---
title: "Infrared Spectroscopy"
book: "School Chemistry — Grades 1 to 12"
subject: chemistry
language: en
chapter: 34
exercises: 15
source: https://one-course.com/books/chemistry/1/en/chapter/34-infrared-spectroscopy
license: CC-BY-NC-SA-4.0
credit: "One Chemistry Book, One Course (one-course.com)"
---

# Chapter 34 — Infrared Spectroscopy

On a laboratory shelf stands a bottle of colourless liquid whose label has been torn off. It might be an [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol), a [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) or an acid: three families that look exactly alike in a bottle. A drop placed on the crystal of an infrared spectrometer, two minutes of waiting, and a graph appears on the screen that answers the question. The bonds of a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) vibrate, and each kind of bond absorbs infrared light of its own frequencies: an [infrared spectrum](#def-g11-infrared-spectrum) is a list of the bonds present.

**You already know.**

[Functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) and families ([Chapter 33](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#ch-g11-functional-groups)). An [absorption spectrum](https://one-course.com/books/chemistry/1/en/chapter/29-colour-and-absorbance#def-g11-absorbance-spectrum) shows how much light a substance absorbs at each wavelength ([Chapter 29](https://one-course.com/books/chemistry/1/en/chapter/29-colour-and-absorbance#ch-g11-absorbance)). [Hydrogen bonds](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#def-g11-polarity-and-cohesion-hydrogen-bond) link $\ce{O-H}$ groups to neighbouring [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) ([Chapter 30](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#ch-g11-polarity-and-cohesion)).

## 34.1 Bonds vibrate

A [covalent bond](https://one-course.com/books/chemistry/1/en/chapter/24-lewis-structures-and-the-shape-of-molecules#def-g10-lewis-and-shape-covalent-bond) is not rigid: the two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) vibrate, moving closer and apart many millions of millions of times per second, like two balls joined by a spring. A stiffer spring (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) rather than a single one) or lighter balls (a hydrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) rather than a carbon [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom)) vibrate faster. A bond can absorb infrared light whose frequency matches its own vibration: infrared light, invisible to the eye, has wavelengths of a few micrometres to a few tens of micrometres.

![A bond pictured as a spring between two balls. Its vibration has a frequency set by the stiffness of the bond and the masses of the atoms; infrared light of that frequency is absorbed.](https://one-course.com/images/onecourse/chapters/chemistry-1/g11-infrared/fig-6fa664abff96.svg)

*A bond pictured as a spring between two balls. Its vibration has a frequency set by the stiffness of the bond and the masses of the [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom); infrared light of that frequency is absorbed.*

**Definition 34.1 (Wavenumber).**

The *wavenumber* $\sigma$ of a light is the inverse of its wavelength, $\sigma = 1/\lambda$. In infrared spectroscopy it is expressed in $\mathrm{cm}^{-1}$: the number of wavelengths in one centimetre. A larger wavenumber means a shorter wavelength and a faster vibration.

**Example 34.2 (From a wavenumber to a wavelength).**

A band at $\sigma = 2000\,\mathrm{cm}^{-1}$ corresponds to $\lambda = 1/2000 = 5.0 \times 10^{-4}\,\mathrm{cm} = 5.0\,\text{µ}\mathrm{m}$. Infrared spectra usually run from $4000\,\mathrm{cm}^{-1}$ ($2.5\,\text{µ}\mathrm{m}$) to $500\,\mathrm{cm}^{-1}$ ($20\,\text{µ}\mathrm{m}$).

## 34.2 Reading an infrared spectrum

**Definition 34.3 (Infrared spectrum, transmittance).**

The *transmittance* $T$ of a sample at a given [wavenumber](#def-g11-infrared-wavenumber) is the percentage of the infrared light that passes through it: $100\,\%$ if nothing is absorbed. The *infrared spectrum* of a compound is the graph of $T$ against the [wavenumber](#def-g11-infrared-wavenumber), drawn by convention with the [wavenumbers](#def-g11-infrared-wavenumber) decreasing from left to right.

**Definition 34.4 (Absorption band, fingerprint region).**

An *absorption band* is a dip of the [transmittance](#def-g11-infrared-spectrum): the light of those [wavenumbers](#def-g11-infrared-wavenumber) is absorbed by a bond. Its position tells which bond, its width and its depth complete the picture. Below about $1500\,\mathrm{cm}^{-1}$, the spectrum is crowded with bands that depend on the whole [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule): this *fingerprint region* identifies a compound by comparison with a known spectrum, but is hard to read bond by bond.

