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Isomers having the same molecular formula and same functional group but differ in their spatial arrangement or group of atoms in space are called stereoisomers. They are said to have different configurations or different arrangement of groups in 3-D space.

Conformational isomerism

The number of different arrangement of atoms formed by rotation about C C single bond is called conformations or rotational isomers or rotamers. Rotation about C2 C3 bond in n-butane gives six conformers shown as follows:
Description: 43077.png

The energy profile for the conformers of n-butane by rotation about C2 C3 bond is shown in the adjacent figure.
Description: 43089.png
It is not always that anti or staggered conformation is more stable than skew or gauche. Sometimes, the skew or gauche conformer is more stable than anti conformer because of stabilization of skew form by intramolecular hydrogen bonding.
For example, ethylene glycol and 2-chloroethanol.
Description: 43098.png

Geometrical isomerism

The necessary conditions for a molecule to exhibit geometrical isomerism are as follows:
  1. The molecule must have restricted rotation due to the presence of a C C, C N, N  N, and cyclic structure.
  2. Each of the two atoms having restricted rotation must be attached to different substituents.
    Description: 43110.png
    Energy profile for the conversion of cis-isomer to trans-isomer can be depicted as shown in the adjacent figure.
Description: 43118.png
If there are n numbers of conjugated or isolated double bonds, there will be 2n geometrical isomers provided all the substituents are different; if some of the substituents are identical, isomer number decreases.
  1. The number of geometrical isomers of an unsymmetrical polyene = 2n (where n is the number of double bonds).
  2. The number of geometrical isomers of symmetrical polyene containing even number of double bonds = Description: 43125.png.
  3. The number of geometrical isomers of symmetrical polyene containing odd number of double bonds = Description: 43134.png
Geometrical isomerism is also shown by compound which contains Description: 43144.png structural units. Cyclic compounds also exhibit geometrical isomerism.

Compounds containing Description: 43153.png units are commonly called oximes. Oxime of formaldehyde is incapable of showing geometrical isomerism Description: 43161.png, while oxime of any other aldehyde (other than formaldehyde) will exhibit geometrical isomerism.

The nomenclature for aldoximes is syn (when H and OH are present on the same side of the double bond) and anti (when H and OH are present on the opposite sides of the double bond).

Oximes of symmetrical ketones Description: 43171.png do not show geometrical isomerism, but oximes of unsymmetrical ketones Description: 43180.png are capable of showing geometrical isomerism.

Cyclic compounds too have restricted rotation because of the impossibility of rotation around C–C single bond as the conformation of cyclic compound would twist on rotation.
Description: 43197.png

Appropriately placed substituents on cycloalkanes would be capable of showing geometrical isomerism.
Description: 43216.png

Optical isomerism

Conditions for a compound to exhibit optical activity are as follows:
  1. The compound should be chiral (asymmetrical). The compound should be devoid of any element of symmetry such as plane of symmetry and center (point) of symmetry.
  2. The mirror image of the compound should be non-superimposable on it. A compound or an isomer if fulfills the first condition, the second condition will be automatically fulfilled. If the second condition is seen first and is found to be fulfilled, this means that the first condition would have been obeyed. So, for a compound/isomer, if it is to be checked that it is optically active or not, any one of the above conditions can be checked.
The number of optical isomers is the number of diastereomers essentially. This value is 2n, where n is the number of chiral carbons.
  1. When the molecule is unsymmetrical:
    Number of d and l isomers (a) = 2n, Number of meso forms (m) = 0.
    ∴ Total number of optical isomers (a + m) = 2n
    where n is the number of chiral carbon atom(s). For example, CH3CH(Br)CH(Br)COOH.
  2. When the molecule is symmetrical and has even number of chiral carbon atoms:
    Number of d and l isomers (a) = 2n – 1,
    Number of meso forms (m) = 2(n/2) – 1.
    ∴ Total number of optical isomers = (a + m).
    For example, HOOCCH(OH)CH(OH)COOH.
  3. When the molecule is symmetrical and has an odd number of chiral carbon atoms:
    Number of d and l forms (a) = Description: 43240.png
    Number of meso forms (m) = Description: 43249.png
    ∴ Total number of optical isomers = (a + m) = 2n – 1.
    For example, CH3CH(OH)CH(OH)CH(OH)CH3.
    Let us have an enantiomeric pair of Description: 43260.png. To separate the two isomers of this pair, we treat them with an optically active (chiral) alcohol, Description: 43268.png. The reaction can be outlined as follows:
    Description: 43278.png
The esters produced can be seen that they are not enantiomers (mirror image isomers), in fact they are diastereomers. This means that they have different bulling points and thus can be separated by fractional distillation. d, d, and ld esters are collected as different fractions. Each fraction is separately hydrolyzed. Let us say fraction I which have d, d ester on hydrolysis gives d-acid and d-alcohol, which are different compounds having different boiling points and so can be further separated by fractional distillation.
Description: 43286.png
On the other hand, fraction II having l, d ester on hydrolysis yields l-acid and d-alcohol having quite different boiling points and so can be separated by fractional distillation. Thus, the enantiomeric acids (dl-from) have been separated (resolved).
The two enantiomeric acids have same enthalpies, but the diastereomeric esters have different enthalpies. Hence, the transition states for the formation of esters also have different enthalpies. Thus the activation energy for the formation of d, d esters and l, desters are different and so are their rates of reaction.
When we say that a compound is resolvable it implies that the compound is optically active and is of d and l-forms. But when the esters is non-resolvable, it means that the compound is optically inactive (achiral), which could be due to either the absence of a chiral center or having a plane of symmetry.
Those stereoisomers which are not mirror images are called diastereomers. Diastereomers have different physical properties. For example, melting and boiling points refractive indices, solubility in different solvents, crystalline structures, and specific rotations. Because of their differences in solubility they often can be separated from each other by fractional crystallization. Diastereomers have different chemical properties towards both chiral and achiral reagents. Neither any two diastereomers nor their transition states are mirror images of each other and so will not necessarily have the same energies. The ∆H values will be somewhat different and thus the rates of reaction will differ. However, since the diastereomers have the same functional groups, their chemical properties are not too dissimilar.
You will be astonished to see that there are molecules, such as allenes, biphenyls, and spiran, which can be chiral even when they have no chiral atoms.
Description: 43295.png
Description: 43306.png
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