---
title: "Proton NMR"
book: "School Chemistry — Grades 1 to 12"
subject: chemistry
language: en
chapter: 38
exercises: 15
source: https://one-course.com/books/chemistry/1/en/chapter/38-proton-nmr
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 38 — Proton 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) answers a little differently according to its neighbours, and the spectrum is a map of the hydrogen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule).

**You already know.**

An [infrared spectrum](https://one-course.com/books/chemistry/1/en/chapter/34-infrared-spectroscopy#def-g11-infrared-spectrum) shows which bonds a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) contains ([Chapter 34](https://one-course.com/books/chemistry/1/en/chapter/34-infrared-spectroscopy#ch-g11-infrared)). [Functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group), families and [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) ([Chapter 33](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#ch-g11-functional-groups), [Chapter 32](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#ch-g11-organic-skeletons)).

![An MRI scanner: the same physics as the chemist’s NMR spectrometer.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-proton-nmr/img-de3256a4e991.jpg)

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

## 38.1 Protons in a magnetic field

The [nucleus](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) of a hydrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) is a single [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) around a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) shield it slightly from the field, and that this shielding depends on the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) nearby: a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) next to an electronegative oxygen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), which pulls [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) away, absorbs at a slightly different frequency from a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) in a hydrocarbon chain. The differences are tiny, a few millionths of the frequency, and are given in parts per million.

![The magnet of an NMR spectrometer.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-proton-nmr/img-807eecf21725.jpg)

*The magnet of an NMR spectrometer.*

**Definition 38.1 (NMR spectrum, chemical shift).**

A [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](#def-g12-proton-nmr-spectrum) of a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) depends on the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) close to it: the nearer it is to an electronegative [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) or a [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol), ether, [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid)) | 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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) $\ce{-CHO}$ | 9.7–10.0 |
| $\ce{H-C-X}$ ([halogen](https://one-course.com/books/chemistry/1/en/chapter/23-electron-shells-and-the-periodic-table#def-g10-electron-shells-family)) | 2.5–4.0 | acid $\ce{-COOH}$ | 11.0–12.0 |

**Proof.** Measured on many compounds. An electronegative neighbour draws [electrons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-nucleus) away from the [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-proton-nmr/fig-11fbb15ec184.svg)

*Where [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) absorb, by environment. [Protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) close to oxygen, to a [double bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-multiple-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](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) whose hydrogen [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) are *equivalent protons* if they have the same environment in the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), so that they absorb at the same shift. Each group of equivalent [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) gives one signal. The three [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) of a $\ce{CH3}$ group are always equivalent.

**Example 38.4 (Counting groups).**

Propanone, $\ce{CH3-CO-CH3}$, has six [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) 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](#def-g12-proton-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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) 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+1n+1n+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](#def-g12-proton-nmr-equivalent) whose neighbouring carbon [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) carry $n$ [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) 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](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) $\ce{CH3-CH2-X}$ (X without hydrogen), the $\ce{CH3}$ signal is a triplet (2 neighbouring [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)) and the $\ce{CH2}$ signal a quartet (3 neighbouring [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)). [Protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) bonded to an oxygen or a nitrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) usually give a singlet and do not split their neighbours.

**Proof.** Admitted: each neighbouring [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) on O or N are exchanged quickly between [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule), 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.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-proton-nmr/fig-331e6ff4e79f.svg)

*Pascal’s triangle gives the relative intensities of the $n+1$ lines of a signal split by $n$ neighbouring [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton): 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.](https://one-course.com/images/onecourse/chapters/chemistry-1/g12-proton-nmr/fig-871ecb1a9c02.svg)

*[Proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) NMR spectra (blue) with their [integration curves](#def-g12-proton-nmr-integration) (orange; each step is proportional to the number of [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) at $4.12\,\mathrm{ppm}$ ($\ce{O-CH2}$, next to oxygen and to a $\ce{CH3}$), a singlet of 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) at $2.04\,\mathrm{ppm}$ ($\ce{CH3-C=O}$, no neighbouring [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)) and a triplet of 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) at $1.26\,\mathrm{ppm}$ ($\ce{CH3}$, next to a $\ce{CH2}$). Propanone (C) gives a single singlet of 6 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton).

