Interpreting the Carbon-13 NMR spectrum of 2-methylpropane (isobutane)

Doc Brown's Chemistry Advanced Level Pre-University Chemistry Revision Study Notes for UK IB KS5 A/AS GCE advanced A level organic chemistry students US K12 grade 11 grade 12 organic chemistry courses involving molecular spectroscopy analysing C-13 NMR spectra of 2-methylpropane

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TMS is the acronym for tetramethylsilane, formula Si(CH₃)₄, whose ¹³C atoms are arbitrarily given a chemical shift of 0.0 ppm. This is the 'standard' in ¹³C NMR spectroscopy and all other ¹³C resonances, called chemical shifts, are measured with respect to the TMS, and depend on the individual (electronic) chemical environment of the ¹³C atoms in an organic molecule - 2-methylpropane here.

2-methylpropane  C₄H₁₀         

For more see The molecular structure, classification and naming of alkanes

Interpreting the C-13 NMR spectrum of 2-methylpropane

As you can see from the diagram above there are 2 different chemical shift lines in the C-13 NMR spectrum of 2-methylpropane indicating 2 different chemical environments of the 2 carbon atoms of 2-methylpropane.

CH₃CH(CH₃)CH₃  or  (CH₃)₃CH

(Note the 2 different colours indicating the 2 different chemical environments of the 4 carbon atoms in 2-methylpropane).

¹³C chemical shifts (a) to (b) on the C-13 NMR spectrum diagram for 2-methylpropane.

There are only two possible chemical environments of the carbon atoms because of the symmetry of the 2-methylpropane molecule.

Three of the carbon atoms (of the methyl groups) have the same chemical environment and so have the same 13C chemical shift.

The carbon-13 NMR spectra provides direct evidence of 2 different carbon atom environments for the 4 carbon atoms in the 2-methylpropane molecule, deduced from the presence of 2 different 13C NMR chemical shifts (ppm).

Comparing the infrared, mass, 1H NMR and 13C NMR spectra of the 2 alkane isomers of C4H10 NOTE: The images are linked to their original detailed spectral analysis pages AND can be doubled in size with touch screens to increase the definition to the original butane and 2-methylpropane image sizes.
The infrared spectra of butane and 2-methyl propane are quite similar, mainly due to C-H stretching and deformation vibrations, but you can see significant differences in the fingerprint region at wavenumbers 1500 to 600 cm-1.
The mass spectra of butane and 2-methyl propane are quite similar and both have a base ion peak of m/z 43 [C3H7]+, but here significant differences in the ratios of the m/z ions 27 to 29 [C2H3,4,5]+.
The 1H NMR spectra of butane and 2-methyl propane are quite similar in that both show the 8 hydrogen atoms exist in only 2 different chemical environment. However, they can be distinguished from each other by the different integrated proton ratios. Butane gives a (2) : (3) proton ratio and 2-methylbutane a (1) : (9) proton ratio.
The 13C NMR spectra of butane and 2-methyl propane are quite similar in that both show the 4 carbon atoms exist in only 2 different chemical environments. I'm not sure how reliable the pair of 13C chemical shifts for 2-methylpropane are, which seem surprisingly close together? The other pair are reliable.