Ch. 1 - A Review of General ChemistrySee all chapters
All Chapters
Ch. 1 - A Review of General Chemistry
Ch. 2 - Molecular Representations
Ch. 3 - Acids and Bases
Ch. 4 - Alkanes and Cycloalkanes
Ch. 5 - Chirality
Ch. 6 - Thermodynamics and Kinetics
Ch. 7 - Substitution Reactions
Ch. 8 - Elimination Reactions
Ch. 9 - Alkenes and Alkynes
Ch. 10 - Addition Reactions
Ch. 11 - Radical Reactions
Ch. 12 - Alcohols, Ethers, Epoxides and Thiols
Ch. 13 - Alcohols and Carbonyl Compounds
Ch. 14 - Synthetic Techniques
Ch. 15 - Analytical Techniques: IR, NMR, Mass Spect
Ch. 16 - Conjugated Systems
Ch. 17 - Aromaticity
Ch. 18 - Reactions of Aromatics: EAS and Beyond
Ch. 19 - Aldehydes and Ketones: Nucleophilic Addition
Ch. 20 - Carboxylic Acid Derivatives: NAS
Ch. 21 - Enolate Chemistry: Reactions at the Alpha-Carbon
Ch. 22 - Condensation Chemistry
Ch. 23 - Amines
Ch. 24 - Carbohydrates
Ch. 25 - Phenols
Ch. 26 - Amino Acids, Peptides, and Proteins
Johnny Betancourt

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. 

Practice:

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!


Johnny Betancourt

Johnny got his start tutoring Organic in 2006 when he was a Teaching Assistant. He graduated in Chemistry from FIU and finished up his UF Doctor of Pharmacy last year. He now enjoys helping thousands of students crush mechanisms, while moonlighting as a clinical pharmacist on weekends.


Additional Problems
Determine the index of hydrogen deficiency (degrees of unsaturation) for the following molecule. Antipsychotic - Haloperidol = C21H23NO2ClF
Determine the index of hydrogen deficiency (degrees of unsaturation) for the following molecule  Cancer, a tyrosine kinase inhibitor - Bosutinib  
Determine the molecular formula corresponding to the following structure. Calculate the number of degrees of unsaturation from the molecular formula and evaluate whether your calculations agree with the structure shown.  
A certain hydrocarbon has a molecular formula of C5H8 . Which of the following is not a structural possibility for this hydrocarbon? (a) It is a cycloalkane. (b) It contains one ring and one double bond. (c) It contains two double bonds and no rings.  (d) It is an alkyne. 
Determine the molecular formula corresponding to the following structure. Calculate the number of degrees of unsaturation from the molecular formula and evaluate whether your calculations agree with the structure shown.  
Based on the trends above, answer the following questions about the structure of a compound with molecular formula C24H48. Is it possible for this compound to have a triple bond? Is it possible for this compound to have a double bond?
Calculate the IHD, index of hydrogen deficiency, for a compound of molecular formula C5H9O2Br.
Calculate the degree of unsaturation for C6H10S.
What is the  unsaturation number of limonene? A. 0 B. 1 C. 2 D. 3 E. 4 F. 5 G. 6 H. 7 I. 8 J. 9
What is the index of hydrogen deficiency of each of the following molecules?
An acyclic alkane has 20 hydrogen atoms. How many carbon atoms are present in this molecule? (A molecule is acyclic if its structure contains no rings.)   A. 6                       B. 7                      C. 8                          D. 9                       E. 10 F. 11                     G. 12                    H. 13                         I. 14                     J. None of these
Which of the following compounds have the same degree of unsaturation? a.I & II b.I & III c.III & IV d.II & III e.I & IV
Determine the degree of unsaturation of the following formulas.
Calculate the IHD, index of hydrogen deficiency, for a compound of molecular formula C12H18N3F2ClNO3.
How many degrees of unsaturation does the following compound have? A)        4 B)        5 C)        6 D)        7  E)       8
What is the index of hydrogen deficiency of each? (Hint: Think about their MF's)
In each pair below, circle the compound with the largest index of hydrogen deficiency; circle both if the index of hydrogen deficiency is the same.
Expand the following structural representations so as to more clearly show all the atoms and any unshared electron pairs. What are their molecular formulas? Are any of them isomers? 
Expand the following structural representations so as to more clearly show all the atoms and any unshared electron pairs. What are their molecular formulas? Are any of them isomers? 
Expand the following structural representations so as to more clearly show all the atoms and any unshared electron pairs. What are their molecular formulas? Are any of them isomers?
Expand the following structural representations so as to more clearly show all the atoms and any unshared electron pairs. What are their molecular formulas? Are any of them isomers?
The general molecular formula for alkanes is  CnH2n+2. What is the general molecular formula for:(d) Cyclic hydrocarbons that contain one double bond 
Are there any cyclic alkenes with molecular formula C41H82?
Can a molecule with the molecule formula C34H70O be a ketone? Could it be an alcohol? Could it be an ether? Why or why not?
How many unsaturations are present in the following compound?A. noneB. 2C. 3D. 5E. 6
Which of the above sections of this molecule would be considered a saturated portion of the molecule? 
The index of hydrogen deficiency for C7H6Br4O2 is 3. Select one: a. True b. False 
An organic compound, pictured below, has the chemical formula C 7H10Cl2. How many degrees of unsaturation are present?a. 1b. 2c. 3d. 4  
A compound with the formula C5H8 can be either an alkene or an alkyne.a. Trueb. False 
Which of the following molecules have a Hydrogen Deficiency Index of 2? Select all of the molecules that apply.