## 38.5 Using infrared and NMR together

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

1. From the [molecular formula](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) , list the possible [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) and their [functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) .
2. 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](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) that do not fit.
3. NMR: count the signals (groups of [equivalent protons](#def-g12-proton-nmr-equivalent) ), read the integration ( [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) per group), the multiplicities (neighbours) and the shifts (environments).
4. Assemble the pieces into one structure, and check it against every observation.

**Example 38.11 (Two isomers CX3HX6OX2\ce{C3H6O2}CX3​HX6​OX2​).**

Propanoic acid $\ce{CH3-CH2-COOH}$ and methyl ethanoate $\ce{CH3-CO-O-CH3}$ are [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer). 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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) gives two singlets of 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) each, at 3.66 ($\ce{O-CH3}$) and $2.05\,\mathrm{ppm}$ ($\ce{CH3-C=O}$), since no carbon of the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) carries [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) next to another protonated carbon.

## 38.6 Exercises

**Exercise 38.1 ★.**

How many groups of [equivalent protons](#def-g12-proton-nmr-equivalent), and so how many signals, do these [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) give: methane; ethane $\ce{CH3-CH3}$; propane; methanol $\ce{CH3-OH}$; methoxymethane $\ce{CH3-O-CH3}$?

**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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) has 2 neighbouring [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) on the next carbon. How many lines has its signal, and in which ratios? Same question for 3 and for 0 neighbours.

**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](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) has 8 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton). How many [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) does each signal represent?

**Solution of Exercise 38.3.**

Total $40\,\mathrm{mm}$ for 8 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton): $5\,\mathrm{mm}$ per [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton). The signals represent 3, 2 and 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton).

**Exercise 38.4 ★.**

Using the table of shifts, where would you expect the signal of a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) of an [aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) group? Of a $\ce{CH3}$ group in a chain?

**Solution of Exercise 38.4.**

[Aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl): 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) are all equivalent? Why is the [solvent](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) deuterated?

**Solution of Exercise 38.5.**

Its twelve [equivalent protons](#def-g12-proton-nmr-equivalent) give a single, sharp, intense line, easy to place at zero. The deuterated [solvent](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) gives no [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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 of Exercise 38.6.**

Two signals. $\ce{CH2}$ next to chlorine: 2 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton), a quartet (3 neighbours), in the range 2.5–$4.0\,\mathrm{ppm}$. $\ce{CH3}$: 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton), a triplet (2 neighbours), near the usual $\ce{CH3}$ range, a little higher because the chlorine is two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) 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 of Exercise 38.7.**

Three signals: the two $\ce{CH3}$, 6 [equivalent protons](#def-g12-proton-nmr-equivalent), a doublet (1 neighbour, the $\ce{CH}$); the $\ce{CH}$, 1 [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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 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 of Exercise 38.9.**

The $\ce{CH2}$ is bonded to the oxygen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) of the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid), which is electronegative and deshields its [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton): $\ce{H-C-O}$ 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 of Exercise 38.10.**

Propanone: a $\ce{C=O}$ ([ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl), $1715\,\mathrm{cm}^{-1}$) and six [equivalent protons](#def-g12-proton-nmr-equivalent), one singlet. Propanal would give three signals, one of them, the [aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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 of Exercise 38.11.**

The $\ce{OH}$ [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) is exchanged quickly between [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule): it gives a singlet and does not split its neighbours. The $\ce{CH2}$ is therefore split only by the 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) of the $\ce{CH3}$: a quartet.

**Exercise 38.12 ★★★.**

Give the structures of four [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) $\ce{C4H8O2}$ that are [esters](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) or acids (butanoic acid, ethyl ethanoate, methyl propanoate, propyl methanoate, …) and predict, for each, the number of NMR signals and their multiplicities.

