Question

How can you draw the diastereomers of 2,3-dibromobutane? Does it follow the $2^{\text{n}}$ rule for stereoisomers?

Answer 1

Hint: Stereoisomers which are non-superimposable images of one another are called diastereomers. The total number of stereoisomers of any compound is equal to $2^{\text{n}}$ , where n is the number of chiral centers in the molecule. But in the case of symmetrical compounds, this rule does not hold true.

Complete step by step answer: Stereoisomers are the isomers that have the same molecular formula but differ in the spatial arrangement of atoms. These are further divided into two types –
-Geometrical isomers: This type of isomerism arises due to the restricted rotation of the bond in a molecule. Compounds having a double bond with different groups of atoms on both sides of the bond show this type of isomerism. The most basic example is but-2-ene.

-Optical isomers: Stereoisomers which are non-superimposable mirror images of each other come under this category. A pair of such stereoisomers are called enantiomers and are distinguished by the rotation of plane polarized light. Dextro enantiomers rotate the plane of polarized light to the right and laevo enantiomers rotate the plane to the left. An example of optical isomers is shown below -

Now, the number of possible stereoisomers of any compound can find out using $2^{\text{n}}$ rule which states that maximum possible number of stereoisomers is equal to $2^{\text{n}}$ where n is the number of stereocenters in the compound. Stereocenter is an atom about which an exchange of two groups produces a stereoisomer.
Below is the structure of 2,3-Dibromobutane and we can see that it is having 2 stereocenters (marked by *).

So, it is supposed to have: $2^2=4$ stereoisomers. But there exist only 3 stereoisomers of it because of the presence of a plane of symmetry in the compound.
Let’s draw the 4 possible optical isomers of 2,3-Dibromobutane to check this.

We can see that structure (1) and (4) are a pair of enantiomers but structures (2) and (3) are identical. Therefore, this compound has a total of 3 stereoisomers. So, we can say that 2,3-Dibromobutane does not obey $2^{\text{n}}$ rule of stereoisomers due to its symmetrical structure.

Additional information: The structure given by (2) and (3) are identical and known as meso-compound. An achiral compound having a superimposable mirror image is known as a meso compound.

Note: The chiral center is an atom in a molecule which is bonded to 3 or more than 3 different atoms or groups of atoms. The stereocenter is an atom about which an exchange of two groups produces a stereoisomer. All chiral centers are stereocenters but all stereocenters cannot be chiral centers.