a) The chemical shift from a certain frequency increases if the nucleus' frequency is high and if the frequency of the reference's nuclei is low. Given that 1H nuclei have high magnetic moments, how can I demonstrate why 1H nuclei show small chemical shifts (in the range of 0-12 ppm) whereas 13C nuclei show larger chemical shifts (in the range -10 to 240 ppm).
Let's try this again: chemical shift is the magnitude of the variation (compared to the resonance frequency), divided by the resonance frequency. Let's say the magnitude of the shielding is roughly the same for proton and carbon nuclei, because the types of chemical environments they are exposed to are going to be similar. But the reference point for proton nuclei is different than for carbon nuclei. Specifically the Larmor frequency of proton nuclei (the magnetic moment) is much bigger in the former than the latter. So similar magnitude variations are going to be smaller, relatively, for protons than for carbon nuclei. This translates into larger chemical shifts, generally, for carbon nuclei.
Analogy: let's say two people start a diet program. One of them weighs 100 pounds and one of them weighs 300 pounds. At the end of the month, the 100 pound person weighs 95 pounds and the 300 pound person weighs 295 pounds. Both have a wieght difference of five pounds. The diet company is interested in the % weight loss as a metric for success. Even though both have lost the same amount of weight, the 100 pound person lost 5% of their weight, but the 300 pound person lost 1.7% of their weight. The "weight shift" for lighter people tends to be larger than the "weight shift" for larger people. Carbon = light people. Hydrogen = heavy people. The "weight loss divided by initial reference weight" is chemical shift.
Make sense?
(This analogy pretends light people and heavy people tend to lose the same amount of weight when on a diet. This probably isn't true. But the analogous feature when "changes in resonance frequency" for carbon and hydrogen is roughly true.)
Obviously, this is likely a pretty big simplification of what is going on. Phosphorous NMR has large ppm ranges as well, but this is because the type of magnetic shielding is different*, and I can't say whether the large range of carbon may not have some similar reasoning. Calculating the actual magnetic field a nucleus experiences relies a lot on gradient and tensor math and complicated physics, but I still think the above explanation gives a reasonable picture - and is the way it was explained to me way back when. A true expert in NMR may have a much better explanation, though.
*The shielding constant is actually a tensor with both diamagnetic and paramagnetic terms. Phosphorus shifts are dominated by paramagnetic terms. If you really want to know the answer to this question, I have a book which provides a whole chapter's worth of information on factors which impact the shielding constant. I suspect the chemical shift range of carbon probably also has something to do with this. I can look through my materials and see what I can find, but I cannot provide an answer to you in the immediate future. Reason: I will be out of town for a while on business.
b) Where are the planes of symmetry in the chair conformation of cyclohexane? I've seen some weird NMR spectra to do with cyclohexane (leading on to adamantane etc.)
A tricky question. Cyclohexane is in D3d point group in a chair conformation. In a single chair there is a 3-fold axis of symmetry going down the middle of the molecule, 3 mirror planes which bisect the molecule and which include the principle rotation axis, a few improper rotation axes, as well as an inversion center. Anyway, there is rapid equilibrium between the two chairs at room temperature, so the axial and equatorial positions are actually averaged into a single peak, and every position becomes functionally equivalent (effectively one might think of it as D6h point group). This is why the NMR spectrum of cyclohexane consists of a single sharp resonance. If you cool the sample down enough, you'd see it split into two - one for the axial positions and one for the equatorial - but they'd still not split each other because each position is equivalent through symmetry.
c) How many peaks are there in the 31P spectrum of P4O6 and P4O10, and which nuclei do they correspond to?
My brief research establishes that P4O6 has a single resonance at -112.5 ppm (wrt phosphoric acid). I suspect P4O10 would be similar, although given that it's an anhydride of phosphoric acid, it is certainly possible that its spectrum might become complicated if there is any chemistry going on when the spectrum is acquired.
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Topic: NMR Coupling (Read 4140 times)