Double bond equivalents from the formula
Double bond equivalents (DBE, degree of unsaturation) tell you how many rings and multiple bonds a molecule has. They are the first step of every structure elucidation.
Rules and values
- DBE = C − (H + X)/2 + N/2 + 1 (X = halogens)
- Oxygen and sulfur do not count
- Each ring and double bond counts 1, a triple bond 2
- DBE ≥ 4: a benzene ring is likely (1 ring + 3 C=C)
- The result must be a whole number ≥ 0, otherwise the formula is wrong
Your turn
Three problems on this topic. Type whole numbers, choose splitting and structures.
Task
How many double bond equivalents (DBE) does a compound with the formula C₄H₉Cl have?
Formula: C₄H₉Cl
DBE
Type whole numbers, e.g. 3. NMR shifts are typical values (±0.3 ppm), splitting follows the n+1 rule.
Worked example
Work out the double bond equivalents (DBE, degree of unsaturation) of the formula C₄H₈O₂.
Formula: C₄H₈O₂
Solution
- 1.DBE = C − (H + X)/2 + N/2 + 1 = 4 − (8 + 0)/2 + 0/2 + 1 = 1
- 2.Oxygen does not count: it forms two bonds and does not change the number of H.
- 3.DBE 1: exactly one double bond (usually C=O here) or one ring.
- 4.For example ethyl acetate.
Typical mistake: Subtracting O like an H or a halogen. Only H and halogens (X) count negative, nitrogen counts half positive, oxygen not at all.
How many double bond equivalents (DBE) does a compound with the formula C₄H₁₁N have?
Formula: C₄H₁₁N
Solution
- 1.DBE = C − (H + X)/2 + N/2 + 1 = 4 − (11 + 0)/2 + 1/2 + 1 = 0
- 2.Nitrogen brings one more H: + N/2.
- 3.DBE 0: saturated, no double bond and no ring.
- 4.For example 2-methylpropan-2-amine (tert-butylamine).
Typical mistake: Forgetting nitrogen or subtracting it. N raises the DBE by ½ per atom.
Common questions
Why does oxygen not count?
Oxygen forms two bonds and can be inserted into a chain without changing the number of H, so it drops out of the formula.