Basic Organic NomenclatureAn IntroductionDave Woodcock,

7. Stereochemistry (iii)

It is possible to have more than one chirality
centre in any molecule.
For each such centre, there exists two spacial arrangements of the four groups attached to the steregenic carbon centre. So for 2 such centres the number of possibilities is four. This is readily seen by counting:
1a + 2a; For 3 such centres, the number of possibilities is eight. (For each of the above four arrangements for centres 1 and 2, carbon 3 can be a or b.) It is readily seen that the number of isomers possible increases by 2 for each chirality centre in the molecule. Thus for n chirality centres the number of possible stereoisomers is 2^{n}. Symmetry considerationsIn each of the above calculations and statements, about the number of stereoisomers for a given molecule with chirality centres, note the use of the word possible. With the presence of two or more chiral carbons, there exists the possibility of symmetry in the molecule (most often this appears as a plane of symmetry between the centres.)As a consequence, it is possible to have a molecule which contains several chirality carbon centres, but which in total is achiral (that is not chiral). If more than one chirality centre is present, the calculated number of stereoisomers , 2^{n} is, therefore, only a theoretical maximum, and for some structures there will be fewer stereoisomers in fact. Enantiomers and DiastereoisomersEnantiomers (to repeat!) are nonsuperimposable mirror images and as such can only exist in pairs.When a structure has two or more chirality centres we have noted that more than two stereoisomers exist. Therefore some pairs of stereoisomers of the structure will be mirror images (and so enantiomers) and some pairs will not be mirror images. Stereoisomers which are not enantiomers (mirror images) are called diastereoisomers. Examples of diastereoisomers that we have already met are the E and Z stereoisomers of alkenes. 
Selfstudy Question: Without worrying about the possible number of stereoisomers at this point, find the chiral carbon centres (at least two in each) in these structures. Review: One chirality Centre If you need to learn about drawing three dimensional structures on paper:
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