- DBE = (2C + 2 + N − H − X) / 2
C, H, N and X are the numbers of carbon, hydrogen, nitrogen and halogen atoms in the molecular formula. The result counts rings and π bonds together: a ring is one, a double bond one, a triple bond two. Oxygen and sulfur do not appear, because inserting a divalent atom into a chain changes no hydrogen count.
Worked examples
Benzene, C₆H₆: (12 + 2 − 6) / 2 = 4: one ring and three double bonds. Ethanol, C₂H₆O: (4 + 2 − 6) / 2 = 0, a saturated chain, and the oxygen made no difference. Pyridine, C₅H₅N: (10 + 2 + 1 − 5) / 2 = 4, the same as benzene with a nitrogen in the ring.
A chain of C carbons with only single bonds and no rings holds 2C + 2 hydrogens, the alkane count. Every ring or double bond removes two of them. Counting the hydrogens that are missing and halving gives the number of such features. A halogen takes a hydrogen’s place, so it counts like one; a nitrogen brings one extra bond, so it adds one hydrogen to the saturated count.
What it is for
Given a formula from mass spectrometry or elemental analysis, the degree of unsaturation says what the structure must contain before any spectrum is read. A DBE of 4 or more suggests a benzene ring; a DBE of 0 rules out double bonds, rings and carbonyl groups at once.
Common mistakes
- Counting oxygen. It does not enter the formula.
- Forgetting that a triple bond is two. Acetylene, C₂H₂, has DBE 2 and one bond.
- Getting a half-integer. The formula gives a whole number for any neutral molecule; a half means a miscounted atom or an ion.
Frequently asked questions
What is it called elsewhere?
Double bond equivalents, index of hydrogen deficiency, rings plus double bonds: the same count.
Can it be negative?
Not for a real molecule: a formula with more hydrogens than 2C + 2 + N − X cannot exist.
Does it tell rings from double bonds?
No. It gives the sum; the spectra decide the split.