How to Calculate Index of Hydrogen Deficiency (IHD) or Degree of Unsaturation

Degree of unsaturation also known as Index of hydrogen deficiency (IHD) is number of pi bond or ring present in the structure of organic molecule. This value helps to elucidate structure of unknown molecules. 

Key words: Molecular formula, Index of hydrogen deficiency (IHD), Structure analysis.

In this article we will learn about calculation of degree of unsaturation in organic chemistry.

Introduction

Organic compounds are consisting of carbon (C), hydrogen (H) and oxygen (O). Along with these three main elements found in organic molecules there are certain amount of nitrogen (N) and halogens (F, Cl, Br, I) found in organic compounds. As we studied that molecular formula of the compound only gives idea about constituents of the molecule and molecular weight. It does not give any information of structure of the molecule. For the structure analysis there are various methods available like Mass spectrometry, UV, IR and NMR spectroscopy. In the analysis process from molecular formula if we able to know the number of rings, double and triple bonds then it will be very useful for the identification of compounds by above methods. Also we can find out various isomers of compounds which are having same molecular formula.

In this context degree of unsaturation of compound is calculated. It is also known as index of hydrogen deficiency (IHD) or unsaturation index. Each degree of unsaturation is equal to 1 pi bond or ring.

A simplified formula for the degree of unsaturation is;

Figure: 1 Degree of Unsaturation

Example 1

Let’s see the molecular formula C₅H₈NClO, now calculate degree of unsaturation by using above formula;

Example 2

Chemical Formula: C₆H₅Br₂NO

Example 3

Degree of unsaturation helps to find out various structures of given formula.

Suppose an unknown organic compound has molecular formula C₄H₈, what could be the possible structure?

According to the formula; the unknown compound has 4 carbon atoms and 8 hydrogen atoms. Therefore degree of unsaturation is calculated as;

The degree of unsaturation 1 suggests that there is one double bond or ring. Therefore possible structures are A or B or C.

Figure 2: Isomers of the chemical formula C4H8

The compound A, B or C all have same molecular formula but the structures are different. So the spectral features like IR and NMR spectra are different. Calculation of degree of unsaturation helps in identification of possible structures of organic compounds. This is needed to determination of various isomers of the compounds.

Example 4

Consider the molecular formula C₆H₆, now let’s calculate degree of unsaturation for the formula. 

Since degree of unsaturation is 4, that means there are three possibilities

a)           1) 4 pi bonds

b)      2) 3 pi bonds + 1 ring

c)       3) 2 pi bonds + 2 rings 

T      Possible structures of the chemical formula C6H6 are given in Table 1

Table 1: Isomers of the chemical formula C6H6

That's all for this topic. If you have any questions please feel free to ask me in the comment box. Thank you..!