Index of hydrogen deficiency

Each time a ring or π bond is added to an alkane, the number of hydrogens decrease by two.

The index of hydrogen deficiency (IHD), sometimes called the unsaturation index, is the amount of rings or π bonds which a molecule contains. When working out a molecule's structure, this is generally calculated before considering other spectral data. It is calculated by taking the difference between a molecular formula and the general formula for an acyclic alkane, then dividing that difference by two.

Take C₄H₆ for example. Compared to the general formula C_nH_2n+2, there is a difference of four hydrogens. Dividing four by two gives us an unsaturation index of 2.

If other elements are contained in the molecular formula, there are three simple rules to account for them:

1. For group V atom in the molecular formula (N, P, As, Sb, Bi), add one hydrogen to the general formula.

2. For group VI atoms in the molecular formula (O, S, Se, Te), leave the general formula unchanged.

3. For group VII atoms in the molecular formula (F, Cl, Br, I), subtract one hydrogen from the general formula.

These rules are also simple enough to visualize intuitively. Remember that double bonds on these elements count in the unsaturation index. Below are two examples where the rules are applied.

C₇H₁₄O₂:

1. Compared to the general formula C_nH_2n+2 (where n = 7), there is a difference of two hydrogens.

2. The oxygen atoms have no effect on the general formula.

3. The unsaturation index therefore equals one.

The molecule could, for example, be an ester:

C₁₀H₁₄N₂:

1. The general formula for n = 10 is C₁₀H₂₂

2. Since there are two group V atoms, we add two hydrogens to the general formula to give C₁₀H₂₄

3. There is a difference of 10 hydrogens, giving an unsaturation index of 5.

So the structure has 5 rings, 5 double bonds, or a mixture of both. One possibility is nicotine:

C₅H₇O₂Cl

1. The general formula for C₅ is C₅H₁₂

2. Oxygen atoms have no effect

3. There is one halogen atom, so we subtract one hydrogen from the general formular to give C₅ is C₅H₁₁

There is a difference of 4 hydrogens, so there is a IHD of 2.

One possibility is 2-Chloro-1-methylcyclopropanecarboxylic acid: