The Index of Hydrogen Deficiency (IHD), is a count of how many molecules of H₂ need to be added to a structure in order to obtain the corresponding saturated, acyclic species.
Hence it takes a count of how many rings and multiple bonds are present in the structure, so IHD can also be thought of as (multiple bonds + rings) or (p + r).

When you look at a structure, just count them up (but take care not to count any rings twice !)
If you have a molecular formula, C_cH_hN_nO_oX_x, then the following equation can be derived:

Where does this equation come from?

• Well, the maximum number of hydrogen atoms for "c" carbon atoms is 2c+2 (think of the formula of saturated hydrocarbons such as ethane, propane etc.).
• From this number, subtract the "h" hydrogens that you have.
• Since, like hydrogen, a halogen only forms one bond, then they can be treated as if they are hydrogens, so subtract them as well.
• Oxygen forms two bonds, therefore it has no impact (compare H count for methane, CH₄, and methanol, CH₃OH).
• Nitrogen forms three bonds. This means for "n" nitrogens, "n" extra hydrogen atoms are needed (compare the H count for methane, CH₄, and methyl amine, CH₃NH₂), therefore, add "n".
• The factor of 0.5 accounts for us counting H atoms, but adding hydrogen, H₂ , molecules. OK ?

• Seeing what types of structural units maybe possible
• Quickly checking structures to see if they fit the molecular formula rather than simply counting H (when a mistake is possible)

C6H10	C6H6	C4H8O	C4H9N	C2Cl2

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