Now we're going to move on to the 3rd important piece of information that you can get from proton NMR, and that's going to be what we call spin splitting. It's just important to recognize all the different terms that this could be called and how they're all the same concept. If you ever hear of spin-spin coupling or J-coupling or a term I mentioned earlier called multiplicity, these are all the same exact concept. Spin splitting has to do with the concept of neighboring protons interfering with each other, and this will reveal to us the distances between different protons.
I have to throw out a big side note here: this topic can be taught either in a really simple way or a really complex way. And since I have no way of knowing exactly the way your professor taught it this semester, I'm going to teach it to you both ways. I've actually made 2 different videos so you can pick the easy one or pick the hard one depending on how your professor explains it, and I'm going to help you determine which one to watch. Obviously, if you just want to be thorough, you can definitely watch both of them.
But for right now, I'm going to teach this topic without J values. J values are the thing that complicates the spin splitting concept a lot. Now just so you know, I've been teaching organic chemistry. Most likely, you're in one of those classrooms where you don't really need to learn a rigorous explanation of J values. That being said, then this session, this one video would really just cover you for spin splitting. Now if your professor goes deep into J values and starts talking about how to draw a tree diagram, that's where you're going to want to watch the second video.
So awesome, let's get back to the lesson. Basically, if you're not learning J values, then this is a very simple rule. All it says is that adjacent non-equivalent protons will split each other's magnetic response to NMR. There's a really simple rule that we use to predict what these splits would look like and that's what we call the n plus one rule. The n plus 1 rule basically says that n stands for the number of non-equivalent. N is equal to this definition here. It turns out that Pascal's Triangle does a really good job of predicting what these different splits will look like.
You might not have seen Pascal's Triangle since grade school, so I'm just going to go over this really quick just to remind you. Pascal's Triangle is a pattern of numbers where, if you add up the two numbers above, you're going to get the number below. So 1 +1 equals 2 and as you go to multiple layers, you start getting bigger and bigger sums. For example, if you do n+1, and your n is actually equal to 0, meaning that you don't have any protons around that are splitting, then what we're going to call that is a singlet. You're just going to get one peak.
Now let's look at a more complicated example. Let's say that n in your example is actually equal to 2. That means that you have 2 non-equivalent adjacent protons next to your target proton. That's going to be called a triplet. What a triplet predicts according to Pascal's Triangle is that since we're on the 3rd level of the triangle, you're going to get a single split of size 1, a second split of size 2, and a third split again of size 1. You can use Pascal's Triangle to model what your split should look like.
Going all the way to like a quintet, if you have a quintet, your peaks are going to have 5 different splits and they're going to be of the size 1, 4, 6, 4, 1. That is when n would equal 4, so we'd have 4 plus 1 which equals 5, which would be our quintet.
I hope that's making sense in terms of the shapes. Now you just have to actually apply it because I know that it's still a little confusing. Let's do the first problem as a worked example. We'll kind of all do it together. And then the second one, I'll have you guys do on your own. So let's go ahead and analyze this carbon right here. I'm going to make that one my red one. First of all, adjacent means it's within one space. If I go to the left, there's nothing there. If I go to the right, I also have nothing. That means for red, n is equal to 0. Now, using the n plus 1 rule, that means that 0 + 1 equals 1, which means that I'm going to get a singlet. I'm going to get just a single peak for the red hydrogens.
Let's keep going. Now let's look at the blue hydrogens. I do the same thing—I say how many adjacent, non-equivalent protons does it have next to it. Well, if I go to the left, again, nothing. I'm next to a carbon with nothing. But if I go to the right, do I have any hydrogens? Actually yes, I have 3 to the right. That means that this would mean that n is equal to 3. So if I use the n plus one rule, 3+1 equals 4, 4 gives me a quartet. So I would expect that I would get a quartet from those protons.
Now let's look at green. Green is over here. So if I go to the right, nothing. If I go to the left, how many protons do I have? 2. So that means that for green, n is equal to 2. So that means according to n plus 1, it would be 2+1 equals 3, which would be what we call a triplet.
Heteroatoms: Heteroatoms are non-carbon atoms such as nitrogen, sulfur, oxygen, phosphorus, etc. They do not split. Think of it like a wall; you can't split through a heteroatom. When I go to analyze how many different adjacent hydrogens are next to that, well if I go to the right, obviously there's nothing. But if I go to the left, there's also nothing because I hit a wall—that wall is the heteroatom. Other than that, everything else is still the same, so go ahead and try to solve for the rest of to try to figure out how many splits you'd get for proton type 1, proton type 2 and proton type 3. Go for it.
