How many possible stereoisomers exist for a diastereomer with n chiral centers?

For a molecule with chiral centers, the number of stereoisomers can be derived from understanding the nature of stereochemistry. Each chiral center can exist in two configurations: R (rectus) or S (sinister). Consequently, if there are n chiral centers in a molecule, the number of possible stereoisomers can be calculated using the formula (2^n).

This formula arises because each chiral center independently contributes two options (R or S) to the overall combination of stereochemical arrangements. Therefore, when you have n chiral centers, you multiply the number of possibilities for each center together, which results in (2 \times 2 \times \ldots) (n times), leading to (2^n) distinct stereoisomers.

In the case of diastereomers, they are stereoisomers that are not mirror images of each other and usually result when you have multiple chiral centers. Any arrangement of these chiral centers will yield a corresponding diastereomer if at least one chiral center differs between the stereoisomers under consideration.

Thus, the correct choice reflects the fundamental principles of stereochemistry, and the answer is indeed (2^n).