Degrees of Unsaturation - Online Tutor, Practice Problems & Exam Prep

The Index of Hydrogen Deficiency (IHD) indicates a molecule's saturation level, calculated using the formula $2^n+2$, where n is the number of carbons. Each pi bond or ring reduces hydrogen count by 2, while a triple bond counts as 2 IHD. For molecular formulas, halogens count as one hydrogen, oxygens are ignored, and nitrogens count as negative one. Understanding IHD aids in identifying constitutional isomers and their structures.

The difference between saturated and unsaturated molecules.

Hey guys. So now we're going to talk about a topic called index of hydrogen deficiency, and this is a topic that usually isn't covered in the first chapter of most textbooks. So you're probably thinking, "Johnny, why are you teaching this to me if I don't need to know it yet?" Well, because there's this other topic called constitutional isomers, and that topic is much easier to understand if you already know the IHD rules. So what I'm going to do here is jump a little bit forward and teach you something that you don't need to know yet because it's going to make isomers so much easier to understand for this chapter. So let's go ahead and begin.

There are actually two different ways to compute the IHD, and that is one structural and the other one is with the molecular formula. What I'm going to do on this page is just show you the structural one, which is actually the easier one, and then we'll move on to the molecular formula. So first of all, let's just talk about what index of hydrogen deficiency is. Well, what it has to do with is how unsaturated or saturated a molecule is. So what's that word saturated? Well, a saturated molecule is any molecule that has as many hydrogens as possible.

There's this formula that we can use in all chemistry to figure out if it has as many hydrogens as possible, and that formula is, maybe you remember it from general chemistry, It's n=2n+2, where n is equal to the number of carbons. So I have my 2n+2 rule, and what that's going to do is it's going to predict for me how many hydrogens I need for my structure for it to be fully saturated, meaning it has as many hydrogens as it can possibly hold. Any molecule that has less than that number, 2n+2, is going to be considered to be unsaturated. And these are words, saturated and unsaturated; they might sound familiar to you, and that's because these are words we use actually in cooking.

So, saturated fat would actually be a fat. Fats are these long carbon chains. There would be this fat that has as many hydrogens as possible. Okay. An unsaturated fat would be one that's missing a few hydrogens. So you might be wondering, "Okay, Johnny, what makes carbons miss hydrogens? Why would you be missing some?" It turns out it only happens for two different reasons. Okay? So I'm going to write this down. It happens for pi bonds. Remember that pi bonds just have to do with double bonds or triple bonds; they both have pi bonds. And then also rings. Rings are also going to take away some of the hydrogens from a molecule because what that means is that the end that one of the ends is supposed to be CH3 and the other end is supposed to be CH3. When you make a ring, they have to fuse together, so that means that now you have to make them CH2s. So what I'm trying to say is that a ring actually takes some hydrogens away from the carbon structure.

Is the following molecule saturated?

If we use 2n+2, n in this case equals 5. So I would do 2×5+2 and that would mean that I need to have 12 hydrogens in order to be fully saturated. So then I would go ahead and ask myself, does this have 12 hydrogens? And if you count, what you'd find is that you have 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12. Wow, look at that. I actually do have 12 hydrogens. So that means that is this molecule saturated or unsaturated? This would be saturated. Okay. So that's the first thing. So now I just showed you a molecule that's saturated. Now another way that you could have known that this was saturated besides doing the formula is you could have also asked yourself, okay, what makes things unsaturated? Well, pi bonds and rings. Did this chain have any pi bonds in it? No. It's all single bonds. Did it have any rings? No. So also by looking at that, you could have said, oh, this is going to be a saturated molecule. See that's how this gets really easy.

Is the following molecule saturated?

And it turns out that this one would be x 2x6+2. So it should have 14 hydrogens. But how many does it actually have? That's right. 12. Okay. I know you counted like every one, each one has 2. So this one actually has 12 hydrogens. Is it missing any hydrogens? Yes. It's actually missing 2 hydrogens. Okay. Does that make sense? So this would be considered unsaturated.

Is the following molecule saturated?

So, this was also the same formula. \(2 \times 6 + 2\). It should have 14 H's, but how many does it actually have? Well, if you think about bond line structure, there's only supposed to be 1 H in each of these positions, meaning that I only have 6 H's, meaning that I'm actually missing how many? I'm missing 8 H's. That's huge. So in the first one, I had all the H's possible. In the second one, I'm missing 2, and in the third one, I'm missing 8.

What index of hydrogen deficiency is.

