Number of Rings or Unsaturations

When the elemental analysis of a molecule or of a fragment is known, the number of rings or unsaturations can be calculated. Even though this does not hold just for mass spectrometry, let us recall the principle. 

An aliphatic hydrocarbon has a formula C H2 + 2. Each ring or unsaturation that is present in a hydrocarbon decreases the number of hydrogen atoms by two units. Let x be the number of hydrogen atoms observed then, if N, is the number of rings and unsaturations, we have 

Benzene indeed contains one ring and three unsaturations. 

The presence of an oxygen or a sulfur atom in the molecule does not modify these numbers, as we can see when comparing CH4 with CH3OH and CH3SH, or CH3CH3 with CH3OCH3 and CH3SCH3. 

Each halogen atom replaces a hydrogen atom and decreases the number of hydrogen atoms by an equal number, as is shown by CH4 and CH2C12. 

---

Let n be the number of carbon atoms, and nX and N be those of halogens and nitrogen (or phosphorus), respectively. The following rule can be deduced, where A, is the number of rings or unsaturations and x is the number of hydrogen atoms that are found experimentally ... 

---