School Chemistry — Grades 1 to 12 · Grades 1–12

38Proton NMR

In a hospital, a patient lies inside the ring of an MRI scanner, and an image of the soft tissues of the body appears on the screen, built from the answers of the hydrogen nuclei of its water and fats. In a chemistry laboratory, a small glass tube holding a few milligrams of a compound is lowered into the bore of a powerful magnet, and a spectrum appears built the same way: a strong magnet, a radio signal, and hydrogen nuclei answering it. In the chemist’s spectrometer each hydrogen nucleus answers a little differently according to its neighbours, and the spectrum is a map of the hydrogen atoms of the molecule.

You already know

An infrared spectrum shows which bonds a molecule contains (Chapter 34). Functional groups, families and isomers (Chapter 33, Chapter 32).

An MRI scanner: the same physics as the chemist’s NMR spectrometer.

38.1 Protons in a magnetic field

The nucleus of a hydrogen atom is a single proton. Placed in a strong magnetic field, it absorbs radio waves of a precise frequency; how and why belongs to physics, and is not needed here. What matters to the chemist is that the electrons around a proton shield it slightly from the field, and that this shielding depends on the atoms nearby: a proton next to an electronegative oxygen atom, which pulls electrons away, absorbs at a slightly different frequency from a proton in a hydrocarbon chain. The differences are tiny, a few millionths of the frequency, and are given in parts per million.

Definition 38.1 (NMR spectrum, chemical shift)

A proton NMR spectrum (nuclear magnetic resonance) shows the signals absorbed by the hydrogen nuclei of a compound. The position of a signal is its chemical shift $\delta$ , in parts per million ( $\mathrm{ppm}$ ), measured from the signal of a reference compound, tetramethylsilane $\ce{Si(CH3)4}$ (TMS), set at $\delta = 0$ . The $\delta$ axis is drawn increasing from right to left.

Proposition 38.2 (The shift depends on the neighbours)

The chemical shift of a proton depends on the atoms close to it: the nearer it is to an electronegative atom or a double bond, the larger its shift. Typical ranges, in $\mathrm{ppm}$ :

environment	$\delta$	environment	$\delta$
$\ce{CH3}$ in a chain	0.7–1.3	$\ce{H-C-O}$ (alcohol, ether, ester)	3.3–4.5
$\ce{CH2}$ in a chain	1.2–1.6	$\ce{H-C=C}$	4.5–6.5
$\ce{H-C-C=C}$	1.6–2.2	H on a benzene ring	6.5–8.0
$\ce{H-C-C=O}$	2.0–2.4	aldehyde $\ce{-CHO}$	9.7–10.0
$\ce{H-C-X}$ (halogen)	2.5–4.0	acid $\ce{-COOH}$	11.0–12.0

Proof. Measured on many compounds. An electronegative neighbour draws electrons away from the proton, which is less shielded and absorbs at a larger shift. ∎

Where protons absorb, by environment. Protons close to oxygen, to a double bond or to an acid group appear at the left of the spectrum.

In the lab — Preparing an NMR tube

A few milligrams of the compound are dissolved in about $0.6\,\mathrm{mL}$ of a solvent whose hydrogen atoms have been replaced by deuterium ( $\ce{CDCl3}$ , deuterated chloroform), which gives no signal; a trace of TMS is added as the reference. The solution is filtered into a thin glass tube, which is capped, labelled and lowered into the magnet.

38.2 Equivalent protons

Definition 38.3 (Equivalent protons)

Protons are equivalent protons if they have the same environment in the molecule, so that they absorb at the same shift. Each group of equivalent protons gives one signal. The three protons of a $\ce{CH3}$ group are always equivalent.

Example 38.4 (Counting groups)

Propanone, $\ce{CH3-CO-CH3}$ , has six protons but one group: the two $\ce{CH3}$ are alike, one on each side of the $\ce{C=O}$ . Ethanol, $\ce{CH3-CH2-OH}$ , has three groups ( $\ce{CH3}$ , $\ce{CH2}$ , $\ce{OH}$ ), and ethyl ethanoate, $\ce{CH3-CO-O-CH2-CH3}$ , three as well: the $\ce{CH3}$ next to $\ce{C=O}$ , the $\ce{CH2}$ next to $\ce{O}$ , and the $\ce{CH3}$ at the end.

38.3 Integration

Definition 38.5 (Integration curve)

The integration curve of an NMR spectrum is a curve, drawn above the signals, that rises by a step at each signal: the height of each step is proportional to the number of protons that give that signal.

