Chirality, Enantiomers, Racemic mixture and specific rotation

Chirality

• Definition: Chirality refers to a property of a molecule that makes it non-superimposable on its mirror image. This is similar to how your left and right hands are mirror images of each other but cannot be perfectly aligned if superimposed.
• Chiral Center: Often, chirality arises when a carbon atom is bonded to four different groups, known as a chiral center or stereocenter.

Enantiomers

• Definition: Enantiomers are pairs of molecules that are non-superimposable mirror images of each other. These pairs of molecules have the same molecular formula and connectivity but differ in the spatial arrangement of their atoms.
• Properties: Enantiomers have identical physical properties (e.g., melting point, boiling point) and chemical properties (e.g., reactivity) in an achiral environment. However, they interact differently with other chiral substances and can have different biological activities.

Racemic Mixtures

• Definition: A racemic mixture (or racemate) is a 1:1 mixture of two enantiomers of a chiral molecule. This mixture contains equal amounts of both enantiomers.
• Properties: Because the optical activities of the two enantiomers cancel each other out, a racemic mixture is optically inactive. This means it does not rotate plane-polarized light.

Specific Rotation

• Definition: Specific rotation is a measure of how much a chiral compound rotates plane-polarized light. It is a characteristic property of chiral compounds.

• Formula: The specific rotation $[\alpha ]$ is given by the formula:$$[\alpha ]=\frac{\alpha }{l\cdot c}$$where:
  • $\alpha$ is the observed rotation in degrees,
  • $l$ is the path length of the sample cell in decimeters,
  • $c$ is the concentration of the sample in grams per milliliter.
• Positive and Negative Values: The specific rotation can be positive ($+$) or negative ($-$), indicating the direction in which the compound rotates plane-polarized light (clockwise for positive, counterclockwise for negative).

Example to Tie Concepts Together

Consider the molecule lactic acid, which has two enantiomers: $(R)-lactic$ acid and $(S)-lactic$ acid. These two enantiomers have identical physical and chemical properties but differ in their interaction with polarized light and biological systems. A racemic mixture of lactic acid would contain equal amounts of $(R)-lactic$ acid and $(S)-lactic$ acid and would be optically inactive because the rotations caused by each enantiomer would cancel each other out.

In summary:

• Chirality refers to a molecule's ability to exist as non-superimposable mirror images.
• Enantiomers are those non-superimposable mirror images.
• Racemic mixtures contain equal amounts of two enantiomers and are optically inactive.
• Specific rotation quantifies the rotation of plane-polarized light by a chiral compound.