NMR Integration: Videos & Practice Problems

Integration in proton NMR reveals the relative quantities of different hydrogen atoms, expressed as ratios. It considers both peak height and width, representing the area under the curve. The computer calculates these areas, allowing for the determination of hydrogen ratios, such as 1:2:3. This ratio indicates the number of protons of each type, which can be multiples of the total. Understanding chemical shifts, splitting patterns using the n+1 rule, and integration ratios is essential for accurately interpreting NMR spectra.

1H NMR Integration

So guys, now we're finally going to get to the last piece of information that you can derive from a proton NMR and that's going to be what we call the integration. The integration describes the relative quantities of all the different hydrogens that are present and the integration will express them as relative ratios. Something that we've been talking about since the very beginning of proton NMR is that some of your peaks are going to be taller and some of them are going to be shorter. Now what's deceiving is to think that your integration depends only on height. It doesn't. It actually also depends on the width of the peak. As you can see, I have an example NMR here with 3 different peaks of different heights but they also have slightly different widths. We have to take that into account when we look at integration. In fact, integration is just a fancy way of saying that you're taking the area under a curve. You're not just looking at the exact height of it. You're looking at all the little slices underneath that curve and you're adding them up together. And then when you stack them up, you take the area. And that's really going to be what determines the relative ratio of these hydrogens.

For those of you who have already taken Calculus 2, this sounds very familiar to you. This is basically the concept of Riemann sums and taking integrals. But for this course, we're just going to let a computer do the work for us. So no fancy integrals that we're going to have to figure out.. The computer is going to figure out these Areas Under the Curve or these integrals, right? Basically, the integral of a function. It's going to do that work for us and it's going to spit out these different values. This red line at the top is actually what we call the integration. As you can see, they have different heights. One of them appears to be yay high. The next one seems to be about twice as tall as the other one. And the one after that seems to be about 3 times as tall as the other one.

What that means is that the computer actually looked at these functions, looked at this as a function and it added up all the little pieces underneath it and came up with a height of this. Now the important part for us isn't to be able to do the actual integral calculus to figure out the integration. It's to compare these heights and to say, well, how many of this type, let's say this is proton A, proton B, and proton C. How many of A are there? How many of B and how many of C and what are the ratios? In this case, the ratio would be a 1 to 2 to 3 ratio based on the integrations that the computer spit out for us. That's what we mean by relative ratio. Now does that mean that there's exactly 6 protons in this molecule? Actually in this case, it does mean that because it looks like I have 1, 3, 6 protons total. In this case, the ratio actually added up to the total number of protons. But just so you know, this ratio could also work for 12 protons or 18 protons or any multiple of 6. What it would basically tell us is that hey, you might have 18 protons but they're in a ratio of 1 to 2 to 3. And then that would basically tell you that you've got this many of type A, this many of type B, and this many of type C.

That said, we basically have all the information that we need now to draw our own NMR spectra. I know you're getting really excited at this point. What I'm going to do is introduce this cumulative practice problem and then I'll have you guys try it yourselves. I want you to draw the entire NMR spectrum for this molecule. Now what you're going to notice is that I did this is actually an easier way to draw it than just giving you a blank chart because I'm kind of giving you boxes to fill out. As long as you have those 9 boxes filled out, you get it right. Let me just show you what I'm looking for. First of all, notice that we have this PPM line right here. That means this is 0 and that means this is some high number. We're not going to worry about exact numbers here. We're just going to worry about the order that this should be more downfield than this. They should have higher numbers as they go along. What I want you to do is that the type of proton, H A H B H C goes here. You're going to order those protons in order of chemical shift. This is going to be based on basically the chemical shift. If it's very downfield, then that should be the one that goes furthest off to the left. Also, you are going to be responsible for so you don't have to tell me the exact value of the shift. You just have to put them in order. In terms of the splitting, you should be able to draw the types of splits that you would get here and we're going to assume n+1. So assume that the n+1 rule works here. Now by the way, notice that in this question, I didn't say assume n+1. Guess what? That's because it's up to you to determine that. If your teacher, if your professor has not made an explicit request to draw a tree diagram or to use a fancy formula, then you're always going to assume n+1. It's the simplest way to do splitting. I want you to draw the splits that would be predicted by Pascal's Triangle and n+1 there. Then finally the integrations. I want you to express the integrations as basically ratios or number of hydrogens. An example of an integration would be I'll just put it here. An example would be let's say, let me just give 3 H. 3 H would tell me that I have 3 hydrogens that are of that type, that are in that space. Now obviously we're going to go ahead and erase that because that's probably not the right answer for that box. Go ahead and what I would try to do, I'm trying to guide you through this so you can think of it one step at a time. Figure out what the chemical shifts are in terms of order of the protons. You can put that in these boxes here, 1, 2, 3. Then figure out what the splits are going to be. Figure out what types of splits they would be based on n plus 1. And then finally add up the number of hydrogens that would be of that type to get the final integrations. Then I'll go ahead and I'll solve the whole thing for you. Now it's your turn. Go for it.

