Organic Chemistry I For Dummies, 2nd Edition
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You can use integration curves on the nuclear magnetic resonance (NMR) spectrum to show peak intensities. The peak intensity — or the area underneath a peak on the NMR spectrum — is related to the number of hydrogens that the peak represents.

Traditionally, integration is shown on the spectrum by the addition of an integration curve (as shown in the figure), although modern computing has made digital integration common that doesn't require you to do any measuring. The height of this integration curve is proportional to the area underneath a peak, so this height is proportional to the number of hydrogens the peak represents. (The width of the curve is unimportant.)

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Integration curves and hydrogen peaks on an 1H NMR spectrum
To measure the height of an integration, you start at the bottom of the integration curve where it's flat, and measure to where the curve goes flat again. Unfortunately, integration can't tell you how many hydrogens each peak represents — it just tells you the relative ratios of hydrogens in one type of chemical environment compared to those in another environment. This makes integration useful only for organic molecules that contain more than one kind of hydrogen (which, fortunately, is most of them).

For example, if there are two peaks, one with an integration curve that's 2 cm high and one with an integration curve that's 1 cm high, this tells you that the larger peak represents twice as many hydrogens as the smaller one (refer to the first figure).

This does not mean that the larger one represents two hydrogens and the smaller represents one hydrogen, necessarily — although this could be the case. It simply tells you that the ratio of hydrogens in the two chemical environments is 2:1. The next figure shows you how to measure an integration with a ruler.

How to measure the height of integration curves.

Measuring the height of an integration curve

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Arthur Winter, PhD, is a chemistry professor at Iowa State University.

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