Integration Traces

In a ¹H NMR spectrum, the area under each peak is proportional to the number of H atoms in that environment. Peak heights can be misleading, because peaks have different widths and may be split, so spectrometers draw an integration trace.The integration trace is a line that runs across the spectrum and rises in a step over each peak. The height of each step is proportional to the area of the peak below it, and so to the number of H atoms in that environment.To use it, measure each step height and find the simplest whole-number ratio. The ratio gives the relative numbers of H atoms, not necessarily the actual numbers. Use the molecular formula to scale the ratio so it adds up to the total number of H atoms.Worked example: a compound C₄H₈O₂ has three peaks with integration step heights of 0.8 cm, 1.2 cm and 1.2 cm.
Divide by the smallest: 0.8/0.8 = 1, 1.2/0.8 = 1.5, 1.2/0.8 = 1.5. The ratio 1 : 1.5 : 1.5 becomes 2 : 3 : 3 when doubled.
Total 2 + 3 + 3 = 8, which matches the 8 H atoms in the formula. So the environments contain 2, 3 and 3 H atoms, consistent with one CH₂ group and two different CH₃ groups, as in ethyl ethanoate.If the ratio adds up to less than the number of H atoms, multiply it up. For example, a ratio of 1 : 3 for a compound with 8 H atoms means the environments contain 2 and 6 H atoms.