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I do not fully understand the idea of coupling and why chemically equivalent hydrogens do not couple.

I wanted to work with the alkanes, so let's take propane first:

Propane

There would be a triplet signal due to the $\ce{CH3}$ groups in blue and green, due to the $n+1$ rule for neighbouring protons, so the neigbouring carbon for the two $\ce{CH3}$ groups would be the $\ce{CH2}$ group circle in red.

Then the $\ce{CH2}$ group in red would have a septet signal due to the two surrounding $\ce{CH3}$ groups is what I would predict.

Moving on to butane, this is where I get more confused:

Butane

For the $\ce{CH3}$ group in blue, there would be a triplet signal due to the neighbouring $\ce{CH2}$ in red, and the same can be said for the $\ce{CH3}$ in black.

Then for the $\ce{CH2}$ groups, I am not exactly sure what would happen but here is what I think:

The $\ce{CH2}$ group in red will have a quartet signal on the NMR spectrum because equivalent hydrogens do not couple and so the $\ce{CH2}$ will not couple with the green $\ce{CH2}$ group. This means that only the $\ce{CH3}$ group will couple. Using the $n+1$ rule, a quartet will be present and the same can be said for the $\ce{CH2}$ group in green. However, I think that the red $\ce{CH2}$ will have a triplet of quartets or a multiplet if that is correct, with the same being said for the green $\ce{CH2}$ group.

I would like to extend this further to pentane, which I am also confused about. Can this be clarified with the two examples above so that I can attempt to do pentane myself?

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Unfortunately, although the answer given by bon provides a very simplistic answer to a fairly common NMR-101 problem, it is not quite correct. It is fine for the propane case, but falls short for butane. While a very simple molecule, butane has a complicated spectrum because, though the two methylene groups are chemically equivalent, they are in fact magnetically non-equivalent. It serves as an example of how all too often NMR is poorly taught at the introductory level.

First, let's clarify a minor point of confusion that is widely taught at introductory levels - that equivalent protons do not couple to each other. They do; the reason that the coupling is not seen is that the transitions are degenerate and so sit directly on top of each other (ie not observable). Remember that the observed lines in a spectrum are the energy transitions between stable spin states - if the energy difference between two states is equivalent, then the lines in the spectrum are degenerate.

So, a better generalisation for interactions giving rise to splitting in a spectrum is that:

  • Coupling between magnetically equivalent nuclei cannot be detected and does not affect the appearance of the spectrum
  • Coupling between chemically equivalent, but magnetically non-equivalent nuclei will usually affect the appearance of the NMR spectrum; commonly seen in second order effects like that of AA'BB' systems.

Second, then, to see what a 1H spectrum of butane really looks like (well, a more realistic simulation at least):

Below is a more realistic simulated spectrum of butane (at 400MHz), which takes into account the fact that the two methylene groups couple to each other, with an average coupling of about 6.6Hz. Complicated isn't it? Have a read of Glenn Facey's page on his NMR blog, (an excellent NMR resource) where he discusses this very problem.

Simulated 1H NMR spectrum of butane

So why is the case? Well, we need to look at what gives rise to magnetic non-equivalence in molecules. There is an excellent on-line resource to explain about symmetry and non-equivalence at Hans Reich's NMR page. But for butane, let us consider the Newman projections:

Newman projections of butane

At no time is the coupling between H2 and H3 the same as H2' and H3. Either it is psuedo-trans or pseudo-cis, but never the same. So, H2 and H2' are non-equivalent, and this will result in non-degenerate transitions, giving rise to complicated splitting patterns in the NMR spectrum. This is the same for other straight chain alkanes, with decreasing complexity as the chain length grows.

And just to show what a real spectrum of butane looks like: reproduced from Tynkkynen et al. (Magn. Reson. Chem. 2012, 50, 598–607), showing the real and calculated (at 500MHz):

Real spectrum of butane

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  • $\begingroup$ long wrote, "At no time is the coupling between H2 and H3 the same as H2' and H3" (that last H3 should be H3' right?). Aren't those couplings equivalent (or enantiotopic) in the anti-conformation pictured in the center of your figure? $\endgroup$ – ron Aug 19 '15 at 0:33
  • $\begingroup$ For the anti conformer (centre), J2,3 != J2',3, so H2 and H2' are not equivalent in this environment. For the gauche conformers (left and right), the couple pairs J2,3 != J2',3 OR J2,3' != J2',3', again introducing non-degeneracy. Anti/gauche equilibrium is temperature dependent for these molecules, and the observed J2,3, J2,3' couplings can be used to calculate the equilibrium populations of conformers. At 300K, J2,2=-13.3, J2,3=6.12, J2,3'=8.66Hz $\endgroup$ – long Aug 19 '15 at 1:10
  • $\begingroup$ Very interesting - I too was never taught this. $\endgroup$ – bon Aug 19 '15 at 9:44
  • $\begingroup$ I know that this may be a little off topic from what you have just said but what would a multiplet be and how would that form? $\endgroup$ – user258521 Aug 19 '15 at 12:21
  • $\begingroup$ Also, I tried using the simplified spectra predictor from 'bon' and came up with this for pentane. [nmrdb.org/new_predictor/index.shtml?v=v2.17.5] Why does it show 6 peaks for the CH2 group attatched to the CH3's when we just said that equivalent groups do not couple, surely the CH2 groups attatched to the CH3's should produce a quartet if we use the simplified way of looking at the problem? I also noticed the central CH2 group had singlets only, which is what would be predicted as equivalent hydrogens do not couple. Have I gone wrong here? $\endgroup$ – user258521 Aug 19 '15 at 12:27
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Your analysis is mostly correct.

Propane

The blue and green $\ce{-CH3}$ groups are chemically equivalent and so will produce a single triplet signal because they couple to the two hydrogens in the red $\ce{-CH2 -}$ group. The red $\ce{-CH2 -}$ group will produce a septet (split into 7) signal due to the six equivalent hydrogens adjacent to it.

enter image description here

Butane

Note: This is actually a simplified view of butane's spectrum. See @long's answer for a more detailed analysis.
The black and blue $\ce{-CH3}$ groups are chemically equivalent and each couple to two equivalent protons, meaning that the two $\ce{-CH3}$ groups as a whole produce only one triplet signal. The red and green $\ce{-CH2 -}$ groups are chemically equivalent and so will not couple with each other, despite being adjacent, but each one will couple with the $\ce{-CH3}$ group next to it, producing a single quartet signal which represents both groups.

enter image description here

Spectra predicted using the free tool found here.

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  • $\begingroup$ Unfortunately had to give this a -1 because the case for butane is actually incorrect. Butane and short chain alkanes should not really be used in teaching NMR at an introductory level, because they actually have far more complicated spectra than this. Nice answer for propane, though. $\endgroup$ – long Aug 19 '15 at 0:17
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Indeed. The simulated spectrum is not correct. Because to simulate it was necessary to split the system and then the secondary effect of coupling constants is not considered. You need to run a simulation of the whole system. In this case you get the same spectrum as posted before: enter image description here

I'm using the same tool as you, but I set the cluster size to 10 http://www.nmrdb.org/new_predictor/index.shtml?v=v2.17.5

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