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)]