D-fructose has a total of 8 diastereomers.
To understand why, it’s important to consider the structure of D-fructose. It is a ketohexose, meaning it contains six carbon atoms and a ketone group. The number of chiral centers in D-fructose is three, as it has four stereogenic (chiral) carbons: C2, C3, and C4. The general formula for calculating the number of stereoisomers based on the number of chiral centers is 2n, where n is the number of chiral centers. For 3 chiral centers, we have 23 = 8 total stereoisomers.
However, diastereomers are specific types of stereoisomers that are not mirror images of each other. D-fructose has other configurations (both D and L forms) that contribute to its diastereomers. Hence, when you consider the variations in the arrangement of the hydroxyl groups around the chiral centers, it results in 8 distinct diastereomers of D-fructose.