**In the lab — Recording a spectrum.**

Most school and university spectrometers now use a small diamond crystal: a drop of liquid, or a few grains of solid pressed by a clamp, is placed on the crystal, and the infrared beam that grazes its surface probes the sample. The crystal is first recorded clean (the “background”), which plays the part of the blank. The crystal is cleaned with a tissue and a little [solvent](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute) between two samples.

## 34.3 Characteristic bands

**Proposition 34.5 (Each bond type has its band).**

Each type of bond absorbs in a characteristic range of [wavenumbers](#def-g11-infrared-wavenumber), nearly the same from one [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) to the next:

| bond | [wavenumber](#def-g11-infrared-wavenumber) ($\mathrm{cm}^{-1}$) | appearance |
| --- | --- | --- |
| $\ce{O-H}$, not hydrogen-bonded (gas, dilute) | near 3600 | sharp |
| $\ce{O-H}$, hydrogen-bonded (liquid [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol)) | 3300–3400 | broad, strong |
| $\ce{O-H}$ of a [carboxylic acid](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) | 2500–3300 | very broad |
| $\ce{N-H}$ of an [amine](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-amine) | 3300–3500 | medium (two bands for $\ce{-NH2}$) |
| $\ce{C-H}$ of a chain | 2850–2960 | strong |
| $\ce{C=O}$ of an [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) | near 1735 | very strong, sharp |
| $\ce{C=O}$ of an [aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) | near 1730 | very strong, sharp |
| $\ce{C=O}$ of a [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) | near 1715 | very strong, sharp |
| $\ce{C=O}$ of a [carboxylic acid](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) | near 1710 | very strong, broader |
| $\ce{C=C}$ | near 1650 | medium |
| $\ce{C-O}$ of an [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol) | near 1050 | strong |

**Proof.** These ranges are measured on many compounds. They group by bond because the vibration of a bond depends mostly on the bond itself and its two [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), little on the rest of the [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule). ∎

![A benchtop infrared spectrometer with its crystal and clamp.](https://one-course.com/images/onecourse/chapters/chemistry-1/g11-infrared/img-0611bc34a775.jpg)

*A benchtop infrared spectrometer with its crystal and clamp.*

![Where the main bonds absorb. The O-H and N-H bands sit at the left, the C=O band, usually the strongest, near 1700\, cm-1; below 1500\, cm-1 lies the fingerprint region.](https://one-course.com/images/onecourse/chapters/chemistry-1/g11-infrared/fig-f715bc1ffce8.svg)

*Where the main bonds absorb. The $\ce{O-H}$ and $\ce{N-H}$ bands sit at the left, the $\ce{C=O}$ band, usually the strongest, near $1700\,\mathrm{cm}^{-1}$; below $1500\,\mathrm{cm}^{-1}$ lies the [fingerprint region](#def-g11-infrared-band).*

**Proposition 34.6 (Hydrogen bonds broaden the O–H band).**

When $\ce{O-H}$ groups are linked by [hydrogen bonds](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#def-g11-polarity-and-cohesion-hydrogen-bond), as in a liquid [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol), their band is broad and lies at lower [wavenumbers](#def-g11-infrared-wavenumber) (about 3300–$3400\,\mathrm{cm}^{-1}$); without [hydrogen bonds](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#def-g11-polarity-and-cohesion-hydrogen-bond), as in the gas, it is sharp and near $3600\,\mathrm{cm}^{-1}$.

**Proof.** Admitted: a [hydrogen bond](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#def-g11-polarity-and-cohesion-hydrogen-bond) pulls on the hydrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom) and loosens the $\ce{O-H}$ bond, which vibrates more slowly; and since every [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is bonded a little differently, the band spreads over a range. ∎

## 34.4 Identifying functional groups

**Method 34.7 (Reading an infrared spectrum).**

1. Look above $1500\,\mathrm{cm}^{-1}$ first; leave the [fingerprint region](#def-g11-infrared-band) for a comparison with known spectra.
2. Near $1700\,\mathrm{cm}^{-1}$ : a very strong band means a $\ce{C=O}$ group ( [aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) , [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) , acid, [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) , [amide](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-amine) ).
3. Between 2500 and $3700\,\mathrm{cm}^{-1}$ : a broad band near $3350\,\mathrm{cm}^{-1}$ means an [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol) $\ce{O-H}$ ; a very broad band from 2500 to $3300\,\mathrm{cm}^{-1}$ with a $\ce{C=O}$ means a [carboxylic acid](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) ; medium bands at 3300– $3500\,\mathrm{cm}^{-1}$ mean $\ce{N-H}$ .
4. Combine with the [molecular formula](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) to choose the family, then check with the position of the $\ce{C=O}$ band if there is one.

