Question

Draw "saw-horse" and projection formulas for each of the following compounds, and designate whether the particular enantiomer is erythro, threo, cis, or trans: a. ( \(S\) )-hydroxyphenylethanoic acid b. \((1 R, 2 S)-1,2-\) dimethylcyclopropane c. \((2 S, 3 S)\) -3-bromo-2-butanol d. \((2 S, 3 R)\) -3-amino-2-butanol e. \((1 S, 3 S)-1,3\) -cyclohexanediol f. \((2 R, 3 R)\) - 2 -chloro-2,3-dimethylpentanoic acid g.* \((R)-2,3\) -pentadiene

Short answer

a. Erythro; b. Trans; c. Threo; d. Erythro; e. Cis; f. Threo; g. Not easily designated.

Step-by-step solution

Understanding Sawhorse and Newman Projections

Sawhorse formulae are a way to visualize the 3D arrangement of atoms in a molecule by looking along the bond. Newman projections focus on looking down a particular bond axis and showing the orientation of groups attached to the bond ends.

Draw (S)-hydroxyphenylethanoic acid

For (S)-hydroxyphenylethanoic acid, the Sawhorse projection has a central carbon with a hydroxyl group on one side, a phenyl group on the other, a carboxylic acid group pointing in another direction, and a hydrogen opposite the hydroxyl. Viewing along the bond, we arrange groups accordingly. This compound can be assigned as erythro based on its configuration.

Draw (1R, 2S)-1,2-dimethylcyclopropane

In this case, show the methyl groups on the same side of the ring using Sawhorse projection. By assigning R/S, confirm that they orient as trans. This cyclopropane has one methyl above and one below the ring, making it a trans isomer.

Create (2S, 3S)-3-bromo-2-butanol

For this molecule, bromo and hydroxy groups at carbons 3 and 2 are staggered. The Sawhorse formula shows groups (methyl, hydroxyl, bromo) with their stereochemistry identifying it as a threo compound due to opposite side location.

Draw (2S, 3R)-3-amino-2-butanol

Arrange the amino, hydroxyl, and methyl groups at carbons 3 and 2 opposite in saw-horse/form. This molecule is designated as erythro, due to the groups being on the same side in projection.

Sketch (1S, 3S)-1,3-cyclohexanediol

Using Sawhorse, place hydroxyl groups on carbons 1 and 3 of the cyclohexane. Confirm configuration aligns as cis for both hydroxyl groups being on the same face up.

Draw (2R, 3R)-2-chloro-2,3-dimethylpentanoic acid

Position the chloro and methyl substituents on carbons 2 and 3 to reflect their stereochemistry. Sawhorse projection suggests threo arrangement due to opposite side orientation.

Diagram (R)-2,3-pentadiene

This compound does not possess typical R/S stereochemistry as a diene. Instead, depict this linear molecule using the "allenic" nature of substituents perpendicular due to its electronic overlap. Cannot readily designate as erythro/threo, cis/trans.

Key concepts

Sawhorse Projections

Sawhorse projections offer a clear way to visualize the 3D geometry of molecules, which is especially helpful in organic chemistry stereochemistry. When using a sawhorse projection, you look along the axis of a particular bond and position the rest of the molecule with a slanted perspective. In this manner, the carbon-to-carbon bond appears diagonal. The groups attached to each carbon atom are then placed in space, allowing us to see their 3D arrangement relative to each other.

This technique helps in distinguishing stereoisomers by visually identifying the interaction of attached substituents. For example, consider two carbon atoms connected by a single bond, with each carbon bonded to different substituents. Sawhorse projections would place these carbon atoms on either end of a diagonal line and stretch out their respective substituents in space. This simple format aids in recognizing stereochemical configurations such as cis or trans, and erythro or threo, based on how the groups align in the projection.

Newman Projections

Newman projections are another fundamental tool for representing the stereochemistry of molecules. A Newman projection involves looking directly down the axis of a chemical bond. This effectively renders one atom in front of the other, simplifying the analysis to a single plane between the observer and the rest of the molecule.

In this visualization, the front carbon atom is represented by a point, and its three substituents extend outward. The rear carbon is shown as a circle with attached groups pointing outward as well. This helps to easily display staggered or eclipsed conformations, which are important for understanding the molecule’s stability and interactions.

• Staggered conformation: Substituents are positioned with minimal overlap, often leading to more stability.
• Eclipsed conformation: Substituents overlap when viewed down the bond axis, causing a less stable configuration due to steric hindrance or torsional strain.

Newman projections are particularly handy for comparing molecule conformers and quickly assessing whether groups on adjacent carbons are aligned or anti-aligned.

Enantiomers

Enantiomers are chiral molecules that are non-superimposable mirror images of each other. Much like your left and right hand, their structures are identical in connectivity but opposite in spatial arrangement. This property makes enantiomers crucial in stereochemistry since they can interact differently in chiral environments, such as enzymes or receptors in biology.

The R/S configuration system helps determine the specific type of enantiomer. Each chiral center in the molecule is assigned an R (rectus) or S (sinister) designation based on the priority of connected groups, following the Cahn-Ingold-Prelog rules. For example, the position of a hydroxyl group can determine whether a particular enantiomer is considered (R) or (S).

In practical terms, enantiomers can have vastly different effects or functions despite their similar structures. Therefore, understanding and identifying enantiomers is critical when discussing chemical reactions, synthesizing pharmaceuticals, or simply describing organic compounds.

Cis-Trans Isomerism

Cis-trans isomerism is a type of stereoisomerism where the spatial orientation of substituents around a rigid bond or ring creates distinct isomers. Understanding this phenomenon is vital in organic chemistry as it can dramatically influence the physical and chemical properties of a compound.

In a cis isomer, two similar or identical groups are on the same side of a double bond or ring structure. Conversely, in a trans isomer, these groups are positioned on opposite sides. For example, in cyclopropane derivatives, methyl groups can be either both facing the same side (cis) or one pointed up and the other down (trans).

Cis-trans isomerism can affect boiling points, melting points, and reactivity due to the differences in the overall shape of the molecule and its dipole moment. When these isomers are part of a larger synthesis or reaction, precise designation (cis or trans) becomes crucial for accurate communication in chemistry.