Topic 15 · page 24 of 28

Splitting and the (n + 1) rule

At high resolution a peak splits into a pattern. A hydrogen with n hydrogens on the adjacent carbon atoms gives n + 1 lines, with heights in the ratio of Pascal's triangle.

14 min read15.20(iii)

Read first: Proton NMR, environments and peak areas

Splitting at high resolution 15.20(iii)

At high resolution each peak you saw at low resolution splits into a group of lines. The splitting happens because the hydrogens on neighbouring carbon atoms act as tiny magnets and slightly change the field felt by the hydrogen being observed.

Number of neighbouring H, n Lines Name Relative heights
0 1 singlet 1
1 2 doublet 1 : 1
2 3 triplet 1 : 2 : 1
3 4 quartet 1 : 3 : 3 : 1
Four splitting patterns with line heights. A singlet has 1 line from no neighbouring hydrogens. A doublet has 2 lines in the ratio 1 to 1 from one neighbouring hydrogen. A triplet has 3 lines in the ratio 1 to 2 to 1 from two neighbouring hydrogens. A quartet has 4 lines in the ratio 1 to 3 to 3 to 1 from three neighbouring hydrogens.
The line heights follow Pascal's triangle: 1, 1 1, 1 2 1, 1 3 3 1.

Two rules about which hydrogens count:

Reading the splitting 15.20(iii)

Count the neighbouring hydrogens to predict the pattern.

Worked exampleEthyl ethanoate, CH₃COOCH₂CH₃

Predict the splitting of each peak.

  1. CH₃ next to C=O (a): the adjacent atom is the carbonyl carbon, which has no hydrogens, so n = 0 and the peak is a singlet (3 H, δ about 2.0).
  2. OCH₂ (b): the adjacent carbon is the CH₃, with 3 hydrogens, so n = 3 and the peak is a quartet (2 H, δ about 4.1).
  3. CH₃ of the ethyl group (c): the adjacent carbon is the CH₂, with 2 hydrogens, so n = 2 and the peak is a triplet (3 H, δ about 1.2).

A pair of linked groups split each other. In an ethyl group, CH₃–CH₂–, the CH₂ is a quartet because of the CH₃, and the CH₃ is a triplet because of the CH₂. This triplet plus quartet pair is the sign of an ethyl group in a spectrum.

Group Neighbouring H Pattern
CH₃ in CH₃CH₂– 2 triplet
CH₂ in –CH₂CH₃ 3 quartet
CH₃ in CH₃CHO 1 doublet
CHO in CH₃CHO 3 quartet
CH₃ bonded to C=O in a ketone, CH₃COCH₃ 0 singlet
CH₃ in (CH₃)₂CHOH, each 1 doublet

The area of a multiplet gives the number of hydrogens in the group, not the number of lines. The number of lines tells you about the neighbours. For example, a quartet with area 2 is a CH₂ (area 2) next to a CH₃ (3 neighbours).

Check yourself

  1. State the splitting pattern, with the number of lines, of a CH₂ group whose neighbouring carbon is a CH₃.
  2. Predict the splitting patterns of the hydrogens in (a) propanone, (b) CH₃CH₂Cl and (c) ethanal.
  3. In the spectrum of butanone, CH₃COCH₂CH₃, predict the pattern and area of each peak.
  4. Explain why the CH₃ in an ethyl group gives a triplet.
  5. A peak is a doublet with an area for 3 hydrogens. What group is next to this CH₃?

Answers cover these until you have tried the questions

  1. Quartet: 3 neighbouring hydrogens give 3 + 1 = 4 lines, in the ratio 1 : 3 : 3 : 1.
  2. (a) Propanone: a single singlet (all six hydrogens equivalent, no neighbouring H). (b) CH₃CH₂Cl: the CH₃ is a triplet and the CH₂ is a quartet. (c) Ethanal: the CH₃ is a doublet (1 neighbour, the CHO hydrogen), and the CHO hydrogen is a quartet (3 neighbours).
  3. CH₃CO–: singlet, area 3 (no neighbouring H). –CH₂–: quartet, area 2 (next to CH₃). –CH₃: triplet, area 3 (next to CH₂).
  4. The CH₃ has two hydrogens on the adjacent CH₂, so n = 2, and it gives 2 + 1 = 3 lines, in the ratio 1 : 2 : 1.
  5. A doublet means one neighbouring hydrogen, so the CH₃ is next to a CH group, as in (CH₃)₂CHOH or CH₃CHO.