![Infrared spectra of six compounds, wavenumber in cm-1 (decreasing to the right). Only the bands discussed in the chapter are drawn; their positions come from measured spectra and tables, their shapes from a simple model.](https://one-course.com/images/onecourse/chapters/chemistry-1/g11-infrared/fig-5adb040a74e9.svg)

*Infrared spectra of six compounds, [wavenumber](#def-g11-infrared-wavenumber) in $\mathrm{cm}^{-1}$ (decreasing to the right). Only the bands discussed in the chapter are drawn; their positions come from measured spectra and tables, their shapes from a simple model.*

**Example 34.8 (Reading the six spectra).**

Ethanol (A) shows a broad $\ce{O-H}$ band near $3350\,\mathrm{cm}^{-1}$, the $\ce{C-H}$ bands just below $3000\,\mathrm{cm}^{-1}$ and a strong $\ce{C-O}$ band near $1050\,\mathrm{cm}^{-1}$, but nothing near $1700\,\mathrm{cm}^{-1}$. In the gas (B), its $\ce{O-H}$ band becomes a sharp line at $3666\,\mathrm{cm}^{-1}$. Propanone (C) has no $\ce{O-H}$ band but a very strong $\ce{C=O}$ at $1715\,\mathrm{cm}^{-1}$. Ethanoic acid (D) shows both: an enormous $\ce{O-H}$ band from 2500 to $3300\,\mathrm{cm}^{-1}$ and a $\ce{C=O}$ at $1710\,\mathrm{cm}^{-1}$. Ethyl ethanoate (E) has its $\ce{C=O}$ at $1735\,\mathrm{cm}^{-1}$ and a strong $\ce{C-O}$ near $1240\,\mathrm{cm}^{-1}$, and no $\ce{O-H}$. Ethanamine (F) shows two medium $\ce{N-H}$ bands above $3300\,\mathrm{cm}^{-1}$.

## 34.5 Exercises

**Exercise 34.1 ★.**

Convert into a wavelength in micrometres: $\sigma = 3300\,\mathrm{cm}^{-1}$ and $\sigma = 1050\,\mathrm{cm}^{-1}$. Which corresponds to the faster vibration?

**Solution of Exercise 34.1.**

$\lambda = 1/3300 = 3.03 \times 10^{-4}\,\mathrm{cm} = 3.03\,\text{µ}\mathrm{m}$; $\lambda = 1/1050 = 9.52 \times 10^{-4}\,\mathrm{cm} = 9.52\,\text{µ}\mathrm{m}$. The band at $3300\,\mathrm{cm}^{-1}$, of larger [wavenumber](#def-g11-infrared-wavenumber), belongs to the faster vibration.

**Exercise 34.2 ★.**

A wavelength of $10\,\text{µ}\mathrm{m}$ is absorbed. Give the [wavenumber](#def-g11-infrared-wavenumber) in $\mathrm{cm}^{-1}$.

**Solution of Exercise 34.2.**

$10\,\text{µ}\mathrm{m} = 1.0 \times 10^{-3}\,\mathrm{cm}$, so $\sigma = 1/1.0 \times 10^{-3} =
1000\,\mathrm{cm}^{-1}$.

**Exercise 34.3 ★.**

Which bond absorbs: near $1715\,\mathrm{cm}^{-1}$; near $3350\,\mathrm{cm}^{-1}$ (broad); between 2850 and $2960\,\mathrm{cm}^{-1}$?

**Solution of Exercise 34.3.**

The $\ce{C=O}$ of a [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl); a hydrogen-bonded [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol) $\ce{O-H}$; $\ce{C-H}$ bonds of a carbon chain.

**Exercise 34.4 ★.**

On spectrum C (propanone), find the strongest band. Which bond does it belong to?

**Solution of Exercise 34.4.**

The band at $1715\,\mathrm{cm}^{-1}$: the $\ce{C=O}$ bond.

