Question

Draw stereochemical formulas for all the possible stereoisomers of the following compounds. Label pairs of enantiomers, and meso comounds. Tell which isomers, if separated from all other stereoisomers, will be optically active. (a) 1,2 -dibromopropane (b) \(1,2,3,4\) -tetrabromobutane

Short answer

For 1,2-dibromopropane, there are 4 possible stereoisomers with 2 pairs of enantiomers (Pair 1: first and third, Pair 2: second and fourth). There are no meso compounds and all stereoisomers will be optically active if separated. For 1,2,3,4-tetrabromobutane, there is at least one meso compound and corresponding pairs of enantiomers, which will be optically active if separated from all other stereoisomers.

Step-by-step solution

(a) 1,2-dibromopropane

For 1,2-dibromopropane, there are two stereocenters (2 chiral centers). Thus, there are a total of 2^2 = 4 possible stereoisomers. 1. Draw the Fischer projection of the first stereoisomer: Br | H - C - C - H | Br 2. Draw the Fischer projection of the second stereoisomer: Br | H - C - C - Br | H 3. Draw the Fischer projection of the third stereoisomer: H | Br - C - C - H | Br 4. Draw the Fischer projection of the fourth stereoisomer: H | Br - C - C - Br | H Pair 1 (first and third) and Pair 2 (second and fourth) are enantiomers of each other. There are no meso compounds in this case. Since all of the stereoisomers have chiral centers, they will all be optically active if separated from the other stereoisomers.

(b) 1,2,3,4-tetrabromobutane

For 1,2,3,4-tetrabromobutane, there are four stereocenters. Thus, there are a total of 2^4 = 16 possible stereoisomers. But drawing all 16 structures can be tedious. It is better to identify meso compounds and enantiomers: 1. Identify meso compounds One possible meso compound is when each pair of adjacent carbons contain the same (either trans or cis) configuration: Br Br | | H - C - C - C - C - H | | Br Br Here, the two middle carbons are connected by a plane of symmetry making the molecule optically inactive. 2. Identify enantiomers Once we identify meso compounds, the remaining possible combinations of the four stereocenters will give enantiomer pairs. Each of these pairs will be optically active if separated from all other stereoisomers. So, for 1,2,3,4-tetrabromobutane, we have at least one meso compound and corresponding pairs of enantiomers.

Key concepts

Stereoisomers

Stereoisomers are molecules that share the same molecular formula and sequence of bonded atoms (constitution), but differ in the three-dimensional orientations of their atoms in space. This concept is crucial in organic chemistry because stereoisomers can have vastly different biological activities and properties.

Illustrating this with an example from the exercise, 1,2-dibromopropane and 1,2,3,4-tetrabromobutane can each form multiple stereoisomers. These compounds have the same connectivity of atoms but can exist in different forms based on how their atoms are oriented in space. In such cases, a method such as the Fischer projection helps in visualizing and distinguishing these stereoisomers on paper.

Enantiomers

Enantiomers are a subtype of stereoisomers. They are mirror images of each other that are not superimposable, much like one's left and right hands. They have identical physical properties except for the direction in which they rotate plane-polarized light and their reactions in a chiral environment.

In the exercise, for both compounds, specific pairs of stereoisomers are identified as enantiomers. It's important to grasp that each enantiomer in such a pair will have the opposite optical rotation. Because of their non-superimposability, they will have distinct interactions with chiral biological molecules, informing the development of pharmaceuticals and understanding of biochemical processes.

Meso Compounds

Meso compounds are a fascinating type of stereoisomer. Even with two or more stereocenters, they are achiral because they have an internal plane of symmetry. This symmetry results in the cancelling out of the optical activity, making the compound optically inactive. In simpler terms, its mirror images are superimposable.

The exercise pointed out that in the case of 1,2,3,4-tetrabromobutane, one can identify meso compounds due to this internal symmetry, indicating that not all molecules with multiple chiral centers are optically active. The existence of meso compounds reinforces the lesson that the arrangement of atoms in three-dimensional space has dramatic effects on the properties of molecules.

Optical Activity

Optical activity refers to a molecule's ability to rotate the plane of polarized light as it passes through a solution of the chiral molecules. This property is exclusive to chiral substances—those that cannot be superimposed on their mirror images. Enantiomers will rotate light in opposite directions: clockwise, or to the right (dextrorotatory), and counter-clockwise, or to the left (levorotatory).

Regarding the stereoisomers identified in the problem, the optically active ones are those that do not possess a plane of internal symmetry; in the case of 1,2-dibromopropane, all stereoisomers are optically active, while for 1,2,3,4-tetrabromobutane, the meso compound is not.

Fischer Projection

The Fischer projection is a two-dimensional representation tool for three-dimensional organic molecules. It's especially helpful for visualizing and differentiating between stereoisomers, including enantiomers and meso compounds. In a Fischer projection, the longest carbon chain is drawn vertically with the most oxidized carbon at the top. Horizontal lines represent bonds that project towards the viewer, while vertical lines represent bonds going away from the viewer's plane.

In the solution process, Fischer projections effectively illustrated the stereoisomers of 1,2-dibromopropane. This method allows us to discern the unique arrangement of atoms for each stereoisomer, which is paramount in understanding their properties and reactions.

Chiral Centers

A chiral center, commonly a carbon atom, is one that has four different groups attached to it. This unique arrangement grants the molecule a non-superimposable mirror image, making it chiral. The presence of chiral centers is a prerequisite for the existence of enantiomers.

As revealed in the exercise, 1,2-dibromopropane has two chiral centers, leading to the formation of four possible stereoisomers. Each chiral center contributes to the molecule's potential for optical activity. Understanding the role of chiral centers allows students to predict the number of potential stereoisomers for a given molecule, thus refining their structural drawing skills and their grasp of stereochemistry.