Question

Double bond equivalent of Cubane is:

A.4
B.5
C.6
D.7

Answer 1

Hint: The double bond equivalent number can be calculated from the formula using the following equation:
DBE = UN = PBoR = $C = \left( {\dfrac{H}{2}} \right) + \left( {\dfrac{N}{2}} \right) + 1$ ,
Where, C = number of Carbon atoms
H = number of hydrogen and halogen atoms
N = number of Nitrogen atoms
One DBE = one ring or one double bond

Complete step by step answer:
Cubane $({C_8}{H_8})$ is a synthetic hydrocarbon molecule and it consists of eight carbon atoms. These carbon atoms are arranged at the corners of a cube and one hydrogen atom is attached to each carbon atom. DBE or double bond equivalent also known as level of unsaturation is the number of unsaturation present in an organic molecule. The term unsaturated means a double bond or a ring system.
Cubane appears to possess six rings, corresponding to the six faces of a cube. However, in the case of hydrocarbons, you can use a simple trick- count the deficiency of hydrogens as compared to saturated open chain alkanes for a given number of carbons and then double bond equivalent is half of this deficiency.
Here, compared with ${C_8}{H_8}$ , octane and then a deficiency in hydrogens in Cubane is 10 so, Double Bond Equivalent \[ = \dfrac{{10}}{2}\] = 5.
Hence, the level of unsaturation is the number of unsaturation present in an organic molecule.

Therefore, the correct answer is option (B).

Note: This can also be solved by an alternative Method:
For a compound with formula ${C_a}{H_b}{N_c}{O_d}{X_e}$ where X is halogen, the double bond equivalent is given by:
double bond equivalent \[ = \left( {\dfrac{1}{2}} \right) \times (2 + 2a - b + c - e)\left( {\dfrac{1}{2}} \right) \times \left( {2 + 2a - b + c - e} \right)\]
For Cubane, Formula : ${C_8}{H_8}$
double bond equivalent \[ = \;\left( {\dfrac{1}{2}} \right)(2 + 2 \times 8 - 8) = 5\]