7.3: Degree of Unsaturation
The degree of unsaturation (U), or index of hydrogen deficiency (IHD), is defined as the difference in the number of pairs of hydrogen atoms between the compound and the acyclic alkane with the same number of carbon atoms. Each double bond or ring costs two hydrogen atoms compared to a saturated analog and results in one degree of unsaturation.
The degree of unsaturation for hydrocarbons is U = (2C + 2 − H) / 2, where C is the number of carbon atoms and H is the number of hydrogen atoms.
For substituted hydrocarbons and ions, the degree of unsaturation is calculated by adjusting the equation for the difference in valency.
In organohalogen compounds, the halogen atoms, being monovalent, are treated as equivalent to hydrogen atoms. Thus, the formula to calculate the degree of unsaturation for compounds containing halogen atoms is U = (2C + 2 − (H + X)) / 2, where X is the number of halogen atoms.
Divalent oxygen atoms in organooxygen compounds are ignored while calculating the saturation number. Each trivalent nitrogen atom in organonitrogen compounds adds to the numerator: U = (2C + 2 + N − H) / 2, where N is the number of nitrogen atoms.
Accordingly, the overall formula for degree of unsaturation is U = (2C + 2 + N − (H + X)) / 2.