Example 38.6 (Reading the steps)

In the spectrum of ethanol, the steps above the three signals measure 2, 1 and 3 units, from left to right: $\ce{CH2}$ , $\ce{OH}$ and $\ce{CH3}$ . Only the ratios count: steps of 12, 6 and 18 mm say the same thing.

38.4 Multiplicity and the $n+1$ rule

Definition 38.7 (Multiplet, $n+1$ rule)

A signal is often split into several close lines: a multiplet (singlet, doublet, triplet, quartet, … for 1, 2, 3, 4 lines). By the $n+1$ rule, a group of equivalent protons whose neighbouring carbon atoms carry $n$ protons in all, not equivalent to it, gives a signal of $n+1$ lines, with intensities in the ratios of Pascal’s triangle.

Proposition 38.8 (Splitting by neighbours)

In a molecule $\ce{CH3-CH2-X}$ (X without hydrogen), the $\ce{CH3}$ signal is a triplet (2 neighbouring protons) and the $\ce{CH2}$ signal a quartet (3 neighbouring protons). Protons bonded to an oxygen or a nitrogen atom usually give a singlet and do not split their neighbours.

Proof. Admitted: each neighbouring proton slightly shifts the signal up or down according to its own state, and the combinations give $n+1$ lines; the physics is explained in the Year 1 volume. Protons on O or N are exchanged quickly between molecules, which averages out their effect. ∎

Pascal’s triangle gives the relative intensities of the n+1 lines of a signal split by n neighbouring protons: 1:1, 1:2:1, 1:3:3:1. — Pascal’s triangle gives the relative intensities of the $n+1$ lines of a signal split by $n$ neighbouring protons: 1:1, 1:2:1, 1:3:3:1.

Proton NMR spectra (blue) with their integration curves (orange; each step is proportional to the number of protons of the signal below it). Shifts are those of measured spectra in CDCl3; line shapes and spacings are drawn from a simple model. — Proton NMR spectra (blue) with their integration curves (orange; each step is proportional to the number of protons of the signal below it). Shifts are those of measured spectra in $\ce{CDCl3}$ ; line shapes and spacings are drawn from a simple model.

Example 38.9 (Reading the spectra)

Ethyl ethanoate (B) gives a quartet of 2 protons at $4.12\,\mathrm{ppm}$ ( $\ce{O-CH2}$ , next to oxygen and to a $\ce{CH3}$ ), a singlet of 3 protons at $2.04\,\mathrm{ppm}$ ( $\ce{CH3-C=O}$ , no neighbouring proton) and a triplet of 3 protons at $1.26\,\mathrm{ppm}$ ( $\ce{CH3}$ , next to a $\ce{CH2}$ ). Propanone (C) gives a single singlet of 6 protons at $2.16\,\mathrm{ppm}$ . Propanoic acid (E) has a quartet at $2.39\,\mathrm{ppm}$ , a triplet at $1.16\,\mathrm{ppm}$ , and a singlet far to the left, at $11.7\,\mathrm{ppm}$ , its acid proton.

38.5 Using infrared and NMR together

Method 38.10 (Identifying a molecule from its IR and NMR spectra)

From the molecular formula, list the possible isomers and their functional groups.
Infrared: look for a $\ce{C=O}$ band near $1700\,\mathrm{cm}^{-1}$ and for $\ce{O-H}$ or $\ce{N-H}$ bands; strike out the isomers that do not fit.
NMR: count the signals (groups of equivalent protons), read the integration (protons per group), the multiplicities (neighbours) and the shifts (environments).
Assemble the pieces into one structure, and check it against every observation.

Example 38.11 (Two isomers $\ce{C3H6O2}$ )

Propanoic acid $\ce{CH3-CH2-COOH}$ and methyl ethanoate $\ce{CH3-CO-O-CH3}$ are isomers. In infrared, only the acid shows the very broad $\ce{O-H}$ band. In NMR (spectra E and D), the acid gives a triplet, a quartet and a singlet near $11.7\,\mathrm{ppm}$ ; the ester gives two singlets of 3 protons each, at 3.66 ( $\ce{O-CH3}$ ) and $2.05\,\mathrm{ppm}$ ( $\ce{CH3-C=O}$ ), since no carbon of the ester carries protons next to another protonated carbon.

38.6 Exercises

Exercise 38.1 ★

How many groups of equivalent protons, and so how many signals, do these molecules give: methane; ethane $\ce{CH3-CH3}$ ; propane; methanol $\ce{CH3-OH}$ ; methoxymethane $\ce{CH3-O-CH3}$ ?

Solution

Solution of Exercise 38.1.

