Index of Hydrogen Deficiency

Degree of unsaturation (Index of Hydrogen Deficiency or IHD) is a measure to how many hydrogen atoms a molecule is missing in order to be fully saturated. A compound that does not have the maximum number of hydrogens per its structure is said to be unsaturated. 

What does it mean for a compound to be saturated?

A molecule that has the maximum number of hydrogen atoms is said to be saturated. A saturated alkane’s molecular formula is as follows: CnH2n+2. For example, hexane (C6H14) is saturated but cyclohexane (C6H12) is not. Hexane and cyclohexane have the exact same number of carbons, but cyclohexane actually has two fewer hydrogens than does hexane. 

hexane-(left)-and-cyclohexane-(right)hexane (left) and cyclohexane (right)

How do we determine degrees of unsaturation?

Luckily, determining degrees of unsaturation (AKA index of hydrogen deficiency, hydrogen deficiency index, etc.) isn’t bad at all! There are actually two different ways to do it: 1) when given a molecular formula and 2) when given a structure that’s already drawn-out. Let’s go ahead and break those down below:

1. Determining degrees of unsaturation from a molecular formula:

On an exam, you might be given a prompt like this one: “Please provide the degree(s) of unsaturation for each of the following compounds.” Some of those might be molecular formulas like C6H14 or C6H12. For this type of problem, it’s easiest to start with a nice equation. In it, “IHD” will stand for index of hydrogen deficiency (also sometimes represented as DoU).

Degrees of-Unsaturation-general-formulaDegrees of Unsaturation general formula

So, now that we’ve got the formula, let’s apply it to our friends hexane and cyclohexane before testing other molecules. 

DoU-hexane-formulaIHD hexane formula

DoU-cyclohexane-formulaIHD cyclohexane formula

2. Determining degrees of unsaturation from a structure: 

Are you ready for some good news? It turns out that determining IHD from a structure is actually even easier than doing so for a molecular formula. Here’s what you need to know: rings and pi bonds equal 1 IHD (two hydrogens missing). Let’s try working that out with hexane and cyclohexane and see if our results match with those of the formula. 

DoU-of-hexane-and-cyclohexane IHD of hexane and cyclohexane

Okay, cool! So, even though hexane and cyclohexane have the same number of carbons, cyclohexane has one degree of unsaturation while hexane is completely saturated. Cyclohexane and hexene would have the same IHD since a ring is a double bond equivalent. What would the IHD of cyclohexene be? Cyclohexene would have two degrees of unsaturation because it has a pi bond and a ring. 


Molecular formula questions: 

Calculate the degree of unsaturation in the following formulas.

Molecular-formula-blankMolecular formula blank

Structure questions: 

How many degrees of unsaturation are present in the molecules drawn below? Let’s look at benzene, naphthalene, 3-hexyne, and styrene. 

structures-blankStructure questions blank

Molecular formula answers:

Molecular-formula-answeredMolecular formula answered

Structure answers:

Structure-questions-answeredStructure questions answered

Benzene has four degrees of unsaturation, naphthalene seven degrees, 3-hexyne two degrees, and styrene has five degrees of unsaturation. 

Alright! So, we’ve officially learned how to calculate the degrees of unsaturation of hydrocarbons. Your professor is likely going to ask about molecules including heteroatoms like halides, oxygen, and nitrogen. To learn how to calculate degrees of unsaturations for molecules with heteroatoms, check out my videos on Index of Hydrogen Deficiency. Hope this helps, and good luck studying!