Question

The double bond equivalent of ${C_4}{H_6}$ is:
A. $0$
B. $1$
C. $2$
D. $3$

Answer 1

:Hint:Double bond equivalent is the level of unsaturation present in an organic compound. Unsaturation is defined as the presence of double bond or triple bond in the organic molecule. Ring is also considered in unsaturation. It is represented as DBE.
Formula used:
$DBE = C + 1 - \dfrac{H}{2} - \dfrac{X}{2} + \dfrac{N}{2}$
Where,
$C$ = Number of carbon atoms present in organic molecules.
$H$ = Number of hydrogen atoms present in organic molecules.
$X$ = Number of halogen atoms present in organic molecules.
$N$ = Number of nitrogen atoms present in organic molecules.

Complete step by step answer:
As in simple words, the double bond equivalent is the number of double bonds and number of triple bonds present in organic molecules. For example, in the case of benzene, there are three double bonds and one ring so its double bond equivalent is four.
Similarly in the case of ${C_4}{H_6}$ ,
The molecular structure of ${C_4}{H_6}$ is $C{H_2} = CH - CH = C{H_2}$
As it is clearly seen that there are two double bonds present in ${C_4}{H_6}$ , so its level of unsaturation is two hence, its double bond equivalent is two.
Now, by the formula:
Here, in ${C_4}{H_6}$ there are four numbers of carbon atoms, and six numbers of hydrogen atoms.
By substituting the value in formula:
$DBE = C + 1 - \dfrac{H}{2} - \dfrac{X}{2} + \dfrac{N}{2}$
Where,
$C$ = Number of carbon atoms present in organic molecules.
$H$ = Number of hydrogen atoms present in organic molecules.
$X$ = Number of halogen atoms present in organic molecules.
$N$ = Number of nitrogen atoms present in organic molecules.
We will get:
$
   \Rightarrow DBE = 4 + 1 - \dfrac{6}{2} - 0 + 0 \\
   \Rightarrow DBE = 5 - 3 \\
   \Rightarrow DBE = 2 \\
$
So, the double bond equivalent of ${C_4}{H_6}$ is $2$ .

Hence, option C is correct.
Note:
 A triple bond can be regarded as $DBE = 2$ . It must be noted that $X$ is the total number of halogens, namely chlorine, fluorine and iodine present in the structure. Presence of an oxygen atom does not affect the double bond equivalent calculation.