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# Integration

See how the area under each proton NMR signal can tell us the number of protons in a certain chemical environment. Created by Jay.

## Want to join the conversation?

• How are the 5 protons in the benzene ring in the same environment?
(16 votes)
• They aren't, but there is so little difference between them that they appear to be in the same environment.
(11 votes)
• how do you integrate when you're just given the lines and not the numbers on the bottom?
(15 votes)
• This method doesn't really work for the MCAT exam where calculators are not allowed. It's much easier if you find the total area of all the signals and divide it by the total number of signals (eg. 116.4/10 =11.64). Then divided the area of each signal by 11.64....it's easier and the value is much closer to the actual value (eg. 57.9/11.64 = 60/12 = 5)
(11 votes)
• do you mean 'divide by the total number of *protons' ?
(1 vote)
• Why is it that we multiply all the ratios by 2?, is it always 2?
(4 votes)
• No, it can be a range of numbers, 1 and 2 will be the most common though. First, you divide all of the integration values by the lowest value; if you get integers, multiply all of them by 1 (aka do nothing); if you get a half number (like 2.5 in the video), multiply by two; if you get x.333, multiply by 3; x.25 by 4; etc.
Once you have these numbers, add them all together. They should add up to the number of hydrogens on your molecule (if your molecule is symmetrical, you might need to multiply by 2 again).
(side note, these will all be rounded values, sometimes heavily rounded)
(8 votes)
• What if youre only given the skeletal structure?
(4 votes)
• How are there only 3 signals, I thought that the two hydrogen atoms attached to the benzene ring would each have a separate signal due to the fact that one hydrogen atom is closer to an oxygen atom than the other?
(2 votes)
• There will be 2-3 different signals in the aromatic region but unless you're given a zoomed in spectrum you will not be able to see these.
Often the aromatic signal is just a mess, rely on the integrations to tell you how many protons there are.
(3 votes)
• In our class, we were told that the area under the peaks are exactly proportional to the number of protons, is that wrong?
(2 votes)
• No that's right. They're proportional but they won't always be exactly equal to the number of protons.
Sometimes you'll need to adjust the numbers like in this video so that they equal the number of protons in the molecule.
(3 votes)
• Since you know that you have ten protons, isn't it easier to add up the area under all the curves, divide by ten, and then use that as the number for a single proton? Then you don't have to guess at the scaling factor. Just divide the area under a single curve by the area for a single proton.
(2 votes)
• At , the CH-2 group is attached to (O), shouldn't it be in the range 3-4 ppm. Why is it in the 5.1 ppm chemical shift?
(2 votes)
• That is because of the benzene ring that it is also attached to
(1 vote)
• In my organic chemistry class we are not given the numbers below the signals (57.9, 23.1, 35.4) so without having those numbers and being able to do the math to figure out which group of hydrogen goes with which signal, how else can I figure that out?
(1 vote)
• Next video about spin-spin splitting and multiplicity rule should answer your question.
(1 vote)

## Video transcript

- [Voiceover] Integration is the area under each signal and it tells us the number of protons in that signal. And so here we have the proton NMR spectrum of Benzyl Acetate including the integration values. So the computer calculates the area under the signal, so for example, for this signal, the area under the signal's calculated by the computer, and gives us this number. The computer gives us 57.9. For this signal, the computer gives us 23.1. And finally, for this signal, we get integration value of 35.4. Let's go back up here to the dot structure of Benzyl Acetate and let's see how many protons that we need to account for in our proton NMR spectrum. This carbon right here has three protons. Let me go ahead and draw those protons in. Alright, this carbon has two protons on it. And that's five so far. And then on our ring, right, we have five more protons. So going around the ring here we have five more for a total of 10. So we need to account for 10 protons in our spectrum. Alright, so going back to the integration values, you find the smallest integration values. So out of those three numbers, 23.1 is the smallest integration value. And we're going to divide all three integration values by the smallest one. And we'll start with 57.9. So 57.9 divided by 23.1. Let's get out the calculator here. 57.9, divide that by 23.1, and we get 2.5. So I'll write 2.5 right here. 23.1 divided by 23.1 is obviously equal to one. and then finally, 35.4, we need to divide that by the smallest integration value, so 35.4 divided by 23.1 gives us about 1.5. So we have 1.5 here. This gives us a ratio of the protons that are giving these three signals. So the ratio would be 2.5 to 1 to 1.5. But you can't have 2.5 protons, right, you can't have half a proton, here. And so those aren't the exact number of protons, right. We need to account for 10 protons in our molecule. And so if you think about it, if you multiply these numbers by two, alright, then that gives us what we want. Because if you multiply 2.5 by two, that gives us five. If you multiply one by two, that gives us two. If you multiply 1.5 by two, that gives us three. And obviously five plus two plus three gives us 10, and 10 protons is how many protons that we need to account for for our molecule. And so therefore, this signal right here corresponds to five protons, this signal corresponds to two protons, and this signal corresponds to three protons. So if we go back up here to our dot structure, and I look at these protons, right, so we have three equivalent protons, the chemical shift for these protons were next to a carbonyl so we would expect the chemical shift to be just past two. And that's of course what we see right here. So the shift is just past two, this signal represents three protons, and it's these three protons right here. Alright, next, let's look at these two protons. So these two protons are next to an Oxygen, so the Oxygen deshields that. Those two protons are also next to this Benzene ring over here, so we would expect a higher chemical shift. Alright, and we have two protons and of course, it's this signal, which corresponds to two protons. Finally, we have five nearly equivalent protons on our ring, so they might not be exactly the same, but for the signal here, right, we have five protons giving us this signal, and it's a little more complex than the other ones, but, notice where it is. Right where-- aromatic region, in terms of a chemical shift. And so this signal must represent these five aromatic protons on our ring. And so this shows you how useful the integration values are. They tell you how many protons are giving that signal, which allows you to figure out the structure of the molecule.