Stereochemistry: Drawing Enantiomers and Diastereomers
Exercise Solutions
You may find it useful to build models of your answer and the answers
given here for comparison purposes. Alternately, relative stereochemical
relationships can be compared by assigning the stereocenters as R or S.
Recall that all the stereocenters are inverted between a pair of mutual
enantiomers, and at least one, but not all, stereocenters will be identical
in mutual diastereomers.
Drawing enantiomers
d. This is a meso compound. It has a mirror image
(as do all things except a vampire), but the original object and mirror
image are superposable. Therefore the original object and the mirror
image are identical, and not enantiomers.
Drawing diastereomers
a. This molecule has two stereocenters, so there are four possible stereoisomers:
two pairs of enantiomers. Thus this compound can have two diastereomers
that make up a set of enantiomers.
Other diastereomers: 
b. This compound has two stereocenters, so it can have
at most four stereoisomers: two enantiomeric sets of diastereomers.
However, since the two stereocenters are mirror images, this compound is
meso. A meso compound is identical with it's mirror image, so it
cannot have an enantiomer. Thus the compound has three total stereoisomers.
The other two stereoisomers are diastereomers of the original meso compound.
Other diastereomers: 
c. Like the previous question, this compound has two stereocenters
and thus four possible stereoisomers. However, the trans compound
is meso, so there are at most three stereoisomers for this compound.
The two new diastereomers also happen to be conformational isomers that
are interconverted by cyclohexane ring flip.
Other diastereomers: 
d. This compound has but one stereocenter. The "stereocenter"
on the right has two methyl groups, so it is not actually a stereocenter.
Because this compound has a single stereocenter, it has an enantiomer,
but no diastereomer.
e. This is b-D-glucopyranose
(glucose), the most common carbohydrate. It has five stereocenters
and therefore 25 = 32 possible stereoisomers. Many of
these stereoisomers occur in nature as other carbohydrates such as b-D-galactopyranose.
There are two diastereomers that are called D-glucopyranose; they differ
in the stereochemistry of the anomeric carbon.
(You can read more about carbohydrates in the text.)
f. This compound has three stereocenters. However,
changing one of the two bridgehead stereocenters (indicated by arrows)
without inverting the other one as well would result in an impossibly strained
"inside out" molecule. (Try this with your molecular models).
The only stereocenter that may be changed and still result in a reasonable
molecule is the amine stereocenter.
Only other reasonable diastereomer: 
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Copyright 2000 by Steven A. Hardinger and Harcourt Brace & Company.
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