Chapter 13: Spectroscopy

Integration

The issues to understand from this page are:

• What do we mean by integration ?
• How do we measure the integration ?
• Using the information
• Practical limitations

What do we mean by integration ?

Integration is a mathematical term that means the area under a curve. In NMR, the curve is the spectra, and the integration is a measure of the area of the peaks in the spectra. The key thing, is that the area of the peak is proportional to the number of atoms that it represents. So in an H NMR, the integration of a peak gives the area of the peak and this area gives us a measure of the number of H atoms it represents, i.e. the number of H of that type. In many modern NMR spectra, the peaks on the spectra often look to be "lines" rather than peaks, and this tends to lead to students thinking about peak height rather than area... but it is the area that is important.

How do we measure the integration ?

There are two methods that may be encountered. First though, we should point out that the area is measured by the spectrometer itself and plotted on the spectra, we are talking about what we need to do to interpret that information:

1. Numbers on spectra method (modern) The numbers are typically printed under the peak, often with a bar or two marks that represent the limits of the integration (i.e. the x axis start and end points for the area measurement). FYI : the limits are set by the person processing the spectrum. In the example to the right, the green bar shows the limits and the area = 3.00

2. Steps on integration curve (traditional) Older instrumentation used to plot a second curve (in the example to the right in blue) above the actual spectra where the integration was recorded as a series of steps. The height (represented by the arrow in the furthest right image) of this step needs to be measured with a ruler and recorded (e.g. in mm) and then compared to other steps in the same spectrum to get the relative ratio.

Using integration information

• Integration can only tell you the relative ratio of the number of H of each type. So for example, you can't get a useful integral if there is only 1 type of H.
• The sum of the integrals represents the empirical number of H and can the related to the molecular formula.
• So (integral sum) x (an integer) = number of H in molecular formula.
• Number of aromatic H on a benzene ring or vinyl H on an alkene can establish the number of substituents present.

Limitations

• Under normal conditions, the accuracy is likely close to + or - 5%. This can be improved if required by modifying the experimental conditions.
• Overlapping peaks make the situation more difficult, but a total area for the overlapping peaks should be possible.
• Exchangeable H (e.g. -OH) often integrate low. This can be improved if required by modifying the experimental conditions.
• Integral accuracy is affected by sample quality and processing so it is important to pay attention to these factors.

© Dr. Ian Hunt, Department of Chemistry