**Exercise 34.5 ★.**

Why is an [infrared spectrum](#def-g11-infrared-spectrum) drawn with a [transmittance](#def-g11-infrared-spectrum) axis, the bands pointing down? What does $T = 100\,\%$ mean?

**Solution of Exercise 34.5.**

The instrument measures the light that passes through the sample; where a bond absorbs, less light passes and the curve dips. $T =
100\,\%$ means that none of the light of that [wavenumber](#def-g11-infrared-wavenumber) is absorbed.

**Exercise 34.6 ★★.**

A compound $\ce{C4H8O}$ shows a very strong band at $1715\,\mathrm{cm}^{-1}$ and no band above $3000\,\mathrm{cm}^{-1}$. Another, $\ce{C4H10O}$, shows a broad band near $3350\,\mathrm{cm}^{-1}$ and none near $1700\,\mathrm{cm}^{-1}$. To which families do they belong? Propose a name for each.

**Solution of Exercise 34.6.**

The first has a $\ce{C=O}$ band at $1715\,\mathrm{cm}^{-1}$ and no $\ce{O-H}$ band. It is a [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl): $\ce{CH3-CO-CH2-CH3}$, butanone (also called butan-2-one). The second has an $\ce{O-H}$ band and no $\ce{C=O}$: an [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol), for example butan-1-ol.

**Exercise 34.7 ★★.**

Explain why the $\ce{O-H}$ band of ethanoic acid is so broad, broader even than that of liquid ethanol.

**Solution of Exercise 34.7.**

The $\ce{O-H}$ groups of the acid are very strongly hydrogen-bonded (the [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) pair up, each $\ce{O-H}$ bonded to the $\ce{C=O}$ of the other), and every [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) is bonded a little differently: the band is loosened further and spread over a very wide range.

**Exercise 34.8 ★★.**

Compare spectra A and B of ethanol. What changes, and why?

**Solution of Exercise 34.8.**

In the liquid (A) the $\ce{O-H}$ band is broad, near $3350\,\mathrm{cm}^{-1}$; in the gas (B), where the [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) are far apart and form no [hydrogen bonds](https://one-course.com/books/chemistry/1/en/chapter/30-electronegativity-polarity-and-intermolecular-forces#def-g11-polarity-and-cohesion-hydrogen-bond), it is a sharp band near $3666\,\mathrm{cm}^{-1}$.

**Exercise 34.9 ★★.**

Propanal and propanone are both $\ce{C3H6O}$. Both show a strong $\ce{C=O}$ band. Can infrared tell them apart from that band alone? What else could help?

**Solution of Exercise 34.9.**

Hardly: near $1730\,\mathrm{cm}^{-1}$ for the [aldehyde](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) and $1715\,\mathrm{cm}^{-1}$ for the [ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl), close values. Comparison of the whole spectrum, [fingerprint region](#def-g11-infrared-band) included, with reference spectra would decide, or another technique.

**Exercise 34.10 ★★.**

A compound shows a strong band at $1735\,\mathrm{cm}^{-1}$, a strong band near $1240\,\mathrm{cm}^{-1}$ and nothing above $3000\,\mathrm{cm}^{-1}$. Its formula is $\ce{C4H8O2}$. Which family? Is ethanoic acid a possibility? Butanoic acid?

**Solution of Exercise 34.10.**

An [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) ($\ce{C=O}$ near $1735\,\mathrm{cm}^{-1}$, strong $\ce{C-O}$, no $\ce{O-H}$), for example ethyl ethanoate. Ethanoic acid is $\ce{C2H4O2}$, not $\ce{C4H8O2}$. Butanoic acid has the right formula but would show the very broad $\ce{O-H}$ band of acids: excluded.

**Exercise 34.11 ★★.**

Which of the six spectra would a [molecule](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule) of propan-1-ol most resemble? Of propanoic acid? Explain.

**Solution of Exercise 34.11.**

Propan-1-ol is an [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol): like A. Propanoic acid is a [carboxylic acid](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid): like D.

**Exercise 34.12 ★★★.**

Propan-2-ol can be oxidised into propanone. A student follows the reaction by recording spectra of samples taken every ten minutes. Describe how the spectra change. How does she know the reaction is complete?

**Solution of Exercise 34.12.**

The broad $\ce{O-H}$ band near $3350\,\mathrm{cm}^{-1}$ shrinks while a strong $\ce{C=O}$ band near $1715\,\mathrm{cm}^{-1}$ grows. The reaction is complete when the $\ce{O-H}$ band has disappeared and the $\ce{C=O}$ band no longer grows.

