Ebook Introduction to spectroscopy (4th edition) Part 2

(BQ) Part 2 book Introduction to spectroscopy has contents: Ultraviolet spectroscopy, mass spectrometry, combined structure problems, nuclear magnetic resonance spectroscopy. (BQ) Part 2 book Introduction to spectroscopy has contents: Ultraviolet spectroscopy, mass spectrometry, combined structure problems, nuclear magnetic resonance spectroscopy.

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Spectroscopy

F o u r t h E d i t i o n

Pavia / Lampman / Kriz / Vyvyan’s Introduction to Spectroscopy, 4e,

is a comprehensive resource that provides an unmatched, tematic introduction to spectra and basic theoretical concepts

sys-in spectroscopic methods that creates a practical learnsys-ing source, whether you’re an introductory student or someone who needs a reliable reference text on spectroscopy

re-This well-rounded introduction features updated spectra, a modernized presentation of one-dimensional Nuclear Magnetic Resonance (NMR) spectroscopy, the introduction of biological molecules in mass spectrometry, and inclusion of modern tech- niques alongside DEPT, COSY, and HECTOR Count on this book’s exceptional presentation to provide the comprehensive cover- age needed to truly understand today’s spectroscopic techniques

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INTRODUCTION

TO SPECTROSCOPY

Donald L Pavia Gary M Lampman George S Kriz James R Vyvyan

Department of ChemistryWestern Washington UniversityBellingham, Washington

F O U R T H E D I T I O N

TOALL OFOUR“O-SPEC” STUDENTS

© 2009, 2001 Brooks/Cole, Cengage Learning ALL RIGHTS RESERVED No part of this work covered by the copyright herein may be reproduced, transmitted, stored, or used in any form

or by any means graphic, electronic, or mechanical, including but not limited to photocopying, recording, scanning, digitizing, taping, Web distribution, information networks, or information storage and retrieval systems, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without the prior written permission of the publisher.

Library of Congress Control Number: 2007943966 ISBN-13: 978-0-495-11478-9

ISBN-10: 0-495-11478-2

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Introduction to Spectroscopy, Fourth Edition

Donald L Pavia, Gary M Lampman, George S Kriz, and James R Vyvyan

Acquisitions Editor: Lisa Lockwood Development Editor: Brandi Kirksey Editorial Assistant: Elizabeth Woods Technology Project Manager: Lisa Weber Marketing Manager: Amee Mosley Marketing Assistant: Elizabeth Wong Marketing Communications Manager:

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Printed in the United States of America

1 2 3 4 5 6 7 12 11 10 09 08

This is the fourth edition of a textbook in spectroscopy intended for students of organic

chemistry Our textbook can serve as a supplement for the typical organic chemistry lecturetextbook, and it can also be used as a “stand-alone” textbook for an advanced undergraduatecourse in spectroscopic methods of structure determination or for a first-year graduate course inspectroscopy This book is also a useful tool for students engaged in research Our aim is not only toteach students to interpret spectra, but also to present basic theoretical concepts As with the previ-ous editions, we have tried to focus on the important aspects of each spectroscopic technique with-out dwelling excessively on theory or complex mathematical analyses

This book is a continuing evolution of materials that we use in our own courses, both as a ment to our organic chemistry lecture course series and also as the principal textbook in our upperdivision and graduate courses in spectroscopic methods and advanced NMR techniques Explana-tions and examples that we have found to be effective in our courses have been incorporated intothis edition

supple-This fourth edition of Introduction to Spectroscopy contains some important changes The

discussion of coupling constant analysis in Chapter 5 has been significantly expanded Long-rangecouplings are covered in more detail, and multiple strategies for measuring coupling constants arepresented Most notably, the systematic analysis of line spacings allows students (with a littlepractice) to extract all of the coupling constants from even the most challenging of first-ordermultiplets Chapter 5 also includes an expanded treatment of group equivalence and diastereotopicsystems

Discussion of solvent effects in NMR spectroscopy is discussed more explicitly in Chapter 6,and the authors thank one of our graduate students, Ms Natalia DeKalb, for acquiring the data inFigures 6.19 and 6.20 A new section on determining the relative and absolute stereochemical con-figuration with NMR has also been added to this chapter

The mass spectrometry section (Chapter 8) has been completely revised and expanded in thisedition, starting with more detailed discussion of a mass spectrometer’s components All of thecommon ionization methods are covered, including chemical ionization (CI), fast-atom bombard-ment (FAB), matrix-assisted laser desorption ionization (MALDI), and electrospray techniques.Different types of mass analyzers are described as well Fragmentation in mass spectrometry is dis-cussed in greater detail, and several additional fragmentation mechanisms for common functionalgroups are illustrated Numerous new mass spectra examples are also included

Problems have been added to each of the chapters We have included some more solved lems, so that students can develop skill in solving spectroscopy problems

prob-PREFACE

v

The authors are very grateful to Mr Charles Wandler, without whose expert help this projectcould not have been accomplished We also acknowledge numerous contributions made by our stu-dents who use the textbook and who provide us careful and thoughtful feedback.

