Certainly! Let's go through the solution step-by-step to determine the number of stereoisomers possible for the given structure.
To determine the total number of stereoisomers for a given molecule, we need to consider the chiral centers and any geometrical isomerism (cis/trans isomerism). The general formula for calculating the number of stereoisomers is:
\(2^n\)
Here, n is the number of chiral centers in the molecule.
Let's analyze the given structure:
1. Identify Chiral Centers: Look for carbon atoms bonded to four different groups. In this molecule, we see that there are two such chiral centers, each marked with a red dot:
2. Calculate Possible Stereoisomers: Since there are two chiral centers, apply the formula:
\(2^n = 2^2 = 4 \times 2 = 8\)
The factor of 2 in this case accounts for the potential geometrical isomerism (cis/trans), due to double bonds if present.
3. Reason for Options: The options were given as 8, 2, 4, and 3. Based on our calculation, the correct number of stereoisomers is 8.
Thus, the correct answer is 8, taking into consideration both the number of chiral centers and any geometrical configurations.
This explanation focuses on understanding and identifying all elements contributing to stereoisomerism. The presence of chiral centers and possible geometrical configuration is crucial to the solution.
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Approach Solution -2
The molecule has three chiral centers, each of which can exist in R or S configurations. The total number of stereoisomers is 2n, where n is the number of chiral centers. Here, n = 3, so: Total stereoisomers = 23 = 8.
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