Question

Write projection formulas for the following compounds and rename them by the \(R, S\) system: a. threo-1,2-diphenyl-1-bromo-2-chloroethane b. erythro-3-deuterio-2-butanol (or erythro-2-butanol-3- \(\left.{ }^{2} \mathrm{H}\right)\) c. meso-2,3-dimethylbutanedioic acid d. the diastereomers of the salt from \(D, L\) -1-phenylethanamine and \(D\) -2-hydroxybutanedioic acid (hydroxysuccinic acid)

Short answer

Renamed compounds: a. (R)-1-bromo-(S)-2-chloro-1,2-diphenylethane; b. (S,S)-3-deuterio-2-butanol; c. meso-compounds are not renamed by R/S due to symmetry; d. salt produces two diastereomers based on chiral centers.

Step-by-step solution

Understanding Fischer Projections

Before assigning the R/S configuration to each compound, we need to draw the Fischer projection, which is useful for visualizing stereochemistry. In Fischer projections, horizontal lines represent bonds coming out of the plane, and vertical lines represent bonds going behind the plane.

Assign Priorities

Use the Cahn-Ingold-Prelog priority rules to assign priorities to the substituents attached to the chiral center. These rules state that the higher the atomic number, the higher the priority.

Determine Configuration R/S

Look at the configuration by arranging the lowest priority group in the vertical or behind the plane in Fischer projection. Trace a path from the highest priority to the lowest (ignoring the lowest priority group), determining whether it follows a clockwise (R) or counterclockwise (S) sequence.

Analyze Each Compound

Apply the steps to each given compound to determine the R/S configuration: a. Draw the Fischer projection for threo-1,2-diphenyl-1-bromo-2-chloroethane and determine configuration. b. Draw the Fischer projection for erythro-3-deuterio-2-butanol and determine configuration. c. For meso-2,3-dimethylbutanedioic acid, determine if it is optically inactive because of symmetry. d. Evaluate for diastereomers of the given salt, considering the combination of stereochemistry from both amine and acid components.

Assign Final Names

With each compound's stereochemistry determined, rename them using the R/S nomenclature. Ensure all chiral centers are included in the name.

Key concepts

Fischer Projections

Fischer projections are a specialized way to depict molecules, especially useful for showing stereochemistry without complex three-dimensional drawings. They help in simplifying the visualization of chiral molecules.
Horizontal lines in a Fischer projection indicate bonds projecting out from the plane (towards the viewer), while vertical lines show bonds going behind the plane (away from the viewer). The intersections of these lines represent the chiral centers, making it easier to analyze such molecules.
When drawing a Fischer projection, always maintain the orientation of atoms. Both horizontal groups should be considered as forward-facing. Remember, rotating a Fischer projection by 180° maintains its representation, but at 90°, it alters the stereochemistry and should be avoided. These projections are essential before moving to assign R/S configurations.

Cahn-Ingold-Prelog Priority Rules

The Cahn-Ingold-Prelog (CIP) priority rules are critical when dealing with chiral molecules, as they help in determining the configuration at a chiral center. The process starts by assigning priorities to substituents attached to each chiral center.

• The priority is assigned based on the atomic number: the higher the atomic number, the higher the priority. For instance, bromine (atomic number 35) has a higher priority than chlorine (atomic number 17).
• If two substituents have the same atomic number, move to atoms bonded to them sequentially until a difference is found.
• Isotopes follow this rule; for example, deuterium (D) has higher priority than hydrogen (H) because deuterium has a higher atomic mass.

These priority assignments are foundational for determining the R or S configuration, which are forms of chiral assignment.

Diastereomers

Diastereomers are stereoisomers with two or more chiral centers that are not mirror images of each other. This contrasts with enantiomers, which are mirror images. Diastereomers differ in physical properties such as melting points and solubilities, allowing them to be separated more easily.
When analyzing diastereomers through exercises like determining configurations of salts with multiple stereocenters, consider the different combinations of R/S configurations possible. Each unique combination creates a distinct diastereomer. A thorough understanding of these principles allows one to methodically examine compounds, distinguishing between non-mirror image stereoisomers.

R/S Configuration

The R and S configurations are a standardized system used to describe the absolute configuration of chiral centers. It helps to specify the three-dimensional arrangement of groups around a chiral center.

• Once priorities are assigned to substituents using CIP rules, place the lowest priority group at the back (away from the viewer).
• Trace a path from the highest priority group to the lowest (ignoring the lowest group). If this path is clockwise, the configuration is R (from the Latin 'rectus' meaning right).
• If the path is counterclockwise, the configuration is S (from 'sinister' meaning left).

This method allows recognizable determination of configuration and proper naming of stereocenters, crucial in naming the compounds accurately with the R/S system.