Degree of unsaturation


In the analysis of the molecular formula of organic molecules, the degree of unsaturation ', 'double bond equivalents is a calculation that determines the total number of rings and π bonds. A formula is used in organic chemistry to help draw chemical structures. It does not give any information about those components individually—the specific number of rings, or of double bonds, or of triple bonds. The final structure is verified with use of NMR, mass spectrometry and IR spectroscopy, as well as qualitative inspection. It is based on comparing the actual molecular formula to what would be a possible formula if the structure were saturated—having no rings and containing only σ bonds—with all atoms having their standard valence.

General formula

The formula for degree of unsaturation is:
where ni is the number of atoms with valence vi.
That is, an atom that has a valence of x contributes a total of x − 2 to the degree of unsaturation. The result is then halved and increased by 1.

Simplified formulae

For certain classes of molecules, the general formula can be simplified or rewritten more clearly. For example:
where
or
where C = number of carbons, H = number of hydrogens, X = number of halogens and N = number of nitrogens, gives an equivalent result.
In either case, oxygen and other divalent atoms do not contribute to the degree of unsaturation, as 2 − 2 = 0.

Explanation

For hydrocarbons, the DBE tells us the number of rings and/or extra bonds in a non-saturated structure, which equals the number of hydrogen pairs that are required to make the structure saturated, simply because joining two elements to form a ring or adding one extra bond in a structure reduces the need for two H's. For non-hydrocarbons, the elements in a pair can include any elements in the lithium family and the fluorine family in the periodic table, not necessarily all H's.
A popular form of the formula is as follows:
where,, and represent the number of carbon, nitrogen, hydrogen and halogen atoms, respectively. Each of the terms on the RHS can be explained, respectively, as follows:
  • Except for the terminal carbons, every carbon chained to the structure with two single bonds requires a pair of hydrogen atoms attached to it. The number of carbons in the formula actually represents the number of hydrogen pairs required for that number of carbons to form a saturated structure.
  • Each of the two terminal carbons in the backbone chain needs one extra hydrogen – that is why "1" is added to the formula.
  • Except the terminal nitrogens, each nitrogen in the chain only requires one H attached to it, which is half a pair of hydrogens—that is why is in the formula, which gives a value of 1 for every two nitrogens.
  • The represents the number of hydrogen pairs because it gives a value of 1 for every two hydrogen atoms. It is subtracted in the formula to count how many pairs of hydrogen atoms are missing in the unsaturated structure, which tells us the degree of hydrogen deficiency.
  • The presence of is for a reason similar to.
Adding an oxygen atom to the structure requires no hydrogen added, which is why the number of oxygen atoms does not appear in the formula.
Furthermore, the formula can be generalised to include all elements of Group I, Group IV, Group V and Group VII of CAS A group in the periodic table as follows:
Or simply,