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Analytical Chemistry

Pascal's triangle

Definition and meaning of Pascal's triangle in chemistry.

Pascal's triangle is a famous triangular array of binomial coefficients that is practically utilized in chemistry to accurately predict the relative intensity ratios of multiplet peaks in NMR spectroscopy.

In more detail

In nuclear magnetic resonance (NMR) spectroscopy, the phenomenon of spin-spin coupling causes the signal peak to undergo observable splitting. When a target nucleus couples with equivalent neighboring nuclei possessing a specific spin, the resulting signal cleanly splits into a multiplet. The relative intensity ratios of these split peaks directly correspond to the numerical coefficients found in the specific row of Pascal's triangle. This reliable mathematical relationship makes the triangle an essential diagnostic tool for structurally interpreting complex NMR spectra.

Key facts

FieldAnalytical Chemistry
Analytical applicationNuclear magnetic resonance spectroscopy
Primary usePredicting multiplet peak intensity ratios
Governing ruleThe n+1 splitting rule
Example

If a specific proton in an NMR spectrum is directly adjacent to two equivalent protons, its signal splits into a distinct triplet with peak intensities in a 1:2:1 ratio, matching the second row of Pascal's triangle.

Frequently asked questions

Does Pascal's triangle apply to all observed NMR peak splitting?

No, it applies specifically to first-order splitting generated by equivalent neighboring nuclei with a spin of 1/2, such as common protons or carbon-13 atoms.