We wish to alert persons who adopt this book that answers to all of the problems are available online from the publisher Authorization to gain access to the web site may be obtained through thelocal Cengage textbook representative

Finally, once again we must thank our wives, Neva-Jean, Marian, Carolyn, and Cathy for theirsupport and their patience They endure a great deal in order to support us as we write, and theydeserve to be part of the celebration when the textbook is completed!

Donald L PaviaGary M LampmanGeorge S KrizJames R Vyvyan

C H A P T E R 1MOLECULAR FORMULAS AND WHAT CAN BE LEARNED

1.1 Elemental Analysis and Calculations 1

1.4 Index of Hydrogen Deficiency 6

1.6 A Quick Look Ahead to Simple Uses of Mass Spectra 12

A Dispersive Infrared Spectrometers 23

B Fourier Transform Spectrometers 252.6 Preparation of Samples for Infrared Spectroscopy 262.7 What to Look for When Examining Infrared Spectra 262.8 Correlation Charts and Tables 28

2.9 How to Approach the Analysis of a Spectrum (Or What You Can Tell at a Glance) 30

viiCONTENTS

2.10 Hydrocarbons: Alkanes, Alkenes, and Alkynes 31

2.21 Alkyl and Aryl Halides 84

C H A P T E R 3NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

3.4 The Mechanism of Absorption (Resonance) 1093.5 Population Densities of Nuclear Spin States 1113.6 The Chemical Shift and Shielding 112

3.7 The Nuclear Magnetic Resonance Spectrometer 114

A The Continuous-Wave (CW) Instrument 114

B The Pulsed Fourier Transform (FT) Instrument 116

3.9 Integrals and Integration 1213.10 Chemical Environment and Chemical Shift 1233.11 Local Diamagnetic Shielding 124

3.18 A Comparison of NMR Spectra at Low- and High-Field Strengths 1413.19 Survey of Typical 1H NMR Absorptions by Type of Compound 142

A Correlation Charts 178

B Calculation of 13C Chemical Shifts 1804.3 Proton-Coupled 13C Spectra—Spin–Spin Splitting of Carbon-13 Signals 181

4.4 Proton-Decoupled 13C Spectra 183

4.6 Cross-Polarization: Origin of the Nuclear Overhauser Effect 1864.7 Problems with Integration in 13C Spectra 189

4.8 Molecular Relaxation Processes 190

4.11 Some Sample Spectra—Equivalent Carbons 195

4.13 Carbon-13 NMR Solvents—Heteronuclear Coupling of Carbon to Deuterium 1994.14 Heteronuclear Coupling of Carbon-13 to Fluorine-19 203

4.15 Heteronuclear Coupling of Carbon-13 to Phosphorus-31 2044.16 Carbon and Proton NMR: How to Solve a Structure Problem 206

C H A P T E R 5NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

5.2 Coupling Constants: The Mechanism of Coupling 234

5.4 Spectra of Diastereotopic Systems 252

A Diastereotopic Methyl Groups: 4-Methyl-2-pentanol 252

B Diastereotopic Hydrogens: 4-Methyl-2-pentanol 2545.5 Nonequivalence within a Group—The Use of Tree Diagrams when the n+1 Rule

5.6 Measuring Coupling Constants from First-Order Spectra 260

A Simple Multiplets—One Value of J (One Coupling) 260

B Is the n+1 Rule Ever Really Obeyed? 262

C More Complex Multiplets—More Than One Value of J 264

A First-Order and Second-Order Spectra 268

B Spin System Notation 269

C The A2, AB, and AX Spin Systems 270

D The AB AX and AB AX Spin Systems 270

E Simulation of Spectra 272

F The Absence of Second-Order Effects at Higher Field 272

G Deceptively Simple Spectra 273

C H A P T E R 6NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

6.2 Exchange in Water and D2O 332

A Acid/Water and Alcohol/Water Mixtures 332

C Peak Broadening Due to Exchange 3376.3 Other Types of Exchange: Tautomerism 338

