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 gonna be what we call the integration. So the integration describes the relative quantities of all the different hydrogen is that air present and the integration will express them as relative ratios. Okay, so something that we've been talking about since the very beginning of proton NMR is that some of your peaks, you're going to be taller, and some of them are going to be shorter. Now, what's deceiving is to think that your integration depends on lien height. It doesn't. It actually also depends on the width of the peak. Okay, As you can see, I have a new example in, um are here with three different peaks of different heights, but they also have slightly different widths. We have to take that into account when you look 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 gonna be what determines the relative ratio of these hydrogen is okay. Now, for those of you have already taken calculus to this sounds very familiar to you. This is basically the concept of Raymond Sums and doing End taking integral. But for this course, we're just gonna let the computer do the work for us. So no fancy, integral, that we're gonna have toe figure out the computer is gonna figure out these a U. C s or these integral right. So basically the integral of a function. It's going to do that work for us and it's going to give us spit out these different distances. So this red line at the top is actually called it integration. And as you can see, they have different heights. One of them appears to be yea high. The next one seems to be about twice as tall as the other one, and the one after that seems to you about three times as tall as the other one. Okay, What that means is that the computer actually looked at these functions looked at. This is a function and it added up all the little pieces underneath it and came up with the height of this. Okay, 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 being Proton. See how many of a are there, How many of B and what's the and how many of C and what's the ratios? In this case, the ratio would be a 1 to 2 to three ratio based on the integrations that the computer spit out for us. Okay? And that's what we mean by a relative ratio. Now, does that mean that there's exactly six protons in this molecule? Actually, in this case, it does mean that because it looks like I have one, 36 protons total. So in this case, the ratio actually added up to the total number of protons. But just you know, this ratio could also work for 12 protons or 18 protons, or any multiple of six would have basically tell us is that Hey, you might have 18 protons but they're in a ratio of 1 to 2 to three. And then that would basically tell you that you've got this many of type A this many of type B in this many of type seat. All right, so 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. So what I'm gonna do is introduce this cumulative practice problem, and then I'll have you guys try it yourself. So I want you to draw the entire NMR spectrum for this molecule. Now, what you're gonna 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 nine boxes filled out, you get it right? Okay. So 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 zero. And that means this is some high number. We're not gonna worry about exact numbers here. We're just gonna worry about the order that this should be more down field than this. They should have higher numbers as they go along. Okay, So what I want you to do is that the type of proton H h B h C goes here. Okay, so you're gonna order those protons in order of chemical shift. So 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. Okay. 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 gonna assume and plus one. So assume that the end plus one rule works here. Now, By the way, notice that in this question, I didn't say assume and plus one guess what? That's because that's up to you to determine that if your teacher, if you're professor, has not made an explicit, um, request to draw tree diagram or to use a fancy formula, then you're always gonna assume n plus one. It's the simplest way to do splitting. So I want you to draw the splits that would be predicted by Paschal's triangle and then plus one there. And then finally, the integrations. I want you to express the integrations as basically ratios or number of hydrogen. So you could An example of an integration would be I'll just put it here. Um, in an example, would be, Let's say, uh, let me just give three h, Okay. Three h would tell me that I have three hydrogen. Is that air of that type that air in that space? Now, obviously, we're gonna go ahead and erase that, because that's probably not the right answer for that box. Okay, so go ahead. And what I would try to do, I'm trying to guide you through this. You can think of it one step at a time. I guess. Figure out what the chemical shifts are in terms of order of the proton. So you can put that in these boxes here. 123 Okay, then figure out what the splits are gonna be. Okay. Figure out what type of splits they will be based on m plus one and then finally add up. The number of hydrogen is that would be of that type to get the final integrations and then I'll go ahead and I'll solve the whole thing for you. Okay, so now it's your turn. Go for it.
Draw Complete NMR Spectrum
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Alright, guys, let's start off with the order of the protons. And what we would see is that the most D shielded should be HC. Because HC is the closest to my electro negative, Adam. And the most shielded should be h A. So my order should have been h a here h b here and h c here because I'm assuming that h a is gonna be the one closest to zero. And h c is gonna be the one furthest downfield cuts the most d shielded. So that takes care of chemical shifts. Now, in terms of splitting we have to use and plus one. So for h A, I would say that, um, N is equal to two. Right? So it's got to here, So that means that it should be a triplet. So I should draw a triplet for h A like that. Okay. Now, for HB, what I see is a little bit more complicated. HB is getting split as by three on one side and by one on the other. Since we're assuming and plus one, we could just add that altogether, and that's gonna be give it a second. That's going to be an equal to four, which means that we get a king Ted. So I remember that cane Ted would be, I believe, the 14641 pattern as predicted by Pascal's triangle. So then we would try to draw that as best we cancel. One, 46 four, one. Okay, If you're not perfect, it's not a big deal, But we'll try to get his best. Do it as best as we can. Then finally, HC. So H c is being split by how many protons? Well, two on this side and to on this side. So once again for H c N is equal to four. So we're going to get another keen tat. So let's do the same exact thing. So it's not as nice. Okay, so there we go. We have our triplet Kane, Tet and Keen Tet. And now all we need is integrations. Okay, so h a has how maney hydrogen that are of that type six. This should be uninterested in of six h. Why? Because I've got these three here. But I've also got these three here. Remember, there was symmetry. Otherwise they would have had their own peak. But they're symmetries that put the same. So that should be six hydrogen czar of type six A six B. How maney type of that. Are there bull? That's gonna be four age? Because I have to and to. And then finally, HC, how many are there? Just one h, Okay, so that is our filled out problem. And now noticed that by making these boxes and putting it kind of order and made it easier to fill out. But this is all the basics of drawing your own an Imar spectra. So really, from here. Now, after you've done this practice problem, I should be able to give you a blank and, um are spectra, and you should be able to draw pretty much every single peak, every single signal, all the different splits, maybe even take a stab at the integration just from all this information. Okay, Um, now, by the way, if you were to represent this as a ratio, the ratio would have been one toe, 46 Okay, so it's that easy. All right? Now, if you do get a ratio that has multiples of numbers, let's say that I'm just gonna give a crazy example. Let's say this molecule had been twice as big. So it was actually to age. He was actually eight h, and it was actually 12 h. Let's just say this is just theoretical, Okay, if that was the ratio, then it could still be expressed like this. Well, it could still be expressed like this because you could simplify all the numbers. You could divide them all by two. And then you'd say, Well, there's more hydrogen, but there's still in a 146 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. All right, So 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?