Question

Is there any formula for calculating the number of isomers in a compound?

Answer 1

There is no formula to calculate the number of structural isomers of an alkane. This is mainly due to the fact that with a certain number of carbons, they can branch out (although most are unstable and do not actually exist).
For example, the formula $C_4{H}_{10}$ represents both butane and 2-methylpropane (both are stable in similar SCTPs) :
The first ten are:
Number of carbons $\to$ Number of structural isomers
$0\to 11\to 12\to 13\to 14\to 25\to 36\to 57\to 98\to 189\to 3510\to 75$
Here is a method to calculate the total no. of stereo isomers of an organic compound,in the following categories:
(A)Compound has n-chiral centres with no symmetry in the molecule
Then, No. of Optical Isomers $\left(X\right)=2^n$
and, No. of Meso-structures (Y)=0
Hence total no. of stereo isomers= $X+Y=2^n$
(B)Symmetry in the molecule and even no. of chiral centres
Then, No. of Optical Isomers $\left(X\right)=2^{(n-1)}$
and, No. of Meso-structures $\left(Y\right)=2^{(\frac{n}{2}-1)}$
Hence total no. of stereo isomers= $X+Y=[2^{(}n-1)]+[2^{(\frac{n}{2}-1)}]$
(C)Symmetry in the molecule and odd no. of chiral centres
Then, No. of Optical Isomers $\left(X\right)=\left[2^{(n-1)}\right]-\left[2^{\left(\frac{[n-1]}{2}\right)}\right]$
and, No. of Meso-structures $\left(Y\right)=2^{\left(\frac{[n-1]}{2}\right)}$
Hence total no. of stereo isomers=$X+Y=2^{(n-1)}$
However you must be careful because in some cases we get
no. of optical isomers=no. of geometric isomers= no. of stereo isomers where the geometric isomers are themselves optically active.