IUPAC name and degree of unsaturation of compound X is

Options

A. 2, 3-dimethyl bicyclo [2, 2, 1] hept-5 ene, 2
B. 1, 2-dimethyl bicyclo [2, 2, 1] hept-4 ene, 3
C. 5, 6-dimethyl bicyclo [2, 2, 1] hept-2 ene, 3
D. 4, 5-dimethyl bicycle [2, 2, 1] hept-1 ene, 2

Answer

C

Explanation

This problem contains conceptual mixing of nomenclature of cyclic hydrocarbon and degree of unsaturation. This problem can be solved by identifying the parent chain functional group, position of functional group substituent and their position one by one and then write the name of compound according to IUPAC names then calculate degree of unsaturation.

Total carbon atom forming the bicyclic ring (hept.)
Functional group `rArr` double bond (ene)
Position of double bond `rArr` 2, 2-ene
Substituents `rArr` 2-methyl group `rArr` dimethyl
Position of substituents `=5,6 rarr 5,6`-dimethyl
Number of cyclic chain = `2 rarr` Bicyclo
3-bridges are of 2 carbons, 2 carbons and one carbon hence,
IUPAC name = 5, 6-dimethyl bicycle [2, 2, 1] hept-2-ene
Molecular formula of compound is `C_(9)H_(14)`
Degree of unsaturation can be calculated as
`u=(C+1) -(H)/(2)+(N)/(2)`
Where, u=degree of unsaturation
C = number of carbons
H = number of hydrogens
N = number of nitrogen
Hence, for a compound having molecular formula `C_(9)H_(14)` the degree of unsaturation may be calculated as
`u=(9-1)-(14)/(2)=10-7=3`