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How do you determine the number of possible isomers for a chiral molecule?

  1. Using the formula 2^n, where n is the number of chiral centers

  2. Using the formula n^2, where n is the number of chirality

  3. Using the formula n! (factorial)

  4. Using the formula 2n, where n is the number of substituents

The correct answer is: Using the formula 2^n, where n is the number of chiral centers

The determination of the number of possible isomers for a chiral molecule is rooted in the concept of stereoisomerism, which arises from the presence of chiral centers—carbon atoms bonded to four different substituents. The correct approach involves applying the formula \(2^n\), where \(n\) represents the number of chiral centers in the molecule. Each chiral center can adopt two configurations, typically referred to as "R" (rectus) and "S" (sinister). Therefore, if a molecule has one chiral center, there are two possible stereoisomers. If there are two chiral centers, each can independently take on either configuration, leading to a total of \(2 \times 2 = 4\) stereoisomers. This pattern continues such that for \(n\) chiral centers, the total number of stereoisomers becomes \(2^n\) because each additional chiral center doubles the number of possible configurations. This makes the formula \(2^n\) a straightforward method for calculating the maximum number of stereoisomeric forms a chiral molecule can exhibit. It's important to note that while \(2^n\) gives the theoretical maximum, actual observed isomers