Neglecting stereoisomers for the moment, draw all isomers of the formula \(\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{DCl}\). (b) Decide which of these are chiral.

In order to draw isomers of C3H6DCl, first count the number of carbon atoms (3) and arrange them in different possible ways to create distinct structures. Ignore the hydrogen and deuterium atoms for now since the positions of these atoms will be inferred from bonding later. We'll only create structures where D is bonded to a carbon and not to chlorine. We have two possible isomer structures with 3 carbon atoms: 1. A linear chain of 3 carbons 2. A branched chain with 2 carbons, and the third carbon attached to the middle carbon Now let's add the appropriate number of hydrogen atoms to each carbon to complete the isomer and replace one hydrogen atom with the deuterium (D) atom. Lastly, add the chlorine (Cl) atom to the structure. For the linear chain isomer: Isomer 1: H-C(1)-C(2)-C(3)-H Replace one hydrogen atom with deuterium and add the chlorine atom: Isomer 1a: D-C(1)-C(2)-C(3)-Cl For the branched chain isomer: Isomer 2: H-C(1)-C(2)-H | C(3)-H Replace one hydrogen atom with deuterium and add the chlorine atom: Isomer 2a: H-C(1)-C(2)-Cl | D-C(3)-H

In order to determine if a molecule is chiral, we need to examine the stereocenters in the molecule, which are carbons with four different substituents attached. A molecule is chiral if it has at least one chiral center and is nonsuperimposable on its mirror image. Isomer 1a: D-C(1)-C(2)-C(3)-Cl The carbons in Isomer 1a have the following substituents: C(1): H, D, and C(2) C(2): C(1), C(3) C(3): H, Cl, and C(2) There are no chiral centers in isomer 1a since no carbons have four different substituents attached. Isomer 2a: H-C(1)-C(2)-Cl | D-C(3)-H The carbons in Isomer 2a have the following substituents: C(1): H, C(2) C(2): C(1), Cl, and C(3) C(3): H, D, and C(2) Carbon C(2) is a chiral center since it has four different substituents attached (C(1), Cl, C(3), H). This means isomer 2a is chiral. In conclusion, isomer 2a is chiral, whereas isomer 1a is achiral.