Compare ethane to ethylene to acetylene,
i.e. #H_3C-CH_3, H_2C=CH_2, HC-=CH#
Ethane is fully saturated, and has a formula of #C_nH_(2n+2)#; here #n=2#, and there are 6 hydrogen atoms.
Ethylene has a so-called #1^@# degree of unsaturation, with #2# hydrogens LESS than the equivalent saturated formula. That is ethylene has 4 hydrogens, 2 hydrogens LESS than the saturated formula.
And acetylene has #2^@# so-called degrees of unsaturation, with #4# hydrogens LESS than the equivalent saturated formula.
And so for a given formula each #"degree of unsaturation"# corresponds to a double bond OR a ring. When we add oxygen to the formula, we assess the degree of unsaturation directly. Where there is nitrogen we substract #NH# from the formula before assessment. Halogens count for 1 hydrogen.
And thus cyclohexanone, #C_6H_10O# has #2^@# of unsaturation. Acetylene, #H-C-=CH#, also has #2^@# of unsaturation. Napthalene, #C_10H_8# has how many degrees of unsaturation?
What is trivial in these simple case, becomes useful in a more complicated formula. If you are given a chemical formula, without knowing ANYTHING else, you can assess the #"degree of unsaturation,"# and accurately forecast the number of olefinic bonds, and ring junctions the molecule is likely to have.
