How Many Stereoisomers Can Aldoheptose Have?

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Aldoheptose has five asymmetric centers, leading to 32 possible stereoisomers, as calculated by 2^5. In contrast, a 2-ketoheptose, which has four asymmetric centers, results in 16 stereoisomers (2^4). A ketotriose, lacking any asymmetric centers, has only one stereoisomer (2^0). The calculations confirm the understanding of isomerism in these carbohydrate structures. Overall, the discussion emphasizes the importance of asymmetric centers in determining the number of stereoisomers.
kasse
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Just to check that I've understood the concept of isomerism:

Homework Statement



How many stereoisomers are possible for

a) a 2-ketoheptose
b) an aldoheptose
c) a ketotriose

2. The attempt at a solution

a) First: does the "2" mean that the carbonyl carbon is the second C-atom?

The molecule has 4 asymmetric centers and hence 2^4 = 16 possible stereoisomers.

b) 5 asymmetric centers, so 2^5 = 32 possible stereoisomers

c) No asymmetric centers, therefore 2^0 = 1 possible stereoisomer


Correct?
 
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Looks OK to me, but second opinion won't hurt.
 

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