Stereoisomers-molecules that have the same constitution, but different
disposition of groups in space. In other words the atoms are connected
to each other in the same way, they only differ with respect to relative
orientation in three dimensional space.
Chiral-General Definition-Any object that is not superimposable
on its mirror image. Your hands are chiral, that is why you need two different
leather gloves, one that only fits your right hand, and one that only fits
your left hand. If your hands were superimposable, then you would only
need one kind of glove and it would fit both hands.
Chemistry Definition; Atom-Any tetrahedral carbon atom that has
four differ-ent substituents is a stereogenic center. Any tetrahedral carbon
atom that has four different sub-stituents is a stereogenic center (it
was worth repeating). This is a simple consequence of geometry; there are
two different ways to place four different substituents in
a tetrahedral arrangement. Looking for four different substituents on a
single carbon atom is the easiest way to identify a chiral molecule.

A carbon atom is not a stereogenic center if even two of
the substituents are the same. A carbon atom is not a stereogenic
center if even two of the substituents are the same (it was worth repeating).
Historical note: in the past, stereogenic centers have also been called;
asymmetric carbon atoms, asymmetric centers, chiral centers, or chiral
atoms even though these latter names can be confusing in certain situations.
Chemistry Definition; Molecule- A molecule is not chiral (even if
it has stereogenic centers) if it has a plane or center of symmetry. A
plane of symmetry is any plane cutting through the molecule such that
one side is a perfect reflection of the other. When looking for a plane
of symmetry you have to put the molecule in the most symmetric conformation
possible, DO NOT WORRY ABOUT WHICH CONFORMATION IS MOST STABLE, STABILITY
OF CONFORMATION IS NOT IMPORTANT FOR STEREOCHEMISTRY. This means you
look for symmetry in cyclohexane derivatives that are drawn flat and alkanes
that are eclipsed !
A center of symmetry is any point is space such that any group on
the molecule can be reflected back through that point an equal distance
but opposite direction and an equivalent group is found. This is relatively
rare in organic chemistry.
As a further consequence of simple geometry, there are only two different
ways to place four substituents around a stereogenic center, and as shown
above the result-ing two different molecules are mirror images of each
other. They are non-superimposable mirror images of each other. You should
make models of the above molecules and prove to yourself they are different
and non-superimposable if you haven't done this already. This pair of chiral
molecules that are mirror images of each other are called enantiomers,
a chemistry name given to represent this spe-cial mirror image relationship
between molecules.
Molecules With More Than One Chiral Center If there are two stereogenic
centers in a single molecule, there are four possible stereoisomers. This
is because each carbon atom can be in one of two possible forms (R or S)
as we saw above, so there are 2x2=4 possible combinations. Now refer to
the general figure below as well as the figure on the following page with
the four chemical structures. Make sure you understand all the relationships
of the four different molecules shown. It is easiest to remember that enantiomers
must be mirror images of each other. Diastereomers is the chemistry
term that describes the relationship be-tween the pairs of molecules in
the figures that are not even mirror images of each other. In other words,
each pair of molecules in the figures must be related because they are
all stereoisomers of each other, so they are either enantiomers (mirror
im-ages) or diastereomers (not mirror images). Thus, diastereomers are
stereoisomers that are not enantiomers. If a molecule happens to be
sym-metric so that two of the four possible stereoisomers are identical
(the S,R is identi-cal to the R,S; the S,S and R,R will always be enantiomers),
this form of the molecule is called the meso form. Since
this situation requires some special symmetry (usually a plane of symmetry)
to be present, it is the rare exception, not the rule.
1). Determine the absolute (R or S) stereochemistry at each chiral
atom.
2). Use the following table to determine relationship.

3). If the molecule happens to be symmetric, check for meso compound,
remembering that only the R,S or S,R molecules can be meso (the S,S and
R,R forms of even symmetric molecules are not meso compounds, they are
enantiomers).
* This method is much easier than simply trying to look for mirror images
etc. by rotating molecule in your mind or redrawing structures in various
orientations.
Other Important Ideas:
1). Different enantiomers can only be distinguished by chiral things
(optical activity etc.). Living systems and biological molecules are chiral,
so chiral molecules are almost always distinguished by living systems.
2). Different diastereomers can be distinguished by all of their
chemical properties.
3). A racemic mixture is defined as being a one-to-one mixture
of two enantiomers.