1H NMR:Spin-Splitting Complex Tree Diagrams

So now we're moving on to drawing complex tree diagrams, which really should be the Onley type of tree diagram you ever draw, since I already proved to you that you don't need to draw simple tree diagrams to get the right shape. So, as I said, we're gonna have to use multiple J values in the same problem in order to really justify using a tree diagram. And when you have these multiple J values involved, it's important toe always split in order of the highest value first, and then go to your lower J values later. So always go from the highest hurts toe. The lowest hurts. OK now, before kicking this question, often really drawing the whole thing. I want to analyze it according to end plus one, and then compare answer at the end to what end plus one would have predicted. So it says here, use a tree diagram to predict the splitting pattern of the bold ID proton, which in this case is age seat. And first of all, what would end plus one rule and Pascal's triangle say about this split? What should it look like? Well, if we go to the left How many protons are we getting split by? So we're getting split by zero, right? Because there's nothing there. If we go to the right, how many protons are we getting? Split by to H A and H B. So that means according toe end plus one and equals two. So then it should be two plus one equals three. So the end plus one rule if I were just to stick with that should be a triplet. Okay? And we know that triplets come with a 1 to 1 ratio. So that's what Paschal's rule tells me. And unfortunately, if you stop there, you would actually get this question completely wrong. Why? Because look thes J Values for H A and H b are actually not the same. They're different. J. H A does not equal J h b. So I can't use Pascal's triangle. I can't use n plus One. Okay, I have to use a tree diagram. So let's go ahead and do the tree diagram like we did before and which proton or which J value split with first. Should I split with the J value from H A or the J Value from H B A J because it's bigger. Remember? Said you always start with the bigger value first. So I'm going to start off with the single it that HC would have given me. Okay, so this is HC. If it wasn't being split, it would just be a single. But I'm going to start off with H A. The split from H A is a value of 16 now. I don't have enough. Um, I guess Cubes, whatever. I don't have enough units here so that every single, um, unit air box is gonna be equal toe one. So instead, let's use to let's say that every box is equal to have split to hurts. Okay, so if we're trying to split by 16 hurts at the beginning, that means that I have to go, um, four to the right and four to the left to make eight boxes or equal to 16. So, basically, what I'm saying here is that one of these is equal to two hertz. Hope you guys can can get Let me get away with that one. Okay, so we're gonna go four to the right, four to the left. That's going to give me a split of that's H A and that's going to give me a split of 16 hurts. OK, and so far, what we're getting we are getting a double it. Okay, so So far, so good. Looks like a double it. It looks like a one toe one ratio. So nothing too crazy. Okay, this is exactly what you'd expect to see with n plus One. Okay, Now, the difference is that if I was using in plus one, the split for HB would have to be what number as well, 16. I would have to have the same coupling constant for and plus one in Pascal's triangle toe work. But notice that my second coupling constant is a different value. It's 10. So now let's go ahead and use the same strategy. But now I have to go. Dammit! I didn't use the right number. Um, I have to go to and a half to the right and 2.5 to the left. So I'm just I said, damn it, because I have to go 0.5, um, 2.5 to 1 side and 2.5 to the other so I can make hertz on this side and I do the same thing. 2.5 on one side to five on the other, so I could go 10 hertz on the other. Now. What's going on, guys? What kind of shape am I getting? Okay, that's actually it. That's the final answer. So notice. First of all, what is the ratio is gonna be here for these splits. It's gonna actually be since nothing is overlapping, it's going to be one toe, one toe, one toe one. Okay, Now, notice that if the J value for H B had been the Samos h A, I would have that overlap in the middle, and I would get a triplet. But since the second J value is smaller, I don't get that overlap, and I get separate peaks instead. Okay, So notice that when I get here, if I were to troll it out, actually looks like this. It's just a bunch of single peaks. But now how maney do I get? I actually get four peaks instead of three. I would have expected three, but I'm getting four. It turns out that this type of arrangement is actually called a doublet of double. It's okay. So basically you had a doublet, and then you split it into another doublet. Okay? And any time you hear things like this doublet of doublet, there's even there's doublet of quartets. There's triplet, triplet, all this kind of stuff. If you hear anything like that, that has to do with Jay. Values being different. Okay, if you if you're Jay values are different from each other, then you get weird shapes, like double it of Dublin's. Okay, so now just once again to compare this and plus, one would have told me that I'm going to get a triplet and a 1 to 1 ratio when really what I'm getting is a doublet of doublet with a + ratio. So this is exactly the reason that we need to be able to draw tree diagrams. Because if you're professor wants you to be able to use different J values and plus one just doesn't cut it, you need to actually draw the entire thing to know what the shape is. Okay, now, just, you know, it could get more complicated. So imagine that instead of being split by two protons, I throw in the third one so Let's say that there was a J H. D. And it had another value of, let's say, 20 Hertz. Whatever. Let's say a smaller number, Let's say eight Hertz. Okay, then you would just keep going and you keep splitting. Do another layer until you split with all of your protons. Okay, In the end of the day, when you're drawing these things, the most important part is that you can get your ratios and they can draw right. If you don't remember the exact name of the weird arrangement, that's usually not a big deal. Okay, but if you draw it correctly, then you should be fine. Okay. So, guys, I hope that that helps to settle J values versus no J values. Andi, I hope that you can see that there's actually really related. It just depends on how complex your professor wants to make your life, how complicated they want to make it this semester. Okay, so that being said, let's move onto the next topic