1H NMR: Spin-Splitting Complex Tree Diagrams

So now moving on to drawing complex tree diagrams which really should be the only type of tree diagram you ever draw since I already proved to you that you don't need to draw a simple tree diagrams to get the right shape so as I said we're going to 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 to always split an order of the highest J value first and then go to your lower J values later so always go from the highest Hertz to the lowest Hertz, OK? Now before kicking this question off and really drawing the whole thing I want to analyze it according to N+1 and then compare our answer at the end to what N+1 would have predicted so it says here use a tree diagram to predict the splitting pattern of the bolded proton which in this case is Hc and first of all What Would N+1 one 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 the 0, right? Because there's nothing there if we go to the right how many protons are we getting split by? 2, Ha and Hb so that means according to N+1 and N equals 2 so then it should be 2+1=3 so that N+1 rule if I were just to stick with that should be a triplet, OK? And we know that triplets come with a 1:2:1 ratio so that's what Pascal's rule tells me and unfortunately if you stop there you would actually get this question completely wrong, why? Because look these J values for Ha and Hb are actually not the same they're different JHa does not equal JHb so I can't use Pascal's Triangle I can't use N+1, OK? 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 should I get to split with the first, should I split with the J value from Ha or the J value from Hb? Ha because it's bigger remember I said you always start with the bigger value first so I'm going to start off with the singlet that Hc would have given me, OK? So this is Hc if it wasn't being split it would just be a singlet but I'm going to start off with Ha the split from Ha is a value of 16, now I don't have enough I guess cubes whatever I don't have enough units here so that every single unit or box is going to be equal to 1 so instead let's use 2 let's say that every box is equal to a split to 2 Hertz, OK? So if we're trying to split by 16 Hertz at the beginning that means that I have to go 4 to the right and 4 to the left to make 8 boxes or equal to 16 so basically what I'm saying here is that one of these is equal to 2 Hertz hope you guys can Let me get away with that one, OK? So we're going to go 4 to the right for the left that's going to give me a split of that's Ha and that's going to give me a split of 16 Hertz, OK? And so far, what we get we are getting? We are getting a doublet, OK? So far so good looks like a double it looks like a 1:1 ratio so nothing too crazy, OK? This is exactly would expect to see with N+1, OK? Now the difference is that if I was using N+1 the split for Hb would have to be what number as well? 16, it would have to have the same coupling constant for N+1 in Pascal's Triangle to 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....Damn it I didn't use the right number I have to go 2.5 to the right and 2.5 to the left so I said damn it because I have to go 0.5, 2.5 to one side and 2.5 to the other so I can make 10 hertz on this side and I do the same thing 2.5 on one side 2.5 on the other so I can go 10 Hertz on the other now what's going on guys? What kind of shape am I getting, OK? That's actually it that's the final answer so notice first of all what are the ratios going to be here for these splits? It's going to actually be since nothing's overlapping it's going to be 1:1:1:1, OK? Now notice that if the J value for Hb had been the same as Ha I would have that overlap in the middle and I would get a triplet but since the second J value smaller I don't get the overlap and I get separate peaks instead, OK? So notice that what I get here if I were to draw it out actually looks like this it's just a bunch of single peaks but now how many do I get? I actually get 4 peaks instead of 3, I would have expected 3 but I'm getting 4 it turned out that this type of arrangement is actually called a doublet of doublets, OK? So basically you had doublet and then you split it into another doublet, OK? And any time you hear things like this Doublet of doublet there's even there's doublet of quartet there's triplet of triplet all this kind of stuff if you hear anything like that that has to do with J values being different, OK? If your J values are different from each other then you get weird shapes like doublet of doublets, OK? So now just once again to compare this N+1 would have told me that I'm going to get a triplet and a 1:2:1 ratio when really what I'm getting is a doublet of doublet with a 1:1:1:1 ratio so this is exactly the reason that we need to be able to draw tree diagrams because if your professor wants you to be able to use different J values N+1 just doesn't cut it and you need to actually draw the entire thing to know what the shape is, OK? Now just so you know it can get more complicated so imagine that instead of being split by 2 protons I throw in a third one so let's say that there was a JHd and it had another value of let's say 20 hertz or whatever let's say a smaller number let's say 8 hertz, OK? Then you just keep going and you keep splitting to do another layer until you split with all of your protons, OK? In the end of the day when you're drawing these things the most important part is that you can get your ratios and that you can draw it right if you don't remember the exact name of the weird arrangement that's usually not a big deal, OK? But if you draw it correctly then you should be fine, OK? So guys I hope that that helps to settle J Values No J values and I hope that you can see that there's actually really related it's just depends on how complex your professor wants to make your life, how complicated they want to make it the semester, OK? So that being said let's move on to the next topic.