So we know that we can use the words saturated and unsaturated to describe this, but is there a way to compare these guys? So is there a way to say, okay, which one is more unsaturated and which one is less unsaturated because they're both very different? The answer is yes. What we do is we use the IHD rules to really be very explicit about which one is the most unsaturated and which one is the least. So the way that we do this is really easy. All we do is that we say that one IHD is the equivalent of missing 2 hydrogens. So if you're missing 2 hydrogens, that would be the equivalent of 1 index of hydrogen deficiency. That's just like the conversion. Alright. And the way that this works is that a ring or a double bond is going to count as 1 IHD. Then a triple bond is going to count as 2 IHD. Because if you think about it, a triple bond has 2 pi bonds in it. So that would be 2 IHD. All right. And really, that is it. Now instead of having to use that complicated formula, I mean, the formula isn't hard, but it's just a little tedious sometimes. Imagine if you had like 11 carbons or something and you're having to maybe use more times tables than just your fingers or whatever. What I'm trying to say is that it can get tedious counting all those hydrogens out, so instead, we use these rules.

What is the IHD of the following molecule?

Alright. So the answer is: how many double bonds did I have? 1, 2, 3, 4. How many rings did I have? 1. Okay. All of these count exactly the same. So this is going to be 5 IHD. Isn't that easy? Okay. That's 5 IHD. That means how many hydrogens are missing so that this would be a saturated molecule. Well, then I would just multiply this by 2 because I said that one IHD equals 2 hydrogens. So that means that 10 Hs are missing. Does that make sense? See how much easier that was than counting up each individual hydrogen? That would take forever. You’d probably make some mistakes too.

What is the IHD of the following molecule?

All right guys, so maybe you're getting fast at this. Just so you know, this one had nitrogens in it and oxygens in it. Does that matter? For structures, absolutely not. When you're just looking at a structure, it doesn't matter what the atom is. All we're looking for is double bonds and rings. So this is just going to be 1, 2, 3. So 3 IHD and then what are we missing? 6 hydrogens are missing.

What is the IHD of the following molecule?

Little bit tricky, but it wasn't that bad. This one has 0 IHd because it has no double bonds and it has no rings. So that means how many hydrogens are missing? Zero, which means what kind of molecule is this? This is actually saturated. Okay. Because it already has the most amount of hydrogens it can. Does that kind of make sense? What I just showed you guys right now is the easiest way to calculate IHG because you just have to look at it and you have your answer right there. What I'm going to show you in the next video is how to calculate it with if you're given molecular formula instead, which is a little bit different. If you have any questions about this, let me know.

How to use IHD with molecular formula.

When you're given a molecular formula to calculate IHD, you don't have the same clues that you had, let's say if it was a structure. If you remember, we could use pi bonds or rings to figure out how many hydrogens were missing from a molecule. But when you're just given a molecular formula, let's say like this example, C4H7Cl1, I have no clue if there are rings there, if there are double bonds there. I really all I have is the atoms. So for this, we're going to have to use our own rule and our own formula because that's really the only way to solve it. Now your professor may have used a different rule in class and in fact, most of the rules that I've seen are different from mine. The only reason I've settled on this one is because it worked for a lot of my students and they like it better. But if you have a rule that your professor taught you that you like better, please by all means use that one. All right. But this is the way it works. Basically, we need to calculate IHD and the way we do that is by calculating the theoretical H's. The way we do that is by using the formula 2N+2. So basically, we calculate N2+2. Then we subtract the actual number of 8 hydrogens. But the thing is that for this we don't just use hydrogens, we also take into consideration other atoms that might act as hydrogen equivalents. So for example, when I'm calculating the number of hydrogens in a molecule, I don't just look at H, I also look at Xs. Do you guys remember what X is? X would be a halogen and that counts as 1 hydrogen. For this formula, I count a halogen and a hydrogen exactly the same. Okay? So then oxygen. What about if I see an oxygen in my compound? What do I count that as? Actually, I count that as 0. I ignore it. Okay. So whenever you see oxygen in this compound, just ignore it. That doesn't go into your equation. Then how about nitrogen? Nitrogen is a special case. Nitrogen is actually going to count as negative one hydrogen for your overall compound. So that means that I'm not just counting Hs. I'm also counting all halogens and all nitrogens and I'm ignoring the oxygens. All right. So then finally, I get that number. That number is going to go here. This is going to be number of H's total. Then I'm going to take that number and I'm going to divide it all by 2, which is what I have here and that's going to be your IHD. Now I know that sounds a little bit complicated, but once you get going with it, you can actually do it pretty fast.

What is the IHD for C4H7Cl?

