Spectroscopy

By James Ashenhurst

Degrees of Unsaturation (or IHD, Index of Hydrogen Deficiency)

Last updated: October 31st, 2022 |

Degrees of Unsaturation (Index Of Hydrogen Deficiency)

  • The molecular formula of a compound can give clues about its structure.
  • The formula for an alkane follows the pattern CnHn+2  where n is the number of carbons.
  • Every pi bond or ring reduces the number of hydrogens by 2.
  • Therefore the molecular formula can tell us the number of pi bonds or rings in an unknown structure.
  • This is called the index of hydrogen deficiency (IHD) or degrees of unsaturation.
  • The full formula has modifications that account for halogens and nitrogens

summary for index of unsaturation formula degrees of unsaturation carbon hydrogen nitrogen halogens

Table of Contents

  1. What’s So Great About The IHD?
  2. Playing Around With Molecular Formulae: Degrees of Unsaturation
  3. For A Hydrocarbon With No Rings Or Double Bonds The Number Of Hydrogens Is Equal To Twice The Number Of Carbons, Plus 2
  4. Each Double Bond or Ring Reduces The Hydrogen Count By 2
  5. Each Ring Or Double Bond Is Called A “Degree Of Unsaturation”
  6. Example: Benzene (4 Degrees Of Unsaturation)
  7. What About Molecules Containing Oxygen?
  8.  What About Halogens?
  9. Nitrogen Is A Little Bit Tricky
  10. A Unified Formula For Degrees of Unsaturation
  11. Applying The IHD Formula To Four Real-Life Examples
  12. Quiz Yourself!

1. What’s So Great About The IHD?

The best thing about the IHD is that it is an easy equation to use that gives you useful information about the structure of an unknown compound. It literally takes a minute to do. Calculating the degrees of unsaturation is THE first task I recommend doing when you are faced with determining the structure of an unknown compound with a known molecular formula. In this post, we see that this calculation was clutch in the determination of the structure of the side chain of deer tarsal pheromone.

Before we get going, see if you can apply the equation in the box above to find the degrees of unsaturation in these extremely well known molecules whose formulae are given below.

  • C9H8O4
  • C21H30O2
  • C17H21NO4
  • C11H15NO2

The latter three molecules are somewhat “naughty” examples, being illegal in most, if not all states. Hopefully that’s an incentive for you to actually do the calculation!  (answers at the bottom of the post).

2. Playing Around With Molecular Formulae: Degrees of Unsaturation

 Let’s start this discussion by looking for patterns in molecular formulae. We’ll start with hydrocarbons containing no double bonds or rings.

Can you see a relationship between the number of carbons and the number of hydrogens?

More specifically, can you come up with a formula?

hydrocarbons with no rings or multiple bonds have the formula number of hydrogens equals 2 times number of carbons plus 2

3. For A Hydrocarbon With No Rings Or Double Bonds The Number Of Hydrogens Is Equal To Twice The Number Of Carbons, Plus 2

You should be able to see that for a hydrocarbon with no rings or double bonds, the number of hydrogens is equal to twice the number of carbons, plus 2.

So for a molecule like dodecane (C12) we’d expect to see (12 x 2) + 2 = 26 hydrogens.

Now: what happens to the molecular formula when we add a double bond to the molecule?

index of hydrogen deficiency effect of doubld bonds on hydrogen count each double bond reduces it by 2

4. Each Double Bond or Ring Reduces The Hydrogen Count By 2

You should be able to see that each multiple bond (π bond ) the number of hydrogens in the formula decreases by two. Ethyne (2 π bonds) has two fewer hydrogens than ethene (1 π bond), which has two fewer hydrogens than ethane (zero π bonds).

Hydrocarbons containing  π bonds are often called “unsaturated” hydrocarbons. They can be treated with hydrogen (Pd/C, H2 ) to give the corresponding alkane with no  π bonds, which is then said to be “saturated” with hydrogen. (Compare “unsaturated fats“, which contain alkenes, and “saturated fats” which do not).

Since every pi bond results in a loss of 2 hydrogens from the molecular formula, we refer to this to as a “degree of unsaturation“.

Let’s turn our attention to cyclic compounds. Do you notice a similar effect?

index of hydrogen deficiency index of unsaturation each ring reduces number of hydrogens by two

You should! Every ring in the molecule decreases the number of hydrogens by two.

5. Each Ring Or Double Bond Is Called A “Degree Of Unsaturation”

Therefore, each ring introduces a “degree of unsaturation” into the molecule. 

