Quick questions on Proton and carbon-13 NMR explained: HSC Chemistry Module 8

Nuclei with a non-zero spin (spin-half nuclei like $^1H$ and $^{13}C$) behave as tiny magnets. In a strong external magnetic field they take one of two orientations (aligned or opposed) with a small energy gap between them. Irradiating the sample with radiofrequency energy matched to that gap causes the lower-energy nuclei to flip to the higher state; this is resonance. The frequency at which resonance happens depends slightly on the local electron density around the nucleus, which differs for each chemical environment.

Tetramethylsilane $(CH_3)_4Si$ has 12 equivalent protons in a single environment, all with very low resonance frequency (silicon is more electropositive than carbon, so the methyls are electron-rich and shielded). Chemical shifts are positive to the left (downfield, deshielded) and zero at TMS.

1. Number of signals. Each unique proton environment gives one signal. Symmetry can make two formally different protons equivalent. For example, all three protons in $CH_3$ are equivalent.

$^{13}C$ NMR is run proton-decoupled as standard, which collapses all couplings and gives a singlet for each unique carbon environment. The spectrum tells you two things:

1. From molecular formula (from mass spectrometry), compute the degree of unsaturation $= (2C + 2 - H + N - X)/2$. 2. Count $^{13}C$ peaks. That fixes the number of unique carbon environments.

NMR is the most informative single technique for organic structure determination. Combined with mass spectrometry (molecular mass) and IR (functional groups), the three give an essentially complete picture.

Strengths. Non-destructive (sample is recovered after analysis), enormously information-rich, distinguishes isomers that IR and mass spectrometry cannot (e.g. propan-1-ol vs propan-2-ol from chemical shift and multiplicity patterns).

Each unique proton environment gives one signal. Symmetry can make two formally different protons equivalent. For example, all three protons in $CH_3$ are equivalent.

Tells you the electronic environment of the proton.

The area under each signal is proportional to the number of equivalent protons in that environment. The spectrometer reports areas as a step trace; the ratio of step heights gives the proton ratio. Integration is what distinguishes a methyl (3H) from a methylene (2H) at similar chemical shift.

Spin-spin coupling to neighbouring protons splits each signal into a multiplet. The rule:

Non-destructive (sample is recovered after analysis), enormously information-rich, distinguishes isomers that IR and mass spectrometry cannot (e.g. propan-1-ol vs propan-2-ol from chemical shift and multiplicity patterns).

Needs tens of milligrams of dissolved sample (compared to nanograms for mass spec). $^{13}C$ has poor sensitivity due to 1.1% natural abundance. Solvent peaks (and water from $-OH$) can obscure regions of the spectrum.

The $n+1$ rule uses the number of protons on the adjacent carbon, not on the carbon itself.

Three equivalent protons of a $CH_3$ do not split each other. They appear as a single multiplet with shape determined by the neighbours.