Methane: 1. Ethane: 1 (the two $\ce{CH3}$ are alike). Propane: 2 (two $\ce{CH3}$ alike, one $\ce{CH2}$ ). Methanol: 2 ( $\ce{CH3}$ and $\ce{OH}$ ). Methoxymethane: 1.

Exercise 38.2 ★

A group of protons has 2 neighbouring protons on the next carbon. How many lines has its signal, and in which ratios? Same question for 3 and for 0 neighbours.

Solution

Solution of Exercise 38.2.

2 neighbours: a triplet, 1:2:1. 3 neighbours: a quartet, 1:3:3:1. 0 neighbours: a singlet.

Exercise 38.3 ★

A spectrum has three signals with integration steps of 15, 10 and 15 mm. The molecule has 8 protons. How many protons does each signal represent?

Solution

Solution of Exercise 38.3.

Total $40\,\mathrm{mm}$ for 8 protons: $5\,\mathrm{mm}$ per proton. The signals represent 3, 2 and 3 protons.

Exercise 38.4 ★

Using the table of shifts, where would you expect the signal of a proton of an aldehyde group? Of a $\ce{CH3}$ group in a chain?

Solution

Solution of Exercise 38.4.

Aldehyde: 9.7 to $10.0\,\mathrm{ppm}$ . A $\ce{CH3}$ of a chain: 0.7 to $1.3\,\mathrm{ppm}$ .

Exercise 38.5 ★

Why is the reference TMS chosen so that its protons are all equivalent? Why is the solvent deuterated?

Solution

Solution of Exercise 38.5.

Its twelve equivalent protons give a single, sharp, intense line, easy to place at zero. The deuterated solvent gives no proton signal of its own, which would otherwise swamp those of the few milligrams of sample.

Exercise 38.6 ★★

Predict the spectrum of chloroethane $\ce{CH3-CH2-Cl}$ : number of signals, integration, multiplicities, approximate shifts.

Solution

Solution of Exercise 38.6.

Two signals. $\ce{CH2}$ next to chlorine: 2 protons, a quartet (3 neighbours), in the range 2.5– $4.0\,\mathrm{ppm}$ . $\ce{CH3}$ : 3 protons, a triplet (2 neighbours), near the usual $\ce{CH3}$ range, a little higher because the chlorine is two atoms away.

Exercise 38.7 ★★

Predict the spectrum of propan-2-ol, $\ce{(CH3)2CH-OH}$ : in particular, the multiplicity of the $\ce{CH3}$ signal and of the $\ce{CH}$ signal (assume the $\ce{OH}$ gives a singlet and does not split).

Solution

Solution of Exercise 38.7.

Three signals: the two $\ce{CH3}$ , 6 equivalent protons, a doublet (1 neighbour, the $\ce{CH}$ ); the $\ce{CH}$ , 1 proton, split by 6 neighbours into 7 lines, in the $\ce{H-C-O}$ range (3.3– $4.5\,\mathrm{ppm}$ ); the $\ce{OH}$ , 1 proton, a singlet.

Exercise 38.8 ★★

Three spectra: (a) one singlet; (b) a quartet, a singlet and a triplet, integrations 2:3:3; (c) a quartet, a triplet and a singlet far left, integrations 2:3:1. Match them with ethyl ethanoate, propanone and propanoic acid.

Solution

Solution of Exercise 38.8.

(a) propanone; (b) ethyl ethanoate; (c) propanoic acid.

Exercise 38.9 ★★

Using the shift chart, explain why the $\ce{CH2}$ of ethyl ethanoate ( $4.12\,\mathrm{ppm}$ ) is far to the left of the $\ce{CH3}$ of the same ethyl group ( $1.26\,\mathrm{ppm}$ ).

Solution

Solution of Exercise 38.9.

The $\ce{CH2}$ is bonded to the oxygen atom of the ester, which is electronegative and deshields its protons: $\ce{H-C-O}$ range, 3.3– $4.5\,\mathrm{ppm}$ . The $\ce{CH3}$ is one carbon further away and stays in the chain range.

Exercise 38.10 ★★

A compound $\ce{C3H6O}$ shows a strong infrared band at $1715\,\mathrm{cm}^{-1}$ and a single NMR singlet. Identify it. Why is propanal excluded?

Solution

Solution of Exercise 38.10.

Propanone: a $\ce{C=O}$ (ketone, $1715\,\mathrm{cm}^{-1}$ ) and six equivalent protons, one singlet. Propanal would give three signals, one of them, the aldehyde proton of $\ce{CH3-CH2-CHO}$ , near 9.7– $10.0\,\mathrm{ppm}$ .

Exercise 38.11 ★★

In the spectrum of ethanol, why is the $\ce{OH}$ signal a singlet, and why does the $\ce{CH2}$ appear as a quartet rather than as a more complex signal?

