Integration

- [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.