Chapter 5: Stereoisomerism

Learning Objectives

• Differentiation of Isomers: Understand the distinction between stereoisomers and constitutional isomers.

• Symmetry and Chirality: Compare rotational and reflectional symmetry, and describe how axes and planes of symmetry affect chirality.

• Chirality Center Configuration: Assign configurations to chirality centers using the Cahn-Ingold-Prelog system.

• Fischer Projections: Draw Fischer projections of sugars and convert them to bond-line drawings.

• Optical Activity: Compare the effects of enantiomers on plane-polarized light and relate enantiomeric composition to observed rotation.

• Stereoisomer Classification: Distinguish between stereoisomers and diastereomers, and determine the maximum number of stereoisomers for a given structure.

• Stereodescriptors for Alkenes: Assign E/Z configurations to trisubstituted and tetrasubstituted alkenes.

• Enantiomeric Excess: Describe and calculate enantiomeric excess (ee).

• Resolution of Enantiomers: Explain methods for separating enantiomers.

• Optical Activity of Interconverting Conformations: Determine optical activity in compounds with rapidly interconverting, nonsuperimposable mirror images.

• Chirality Without Chiral Centers: Describe how a compound can be chiral without a chiral center.

Introduction to Stereoisomerism

Types of Isomers

Isomers are compounds with the same molecular formula but different arrangements of atoms. They are classified as:

• Constitutional Isomers: Same molecular formula, different connectivity of atoms.

• Stereoisomers: Same molecular formula and connectivity, but different spatial arrangement of atoms.

Examples of Stereoisomers

Compounds such as cis-1,2-dimethylcyclohexane and trans-1,2-dimethylcyclohexane are stereoisomers. The cis isomer has both methyl groups on the same side of the ring, while the trans isomer has them on opposite sides. These prefixes are used in IUPAC nomenclature to distinguish such compounds.

Restricted Rotation and Stereoisomerism

Double bonds (C=C) restrict rotation, leading to cis-trans isomerism in alkenes. For example:

• cis-2-butene: Both methyl groups on the same side of the double bond. Boiling point = 4°C.

• trans-2-butene: Methyl groups on opposite sides. Boiling point = 1°C.

Chirality and Chiral Molecules

Definition of Chirality

Chirality refers to the property of a molecule being non-superimposable on its mirror image. A chiral object is asymmetric and lacks a plane of symmetry. To test chirality, check if the object is superimposable on its mirror image.

Importance of Chirality

• Chiral molecules often have identical physical properties but can differ significantly in biological activity (pharmacology).

• Visualizing chirality often requires 3D models.

Chiral Centers

A chiral center (usually a carbon atom) is bonded to four unique groups. This tetrahedral arrangement leads to non-superimposable mirror images.

• Practice: Identify chiral centers in molecules such as Vitamin D3.

Enantiomers

Enantiomers are pairs of stereoisomers that are mirror images but not superimposable. Only chiral compounds can have enantiomers.

R/S Configurations of Chiral Centers

Cahn-Ingold-Prelog System

The Cahn-Ingold-Prelog (CIP) system assigns absolute configuration to chiral centers as either R (rectus, right) or S (sinister, left).

1. Assign priorities to the four groups attached to the chiral center based on atomic number (highest = 1, lowest = 4).

2. Orient the molecule so the lowest priority group (4) is pointing away.

3. Trace a path from priority 1 → 2 → 3. If the path is clockwise, the configuration is R; if counterclockwise, it is S.

For ties, compare atomic numbers one layer outward from the chiral center. Double bonds are treated as two single bonds for priority assignment.

Use in Nomenclature

The R/S configuration is included in the IUPAC name to distinguish enantiomers, e.g., (R)-3-methylhexane vs. (S)-3-methylhexane.

Fischer Projections

Representation of Chiral Molecules

Fischer projections are 2D representations of molecules with chiral centers, commonly used for sugars and amino acids.

• Horizontal lines: bonds coming out of the plane.

