The Calculations of Hydrogen Deficiency Index or Unsaturation Index

The Hydrogen Deficiency Index is sometimes referred to as “units of unsaturation” and similar terms. The hydrogen deficiency measures the number of H₂ that must be supplied to a structure to produce the equivalent saturated, acyclic species. As a result, the IHD counts the number of rings and multiple bonds in the structure. Hence, the IHD can alternatively be thought of as many bonds + rings, or π + r = IHD. When confronted with establishing the structure of an unknown chemical with a known molecular formula, the first job of advice is to assess the degrees of unsaturation. It is important to remember that the IHD for neutral organic substances has to be a positive number (i.e. 0, 1, 2 etc.).

Hydrogen Deficiency Index Formula

The degree of unsaturation was formerly known as the hydrogen deficiency index. It corresponds to the number of units of H₂ required to completely saturated the organic chemical in question. All that is required to calculate the IHD is the compound’s molecular formula.

The degree of unsaturation informs you how many rings and multiple bonds are prevalent in a compound, if you know the molecular formula. 

For hydrocarbons, compute the units of H₂ required to convert it to an alkyl group, to yield the formula C_nH_(2n+2). As a result, C₆H₁₂ has a Hydrogen Deficiency Index of just one. Because all isomers of the exact chemical have a similar Hydrogen Deficiency Index, it makes no difference if C₆H₁₂ refers to an alkene or a cyclic compound.

If elements other than C and H are present, their presence is determined by the group of the periodic table they belong to:

• 17th Group: For halogens, or elements in Group 17, replace the halogen atom with a hydrogen atom. This works because four single bonds surround each carbon atom in chloroethane. Thus, according to the hydrogen deficiency index formula, chloroethane (C₂H₅Cl) becomes C₂H₆. Its Hydrogen Deficiency Index will be zero. Similarly, C₂H₂Br₂ becomes C₂H₄ with an IHD of 1.
• 16th Group: In ethanol, the two carbon atoms still have four single bonds. Adding an oxygen atom in ethane will not change the hydrogen deficiency index. Thus, oxygen atoms can be removed when calculating the Hydrogen Deficiency Index. For example, ethanol (C₂H₆O) will become C₂H₆ with a Hydrogen Deficiency Index of zero. In the same way, acetone (C₃H₆O) becomes C₃H₆ with a Hydrogen Deficiency Index of one.

Hydrogen Deficiency Index Calculator

Let’s consider three compounds to understand this better – pentane, 1-pentene and cyclopentane.

C₅H₁₂ is the chemical formula for pentane. The greatest number of hydrogens that can be added to a molecule with 5 carbons is 12. Thus, the structural composition of pentane is saturated (which means not any more hydrogen atoms may be added). It can also be said that pentane has zero level of unsaturation.

There are two fewer hydrogens in 1-pentene C₅H₁₀ than in the saturated state (pentane), indicating that the 1-pentene has 1 degree of unsaturation. With the addition of a ring, cyclopentane (C₅H₁₀) must also surrender two hydrogens. Thus, cyclopentane will have one grade of unsaturation. When a dual bond or ring is indicative of the presence, it results in 1 degree of unsaturation of the molecular compound.

Regardless of the degree of unsaturation, any hydrocarbon may be transformed into a monohalide by withdrawing a hydrogen atom and substituting it with a halogen. As a result, the monohalide would have an uneven amount of hydrogens. Similarly, a dihalide will contain an odd number of hydrogens, and so on. Remember that this rule only applies to alkyl halides. 

Eliminate the halogen from the equation and substitute it with hydrogen to calculate the extent of unsaturation of a halide. C₅H₇Cl, for example, yields C₅H₈, which has 2 degrees of unsaturation.

Conclusion

The hydrogen deficiency index’s strongest feature is a simple equation and only takes a few minutes to complete. The hydrogen deficiency index formula provides important structural information about an unknown chemical. 

To calculate the IHD for hydrocarbons, you only need to use the equation C_nH_(2n+2).