**Exercise 34.13 ★★★.**

Butanoic acid and ethyl ethanoate are [isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer), $\ce{C4H8O2}$. Describe two differences between their infrared spectra, and explain them.

**Solution of Exercise 34.13.**

Butanoic acid shows a very broad $\ce{O-H}$ band from 2500 to $3300\,\mathrm{cm}^{-1}$, the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) none; the acid’s $\ce{C=O}$ lies near $1710\,\mathrm{cm}^{-1}$, broader, the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid)’s near $1735\,\mathrm{cm}^{-1}$, sharp, with a strong $\ce{C-O}$ band near $1240\,\mathrm{cm}^{-1}$. The acid has an $\ce{O-H}$ group, hydrogen-bonded, which also slightly loosens its $\ce{C=O}$.

**Exercise 34.14 ★★★.**

A sample of ethyl ethanoate shows, besides the expected bands, a weak broad band near $3350\,\mathrm{cm}^{-1}$. Suggest two impurities that could cause it (think of how [esters](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) are made, and of the [air](https://one-course.com/books/chemistry/1/en/chapter/4-air-a-mixture-of-gases#def-g4-air-a-mixture-of-gases-air)). How could the sample be checked?

**Solution of Exercise 34.14.**

Leftover ethanol (the [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol) the [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) is made from) or water (from the [air](https://one-course.com/books/chemistry/1/en/chapter/4-air-a-mixture-of-gases#def-g4-air-a-mixture-of-gases-air) or the washing): both have hydrogen-bonded $\ce{O-H}$ groups. The sample can be compared with a reference spectrum, dried, distilled, or its boiling temperature measured.

**Exercise 34.15 ★★★.**

The $\ce{C=O}$ band of [ketones](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl) lies near $1715\,\mathrm{cm}^{-1}$, that of a $\ce{C=C}$ near $1650\,\mathrm{cm}^{-1}$, and the $\ce{C-O}$ band near $1050\,\mathrm{cm}^{-1}$. Using the picture of two balls on a spring, explain why 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) $\ce{C=O}$ vibrates faster than a single bond $\ce{C-O}$. Why are $\ce{O-H}$, $\ce{N-H}$ and $\ce{C-H}$ bands all at high [wavenumbers](#def-g11-infrared-wavenumber)?

**Solution of Exercise 34.15.**

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) is a stiffer spring than a single bond between the same [atoms](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom): it vibrates faster, at a higher [wavenumber](#def-g11-infrared-wavenumber) (1715 against $1050\,\mathrm{cm}^{-1}$). The $\ce{O-H}$, $\ce{N-H}$ and $\ce{C-H}$ bonds all involve a hydrogen [atom](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-atom), the lightest of all: light balls on a spring vibrate fast, hence [wavenumbers](#def-g11-infrared-wavenumber) near 2900–$3600\,\mathrm{cm}^{-1}$.

## 34.6 Problem: Three Unlabelled Bottles

**Problem 34.1.**

Weekend problem — three bottles have lost their labels: which is which, and what wavelength does the ketone absorb most?

Three bottles of colourless liquid have lost their labels. The stock list says they contain ethanol, propanone and ethanoic acid. Their spectra are recorded: bottle 1 gives a spectrum like A, bottle 2 like D, bottle 3 like C.

**Part I — The candidates.**

1. Write the [semi-structural formulas](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) of ethanol, propanone and ethanoic acid.
2. Give their [molecular formulas](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) .
3. Name the [functional group](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) of each.
4. Which bonds of each should give a band above $1500\,\mathrm{cm}^{-1}$ ?

**Part II — The spectra.**

5. Bottle 1: is there a $\ce{C=O}$ band? An $\ce{O-H}$ band? Which compound is it?
6. Bottle 2: describe its two strongest features. Which compound?
7. Bottle 3: which compound? Which band decides?
8. Could the smell have told them apart? Why is it better not to try?
9. Why is the $\ce{O-H}$ band of bottle 2 wider than that of bottle 1?

**Part III — [Isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer).**

10. Methoxymethane is an isomer of ethanol. Write its formula. Which band of ethanol would its spectrum lack?
11. Propanal is an isomer of propanone. Which band do they share? Where does it lie for each?
12. Methyl methanoate, $\ce{HCOO-CH3}$ , is an isomer of ethanoic acid. Which band of the acid would be missing? Where would its $\ce{C=O}$ band lie?
13. Why can a [molecular formula](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-formulas) alone not identify a compound, while formula and spectrum together usually can?