Draw Complete NMR Spectrum

All right, guys. Let's start off with the order of the protons. What we would see is that the most deshielded should be H_c because H_c is the closest to my electronegative atom, and the most shielded should be my order should have been here, H_b here and H_c here because I'm assuming that it is going to be the one closest to 0, and H_c is going to be the one furthest downfield because it's the most deshielded. That takes care of chemical shifts. Now, in terms of splitting, we have to use n+1. For H_c, I would say that n is equal to 2. So it's got 2 here. So that means that it should be a triplet. So I should draw a triplet for like that.

Now for H_b, what I see is a little bit more complicated. H_b is getting split by 3 on one side and by 1 on the other. Since we're assuming n+1, we can just add that altogether, and that's going to give it a second. That's going to be n equal to 4, which means that we would get a quintet. Remember that a quintet would be, I believe, the 1-4-6-4-1 pattern as predicted by Pascal's triangle. So then we would try to draw that as best we can. So 1, 4, 6, 4, 1. If you're not perfect, it's not a big deal. But we'll try to do it as best we can.

Then finally, H_c. So H_c is being split by how many protons? Well, 2 on this side and 2 on this side. So once again, for H_c, n is equal to 4. So we're going to get another quintet. So let's do the same exact thing. This one's not as nice. There we go. We have our triplet, quintet, and quintet, and now all we need is integrations. Okay. So H_a has how many hydrogens that are of that type? 6. This should be an integration of 6 H. Why? Because I've got these 3 here, but I've also got these 3 here. Remember there was symmetry? Otherwise, they would have had their own peak, but there's symmetry so they're both the same.

So that should be 6 hydrogens are of type 6 A. 6b, how many types of that are there? Well, that's going to be 4 H because I have 2 and 2. And then finally H_c, how many are there? Just one H. That is our filled-out problem.

Now notice that by making these boxes and putting it kind of in order, it made it easier to fill out. But this is all the basics of drawing your own NMR spectra. Really from here, now after you've done this practice problem, I should be able to give you a blank NMR a marked spectra, and you should be able to draw pretty much every single peak, every single signal, all these different splits. Maybe even take a stab at the integration just from all this information.

Now by the way, if you were to represent this as a ratio, the ratio would have been 1 to 4:6. So it's that easy. Now if you do get a ratio that has multiples of numbers, let's say that I'm just going to give a crazy example. Let's say this molecule had been twice as big. So it was actually 2 H, it was actually 8 H, and it was actually 12 H. Let's just say this is just theoretical. If that was the ratio, then it could still be expressed like this because you could simplify all the numbers. You could divide them all by 2, and then you'd say, well, there are more hydrogens but they're still in a one 4 6 ratio. So just trying to show you that your ratios don't always add up to the amount of protons you have. What they do tell you is the relative amounts of each type of proton that you have. Hope that made sense. Let's go ahead and move on to the next topic.

PRACTICE: Which of the following molecules gives a 1H NMR spectrum consisting of three peaks with integral ratio of 3:1:6 (when signals are counted from left to right)?

• A. 1
• B. 2
• C. 3
• D. 4

Answer: (B)

Here’s what students ask on this topic:

What is NMR integration and how is it used in proton NMR?

NMR integration in proton NMR reveals the relative quantities of different hydrogen atoms in a molecule. It is expressed as ratios and considers both the height and width of the peaks, representing the area under the curve. The computer calculates these areas, allowing for the determination of hydrogen ratios, such as 1:2:3. This ratio indicates the number of protons of each type, which can be multiples of the total. Understanding chemical shifts, splitting patterns using the n+1 rule, and integration ratios is essential for accurately interpreting NMR spectra.

How do you determine the relative number of protons from NMR integration?

To determine the relative number of protons from NMR integration, you compare the heights of the integration lines provided by the computer. These heights represent the area under the curve for each peak. For example, if the integration lines are in a 1:2:3 ratio, it means that the number of protons corresponding to each peak is in that ratio. This could mean 1, 2, and 3 protons, respectively, or any multiple thereof, such as 2, 4, and 6 protons.

What is the significance of the area under the curve in NMR integration?

The area under the curve in NMR integration is significant because it represents the relative quantity of hydrogen atoms contributing to each peak. Unlike just measuring peak height, the area accounts for both the height and width of the peak, providing a more accurate representation of the number of protons. This area is calculated by the computer and is used to determine the integration ratios, which help in identifying the relative number of different types of protons in the molecule.

How does the n+1 rule apply to NMR splitting patterns?

The n+1 rule in NMR splitting patterns states that a proton with n neighboring protons will split into n+1 peaks. For example, a proton with two neighboring protons (n=2) will split into three peaks (a triplet). This rule helps predict the splitting patterns observed in the NMR spectrum, which, combined with integration and chemical shifts, aids in determining the structure of the molecule.

Can NMR integration ratios be used to determine the exact number of protons in a molecule?

NMR integration ratios indicate the relative number of protons but not necessarily the exact number. For instance, a 1:2:3 ratio could correspond to 1, 2, and 3 protons or any multiple thereof, such as 2, 4, and 6 protons. To determine the exact number, additional information about the molecular structure and the total number of protons in the molecule is required.