Question

How many aldooctoses are possible? How many D-aldooctoses are possible?

Short answer

There are a total of 64 possible aldooctoses, and 32 of those are D-aldooctoses.

Step-by-step solution

Identify the chiral carbons in aldooctoses

An aldooctose contains an aldehyde group on carbon 1 and an alcohol group on carbon 8. Carbons 2 through 7 are chiral, meaning that they are bonded to four different atoms or groups of atoms. We can represent the chiral centers as C* within the aldooctose structure.

Determine the number of aldooctoses

To calculate the total number of aldooctoses, we need to find the number of possible stereoisomers. Each chiral carbon can have two different configurations (R or S). As there are 6 chiral carbons in aldooctose, the total number of possible aldooctoses can be determined using the formula: Total aldooctoses = 2^(number of chiral carbons) = 2^6 Total aldooctoses = 64

Determine the number of D-aldooctoses

To find out the number of possible D-aldooctoses, we need to consider the specific configuration at the last chiral carbon, which is carbon 8. For D-aldooctoses, the hydroxyl group (-OH) is in the right-hand side on the last chiral carbon. Since carbon 8 is not a chiral center, we need to look at the remaining chiral centers (carbons 2 through 7). As there are 5 chiral carbons remaining, the number of possible D-aldooctoses can be determined using the formula: Total D-aldooctoses = 2^(number of chiral carbons) = 2^5 Total D-aldooctoses = 32 In conclusion, there are a total of 64 possible aldooctoses, and 32 of those are D-aldooctoses.