Geometrical isomers are a type of stereoisomers that have the same molecular formula and connectivity but differ in the spatial arrangement of their atoms.



The formula to find the number of geometrical isomers of a compound is:

Number of Geometrical Isomers = 2^n

where n is the number of stereocenters or double bonds with restricted rotation.



Geometrical isomers arise due to the presence of double bonds or stereocenters in a molecule. In double bonds, the restricted rotation around the bond axis leads to the formation of cis and trans isomers. In stereocenters, the presence of different substituents leads to the formation of different arrangements of atoms in space.

The number of geometrical isomers of a compound is determined by the number of stereocenters or double bonds with restricted rotation. Each stereocenter or double bond can exist in two different arrangements, leading to the formation of two isomers.

Therefore, the total number of geometrical isomers is calculated by taking the number of stereocenters or double bonds to the power of 2.



Consider the compound 2-butene with a double bond between the second and third carbon atoms. This compound has only one double bond with restricted rotation, and hence only two possible arrangements.

Therefore, the number of geometrical isomers = 2^1 = 2.

The two isomers are cis-2-butene and trans-2-butene.



The formula to find the number of geometrical isomers of a compound is based on the number of stereocenters or double bonds with restricted rotation. By calculating this number and applying the formula, we can determine the total number of possible geometrical isomers for a given compound.

FORMULA TO CALCULATE NUMBER OF GEOMETRICAL ISOMERS FORPOLYENESPolyenes geometrical isomers (i) When a compound has n double bonds and ends of a polyene are different, thenumber of geometrical isomers = 2n C6H5- CH = CH - CH = CH - CH = CH - CH = CH - ClThe given compound has four double bonds and the two ends are different (Oneis C6H5and other is Cl). Therefore, number of geometrical isomers .= 2n= 24= 16(ii) When the ends of polyene are same.Case I :When number of double bonds (=n) is even then the number of geometrical isomers = 2n-1+ 2[(n/2)-1] Cl - CH = CH- CH = CH - CH = CH - CH = CH - Cln=4,evenNumber of geometrical isomers = 2n-1+ 2(n/2)-1]= 23+ 21= 8 + 2 = 10Case II :When number of double bonds (=n) is odd.Number of geometrical isomers = 2n-1+ 2[n+1/2]-1 C6H6- CH = CH - CH = CH - CH = CH - C6H5 (n =3, odd)Number of geometrical isomers = 22+ 22-1=22+ 21= 4 + 2 = 6