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Index of Hydrogen Deficiency (IHD)
 

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 (π + 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, CcHhNnOoXx, then the following equation can be derived:

IHD = 0.5 * [2c+2-h-x+n]

Where does this equation come from ?

  • Well, the maximum number of hydrogen atoms for "c" carbon atoms is 2c+2 (think of the formulae 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 ?
Determining the IHD for molecules can be useful for the following reasons:
  • 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)
What is the IHD of the following molecular formulae ?
 
C6H10
C6H6
C4H8O
C4H9N
C2Cl2
IHD = 2
IHD = 4
IHD = 1
IHD = 1
IHD = 2


 © Dr. Ian Hunt, Department of Chemistry, University of Calgary

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