Chemistry > Isomerism > 6.0 Optical isomerism in compounds having more than one chiral carbons

  Isomerism
    1.0 Isomerism
    2.0 Structural Isomerism
    3.0 Tautomerism
    4.0 Geometrical isomerism in the compounds containing C=N
    5.0 Optical Isomerism
    6.0 Optical isomerism in compounds having more than one chiral carbons
    7.0 Optically active compounds having no asymmetric carbon

6.4 Calculation of number of optical isomers
The number of optical isomers of an organic compound depends on its structure and number of asymmetric carbon atoms. thus, the number of optical isomers may be determined from the knowledge of the structure of the compound as follows:

1. When the molecule is unsymmetrical

No. of optically active isomers, $a = {2^n}$

Number of meso forms $(m) = 0$

Number of racemic mixtures, $r = \frac{a}{2}$

$\therefore $ Total no. of optically active isomers $ = (a + m) = {2^n}$

2. When the molecule is symmetrical and has even no. of asymmetric carbon atoms.

No. of optically active isomers, $a = {2^{(n-1)}}$

No. of meso forms, $m = {2^{[n/2--1]}}$

No. of racemic mixtures, $r = \frac{a}{2}$

$\therefore $ Total no. of optically active isomers $= a + m.$

3. When the molecule is symmetrical and has an odd no. of asymmetrical carbon atoms.

no. of optically active isomers, $a = {2^{(n-1)}}-{2^{(n/2-1/2)}}$
No. of meso forms, $m = {2^{(n/2-\frac{1}{2})}}$

$\therefore $ Total no. of optically active isomers $ = (a + m) = {2^{(n-1)}}$

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