Solution

Solution of Exercise 38.11.

The $\ce{OH}$ proton is exchanged quickly between molecules: it gives a singlet and does not split its neighbours. The $\ce{CH2}$ is therefore split only by the 3 protons of the $\ce{CH3}$ : a quartet.

Exercise 38.12 ★★★

Give the structures of four isomers $\ce{C4H8O2}$ that are esters or acids (butanoic acid, ethyl ethanoate, methyl propanoate, propyl methanoate, …) and predict, for each, the number of NMR signals and their multiplicities.

Solution

Solution of Exercise 38.12.

Butanoic acid $\ce{CH3-CH2-CH2-COOH}$ : 4 signals, a triplet ( $\ce{CH3}$ ), a 6-line signal (central $\ce{CH2}$ , 5 neighbours), a triplet ( $\ce{CH2-C=O}$ ), a singlet near 11– $12\,\mathrm{ppm}$ . Ethyl ethanoate: a singlet, a quartet, a triplet. Methyl propanoate $\ce{CH3-CH2-CO-O-CH3}$ : a triplet, a quartet ( $\ce{CH2-C=O}$ , 2.0– $2.4\,\mathrm{ppm}$ ), a singlet ( $\ce{O-CH3}$ ). Propyl methanoate $\ce{H-CO-O-CH2-CH2-CH3}$ : 4 signals, a singlet far to the left (the H on the $\ce{C=O}$ carbon), a triplet ( $\ce{O-CH2}$ ), a 6-line signal, a triplet ( $\ce{CH3}$ ).

Exercise 38.13 ★★★

A drop of heavy water $\ce{D2O}$ is shaken with a solution of ethanol, and the spectrum is recorded again: one signal disappears. Which, and why? How does this help to recognise $\ce{O-H}$ protons?

Solution

Solution of Exercise 38.13.

The $\ce{OH}$ signal: the $\ce{O-H}$ protons exchange with the deuterium of the heavy water, and $\ce{O-D}$ gives no proton signal. A signal that vanishes on shaking with $\ce{D2O}$ belongs to a proton on O or N.

Exercise 38.14 ★★★

A sample of ethyl ethanoate contains some ethanol. Which extra signals appear in the spectrum? If the integration of the singlet at $2.04\,\mathrm{ppm}$ is 30 mm and that of a small extra triplet at $1.23\,\mathrm{ppm}$ is 3 mm, estimate the ratio of the amounts of ethanol and ester.

Solution

Solution of Exercise 38.14.

Ethanol adds a quartet near $3.69\,\mathrm{ppm}$ , a triplet near $1.23\,\mathrm{ppm}$ and an $\ce{OH}$ singlet. The ester singlet: $30\,\mathrm{mm}$ for 3 protons, $10\,\mathrm{mm}$ per proton of ester. The ethanol triplet: $3\,\mathrm{mm}$ for 3 protons, $1\,\mathrm{mm}$ per proton of ethanol. Since each molecule contributes one $\ce{CH3}$ to these signals, the amounts are in the ratio $1/10$ : about one molecule of ethanol for ten of ester.

Exercise 38.15 ★★★

2-Methylpropan-1-ol is $\ce{(CH3)2CH-CH2-OH}$ . Predict its spectrum: the signals, their integrations, and the multiplicity of the $\ce{CH3}$ and $\ce{CH2}$ signals. Which signal has the most lines?

Solution

Solution of Exercise 38.15.

Four signals: the two $\ce{CH3}$ (6 protons) a doublet; the $\ce{CH}$ (1 proton), split by 6 + 2 = 8 neighbours into 9 lines; the $\ce{CH2}$ (2 protons) next to $\ce{O}$ , a doublet, in the $\ce{H-C-O}$ range; the $\ce{OH}$ (1 proton) a singlet. The $\ce{CH}$ signal has the most lines.

38.7 Problem: The Unknown Solvent

Problem 38.1

Weekend problem — a bottle of solvent labelled only $\ce{C4H8O2}$ : what is it, and how tall is each step of its integration curve?

A bottle of solvent in a storeroom is labelled only “ $\ce{C4H8O2}$ ”. Its infrared spectrum shows a strong band at $1740\,\mathrm{cm}^{-1}$ and no band above $3100\,\mathrm{cm}^{-1}$ . Its NMR spectrum shows three signals: a quartet at $4.12\,\mathrm{ppm}$ , a singlet at $2.04\,\mathrm{ppm}$ and a triplet at $1.26\,\mathrm{ppm}$ . The integration curve rises by a total of $72\,\mathrm{mm}$ .

