How do you find the number of chiral compounds?

Chiral molecules usually contain at least one carbon atom with four nonidentical substituents. Such a carbon atom is called a chiral center (or sometimes a stereogenic center), using organic-speak. Any molecule that contains a chiral center will be chiral, with the exception of a meso compound (see below for how to identify these).

For example, the compound shown here contains a carbon atom with four nonidentical substituents; this carbon atom is a chiral center, and the molecule itself is chiral, because it's nonsuperimposable on its mirror image.

Table of Contents Show

How to identify molecules as meso compounds
How to Identify the Diastereomers of a Molecule
About This Article
About the book author:
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How do you calculate chiral compounds?
How do you find the number of chiral isomers?

A chiral center

You need to be able to quickly spot chiral centers in molecules. All straight-chain alkyl group carbons (CH3 or CH2 units) will not be chiral centers because these groups have two or more identical groups (the hydrogens) attached to the carbons. Neither will carbons on double or triple bonds be chiral centers because they can't have bonds to four different groups.

When looking at a molecule, look for carbons that are substituted with four different groups. See, for example, if you can spot the two chiral centers in the molecule shown here.

A molecule with two chiral centers

Because CH3 and CH2 groups cannot be chiral centers, this molecule has only three carbons that could be chiral centers. The two leftmost possibilities, identified in the next figure, have four nonidentical groups and are chiral centers, but the one on the far right has two identical methyl (CH3) groups and so is not a chiral center.

The chiral centers in a long molecule

How to identify molecules as meso compounds

A meso compound contains a plane of symmetry and so is achiral, regardless of whether the molecule has a chiral center. A plane of symmetry is a plane that cuts a molecule in half, yielding two halves that are mirror reflections of each other.

By definition, a molecule that's not superimposable on its mirror image is a chiral molecule. Compounds that contain chiral centers are generally chiral, whereas molecules that have planes of symmetry are achiral and have structures that are identical to their mirror images.

The plane of symmetry in meso compounds

For example, cis-1,2-dibromocyclopentane (shown in the first figure) is meso because a plane cuts the molecule into two halves that are reflections of each other. Trans-1,2-dibromocyclopentane, however, is chiral because no plane splits the molecule into two mirror-image halves.

Now look at the mirror images of these two molecules in the second figure to prove this generality to yourself.

The mirror images of achiral (meso) and chiral molecules

Even though the cis compound has two chiral centers (indicated with asterisks), the molecule is achiral because the mirror image is identical to the original molecule (and is, therefore, superimposable on the original molecule). Molecules with planes of symmetry will always have superimposable mirror images and will be achiral. On the other hand, the trans stereoisomer has no plane of symmetry and is chiral.

In organic chemistry, you need to be able to spot planes of symmetry in molecules so you can determine whether a molecule with chiral centers will be chiral or meso. For example, can you spot the planes of symmetry in each of the meso compounds shown in the last figure?

Some meso compounds

How to Identify the Diastereomers of a Molecule

When more than one chiral center is present in a molecule, you have the possibility of having stereoisomers that are not mirror images of each other. Such stereoisomers that are not mirror images are called diastereomers.

Typically, you can only have diastereomers when the molecule has two or more chiral centers.

The maximum number of possible stereoisomers that a molecule can have is a function of 2n, where n is the number of chiral centers in the molecule. Therefore, a molecule with five chiral centers can have up to 25 or 32 possible stereoisomers! As the number of chiral centers increases, the number of possible stereoisomers for that compound increases rapidly.

For example, the molecule shown here has two chiral centers.

A molecule with two chiral centers

Because this molecule has two chiral centers, it can have a total of 22, or 4, possible stereoisomers, of which only one will be the enantiomer of the original molecule.

Enantiomers are stereoisomers that are mirror images of each other.

Because both chiral centers in this molecule are of R configuration, the enantiomer of this molecule would have the S configuration for both chiral centers. All the stereoisomers of this molecule are shown in the next figure. Those molecules that are not enantiomers of each other are diastereomers of each other.

The four stereoisomers of a molecule with two chiral centers

About This Article

About the book author:

Arthur Winter, PhD, is the author of the popular Organic Chemistry Help! website chemhelper.com and Organic Chemistry I For Dummies. His professional focus is on the chemistry of magneto-organic materials.

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How do you calculate chiral compounds?

The key to finding chiral carbons is to look for carbons that are attached to four different substituents. We can immediately eliminate any carbons that are involved in double bonds, or that have two hydrogens attached. Given this, we find that there are three chiral carbons.