RACEMIC MIXTURES INVOLVING ENANTIOMRES

Racemic Mixtures: Involving Enantiomers

Enantiomorphic pairs show no rotation of plane‐polarized light if they are in a true 1:1 mixture. Again, such mixtures are referred to as racemic mixtures, or racemates.

Racemic mixtures can be separated, or resolved, into their pure enantiomers by three methods. The first method is to mechanically separate the crystals in such a mixture based on differences in their shapes. This was the method first used by Pasteur, and it is mainly of historical interest.

The second resolution method employs enzymes. Enzymes are stereospecific chiral protein molecules that act as catalysts. Because of their chirality, these molecules react with only one enantiomer in a racemic mixture. The enantiomer that momentarily bonds to an enzyme undergoes reaction, while the enantiomer that does not bond remains unchanged. The unreacted enantiomer can then be removed from the reaction mix by ordinary separation methods, such as distillation or recrystallization.

The third method involves converting the enantiomers of a racemic mixture into diastereomers and then resolving that mixture with ordinary separation techniques. The separated diastereomers are then treated with appropriate reagents to regenerate the original enantiomers.

In this example, the diastereomer salts are separated by recrystallization, and the original acids are regenerated by the addition of a hydrochloric acid solution.

ENANTIOMERS AND DIASTEREOMERS

Enantiomers and Diastereomers

A Fischer projection is the most useful projection for discovering enantiomers. Compare the 2‐chlorobutane enantiomer structures in this diagram.

Rotating structure ( b) 180° in the plane of the paper, the only allowable rotation, does not lead to a form that is superimposable on structure ( a). Rotations of less than or more than 180° are not allowed because in a two‐dimensional projection, it is impossible to see the difference in the position of atoms that are located in front of or behind the plane.

Structures ( a) and ( b) are the only pair of enantiomers for 2‐chlorobutane.The compound 2‐chloro‐3‐bromobutane has two stereogenic centers and a maximum of four enantiomers. Compare these two Fischer projections.

Structure ( b) cannot be superimposed on structure ( a) by rotating it in the plane of the page, so structures ( a) and ( b) are enantiomers. The additional two enantiomers are created by allowing rotation about one of the stereogenic centers while restricting rotation about the other. Structure ( c) is created by allowing rotation about the upper stereogenic center (carbon 2) of structure ( a).

Notice that structure ( c) has a different configuration from structures ( a) and ( b). Structure ( d), the mirror image of ( c), cannot be superimposed on structure ( c) by rotating it in the plane of the page. Therefore, structures ( c) and ( d) are enantiomers. Any further rotation about the stereogenic centers creates a structure that is already drawn. For example, starting with structure ( a) and allowing rotation about the lower stereogenic center (carbon 3) generates structure ( d) again. This situation agrees with the maximum number of enantiomers predicted by the van't Hoff rule: 2 ⁿ = 2 ² = 4.

The relationship between the enantiomers of separate enantiomorphic pairs is called diastereoisomerism. For example, while structures ( a) and ( b), and ( c) and ( d), are enantiomers, the relationship of ( a) to ( c) is one of diastereoisomerism. They are not mirror images, so structure ( a) is a diastereomer of structures ( c) and ( d). Likewise, structure ( b) is a diastereomer of structures ( c) and ( d). In the same fashion, structures ( c) and ( d) are diastereomers of ( a) and ( b). Enantiomers have opposite configurations at all stereogenic centers, while diastereomers have the same configuration at one or more stereogenic centers but opposite configurations at others.

Optically inactive stereogenic centers ( meso forms). Some molecules are optically inactive even though they contain stereogenic centers. These compounds normally contain a plane of symmetry. The compound 2,3‐dichlorobutane should have four enantiomers because it has two stereogenic centers.

Structure ( b) cannot be superimposed on structure ( a) by rotating it in the plane of the page; thus, structures ( a) and ( b) are enantiomers. Rotation about the upper stereogenic center leads to structure ( c), which is a different configuration from ( a) and ( b).

Structure ( d) is the mirror image of ( c). It can be superimposed on ( c) by rotating it 180°. Because these two structures are superimposable mirror images, they are not optically active, even though they contain two stereogenic centers. The reason for this lack of optical activity is the plane of symmetry through the center of the molecule.

These types of molecules are called meso forms. In meso forms , the stereogenic centers are optically active, but due to the molecular symmetry, they rotate plane‐polarized light to the same degree but in opposite directions. This phenomenon results in an internal cancellation of optical activity.

PROJECTIONS

Projections

An explanation of the various drawings, or projections, used to show the three‐dimensional structure of chemicals will help you understand the next section's discussion of enantiomers and diastereomers. The simplest drawing is called a Fischer projection. In this representation, the “backbone” atoms of a carbon chain are represented simply by a straight line, and the terminal carbons are written as groups. The atoms or groups bonded to the chain carbons are “attached” with perpendicular lines. Compare the structural formula and Fischer projection of 2‐bromo‐3‐chlorobutane.

A second type of projection, a sawhorse projection, allows better visualization of the three‐dimensional geometry between adjacent carbon atoms. This projection is customarily used to show interactions between groups on adjacent carbon atoms in mechanisms. In a sawhorse projection, the backbone carbons are represented by a diagonal line, and the terminal carbons are shown in groups, just as in the Fischer projection. You can see in the next illustration that the top carbon group of the Fischer projection of 2‐bromo‐3‐chlorobutane has become the back carbon group of the sawhorse projection.

A sawhorse projection can reveal staggered and eclipsed conformations in molecules. The previous conformation of 2‐bromo‐3‐chlorobutane is referred to as a staggered conformer because the atoms and groups attached to each backbone carbon fit in the voids around the groups on the adjacent carbon. In an eclipsed conformer, the groups and atoms on adjacent carbons are in line with each other.

A third type of projection is called the Newman projection. This type of projection is used mainly to show interaction leading to stress between atoms or groups in three‐dimensional space due to steric crowding. In this representation, a molecule is viewed from one “end.” The “front” carbon of the backbone is represented by a dot, and the “back” carbon of the backbone is shown as a circle. Lines representing the bonds attaching the atoms and groups to the backbone carbons emanate from the dot and the circle at 120° angles. Compare the two conformations of 2‐bromo‐3‐chlorobutane in the Newman projection to the previous sawhorse and Fischer projections.

CHIRALITY

Chirality

Molecules that form nonsuperimposable mirror images, and thus exist as enantiomers, are said to be chiral molecules. For a molecule to be chiral, it cannot contain a plane of symmetry. A plane of symmetry is a plane that bisects an object (a molecule, in this case) in such a way that the two halves are identical mirror images. An example of a structure that has a plane of symmetry is a cylinder. Cutting a cylinder in half lengthwise generates two halves that are exact mirror images of each other. A molecule that possesses a plane of symmetry in any of its conformations is identical to its own mirror image. Such molecules are achiral, or nonchiral. Butane is an achiral molecule, while 2‐bromobutane is chiral.

The most common cause of chirality in an organic molecule is a carbon atom with four different atoms or groups bonded to it. This carbon atom is called a stereogenic, chiral, or asymmetric center. (Such centers are often designated with an asterisk in formulas and projections.)

The van't Hoff rule predicts the maximum number of enantiomers an optically active molecule can possess. This rule states that the maximum number of enantiomers a molecule can have is equal to 2 raised to the nth power, where n equals the number of stereogenic centers. The molecule 2‐chlorobutane has one stereogenic center, so two enantiomers are possible.