n+1 rule
Summary
In ¹H NMR, a proton (or set of equivalent protons) with n equivalent neighboring protons on the adjacent atom is usually split into n + 1 peaks. Testable point: an ethyl group gives a triplet (CH₃) and a quartet (CH₂). Equivalent protons do not split each other, and OH protons often appear unsplit.
Detail
Meaning: Spin-spin coupling occurs because the magnetic fields of neighboring protons slightly add to or subtract from the applied field, so one signal splits into a multiplet. Neighbors are protons on adjacent atoms (H–C–C–H). Peak heights follow Pascal's triangle: doublet 1:1, triplet 1:2:1, quartet 1:3:3:1, and so on. The spacing between peaks is the coupling constant J, which is the same in the two coupled signals.
Equation: Number of peaks = n + 1, where n = the number of equivalent protons on adjacent atoms (a unitless count). Peak spacing is J, in Hz.
On the MCAT: You are given a formula and a spectrum, and you assign the signals. Ethyl: CH₃ has 2 neighbors, so a triplet; CH₂ has 3 neighbors, so a quartet. Isopropyl: the CH is a septet (6 neighbors) and the CH₃ groups are a 6H doublet. A group with no adjacent H, such as the CH₃ of an methyl ketone, is a singlet. Combine splitting with integration (relative number of H) and chemical shift (environment) to choose among isomers.
Common confusion: Students count the protons on the signal's own carbon instead of its neighbors. Protons that are equivalent do not split each other. Protons separated by an O or other heteroatom (CH₃–O–CH₂) are generally too far to couple. OH and NH protons often show as unsplit singlets because of rapid exchange. If the neighbors are not equivalent, the simple n + 1 count does not apply and the pattern is more complex.
Sources
- Organic Chemistry (Clayden)
- Organic Chemistry (Wade)
- Spectrometric Identification of Organic Compounds (Silverstein)
Written for the MCAT and checked before it was published. For study reference only. Spotted an error? Let us know.