How do Chiral centers determine the number of isomers?

I think I read somewhere that if an organic compound has n number of chiral centers, there must exist 2^n number of isomers. Is that true? And why? 




That 2^n number of isomers are ***exactly stereoisomers*** ( ***Not*** "total no. of isomers"). There is no direct formula for calculating the number of structural isomers.Total number of isomers = (number of structural isomers + number of stereoisomers).


Though there are direct formulas for obtaining number of stereoisomers, but there is no direct formula for finding out the total number of structural isomers.


As I said above, we do have formulas for finding out the number of stereoisomers. Here is the exact formulas which you can use to determine number of stereoisomers:


**a) When the molecule is unsymmetrical and contains 'n ' chiral carbon atoms:**


Total no. of stereoisomers = 2^n


**b) When the molecule is unsymmetrical and has even number of stereogenic centres or chiral carbon atoms:**


Total no. of stereoisomers = Number of optical isomers + Number of meso forms = 2(n-1) + 2(n/2-1)


**c) When the molecule is symmetrical and has odd no. of stereogenic centres**


Total no. of stereoisomers = [2(n-1)-2(n/2-1/2)] + 2(n/2-1/2)]


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