• Vertical lines: bonds going back into the plane.

Fischer projections are especially useful for molecules with multiple chiral centers.

Optical Activity

Interaction with Plane-Polarized Light

Enantiomers rotate plane-polarized light in opposite directions but to equal degrees. This property is called optical activity.

• Compounds that rotate plane-polarized light are optically active.

• Only chiral compounds are optically active.

Measurement of Optical Rotation

The degree of rotation depends on sample concentration and pathlength. Standard measurements use 1 g/mL solution and a 1 dm pathlength. Temperature and wavelength also affect rotation.

The specific rotation is given by:

• = observed rotation

• = concentration (g/mL)

• = pathlength (dm)

Sign of Rotation

• (+) = dextrorotatory (right)

• (-) = levorotatory (left)

There is no direct correlation between R/S configuration and the sign of optical rotation.

Stereoisomeric Relationships and Physical Properties

Classification of Stereoisomers

• Enantiomers: Stereoisomers that are mirror images.

• Diastereomers: Stereoisomers that are not mirror images.

Enantiomers have identical physical properties except for their interaction with chiral environments and optical activity. Diastereomers have different physical properties.

Maximum Number of Stereoisomers

The maximum number of stereoisomers for a molecule with n chiral centers is:

For example, a molecule with three chiral centers can have up to eight stereoisomers.

Meso Compounds

A meso compound contains chiral centers but is achiral due to an internal plane of symmetry. Meso compounds have fewer stereoisomers than predicted by the rule.

Symmetry and Chirality

• Rotational symmetry does not affect chirality.

• A plane of symmetry renders a compound achiral.

• Absence of a plane of symmetry usually indicates chirality, with exceptions (e.g., inversion centers).

E/Z Configurations of Alkenes

Assigning E/Z Notation

For alkenes with different groups attached to the double bond, E/Z notation is used instead of cis/trans.

1. Assign priorities to groups on each carbon of the double bond using atomic number.

2. If the highest priority groups are on the same side, the configuration is Z (zusammen, together).

3. If on opposite sides, it is E (entgegen, opposite).

Mixtures of Enantiomers

Racemic Mixtures and Enantiomeric Excess

• Racemic mixture: 50:50 mixture of two enantiomers; optical rotation is zero.

• If one enantiomer is in excess, the mixture is optically active but less so than the pure enantiomer.

Calculating Enantiomeric Excess (ee)

Enantiomeric excess is calculated as:

Alternatively, using optical rotation:

Resolution of Enantiomers

Methods of Separation

• Distillation: Separates compounds with different boiling points.

• Recrystallization: Separates compounds with different solubilities.

• These methods do not separate enantiomers from racemates due to identical physical properties.

Chiral Resolving Agents

Chiral agents convert enantiomers into diastereomers, which can be separated due to differing physical properties.

Affinity Chromatography

Uses a chiral adsorbent in a column to separate enantiomers based on differential interaction rates.

Nonsuperimposable Mirror Images that are Interconvertible

Conformational Isomerism

Some molecules (e.g., butane) have chiral conformations due to rotation around single bonds, but these are rapidly interconvertible, so the compound is not optically active.

Chair Conformations

Chair forms of cyclohexane can be chiral and enantiomeric, but rapid interconversion leads to overall achirality.

Chiral Compounds without Chiral Centers

Atropisomers

Atropisomers are stereoisomers that arise from restricted rotation around a bond, leading to stable, non-interconvertible conformations. These can be chiral without a chiral center, possessing an "axis of chirality."

Allenes

Allenes have two adjacent C=C double bonds. If the groups on each end are different, the molecule can be chiral and exist as enantiomers, even without a chiral center.

Summary Table: Types of Isomers

Key Equations

• Maximum number of stereoisomers:

• Specific rotation:

• Enantiomeric excess:

Additional info: Some context and examples have been expanded for clarity and completeness, including definitions, equations, and applications relevant to college-level Organic Chemistry.