Overview

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.

Procedure

Alkanes contain the maximum possible number of hydrogens, 2n + 2, where n is the number of carbon atoms. They are called saturated hydrocarbons.

Hydrocarbons with multiple bonds are unsaturated and have fewer hydrogens per carbon atom than their saturated analogs. In cyclic compounds, the presence of every ring costs two hydrogens.

A compound possesses one degree of unsaturation for every π bond and ring present in the molecule, which corresponds to each pair of missing hydrogen atoms in hydrocarbons.

In such compounds, the degree of unsaturation, also called the index of hydrogen deficiency, or saturation number, is half the difference between the maximum possible and actual number of hydrogens.

If a molecular formula is C₄H₆, the compound has two degrees of unsaturation. The molecule may have one ring and one double bond or two double bonds. Other possibilities are the presence of two rings or one triple bond.

The degree of unsaturation can also be calculated for ions and functionalized hydrocarbons by adjusting for the differences in valency.

In organohalogen compounds, the monovalent halogens are considered as equivalent to hydrogen. As such, the degrees of unsaturation of 1-bromopropane and propane are both zero.

In contrast, divalent oxygen is ignored when calculating the degree of unsaturation with this equation. Accordingly, acetone and 1-propene have the same degree of unsaturation.

In nitrogen-bearing compounds, each trivalent nitrogen atom adds one to the numerator of the equation, effectively canceling out one hydrogen atom. Thus, 3-buten-1-amine has the same degree of unsaturation that 1-butene does.