Chapter 4 : Stereochemistry B.sc 1st Year Page : 2 Organic Chemistry
Calculation of the number of possible optical isomers in compounds containing different number of asymmetric carbon atoms
Since the number of optical isomers of a compound depends on its structure and the number of asymmetric carbon atoms present in its molecule. Therefore, the number of optical isomers possible for a dissymmetric compound can be calculated by applying the following rules :
 When the molecule can not be divided into two equal halves and consists asymmetric carbonatoms equal to ‘n’ then number of d and lisomers(a) = 2and the number of meso – forms (m) = 0. Thus, the total number of optical isomers = (a + m) = 2^{n} + 0 = 2^{n}.
 When the molecule can be divided into two halves and consists even number of asymmetric carbonatoms. Then number of d and lisomers (a) = 2^{(n1)} and the number of mesoforms (m) = 2^{(0.5n 1).} Thus, the total number of optical isomers = (a + m) = 2^{(n1)} + 2^{(0.5n 1)}^{. }.
 When the molecule can be divided into two equal halves and consists odd number of asymmetric carbon – atoms. Then number of d and I isomers (a) = 2^{(n1)} – 2^{(0.5n1)} and the number of mesoforms (m) = 2^{(0.5n 0.5)}. Thus, the total number of optical isomers = (a + m) = 2^{(n1) }.
in all the above three cases, the number of racemic forms would be α/2.
For example :
The total number of possible isomers for the compounds.
 CH_{2}(CHOH)_{2},COOH and
 HOOC(CHOH)_{2}COOH
can be calculated as follows:

For the compound, CH,(CHOH),.COOH:
Solution :
The above structure shows the compound can not be divided into two equal halves but it consists of two asymmetric carbon atoms.
Hence, The number of d and I isomers(a) = 2^{n} = 2^{2} = 4
anti the number of mesoforms (m) = 0 Thus, the total number of optical isomers = (a + m) = 4 + 0 = 4
For the compound, HOOC(CHOH)_{2}COOH:
Solution :
The above structure shows that the compound can be divided into two equal halves and it consists two asymmetric carbonatoms i.e. it consists even number of asymmetric carbonatoms.
Hence, Number of d and lisomers (a) = 2^{(n1)} = 2^{(21)} = 2 and the number of mesoforms (m) = 2^{(n/21)} = 2^{(11)} = 2^{0} = 1. Thus, the total number of optical isomers = (a + m) = 2 + 1 = 3