Let's just go through it one step at a time. So the first thing I would do is I'd say how many carbons do I have? I have to put that into n+2. Okay. What that's going to give me is that my theoretical H's should be 10 H's. That's the amount I should have. Okay. Now let's calculate how many H's I actually have. Well, there seem to be 7 Hs right there, so I know I have at least 7, but I also have a chlorine. What is a chlorine? A chlorine is a halogen. So that means it's going to be I'm actually going to have 8 hydrogen equivalents here. So I'm going to say 10 minus 8 hydrogens and now I'm going to divide all of that by 2 and that's going to be my IHD. It's really it's not that bad. So that's going to equal 22, which is the same as 1 IHD. So now, I can use that information to figure out okay, if I have 1 IHD, that means that I either have a double bond or what do I have? Do you guys remember? The things that equal one IHD are a double bond or a ring. Isn't that cool? So now I know that in this molecule, even though I don't really know what the structure is, I know at least I have a double bond or a ring because I'm missing 2 hydrogens. How do I know I'm missing 2 hydrogens? Because remember that 1 IHD equals 2 hydrogens that are missed. Okay?

Calculating IHD using molecular formula

According to n+2, what I should have gotten for my theoretical is 14H's. Okay. How many H's do I actually have? Well, I actually have 7, but then I have a nitrogen. What does nitrogen count as? Nitrogen actually counts as a negative. So that means instead of writing the number 7, I'm going to write 6 because basically that nitrogen is taking away one of the hydrogens. So now I have 14-6 divided by 2. What is that going to give you? That's going to give you 4 IHD. Okay. And I'm not going to go over all the possibilities here because obviously that could be a lot of double bonds, a lot of rings, triple bonds, etc. But what's important to know is that now you can convert this into IHG. Now you know how to figure out the IHG for a molecular formula.

Calculating IHD using molecular formula

All right. So in this case, my carbons was 7. So it would be 2×7+2, which would actually equal 16H's. What I'm going to subtract from that is just the number 12. Why is that? Right. Because oxygens don't count. Remember, I ignore the oxygens. So it's 16-12/2, that equals 2IHD.

Here’s what students ask on this topic:

What is the Index of Hydrogen Deficiency (IHD) and how is it calculated?

The Index of Hydrogen Deficiency (IHD) indicates the degree of unsaturation in a molecule, showing how many pairs of hydrogen atoms are missing compared to a fully saturated molecule. The basic formula for calculating IHD is:

$\mathrm{IHD}=\frac{(2n+2)-H-X+N}{2}$

where n is the number of carbons, H is the number of hydrogens, X is the number of halogens, and N is the number of nitrogens. Oxygen atoms are ignored in this calculation. Each pi bond or ring reduces the hydrogen count by 2, while a triple bond counts as 2 IHD.

How do pi bonds and rings affect the Index of Hydrogen Deficiency (IHD)?

Pi bonds and rings both contribute to the Index of Hydrogen Deficiency (IHD) by reducing the number of hydrogen atoms in a molecule. Each pi bond (found in double and triple bonds) and each ring reduces the hydrogen count by 2. Specifically, a double bond or a ring counts as 1 IHD, while a triple bond, which contains two pi bonds, counts as 2 IHD. This reduction in hydrogen atoms indicates the degree of unsaturation in the molecule.

How do you calculate IHD from a molecular formula?

To calculate IHD from a molecular formula, follow these steps:

1. Calculate the theoretical number of hydrogens for a fully saturated molecule using the formula $2n+2$, where n is the number of carbons.
2. Adjust for other atoms: add the number of halogens (X), ignore oxygens (O), and subtract the number of nitrogens (N).
3. Subtract the actual number of hydrogens from the adjusted theoretical number.
4. Divide the result by 2 to get the IHD.

For example, for C₄H₇Cl, the calculation would be:

$\frac{(2*4+2)-7+1}{2}=2$

What role do halogens, oxygens, and nitrogens play in calculating IHD?

When calculating the Index of Hydrogen Deficiency (IHD), halogens, oxygens, and nitrogens are treated differently:

• Halogens (X): Each halogen atom is counted as one hydrogen atom.
• Oxygens (O): Oxygen atoms are ignored in the IHD calculation.
• Nitrogens (N): Each nitrogen atom is counted as negative one hydrogen atom.

These adjustments are made to account for the different ways these atoms affect the hydrogen count in a molecule, ensuring an accurate calculation of the degree of unsaturation.

Why is understanding IHD important for identifying constitutional isomers?

Understanding the Index of Hydrogen Deficiency (IHD) is crucial for identifying constitutional isomers because it provides insight into the degree of unsaturation in a molecule. By knowing the IHD, you can determine the number of rings and pi bonds present, which helps in predicting possible structures. This information simplifies the process of distinguishing between different isomers that share the same molecular formula but have different connectivity of atoms, making it easier to identify and understand their unique properties.