6.5 Protons on Nitrogen: Quadrupole Broadening and Decoupling 342

6.7 The Effect of Solvent on Chemical Shift 347

6.10 Determining Absolute and Relative Configuration via NMR 356

A Determining Absolute Configuration 356

B Determining Relative Configuration 3586.11 Nuclear Overhauser Effect Difference Spectra 359

7.4 Instrumentation 3847.5 Presentation of Spectra 385

7.8 The Effect of Conjugation 3907.9 The Effect of Conjugation on Alkenes 3917.10 The Woodward–Fieser Rules for Dienes 394

7.12 Woodward’s Rules for Enones 4007.13 a ,b-Unsaturated Aldehydes, Acids, and Esters 402

A Substituents with Unshared Electrons 404

B Substituents Capable of p -Conjugation 406

C Electron-Releasing and Electron-Withdrawing Effects 406

D Disubstituted Benzene Derivatives 406

E Polynuclear Aromatic Hydrocarbons and Heterocyclic Compounds 409

7.16 Visible Spectra: Color in Compounds 4127.17 What to Look for in an Ultraviolet Spectrum: A Practical Guide 413

A Electron Ionization (EI) 420

B Chemical Ionization (CI) 421

C Desorption Ionization Techniques (SIMS, FAB, and MALDI) 425

D Electrospray Ionization (ESI) 426

A The Magnetic Sector Mass Analyzer 429

B Double-Focusing Mass Analyzers 430

C Quadrupole Mass Analyzers 430

D Time-of-Flight Mass Analyzers 4328.5 Detection and Quantitation: The Mass Spectrum 4358.6 Determination of Molecular Weight 438

8.7 Determination of Molecular Formulas 441

A Precise Mass Determination 441

B Isotope Ratio Data 4418.8 Structural Analysis and Fragmentation Patterns 445

A Stevenson’s Rule 446

B The Initial Ionization Event 447

C Radical-site Initiated Cleavage:a-Cleavage 448

D Charge-site Initiated Cleavage: Inductive Cleavage 448

U Selected Nitrogen and Sulfur Compounds 488

V Alkyl Chlorides and Alkyl Bromides 4928.9 Strategic Approach to Analyzing Mass Spectra and Solving Problems 4968.10 Computerized Matching of Spectra with Spectral Libraries 497

C H A P T E R 1 0NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY

10.2 Pulse Widths, Spins, and Magnetization Vectors 58910.3 Pulsed Field Gradients 593

10.5 Determining the Number of Attached Hydrogens 598

A An Overview of the COSY Experiment 603

B How to Read COSY Spectra 604

A An Overview of the HETCOR Experiment 608

10.9 Inverse Detection Methods 612

10.11 Magnetic Resonance Imaging 61410.12 Solving a Structural Problem Using Combined 1-D and 2-D Techniques 616

A Index of Hydrogen Deficiency and Infrared Spectrum 616

Appendix 4 1H Chemical Shifts of Selected Heterocyclic and Polycyclic Aromatic

Appendix 5 Typical Proton Coupling Constants A-13Appendix 6 Calculation of Proton (1H) Chemical Shifts A-17Appendix 7 Approximate 13C Chemical-Shift Values (ppm) for Selected Types

Appendix 8 Calculation of 13C Chemical Shifts A-22

Appendix 10 1H and 13C Chemical Shifts for Common NMR Solvents A-33Appendix 11 Tables of Precise Masses and Isotopic Abundance Ratios for Molecular

Ions under Mass 100 Containing Carbon, Hydrogen, Nitrogen,

Appendix 13 A Handy-Dandy Guide to Mass Spectral Fragmentation Patterns A-43

MOLECULAR FORMULAS AND WHAT CAN BE LEARNED FROM THEM

Before attempting to deduce the structure of an unknown organic compound from an

exami-nation of its spectra, we can simplify the problem somewhat by examining the molecularformula of the substance The purpose of this chapter is to describe how the molecular for-mula of a compound is determined and how structural information may be obtained from that for-

mula The chapter reviews both the modern and classical quantitative methods of determining the

molecular formula While use of the mass spectrometer (Section 1.6 and Chapter 8) can supplantmany of these quantitative analytical methods, they are still in use Many journals still require that

a satisfactory quantitative elemental analysis (Section 1.1) be obtained prior to the publication ofresearch results

1

C H A P T E R 1

1.1 ELEMENTAL ANALYSIS AND CALCULATIONS

The classical procedure for determining the molecular formula of a substance involves three steps:

1 A qualitative elemental analysis to find out what types of atoms are present C, H, N,

O, S, Cl, and so on

2 A quantitative elemental analysis (or microanalysis) to find out the relative numbers

(per-centages) of each distinct type of atom in the molecule

3 A molecular mass (or molecular weight) determination.

The first two steps establish an empirical formula for the compound When the results of the third procedure are known, a molecular formula is found.

