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 carbon-atoms equal to ‘n’ then number of d- and l-isomers(a) = 2and the number of meso – forms (m) = 0. Thus, the total number of optical isomers = (a + m) = 2n + 0 = 2n.
• When the molecule can be divided into two halves and consists even number of asymmetric carbon-atoms. Then number of d- and l-isomers (a) = 2(n-1) and the number of meso-forms (m) = 2(0.5n -1). Thus, the total number of optical isomers = (a + m) = 2(n-1) + 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(n-1) – 2(0.5n-1) and the number of meso-forms (m) = 2(0.5n -0.5). Thus, the total number of optical isomers = (a + m) = 2(n-1) .

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.

1. CH2(CHOH)2,COOH and
2. HOOC(CHOH)2COOH

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) = 2n = 22 = 4

anti the number of meso-forms (m) = 0 Thus, the total number of optical isomers = (a + m) = 4 + 0 = 4

For the compound, HOOC(CHOH)2COOH:

Solution :

The above structure shows that the compound can be divided into two equal halves and it consists two asymmetric carbon-atoms i.e. it consists even number of asymmetric carbon-atoms.

Hence, Number of d- and l-isomers (a) = 2(n-1) = 2(2-1) = 2 and the number of meso-forms (m) = 2(n/2-1) = 2(1-1) = 20 = 1. Thus, the total number of optical isomers = (a + m) = 2 + 1 = 3