How many stereoisomers are possible for the following alkenes?
(d)

Verified step by step guidance

1. Step 1: Analyze the structure of the given alkene. The molecule consists of a cyclohexene ring with a double bond and a substituent attached to the ring. The substituent is a chiral center due to the wedge and dash bonds indicating stereochemistry.
2. Step 2: Determine the stereochemical possibilities for the double bond. A double bond in an alkene can exhibit cis-trans (E/Z) isomerism depending on the relative positions of the substituents attached to the double-bonded carbons.
3. Step 3: Evaluate the chiral center. The substituent attached to the cyclohexene ring has a chiral center, which can exist in two configurations: R and S. This adds additional stereoisomeric possibilities.
4. Step 4: Combine the stereochemical possibilities. The total number of stereoisomers is determined by multiplying the possibilities from the double bond (E/Z) and the chiral center (R/S).
5. Step 5: Conclude the calculation. Since there are 2 possibilities for the double bond (E/Z) and 2 possibilities for the chiral center (R/S), the total number of stereoisomers is 2 × 2 = 4.

Key Concepts

Stereoisomerism

Stereoisomerism refers to the phenomenon where compounds have the same molecular formula and connectivity of atoms but differ in the spatial arrangement of their atoms. This can lead to different physical and chemical properties. In alkenes, stereoisomers arise due to the presence of a double bond, which restricts rotation and can create different configurations, such as cis and trans isomers.

Chirality and Enantiomers

Chirality is a property of a molecule that makes it non-superimposable on its mirror image, often due to the presence of a chiral center, typically a carbon atom bonded to four different substituents. Enantiomers are a type of stereoisomer that are mirror images of each other and can exhibit different biological activities. Understanding chirality is crucial for determining the number of stereoisomers in a compound.

Counting Stereoisomers

The number of possible stereoisomers for a compound can be calculated using the formula 2^n, where n is the number of chiral centers in the molecule. For alkenes, the presence of double bonds and the possibility of cis/trans configurations must also be considered. This systematic approach helps in determining the total stereoisomer count for a given alkene structure.