### Integration of ^{1}H NMR spectra

The area under each pattern is obtained from integration of the signal (or better the function that defines the signal) and is proportional to the number of hydrogen nuclei whose resonance is giving rise to the pattern. The integration is sometimes shown as a step function on top of the peak with the height of the step function proportional to the area. The integration of the patterns at 1.1, 2.4, and 3.7 ppm for methyl propanoate is approximately 3:2:3 (see figure 22). Note, the error in integration can be as high as 10% and depends upon instrument optimization. The integration of an ^{1}H NMR spectrum gives a measure of the proton count adjusted for the molecular symmetry. Methyl propanoate has no relevant molecular symmetry and so, the integration gives the actual proton count: 3+2+3=8 protons. In contrast diethyl ether (Et-OEt) has a plane of symmetry which makes the two ethyl groups equivalent, and so, only two signal are observed, a triplet and a quartet, with integration 3:2.

The areas represented by the integration step function is usually integrated by the instrument and displayed as numerical values under the scale. For instance, the normalized integration values for 2-butanone are shown in Figure 27. Note that these values are not exact integers and need to be rounded to the nearest integer to obtain the proper value.

next section: Integration of NMR spectra, ^{13}C

Copyright information: Original content © University of Colorado, Boulder, Chemistry and Biochemistry Department, 2011. The information on these pages is available for academic use without restriction.