Which statement about degrees of unsaturation is correct?

Which statement about degrees of unsaturation is correct?

• A. DBE equals C - H/2 + N/2 + 1
• B. DBE equals H/2 - C
• C. DBE equals the number of rings
• D. DBE applies only to hydrocarbons

Answer: (A)

Degrees of unsaturation counts how many rings and multiple bonds a molecule has relative to a fully saturated open-chain structure with the same carbon and other heteroatom content. The way to capture that globally is to compare the actual hydrogen count to what a saturated reference would have, while accounting for nitrogens. The general formula DBE = C − H/2 + N/2 + 1 comes from that idea: every ring or pi bond reduces the number of hydrogens by two compared with a saturated counterpart, and each nitrogen changes the hydrogen balance slightly because it can substitute for a CH unit in the saturated framework. For a hydrocarbon (no nitrogens or oxygens), this reduces to DBE = (2C + 2 − H)/2, which is consistent with the same interpretation. This expression correctly yields zero for alkanes (CnH2n+2), gives positive integers for rings and/or double bonds (for example, benzene has four degrees of unsaturation due to three double bonds and one ring), and shows why simple counts like H/2 − C or “the number of rings” alone aren’t sufficient. It also applies beyond hydrocarbons; oxygens don’t affect the count directly, and nitrogens are included via the N/2 term, so DBE is meaningful for a wide range of organic compounds.

Degrees of unsaturation counts how many rings and multiple bonds a molecule has relative to a fully saturated open-chain structure with the same carbon and other heteroatom content. The way to capture that globally is to compare the actual hydrogen count to what a saturated reference would have, while accounting for nitrogens.

The general formula DBE = C − H/2 + N/2 + 1 comes from that idea: every ring or pi bond reduces the number of hydrogens by two compared with a saturated counterpart, and each nitrogen changes the hydrogen balance slightly because it can substitute for a CH unit in the saturated framework. For a hydrocarbon (no nitrogens or oxygens), this reduces to DBE = (2C + 2 − H)/2, which is consistent with the same interpretation.

This expression correctly yields zero for alkanes (CnH2n+2), gives positive integers for rings and/or double bonds (for example, benzene has four degrees of unsaturation due to three double bonds and one ring), and shows why simple counts like H/2 − C or “the number of rings” alone aren’t sufficient. It also applies beyond hydrocarbons; oxygens don’t affect the count directly, and nitrogens are included via the N/2 term, so DBE is meaningful for a wide range of organic compounds.