DOUBLE BOND EQUIVALENTS or INDEX NUMBER:

It is a numerical value on the basis of which we can have an idea about the different type of equivalent structures we can have for a given formula.

 

Knowing the DBE the problems on structural isomerism can be more easily solved.

 

Mathematically,  

DBE= {( n(v-2))/2}+1

where n is the number of atoms

v is the valency of the atom.

Eg 1):

Consider C₄H₆

DBE={4(4-2)/2+6(1-2)/2}+1

={(8-6)/2}+1

=2

This implies that the molecule may contain,

1)two double bonds or one triple bond.

2)one ring and one double bond.

3)two rings.

 

Thus by knowing the DBE total number of structural isomers can be formulated.

 

Eg 2):

Consider C₃H₆O

DBE={3(4-2)/2+6(1-2)/2+1(2-2)/2}+1

=1

So the isomers may contain either a double bond or a ring.

 

I hope this is helpful!