Draw all the structural isomers of compounds with the formula \(\mathrm{C}_{4} \mathrm{H}_{8} \mathrm{Cl}_{2} .\) Indicate which isomers are chiral and give them systematic names.

In organic chemistry, constitutional isomers, also known as structural isomers, are molecules with the same molecular formula but different structural formulas. They differ in the way their atoms are connected or the sequence in which their atoms are connected.

For instance, with the molecular formula \(\mathrm{C}_{4}\mathrm{H}_{8} \mathrm{Cl}_{2}\), there are a few ways we can attach the chlorine atoms to the four-carbon backbone. Placing the chlorine atoms on the same carbon will create 1,1-dichlorobutane, but if we place them on adjacent carbons, we generate 1,2-dichlorobutane, and so on. Each of these structural variations represents a different constitutional isomer.

These organizational differences can result in varied chemical and physical properties, hence the significance in being able to recognize and distinguish between these isomers.

Chirality is a property of asymmetry in molecules where an object and its mirror image cannot be superimposed on each other. This concept is essential for understanding the behavior of molecules in biological systems as chirality can significantly affect how different molecules interact with biological receptors.

In the context of the \(\mathrm{C}_{4}\mathrm{H}_{8} \mathrm{Cl}_{2}\) isomers, we identify chiral centers by looking for carbon atoms with four distinct substituents. For example, in 1,2-dichlorobutane, the second carbon has two different alkyl groups and two different halogens attached, qualifying it as chiral. Meanwhile, the other isomers lack this specific type of carbon and are thus not chiral. Chiral molecules are frequently referred to as 'enantiomers' when they come in two non-superimposable mirror images. The existence of chirality in a molecule can lead to different, sometimes opposite, interactions with other chiral molecules, like those in our bodies, making it a fundamental concept in pharmaceuticals and biochemistry.

The IUPAC nomenclature is a standardized system of naming chemical compounds so that each has a unique name. It's based on a set of rules to unambiguously describe the structure of a compound and, by extension, its properties and behavior.

For the compound \(\mathrm{C}_{4}\mathrm{H}_{8} \mathrm{Cl}_{2}\), we would start naming from the end of the molecule closest to the first point of difference, which typically involves a functional group or substituent. Each chlorine's position is indicated by a number, and the longest continuous chain of carbons determines the parent name. Taking 1,1-dichlorobutane as an example, we start numbering from the end nearest a chlorine atom, consequently naming it based on the position of the chlorines relative to the butane chain.

Understanding how to apply these rules and conventions is vital for clear communication in chemistry and enables chemists to deduce the structure of a compound from its IUPAC name and vice versa.