1.7. What Can We Learn? Relative Numbers of H’s

There are four practical pieces of information that can be extracted from a typical ¹H NMR spectrum. The second of these is the relative numbers of different “types” of hydrogens in the sample (the ratio of hydrogen atoms in each different chemical environment in the sample). For now, the differences in shape for each signal (see Section 1.9) should be ignored.

1.7.1. Area Under the Curve and Proportionality

Because of how the data is collected during the FID period the signal strength is directly proportional to the number of hydrogen atoms in that chemical environment. Once this is converted into an NMR spectrum the “area under the curve” for each signal is proportional. Determining these values requires integral calculus, but the computer can do this as part of the data processing.

1.7.2. How To Determine the Relative Numbers of H’s

There are two systems for reporting integration on an NMR spectrum. Under the older system an integral line is added near each signal (Figure 1.19).

Figure 1.19 – Example of a ¹H NMR Spectrum with Traditional Integration.

The height of the line is proportional to the number of hydrogen atoms that gave rise to that signal. The reader is required to interpret the heights and translate them into ratios manually (Figure 1.20). This approach is rarely used in modern practice but may be encountered in some sources.

Figure 1.20 – Example of Interpreting Traditional Integration on a ¹H NMR Spectrum.

Under the newer system an integral line is added near each signal and an integral value is reported (Figure 1.21). Occasionally, only the integral values are shown for simplicity.

Figure 1.21 – Example of a ¹H NMR Spectrum with Modern Integration.

This approach is much more commonly used. Typically, the integral values may be used directly: a signal with integration of 2.0 usually represents two chemically equivalent hydrogen atoms. However, this is not always true. Note that the y-axis in an NMR spectrum is actually unitless. This means the integration values are not directly physically meaningful. Technically, only the ratio between integrals is significant. For example (Figure 1.22), pentan-3-one is symmetrical and has two sets of chemically equivalent hydrogens: a group of four (red) and a group of six (blue). However, instead of a 4:6 ratio of integrations the computer would typically report 2:3 (the reduced fraction). It is important to keep this in mind when predicting or interpreting spectral data (see Sections 1.11 and 1.12). Notably, the actual number of hydrogens represented by each signal will always be an integer multiple of the integrations. In this case multiplying all of the integrations by 2 gives the correct number of hydrogen atoms represented.

Figure 1.22 – ¹H NMR Spectrum for Pentan-3-one with Modern Integration as the Reduced Fraction.