Question

Four stereoisomers exist for 3 -penten \(-2=\mathrm{ol}\). (a) Explain how these four stereoisomers arise. (b) Draw the stereoisomer having the E configuration about the carbon-carbon double bond and the \(R\) configuration at the chiral center.

Short answer

Based on the step by step solution, the origin of the four stereoisomers of 3-penten-2-ol can be explained by the combination of two different types of isomerism: (1) geometric isomerism around the carbon-carbon double bond (E and Z configurations) and (2) chirality at the chiral carbon 2 (R and S configurations). Therefore, the possible combinations are E,R; E,S; Z,R; and Z,S. The E,R stereoisomer is formed by having the higher-priority groups on opposite sides of the double bond (E configuration) and the R configuration at the chiral center (clockwise arrangement when the lowest priority group is pointing away from us).

Step-by-step solution

Structure of 3-penten-2-ol and stereoisomerism elements

The molecule 3-penten-2-ol has five carbon atoms, with a double bond between carbons 3 and 4 and an alcohol (\( \mathrm{-OH} \) group) at carbon 2. The carbon at position 2 is a chiral center because it is attached to four different groups: a hydrogen, an alcohol (\( \mathrm{-OH} \) group), a methyl, and an ethyl. This chiral carbon can give rise to a pair of enantiomers. There is also geometric isomerism around the carbon-carbon double bond, because it cannot freely rotate, leading to cis/trans (or E/Z) isomers.

Explain how the four stereoisomers arise

The four stereoisomers of 3-penten-2-ol result from the combination of two different types of isomerism: (1) geometric isomerism around the carbon-carbon double bond (E and Z configurations) and (2) chirality at the chiral carbon 2 (R and S configurations). Therefore, the possible combinations are E,R; E,S; Z,R; and Z,S.

Determine E/Z and R/S configurations

E/Z configuration: If the higher priority groups are on opposite sides of the double bond, it's E configuration. If they are on the same side, it is Z configuration. We can use Cahn-Ingold-Prelog (CIP) priority rule to assign priorities. R/S configuration: To assign R or S configuration at a chiral center, follow these steps: 1. Assign priority to each of the four groups attached to the chiral center based on the CIP rules. 2. Orient the molecule so that the lowest priority group is pointing away from us. 3. Determine the direction of the three higher priority groups; if the order is clockwise, it's R configuration, and if it's counterclockwise, it's S configuration.

Draw the E,R stereoisomer of 3-penten-2-ol

To draw the E,R stereoisomer of 3-penten-2-ol, you should first draw the carbon skeleton of the molecule and place a double bond between carbons 3 and 4, and an \( \mathrm{-OH} \) group at position 2. Apply the E/Z and R/S rules from Step 3. Draw the higher-priority groups on opposite sides of the double bond (E configuration) and the R configuration at the chiral center (clockwise arrangement when lowest priority group is pointing away from us).

Key concepts

Stereoisomerism

Stereoisomerism is the occurrence of the same molecular formula and sequence of bonded atoms (constitution), but with a different three-dimensional orientation of atoms in space. While geometric isomerism (also known as cis-trans isomerism) considers different orientations around a double bond, the concept also includes chirality, where a molecule has a carbon atom—called a chiral center—bonded to four distinct substituents.

For instance, the molecule 3-penten-2-ol contains both a double bond and a chiral center, allowing for both geometric and chiral stereoisomers. This rich structural variety gives rise to diverse chemical behavior, with each stereoisomer often exhibiting unique physical and chemical properties despite sharing the same molecular formula. Understanding stereoisomerism is key in fields like pharmaceuticals, where the different isomers can have wildly different effects in biological systems.

Chiral Centers

Chiral centers are carbon atoms that are attached to four different groups or atoms, leading to non-superimposable mirror images, called enantiomers. Each enantiomer can't be overlaid on its mirror image even when rotated, much like how left and right hands are mirror images but not identical.

The molecule 3-penten-2-ol has such a chiral center at carbon 2, which significantly contributes to its ability to exist as stereoisomers. The presence of chiral centers in molecules is crucial for the pharmaceutical industry as the two enantiomers of a drug can have very different biological activities. For example, one enantiomer might be therapeutically beneficial while the other could be harmful or inactive.

Geometric Isomerism

Geometric isomerism, a subset of stereoisomerism, occurs due to the restricted rotation around double bonds. There are two types of geometric isomers: cis (where the similar or higher priority substituents are on the same side of the double bond) and trans (where they are on opposite sides). However, the more modern nomenclature uses the terms E (from the German 'entgegen', meaning opposite) and Z (from 'zusammen', meaning together) to distinguish these isomers.

The molecule 3-penten-2-ol exhibits geometric isomerism because of the double bond between carbons 3 and 4. This double bond keeps the molecule rigid, leading to the existence of distinct spatial arrangements, creating the possibility of E and Z isomers.

Cahn-Ingold-Prelog Priority Rules

The Cahn-Ingold-Prelog (CIP) priority rules provide a systematic approach for assigning configuration to stereocenters. The rules help to determine the 'priority' of substituents attached to a chiral center or a double bond. Priority is assigned based on the atomic number of the atoms directly attached to the chiral center or double bond; the higher the atomic number, the higher the priority.

In situations where the atomic numbers are the same, the rule considers the atoms or groups attached to those atoms, branching out until a difference is found. These rules are vital in determining the configuration (R/S and E/Z) of stereoisomers and are extensively used in the naming and classification of organic molecules.

E/Z Configuration

E/Z configuration is the nomenclature used to describe geometric isomers based on the positions of substituents around a double bond. According to the CIP priority rules, if the higher priority groups are on opposite sides of the double bond, the molecule is assigned an E configuration. If the higher priority groups are on the same side, it is given a Z configuration.

Applying this to 3-penten-2-ol, we consider the atomic numbers and other CIP rules to decide which substituents have the highest priority on both sides of the double bond, enabling us to determine the E or Z configuration. Understanding this concept is essential for properly identifying molecular structures, especially since it can impact the molecule's physical properties and reactivity.

R/S Configuration

R (rectus) and S (sinister) configuration relates to the spatial arrangement of the substituents around a chiral center. Following the CIP priority rules, we determine the order of substituents around the chiral center. If the arrangement from highest to lowest priority is clockwise, the configuration is R; if it's counterclockwise, it's S—always viewed with the lowest priority group pointed away.

For the chiral center in 3-penten-2-ol, we identify the priorities of the substituents and then orient them, so the lowest priority group is in the back. If the descending order of priority groups sweeps in a clockwise motion, we denote it with R; if counterclockwise, S. This R/S notation is critical for understanding the three-dimensional arrangement of molecules and for predicting the outcome of chemical reactions involving chiral molecules.