Virtually all organic compounds contain carbon and hydrogen In most cases, it is not sary to determine whether these elements are present in a sample: their presence is assumed.However, if it should be necessary to demonstrate that either carbon or hydrogen is present in acompound, that substance may be burned in the presence of excess oxygen If the combustionproduces carbon dioxide, carbon must be present; if combustion produces water, hydrogen atomsmust be present Today, the carbon dioxide and water can be detected by gas chromatographicmethods Sulfur atoms are converted to sulfur dioxide; nitrogen atoms are often chemically re-duced to nitrogen gas following their combustion to nitrogen oxides Oxygen can be detected bythe ignition of the compound in an atmosphere of hydrogen gas; the product is water Currently,all such analyses are performed by gas chromatography, a method that can also determine the rel-ative amounts of each of these gases If the amount of the original sample is known, it can be

neces-entered, and the computer can calculate the percentage composition of the sample.

Unless you work in a large company or in one of the larger universities, it is quite rare to find aresearch laboratory in which elemental analyses are performed on site It requires too much time toset up the apparatus and keep it operating within the limits of suitable accuracy and precision

Usually, samples are sent to a commercial microanalytical laboratory that is prepared to do this

work routinely and to vouch for the accuracy of the results

Before the advent of modern instrumentation, the combustion of the precisely weighed sample wascarried out in a cylindrical glass tube, contained within a furnace A stream of oxygen was passedthrough the heated tube on its way to two other sequential, unheated tubes that contained chemicalsubstances that would absorb first the water (MgClO4) and then the carbon dioxide (NaOH/silica).These preweighed absorption tubes were detachable and were removed and reweighed to determinethe amounts of water and carbon dioxide formed The percentages of carbon and hydrogen in theoriginal sample were calculated by simple stoichiometry Table 1.1 shows a sample calculation.Notice in this calculation that the amount of oxygen was determined by difference, a commonpractice In a sample containing only C, H, and O, one needs to determine the percentages of only Cand H; oxygen is assumed to be the unaccounted-for portion You may also apply this practice in sit-uations involving elements other than oxygen; if all but one of the elements is determined, the lastone can be determined by difference Today, most calculations are carried out automatically by thecomputerized instrumentation Nevertheless, it is often useful for a chemist to understand the fun-damental principles of the calculations.

Table 1.2 shows how to determine the empirical formula of a compound from the percentage

compositions determined in an analysis Remember that the empirical formula expresses the simplestwhole-number ratios of the elements and may need to be multiplied by an integer to obtain the true

molecular formula To determine the value of the multiplier, a molecular mass is required.

Determination of the molecular mass is discussed in the next section

For a totally unknown compound (unknown chemical source or history) you will have to use thistype of calculation to obtain the suspected empirical formula However, if you have prepared thecompound from a known precursor by a well-known reaction, you will have an idea of the structure

of the compound In this case, you will have calculated the expected percentage composition of your

3 0

1

26 m

m g/

g m

C m

O o

0

5 2

2 m

m g

g /m

H m

2 O ole

1

2 m

m m

m o

o le

le H s

2

H O

(1.056 mmoles H)(1.008 mg/mmole H) = 1.06 mg H in original sample

9.8

6 3

.3 m

5 g

m s

g am

C ple

9.8

1 3

.0 m

6 g

m s

g am

H ple

% O = 100 − (64.6 + 10.8) = 24.6%

sample in advance (from its postulated structure) and will use the analysis to verify your hypothesis.When you perform these calculations, be sure to use the full molecular weights as given in the peri-odic chart and do not round off until you have completed the calculation The final result should begood to two decimal places: four significant figures if the percentage is between 10 and 100; threefigures if it is between 0 and 10 If the analytical results do not agree with the calculation, the sam-ple may be impure, or you may have to calculate a new empirical formula to discover the identity ofthe unexpected structure To be accepted for publication, most journals require the percentages