Part I — The candidates.

Check that $\ce{C4H8O2}$ fits an ester or a carboxylic acid with single bonds only in its chain.
Give the semi-structural formulas and names of butanoic acid and of the three esters ethyl ethanoate, methyl propanoate and propyl methanoate.
Which functional group do they share in pairs?

Part II — Infrared.

What does the band at $1740\,\mathrm{cm}^{-1}$ reveal?
What would butanoic acid show that is missing here? Strike it out.
Can infrared alone choose between the three esters?

Part III — NMR.

How many groups of equivalent protons has the unknown?
What do the quartet and the triplet suggest together?
What does the singlet say about the neighbours of its protons?
Why is the quartet at a large shift?
Predict the spectrum of methyl propanoate $\ce{CH3-CH2-CO-O-CH3}$ (signals, multiplicities, approximate shifts). Is it the unknown?
Predict the spectrum of propyl methanoate. Is it the unknown?

Part IV — Identification and integration.

Identify the unknown and draw its structure, labelling each signal.
How many protons does each signal represent?
The total integration is $72\,\mathrm{mm}$ for 8 protons. How many millimetres per proton?
Compute the height of the step of the singlet and of the triplet.
Check that the three steps add up to $72\,\mathrm{mm}$ .
Ethyl ethanoate smells of pear drops: is that consistent with the family found?
State the final answer: how tall is the integration step of the quartet?

Solution

Solution of Problem 38.1.

1. An alkane with four carbons is $\ce{C4H10}$ ; one $\ce{C=O}$ removes two hydrogens and the two oxygens add none: $\ce{C4H8O2}$ , the formula of acids and esters with four carbons.

2. Butanoic acid $\ce{CH3-CH2-CH2-COOH}$ ; ethyl ethanoate $\ce{CH3-CO-O-CH2-CH3}$ ; methyl propanoate $\ce{CH3-CH2-CO-O-CH3}$ ; propyl methanoate $\ce{H-CO-O-CH2-CH2-CH3}$ .

3. The three esters share the ester group; all four have a $\ce{C=O}$ .

4. A $\ce{C=O}$ , in the ester range (near $1735\,\mathrm{cm}^{-1}$ ).

5. The very broad $\ce{O-H}$ band from 2500 to $3300\,\mathrm{cm}^{-1}$ : absent, so not butanoic acid.

6. No: the three esters have the same groups.

7. Three.

8. An ethyl group $\ce{CH3-CH2-}$ : the $\ce{CH2}$ split by 3 protons (quartet), the $\ce{CH3}$ by 2 (triplet).

9. Its protons have no protons on the neighbouring atoms: a $\ce{CH3}$ bonded to the $\ce{C=O}$ carbon or to the ester oxygen.

10. The $\ce{CH2}$ is bonded to oxygen ( $\ce{H-C-O}$ range).

11. A triplet ( $\ce{CH3}$ ), a quartet near 2.0– $2.4\,\mathrm{ppm}$ ( $\ce{CH2}$ next to $\ce{C=O}$ ) and a singlet in the $\ce{H-C-O}$ range ( $\ce{O-CH3}$ ). The quartet would be far below $4.12\,\mathrm{ppm}$ and the singlet far above $2.04\,\mathrm{ppm}$ : not the unknown.

12. Four signals (a singlet far left, a triplet, a 6-line signal, a triplet): not the unknown, which has three.

13. Ethyl ethanoate, $\ce{CH3-CO-O-CH2-CH3}$ : singlet $2.04\,\mathrm{ppm}$ = $\ce{CH3-C=O}$ ; quartet $4.12\,\mathrm{ppm}$ = $\ce{O-CH2}$ ; triplet $1.26\,\mathrm{ppm}$ = the end $\ce{CH3}$ .

14. Singlet 3, quartet 2, triplet 3.

15. $72 / 8 = 9\,\mathrm{mm}$ per proton.

16. Singlet $3 \times 9 = 27\,\mathrm{mm}$ ; triplet $27\,\mathrm{mm}$ .

17. $18 + 27 + 27 = 72\,\mathrm{mm}$ .

18. Yes: small esters are known for their fruity smells.

19. The quartet’s step is $18\,\mathrm{mm}$ out of $72\,\mathrm{mm}$ .

Terms defined in this chapter

See all 852 terms in the glossary

38.1 Protons in a magnetic field

38.2 Equivalent protons

38.3 Integration

38.4 Multiplicity and the n+1n+1n+1 rule

38.5 Using infrared and NMR together

38.6 Exercises

38.7 Problem: The Unknown Solvent

Terms defined in this chapter

38.4 Multiplicity and the $n+1$ rule