Stereochemistry: Chirality, Fischer Projections, and the R/S System

Stereochemistry

Chirality and Enantiomers

Stereochemistry is the study of the spatial arrangement of atoms in molecules and how this affects their chemical behavior. A molecule is chiral if it contains a carbon atom bonded to four different groups, resulting in non-superimposable mirror images called enantiomers.

• Chiral Carbon: A carbon atom attached to four distinct groups.

• Enantiomers: Two molecules that are mirror images of each other but cannot be superimposed.

• Physical Properties: Enantiomers have identical physical properties except for their interaction with plane-polarized light and reactions in chiral environments.

• Optical Activity: Enantiomers rotate plane-polarized light in opposite directions. One is dextrorotatory (clockwise, +) and the other is levorotatory (counterclockwise, -).

Example: The two enantiomers of 2-butanol:

• ($+)$-2-butanol: dextrorotatory

• ($-$)-2-butanol: levorotatory

Absolute Configuration and the D/L System

The absolute configuration of a molecule refers to the exact spatial arrangement of its atoms. Before modern X-ray crystallography, chemists used the D/L system to describe configurations, based on the structure of glyceraldehyde.

• D-Glyceraldehyde: The OH group is on the right in the Fischer projection.

• L-Glyceraldehyde: The OH group is on the left in the Fischer projection.

Example: Glyceraldehyde can exist as D- and L- enantiomers, which are mirror images:

Form	Fischer Projection
D-Glyceraldehyde	HOCH2–CH(OH)–CHO (OH on right)
L-Glyceraldehyde	HOCH2–CH(OH)–CHO (OH on left)

Fischer Projections

Fischer projections are a two-dimensional way to represent three-dimensional molecules, especially carbohydrates and amino acids. Horizontal lines represent bonds projecting out of the plane (towards the viewer), while vertical lines represent bonds going behind the plane (away from the viewer).

• Horizontal bonds: Project out of the page.

• Vertical bonds: Project into the page.

Example: Fischer projection of D-glyceraldehyde:

Structure	Fischer Projection
D-Glyceraldehyde

Additional info: Fischer projections are widely used for sugars and amino acids to easily compare stereochemistry.

The R/S System (Cahn-Ingold-Prelog Rules)

The R/S system is a universal method for assigning absolute configuration to chiral centers. It uses atomic numbers to assign priorities to the groups attached to the chiral carbon.

• Step 1: Assign priorities (1 = highest, 4 = lowest) based on atomic number.

• Step 2: Orient the molecule so the lowest priority group (4) is pointing away from you.

• Step 3: Trace a path from priority 1 → 2 → 3.

• Step 4: If the path is clockwise, the configuration is R (rectus, right). If counterclockwise, it is S (sinister, left).

Example: Assigning R/S to 2-bromobutane:

• Br (atomic number 35) > CH2CH3 > CH3 > H

• Assign priorities: Br = 1, CH2CH3 = 2, CH3 = 3, H = 4

• Orient H away, trace 1 → 2 → 3

• Clockwise = R, Counterclockwise = S

Formula:

• $\text{Priority:}~Z > O > N > C > H$ (atomic number order)

Assigning R/S from Fischer Projections

To assign R or S from a Fischer projection:

• Assign priorities to the four groups.

• If the lowest priority group is on a vertical line, assign R/S as usual.

• If the lowest priority group is on a horizontal line, the assignment is the opposite of what you determine.

Example: For D-glyceraldehyde, the lowest priority (H) is on the horizontal line, so the configuration is the opposite of the path traced.

Assigning R/S from Newman Projections

Newman projections are used to visualize molecules along a particular bond axis. Assign priorities to the groups attached to the chiral center, orient the lowest priority group away, and trace the path from 1 → 2 → 3 to assign R or S.

Special Cases: Meso Compounds

Meso compounds are molecules with multiple chiral centers that are superimposable on their mirror image due to an internal plane of symmetry. They are optically inactive even though they have chiral centers.

• Example: Meso-tartaric acid is symmetrical and optically inactive.

Optical Rotation

The degree to which a compound rotates plane-polarized light is called its specific rotation ($[\alpha]$). It is measured using a polarimeter and depends on concentration, path length, and temperature.

• $[\alpha] = \frac{\alpha_{\text{obs}}}{l \cdot c}$

• $\alpha_{\text{obs}}$ = observed rotation

• $l$ = path length (dm)

• $c$ = concentration (g/mL)

Summary Table: Stereochemistry Concepts

Term	Definition	Example
Chiral Carbon	Carbon with four different groups	2-butanol
Enantiomers	Non-superimposable mirror images	D- and L-glyceraldehyde
Meso Compound	Has chiral centers but is optically inactive	Meso-tartaric acid
Fischer Projection	2D representation of 3D molecules	Glucose, amino acids
R/S System	Absolute configuration assignment	2-bromobutane (R or S)

Additional info: The notes also discuss the use of swap rules for Fischer projections, the importance of atomic number in priority assignment, and the historical context of stereochemical nomenclature.