In a 1H NMR spectrum, the area under the signals is proportional to the number of hydrogens giving rise to the signal. As a result the integration of the spectrum is a measure of the proton count. In a 13C NMR spectrum the area under the signal is not simply proportional to the number of carbons giving rise to the signal because the NOE from proton decoupling is not equal for all the carbons. In particular, unprotonated carbons receive very little NOE, and their signals are always weak, only about 10% as strong as signals from protonated carbons.
Because the resolution in 13C NMR is excellent, the number of peaks in the spectrum is a measure of the carbon count adjusted for the symmetry of the molecule. For example, hexane gives three peaks: the two methyls are equivalent as are two sets of methylenes. Several examples are analyzed as follows; the chemical shifts shown are not the observed values but calculated values from empirical rules:
Hexane shows three peaks, two methyls and two sets of methylenes.
Acetone shows two peaks, one for the methyls and one for the carbonyl carbon.
Ethyl benzoate shows 7 peaks; the benzene ring shows only 4 peaks because of two sets of equivalent carbons.
Ethyl 3-chlorobenzoate, however, shows 9 peaks, a separate signal for each carbon because it has no symmetry.
Cis-1,2-dimethylcyclohexane shows 4 peaks; because of rapid chair-chair interconversion, we can analyze the NMR spectrum in terms of a flat structure; hence, the methyls are equivalent, as are the methines, and there are two sets of equivalent methylenes.
next section: NMR solvents
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