**Part IV — The wavelength.**

14. What is the [wavenumber](#def-g11-infrared-wavenumber) of the strongest band of propanone?
15. Express it in $\mathrm{m}^{-1}$ .
16. Compute the wavelength absorbed, in metres, then in micrometres.
17. Is that light visible? To which kind of radiation does it belong?
18. Do the same for the $\ce{C-O}$ band of ethanol near $1050\,\mathrm{cm}^{-1}$ .
19. Which of the two bonds vibrates faster?
20. State the final answer: what wavelength does the $\ce{C=O}$ bond of propanone absorb most strongly?

**Solution of Problem 34.1.**

**1.** $\ce{CH3-CH2-OH}$; $\ce{CH3-CO-CH3}$; $\ce{CH3-COOH}$.

**2.** $\ce{C2H6O}$; $\ce{C3H6O}$; $\ce{C2H4O2}$.

**3.** Hydroxyl; carbonyl ([ketone](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carbonyl)); carboxyl.

**4.** Ethanol: $\ce{O-H}$ and $\ce{C-H}$. Propanone: $\ce{C-H}$ and $\ce{C=O}$. Ethanoic acid: $\ce{O-H}$, $\ce{C-H}$ and $\ce{C=O}$.

**5.** No $\ce{C=O}$ band, a broad $\ce{O-H}$ band: ethanol.

**6.** A very broad $\ce{O-H}$ band from 2500 to $3300\,\mathrm{cm}^{-1}$ and a strong $\ce{C=O}$ near $1710\,\mathrm{cm}^{-1}$: ethanoic acid.

**7.** Propanone: the very strong $\ce{C=O}$ band at $1715\,\mathrm{cm}^{-1}$, with no $\ce{O-H}$.

**8.** Probably (vinegar, [solvent](https://one-course.com/books/chemistry/1/en/chapter/9-solutions-and-solubility#def-g6-solutions-and-solubility-solute), [alcohol](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-alcohol)), but sniffing unknown liquids is dangerous; the spectrum is safe and certain.

**9.** The acid’s $\ce{O-H}$ groups are more strongly hydrogen-bonded (paired [molecules](https://one-course.com/books/chemistry/1/en/chapter/11-atoms-and-molecules#def-g7-atoms-and-molecules-molecule)), so the band is lower and much wider.

**10.** $\ce{CH3-O-CH3}$, $\ce{C2H6O}$; it has no $\ce{O-H}$, so no $\ce{O-H}$ band.

**11.** The $\ce{C=O}$ band: near $1730\,\mathrm{cm}^{-1}$ for propanal, near $1715\,\mathrm{cm}^{-1}$ for propanone.

**12.** The $\ce{O-H}$ band: an [ester](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-carboxylic-acid) has no $\ce{O-H}$. Its $\ce{C=O}$ would lie near $1735\,\mathrm{cm}^{-1}$.

**13.** [Isomers](https://one-course.com/books/chemistry/1/en/chapter/32-organic-molecules-skeletons-and-names#def-g11-organic-skeletons-isomer) share a formula; their [functional groups](https://one-course.com/books/chemistry/1/en/chapter/33-functional-groups-and-families#def-g11-functional-groups-functional-group) differ, and the spectrum shows the groups.

**14.** $1715\,\mathrm{cm}^{-1}$.

**15.** $1715 \times 100 = 1.715 \times 10^{5}\,\mathrm{m}^{-1}$.

**16.** $\lambda = 1/1.715 \times 10^{5} = 5.83 \times 10^{-6}\,\mathrm{m} =
5.83\,\text{µ}\mathrm{m}$.

**17.** No: visible light runs from about 0.4 to $0.75\,\text{µ}\mathrm{m}$. It is infrared radiation.

**18.** $1.05 \times 10^{5}\ \mathrm{m}^{-1}$, so $\lambda = 9.52 \times 10^{-6}\,\mathrm{m}
= 9.52\,\text{µ}\mathrm{m}$.

**19.** The $\ce{C=O}$ bond (higher [wavenumber](#def-g11-infrared-wavenumber), shorter wavelength).

**20.** About $5.8\,\text{µ}\mathrm{m}$.