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Organic Chemistry: Enantiomers and Diastereomers



Problems: Enantiomers


In the previous chapter we defined stereoisomers as molecules that have the same connectivity but differ in their spatial arrangement of atoms. We saw that the rigidity of double bonds gave rise to one type of stereoisomerism, cis-trans isomerism. However, it turns out, cis-trans isomers form only a small subset of stereoisomers. A more important type of stereoisomerism arises from molecules that are chiral.

You already have some intuitive notion of what it means for an object to be chiral, which is a Greek word meaning "handed". Consider the relation between your left and right hands. They appear to be the same, and yet there are clearly some ways in which they are distinct. For example, a right glove that fits easily over your right hand will not fit over your left hand. You would have a hard time fitting a left shoe over your right foot. A pair of right-handed scissors works fine in your right hand but feels awkward when you try to use your left hand.

What does it mean for an object to be chiral? To answer this question, again consider your left and right hands. The objects look identical; in fact theyare mirror images of each other. However, they are not the same. The test used to determine whether two objects are identical is superimposability. That is, can two objects be placed in the same space in such a way that all of their components overlap? Try the test of superimposability on your left and right hands, and you should see that they are not superimposable. This allows us to define what it means for an object to be chiral:

a chiral object is one that is not superimposable on its mirror image.
Conversely, an achiral object is one that is identical (superimposable) to its mirror image.

How can we tell whether a given object is chiral? The most straightforward way to determine whether a given object is chiral is to draw or visualize the object's mirror image and see if the two are identical (that is, superimposable). If the object contains an internal plane of symmetry then it must be achiral. However, as we shall see, the converse is not true: an object that has no internal plane of symmetry may also be achiral.

Chiral Molecules

Molecules, like other objects, can be chiral or achiral. For example, build a model of 2-butanol (butane with an -OH substituent on the second carbon) and its mirror image:

Figure %: The mirror images of 2-butanol

Try to physically superimpose these models and you'll see that they're not superimposable. This means that there are two distinct versions of 2-butanol, a right-handed one and a left-handed one. Each version of 2-butanol is a chiral molecule. What is the relation between them? The two molecules are clearly isomers, and since they have the same atomic connectivities they are stereoisomers. Unlike cis-trans isomerism, this stereoisomerism arises from the ability of molecules to be chiral. A chiral molecule and its non-superimposable mirror image are special types of stereoisomers called enantiomers.

Stereogenic Centers

What makes a molecule chiral? It turns out that in the majority of cases chiral molecules result from carbon atoms that are bonded to four different groups. For example, C 2 in 2-butanol is attached to the four distinct groups -H, -Me, -Et, and -OH. There are two different ways to arrange four groups about tetrahedr al carbon, giving rise to chirality. (In fact, chiral molecules gave chemists evidence that carbon is indeed tetrahedral.) Such a carbon atom is called an asymmetric carbon because it lacks a plane of symmetry. Asymmetric carbons are also called "chiral carbons". Because asymmetric carbons give rise to stereoisomerism, they are stereogenic centers or stereocenters. Technica lly, there are other structural motifs that are stereocenters beside asymmetric carbons, but in practice the term "stereocenter" is used in place of "asymmetric carbon" to denote a carbon bonded to four different substituents.

Figure %: General description of asymmetric carbon atoms that are bonded to four different groups.

(R)/(S) Nomenclature

The goal of nomenclature is to allow chemists to unambiguously identify the structure of any molecule given its name. The presence of stereoisomers presents a special problem in this regard. For example, given a particular molecule of 2-butanol, how can we name it so that the name conveys its handedness? How can we convey exactly which enantiomer of 2-butanol we're talking about? Furthermore, what about molecules that contain several stereocenters? What is needed is a nomenclature system to designate the absolute configuration at each stereocenter.

The term "configuration" refers to the fixed spatial positioning of bonds at a particular stereogenic carbon atom. Do not confuse "configuration" with "conformation". Unlike conformations, which are constantly equilibrating back and forth between forms, configurations are fixed and do not change unless bonds are broken. The configurational designation is absolute in the sense that the exact three-dimensional structure of the molecule can be reconstructed using the name alone.

In order to specify the absolute configuration at any stereogenic carbon, first identify the four groups attached to it and assign priorities to them using the Cahn-Ingold-Prelog convention:

  1. Examine the atoms directly attached to the stereogenic carbon. Groups attached with atoms of higher atomic number receive higher priority.
  2. In the case of isotopes, assign higher priority to the group containing the atom of higher atomic mass.
  3. When the attached atoms are identical, move down the next branching bond of the highest priority, and repeat until a difference is found.
Figure %: Assigning priorities to groups on 2-butanol according to the Cahn-Ingold-Prelog convention
After assigning priorities, look at the molecule so that the group of lowest priority is facing away from you. Now trace a circular path from the group of highest priority to the group of second priority to the group of third priority. If this path is c lockwise, the stereocenter has an (R) configuration. If the path is counterclockwise, the stereocenter has an (S) designation.
Figure %: Designating (R)/(S) configurations for 2-butanol

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