How To Calculate Hdi Chemistry

Degrees of Unsaturation (Index Of Hydrogen Deficiency): How the molecular formula of a chemical compound can give helpful hints about its construction.

Today nosotros'll talk about a quick and useful calculation we tin can perform to obtain the number of [multiple bonds + rings] in an unknown structure merely past knowing the molecular formula. We call information technology the Index of Hydrogen Deficiency, or more than commonly, only "Degrees of Unsaturation".

Here'southward the short, condensed version:

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

Table of Contents

What'southward And so Great About The IHD?
Playing Around With Molecular Formulae: Degrees of Unsaturation
For A Hydrocarbon With No Rings Or Double Bonds The Number Of Hydrogens Is Equal To Twice The Number Of Carbons, Plus 2
Each Double Bond or Ring Reduces The Hydrogen Count By 2
Each Ring Or Double Bail Is Chosen A "Caste Of Unsaturation"
Instance: Benzene (iv Degrees Of Unsaturation)
What About Molecules Containing Oxygen?
What About Halogens?
Nitrogen Is A Lilliputian Fleck Tricky
A Unified Formula For Degrees of Unsaturation
Applying The IHD Formula To Four Real-Life Examples
Quiz Yourself!

1. What'due south So Dandy About The IHD?

The best thing almost the IHD is that it is an piece of cake equation to employ that gives yous useful data nigh the structure of an unknown compound. Information technology literally takes a minute to do.Calculating the degrees of unsaturation is THE first task I recommend doing when y'all are faced with determining the construction of an unknown compound with a known molecular formula.In the final postal service, we saw 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 lot tin employ the equation in the box above to notice the degrees of unsaturation in theseextremely well known molecules whose formulae are given below.

C₉H₈O_four
C₂₁ H _thirty O ₂
C ₁₇ H 21 Due north O 4
C ₁₁ H ₁₅ N O ₂

The latter 3 molecules are somewhat "naughty" examples, being illegal in near states. Hopefully that'south an incentive for y'all to really do the calculation! (answers at the bottom of the post).

ii. Playing Around With Molecular Formulae: Degrees of Unsaturation

Let's kickoff this discussion past looking for patterns in molecular formulae. We'll commencement with hydrocarbons containing no double bonds or rings.

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

More than specifically, tin can yous come up upward with a formula?

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

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

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

So for a molecule like dodecane (C₁₂) nosotros'd look 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 exist able to run across that each multiple bond (π bail ) the number of hydrogens in the formula decreases by ii. 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 exist treated with hydrogen (Pd/C, H_ii ) 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 exercise not).

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

Allow'due south plough our attending to cyclic compounds. Exercise you discover a similar effect?

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

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

5. Each Band Or Double Bond Is Chosen A "Caste Of Unsaturation"

Therefore, each band introduces a "degree of unsaturation" into the molecule.

Y'all might inquire: 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 thesum of the number of double bonds and rings.

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

half dozen. Case: Benzene (4 Degrees Of Unsaturation)

For instance, thus the molecular formula C₆H_{half dozen} (4 degrees of unsaturation) is satisfied by molecules with

4 pi bonds
iii pi bonds and a ring (benzene)
two pi bonds and two rings (the very unstable Dewar Benzene, synthesized in 1963)
ane pi bail and 3 rings (the even more unstable benzvalene, a contact explosive, synthesized in 1971)
and yep, even zero pi bonds and 4 rings (prismane, synthesized in 1973).

[Historical side notation: the formula of benzene was known to exist C₆H₆ from Michael Faraday in 1825, merely the correct structure was non proposed until 1865 (Kekule) and non confirmed until 1929, by Catherine Lonsdale's X-ray studies [h/t BRSM]. Just a reminder that knowing the molecular formula but gets you so far. ]

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

7. What About Molecules Containing Oxygen?

And then far, so skillful. Let's move on. What well-nigh 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 aforementioned rules apply! We can summate the number of hydrogens from the number of carbons as if the oxygen didn't be.

Annotation that a π bond which contains oxygen still counts as a "degree of unsaturation" (come across formaldehyde, CH₂O).

8. What About Halogens?

OK. What about halogens similar 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 every bit hydrogens.That is, carbon tetrachloride (CCl_four) has the same degrees of unsaturation (zippo) every bit CH₄.

We can thus alter 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

nine. Nitrogen Is A Picayune Flake Catchy

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, y'all might take noticed that we can't ignore nitrogen like we did oxygen.

The fashion 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 information technology with cadaverine (C_vH₁₄N₂) which contains no double bonds or rings.

ten. A Unified Formula For Degrees of Unsaturation

And so far our equation has only applied to "saturated" compounds with no double bonds or rings.

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

Math time. If we movement the left hand side over to the right, we go this:

Zero equals the degrees of unsaturation in this instance.

If nosotros introduce a double bond or ring, the equation volition return "2".

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

Each successive caste of unsaturation will increase this number past 2. For example, 2-chloropyridine C₅H₄NCl gives united states of america viii:

each degree of unsaturation reduces this number by 2

At present 8 is not the degrees of unsaturation. It'due south merely the number of hydrogens "missing" from the respective non-circadian alkane of the same carbon count.

In order to make this equation give united states of america the bodily degrees of unsaturation, we need to divide everything past ii.

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 correspond 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 yous prefer.

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

OK, now for those existent-life examples I mentioned in a higher place.

C_ixH₈O₄
C₂₁ H _thirty O ₂
C ₁₇ H 21 Northward O₄
C _eleven H ₁₅ Due north O _ii

Allow'due south plug each of them into our formula. You should get:

C_ixH₈O₄[vi degrees of unsaturation]
C₂₁ H ₃₀ O _two[7 degrees of unsaturation]
C ₁₇ H 21 North O₄ [8 degrees of unsaturation]
C ₁₁ H ₁₅ N O ₂[5 degrees of unsaturation]

Now, let's wait at each of the molecules. You'll observe 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 like shooting fish in a barrel.

With the structure in front of you it seems obvious. Simply if you're dealing with an unknown information technology can be very helpful, similar nosotros saw with deer tarsal gland hormone in the last post.

In the adjacent 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 diverse molecules.