**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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)?

**Solution of Exercise 38.13.**

The $\ce{OH}$ signal: the $\ce{O-H}$ [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) exchange with the deuterium of the heavy water, and $\ce{O-D}$ gives no [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) signal. A signal that vanishes on shaking with $\ce{D2O}$ belongs to a [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid).

**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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) singlet: $30\,\mathrm{mm}$ for 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton), $10\,\mathrm{mm}$ per [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) of [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid). The ethanol triplet: $3\,\mathrm{mm}$ for 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton), $1\,\mathrm{mm}$ per [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) of ethanol. Since each [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) contributes one $\ce{CH3}$ to these signals, the amounts are in the ratio $1/10$: about one [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) of ethanol for ten of [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid).

**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 of Exercise 38.15.**

Four signals: the two $\ce{CH3}$ (6 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)) a doublet; the $\ce{CH}$ (1 [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)), split by 6 + 2 = 8 neighbours into 9 lines; the $\ce{CH2}$ (2 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton)) next to $\ce{O}$, a doublet, in the $\ce{H-C-O}$ range; the $\ce{OH}$ (1 [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-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](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) labelled only $\ce{C4H8O2}$: what is it, and how tall is each step of its [integration curve](#def-g12-proton-nmr-integration)?

A bottle of [solvent](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) in a storeroom is labelled only “$\ce{C4H8O2}$”. Its [infrared spectrum](https://one-course.com/books/chemistry/1/en/chapter/34-infrared-spectroscopy#def-g11-infrared-spectrum) shows a strong band at $1740\,\mathrm{cm}^{-1}$ and no band above $3100\,\mathrm{cm}^{-1}$. Its [NMR spectrum](#def-g12-proton-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](#def-g12-proton-nmr-integration) rises by a total of $72\,\mathrm{mm}$.

**Part I — The candidates.**

1. Check that $\ce{C4H8O2}$ fits an [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) or a [carboxylic acid](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) with single bonds only in its chain.
2. Give the [semi-structural formulas](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) and names of butanoic acid and of the three [esters](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) ethyl ethanoate, methyl propanoate and propyl methanoate.
3. Which [functional group](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) do they share in pairs?

**Part II — Infrared.**

4. What does the band at $1740\,\mathrm{cm}^{-1}$ reveal?
5. What would butanoic acid show that is missing here? Strike it out.
6. Can infrared alone choose between the three [esters](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) ?

**Part III — NMR.**

7. How many groups of [equivalent protons](#def-g12-proton-nmr-equivalent) has the unknown?
8. What do the quartet and the triplet suggest together?
9. What does the singlet say about the neighbours of its [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) ?
10. Why is the quartet at a large shift?
11. Predict the spectrum of methyl propanoate $\ce{CH3-CH2-CO-O-CH3}$ (signals, multiplicities, approximate shifts). Is it the unknown?
12. Predict the spectrum of propyl methanoate. Is it the unknown?

**Part IV — Identification and integration.**

13. Identify the unknown and draw its structure, labelling each signal.
14. How many [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) does each signal represent?
15. The total integration is $72\,\mathrm{mm}$ for 8 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) . How many millimetres per [proton](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) ?
16. Compute the height of the step of the singlet and of the triplet.
17. Check that the three steps add up to $72\,\mathrm{mm}$ .
18. Ethyl ethanoate smells of pear drops: is that consistent with the family found?
19. State the final answer: how tall is the integration step of the quartet?

**Solution of Problem 38.1.**

**1.** An [alkane](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) 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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) share the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) group; all four have a $\ce{C=O}$.

**4.** A $\ce{C=O}$, in the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) 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](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) have the same groups.

**7.** Three.

**8.** An ethyl group $\ce{CH3-CH2-}$: the $\ce{CH2}$ split by 3 [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) (quartet), the $\ce{CH3}$ by 2 (triplet).

**9.** Its [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) have no [protons](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton) on the neighbouring [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom): a $\ce{CH3}$ bonded to the $\ce{C=O}$ carbon or to the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) 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](https://one-course.com/books/chemistry/1/en/chapter/16-inside-the-atom#def-g9-inside-the-atom-proton).

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

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

**18.** Yes: small [esters](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) are known for their fruity smells.

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