You might ask: what if we have a molecule with rings and multiple bonds? See for yourself.

effect of double bonds and rings on number of hydrogens degrees of unsaturation the effect is additive

The effect is additive. That is, the “degrees of unsaturation” is the sum of the number of double bonds and rings.

Note that it doesn’t tell you how many double bonds are present or how many rings are present. It merely tells you their sum.

6. Example: Benzene (4 Degrees Of Unsaturation)

For instance, thus the molecular formula C6H6 (4 degrees of unsaturation) is satisfied by molecules with

  • 4 pi bonds
  • 3 pi bonds and a ring (benzene)
  • two pi bonds and two rings (the very unstable Dewar Benzene, synthesized in 1963)
  • one pi bond and three rings (the even more unstable benzvalene, a contact explosive, synthesized in 1971)
  • and yes, even zero pi bonds and four rings (prismane, synthesized in 1973).

[Historical side note: the formula of benzene was known to be C6H6 from Michael Faraday in 1825, but the correct structure was not proposed until 1865 (Kekule) and not confirmed until 1929, by Catherine Lonsdale’s X-ray studies . Just a reminder that knowing the molecular formula only gets you so far. ]

Helpful hint: if you see 4 degrees of unsaturation in an unknown molecule, thinking “benzene ring” is a good place to start.

7. What About Molecules Containing Oxygen?

So far, so good.  Let’s move on. What about molecules with oxygen?

what is effect of oxygen and sulfur on index of hydrogen deficiency formula they have no effect on degrees of unsaturation

The same rules apply! We can calculate the number of hydrogens from the number of carbons as if the oxygen didn’t exist.

Note that a π bond which contains oxygen still counts as a “degree of unsaturation” (see formaldehyde, CH2O).

8. What About Halogens?

OK. What about halogens like chlorine, fluorine, iodine and bromine?

informula for degrees of unsaturation halogens have same effect as hydrogens

For the purposes of our formula relating hydrogens to carbons for molecules without rings or double bonds, halogens can be counted as hydrogens. That is, carbon tetrachloride (CCl4) has the same degrees of unsaturation (zero) as CH4.

We can thus modify the equation for a molecule with no double bonds or rings as follows:

for compound with no double bonds or rings equation for index of hydrogen deficiency index of unsaturation formula is hydrogens plus halogens equals 2 times number of carbons plus 2

9. Nitrogen Is A Little Bit Tricky

We’ve saved nitrogen for last, because it’s a bit weird.  Try to see the pattern of how nitrogen affects our formula.

nitrogen in the formula for index of unsaturation is a special case nh3 has zero degrees of unsaturation this figure shows many examples of nitrogen compounds

OK, you might have noticed that we can’t ignore nitrogen like we did oxygen.

The way to make the equation work with nitrogen is to add the nitrogen count to the right hand side of the equation, like this:

formula for compound with no double bonds or rings formula for index of hydrogen deficiency is here try cadaverine c5h14n2

Try it with cadaverine (C5H14N2) which contains no double bonds or rings.

10. A Unified Formula For Degrees of Unsaturation

So far our equation has only applied to “saturated” compounds with no double bonds or rings.

How can we use this to make a general formula for “degrees of unsaturation”, which is actually… useful?

Math time. If we move the left hand side over to the right, we get this:

modified formula for index of hydrogen deficiency incorporating carbon nitrogen hydrogen and halogens

Zero equals the degrees of unsaturation in this case.

If we introduce a double bond or ring, the equation will return “2”.

compound with 1 degree of unsaturation will return value of 2 for this formula see 3 halo piperidine

Each successive degree of unsaturation will increase this number by 2. For instance, 2-chloropyridine C5H4NCl gives us 8:

each degree of unsaturation reduces this number by 2

Now 8 is not the degrees of unsaturation. It’s merely the number of hydrogens “missing” from the corresponding non-cyclic alkane of the same carbon count.

In order to make this equation give us the actual degrees of unsaturation, we need to divide everything by two.

final modification for formula with degrees of unsaturation is equal to one half times 2 times carbons plus 2 plus nitrogens minus hydrogens minus halogens

We can really condense things by using the symbols H, C, N, and X to represent hydrogens, carbons, nitrogens and halogens, respectively.

unified formula for degrees of unsaturation index of hydrogen deficiency including carbon nitrogen hydrogen halogens

This is our final form for the equation for “degrees of unsaturation”, or “index of hydrogen deficiency” if you prefer.

