carbon atoms, each connected by a single pair of shared electrons. This design ensures that each carbon atom has enough electrons to satisfy its valence requirements. The structural formula lets us appreciate how these single bonds are arranged and how other atoms like hydrogen and chlorine associate with the carbon chain. It's the simplicity of single bonds that allows for a diverse array of molecular shapes and sizes, from intricate rings to long chains, each with their own unique properties.