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how do i calculate the strereoisomers ?

Asked by shanmugamneet2018 | 28 Mar, 2019, 10:19: AM

Expert Answer

Case I: When the molecule has no symmetry (usymmetrical):

The number of d- and l- forms, a = 2ⁿ , where n= number of unsymmetrical carbon atoms.

number of meso isomers m = 0

The total number of optical isomers = a + m = 2ⁿ

For example,

begin mathsize 11px style CH subscript 3 minus straight C with asterisk times on top HOH minus COOH space space left parenthesis lactic space acid right parenthesis end style

in the above compound n= 1, a = 2¹ = 2, m= 0,

hence total optical isomers = 2 + 0 = 2

Case II: When the molecule has symmetry:

1) When the number of asymmetric carbon atoms are even:

The number of d- and l- forms, a = 2^(n-1) , where n= number of unsymmetrical carbon atoms.

number of meso isomers m = 2^(n/2)-1 ,

The total number of optical isomers = a + m = 2^(n-1) +2^(n/2)-1

For example,

HOOC minus straight C with asterisk times on top HOH minus straight C with asterisk times on top HOH minus COOH

where n=2, a=2^(n-1) = 2^(2-1) = 2¹ = 2

m = 2^(n/2)-1 = 2^(2/2)-1 = 2⁰= 1

So, total optical isomers = 2+1 = 3

2) When the number of asymmetric carbon atoms are odd:

The number of d- and l- forms, a = 2^(n-1) - 2^(n-1)/2 where n= number of unsymmetrical carbon atoms.

number of meso isomers m = 2^(n-1)/2

The total number of optical isomers = a + m = 2^(n-1)

For example,

HOOC minus straight C with asterisk times on top HOH minus straight C with asterisk times on top HOH minus straight C with asterisk times on top HOH minus COOH

where n=3, a = 2^(n-1) - 2^(n-1)/2 = 2²- 2¹ = 2

m = 2^(n-1)/2 = 2^(3-1)-2 = 2¹= 2

So, total optical isomers = 2+2 = 4

In all above three cases, the number of racemic forms will be = a/2

We hope you understand the concept, still, you have any query you can ask in doubts and solution section.

Answered by Ramandeep | 28 Mar, 2019, 11:24: AM

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