11. Applying The IHD Formula To Four Real-Life Examples

OK, now for those real-life examples I mentioned above.

  • C9H8O4     
  • C21H30O
  • C17H21NO4 
  • C11H15NO

Let’s plug each of them into our formula. You should get:

  • C9H8O4     [6 degrees of unsaturation]
  • C21H30O[7 degrees of unsaturation]
  • C17H21NO4 [8 degrees of unsaturation]
  • C11H15NO[5 degrees of unsaturation]

Now, let’s look at each of the molecules. You’ll find that the calculated degrees of unsaturation agrees with the sum of [multiple bonds and rings] in the molecule.

examples of index of hydrogen deficiency calculation incorporating aspirin thc cocaine and mdma calculate degrees of unsaturation

Super useful. Super easy.

With the structure in front of you it seems obvious. But if you’re dealing with an unknown it can be very helpful, like we saw with deer tarsal gland hormone in the last post.

In the next post, we’ll start delving into the mysteries of spectroscopy. We’ll start with one of the simplest spectroscopic techniques – UV-Vis spectroscopy – and show how it can be used to deliver clues about the structures of various molecules.


Notes

Quiz Yourself!

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Comments

Comment section

23 thoughts on “Degrees of Unsaturation (or IHD, Index of Hydrogen Deficiency)

  1. I read that in Dewar benzene, the middle C1-C4 linkage in not sigma bond but 2p-2p pi bond (special type of pi without sigma).

  2. In compound R-NO2 (suppose R is an aliphatic saturated compound), will the degree of unsaturation be 1 or 1.5? Shouldn’t we take DU equal to 1.5 due to resonance between the negative charge of oxygen atom and the double bond?
    Which one is correct? Sorry to ask a silly question.

  3. I have been struggling with using IHD to deduce a structural fromula from a spectrum graph.
    Your explanation has help me a lot.
    Thank you.

  4. First problem to be solved using simultaneous equations in two variables.
    A hydrocarbon contains only two elements, viz C and H. Let the formula be CxHy.
    Given IHD= 6.
    Substitute in IHD formula and get the first simultaneous equation as
    2x+2+-y= 6
    Atomic weights of C=12 and H=1. Substitute to calculate formula weight and get 2nd equation in two variables
    12x + y = 284.
    solve for x and y

  5. If we’re given the structure of the molecule, can’t we just calculate degrees of unsaturation by the formula:

    IHD = #rings + #double bonds + 2#triple bonds

    If we only have the molecular formula, this formula isn’t helpful. But if we have the structure, isn’t this formula more simple?

    1. Hi Chris – This is a post about structure determination.

      The usefulness of IHD is that it is a value you can calculate from the molecular formula without knowing anything else about the structure (the molecular formula can be obtained from techniques like elemental analysis, high-resolution mass spectrometry, etc.)

      That’s why I say it’s one of the first calculations to make when you’re dealing with a molecule of unknown structure.

      If you already know the structure, then IHD isn’t really going to help you

  6. I once came a cross a question,
    which spoke of degrees of unsaturation for,
    the oxalate ion, not the acid, beware.
    The answer spoke of degrees 3, not 2,
    as the anionic oxygens could pick up a H2 too,
    I’d like to know if this accepted and right,
    Pray do clear my plight!

  7. Can you explain what a degree of unsaturation of 6 mean? I calculated the degree of unsaturation for C7H5NO3 but I am a bit confused on what a DoU =6 means for the compound’s structure?

    1. It means the the number of [rings + multiple bonds] is equal to 6. That means it could have 6 rings and no double bonds, 5 rings and one multiple bond…. all the way to zero rings and six multiple bonds.

      A quick hint: a benzene ring takes up 4 degrees of unsaturation [1 ring and 3 double bonds], so I would start there. That leaves you with 5 hydrogens, a nitrogen and 3 oxygens to put on the benzene ring…

  8. I’m really thankful for you, I didn’t know What the degrees of unsaturation was and useful, now I know because of you, and it’s very helpful for me to identify molecules by IR spectres given to me as a hometask

  9. You made a mistake in your formula for cocaine and MDMA, you are subtracting the nitrogen instead of adding it… The answer you get is correct, but the operation indicated is incorrect.

  10. I’m sorry you didn’t get the faculty positions you applied for, especially after all of that post-graduate work. All the same, your posts are the truth! Great examples, great explanations. It all makes so much sense now that I think I’ll actually be able to get an A on my Ochem exam.

    Thanks again!

    Renee

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