found to be less than 0.4% off from the calculated value Most microanalytical laboratories can

eas-ily obtain accuracy well below this limit provided the sample is pure

In Figure 1.1, a typical situation for the use of an analysis in research is shown Professor AmylCarbon, or one of his students, prepared a compound believed to be the epoxynitrile with the struc-ture shown at the bottom of the first form A sample of this liquid compound (25 μL) was placed in

a small vial correctly labeled with the name of the submitter and an identifying code (usually onethat corresponds to an entry in the research notebook) Only a small amount of the sample is re-quired, usually a few milligrams of a solid or a few microliters of a liquid A Request for Analysisform must be filled out and submitted along with the sample The sample form on the left side ofthe figure shows the type of information that must be submitted In this case, the professor calcu-lated the expected results for C, H, and N and the expected formula and molecular weight Note thatthe compound also contains oxygen, but that there was no request for an oxygen analysis Twoother samples were also submitted at the same time After a short time, typically within a week, the

1.1 Elemental Analysis and Calculations 3

T A B L E 1 2

CALCULATION OF EMPIRICAL FORMULA

Using a 100-g sample:

64.6% of C = 64.6 g 10.8% of H = 10.8 g

1

2 0

4 0

.6 0

g g

ᎏ

12.0

6 1

4.

g

6 /m

g ole

1.00

1 8

0.

g

8 /m

g ole

16.

2 0

4 g

.6 /m

g ole

which approximates

C3.50H7.00O1.00or

C7H14O2

results were reported to Professor Carbon as an email (see the request on the form) At a later date,

a formal letter (shown in the background on the right-hand side) is sent to verify and authenticatethe results Compare the values in the report to those calculated by Professor Carbon Are theywithin the accepted range? If not, the analysis will have to be repeated with a freshly purified sam-ple, or a new possible structure will have to be considered

Keep in mind that in an actual laboratory situation, when you are trying to determine the ular formula of a totally new or previously unknown compound, you will have to allow for somevariance in the quantitative elemental analysis Other data can help you in this situation since in-frared (Chapter Two) and nuclear magnetic resonance (NMR) (Chapter Three) data will also sug-gest a possible structure or at least some of its prominent features Many times, these other data will

molec-be less sensitive to small amounts of impurities than the microanalysis

Sample ID

PAC599A 67.39

8.20 73.77

9.22 11.25 PAC589B

(circle one) AirMail

Comments: C7H11NO

%OtherMol Wt

Sensitive to :Dry the Sample?

B.P 69 ˚C @ 2.3 mmHg

Other Elements Present :Single Analysis Duplicate AnalysisDuplicate only if results are not in range

Email

PAC599A P.O No :

Phone

OX

pac@www.edu

Professor Amyl CarbonDepartment of ChemistryWestern Washington UniversityBellingham, WA 98225

C, H, N

F I G U R E 1 1 Sample microanalysis forms Shown on the left is a typical submission form that is sent

with the samples (The three shown here in labeled vials were all sent at the same time.) Each sample needs its own form In the background on the right is the formal letter that reported the results Were the results obtained for sample PAC599A satisfactory?

Once the molecular mass and the empirical formula are known, we may proceed directly to the

molecular formula Often, the empirical formula weight and the molecular mass are the same In

such cases, the empirical formula is also the molecular formula However, in many cases, the ical formula weight is less than the molecular mass, and it is necessary to determine how manytimes the empirical formula weight can be divided into the molecular mass The factor determined

empir-in this manner is the one by which the empirical formula must be multiplied to obtaempir-in the molecularformula

Ethane provides a simple example After quantitative element analysis, the empirical formula for ethane is found to be CH 3 A molecular mass of 30 is determined The empirical formula weight

of ethane, 15, is half of the molecular mass, 30 Therefore, the molecular formula of ethane must be2(CH3) or C2H6

For the sample unknown introduced earlier in this chapter, the empirical formula was found to be

C7H14O2 The formula weight is 130 If we assume that the molecular mass of this substance wasdetermined to be 130, we may conclude that the empirical formula and the molecular formula areidentical, and that the molecular formula must be CH O

1.3 MOLECULAR FORMULAS

1.2 DETERMINATION OF MOLECULAR MASS

The next step in determining the molecular formula of a substance is to determine the weight of one mole of that substance This may be accomplished in a variety of ways Without knowledge

of the molecular mass of the unknown, there is no way of determining whether the empiricalformula, which is determined directly from elemental analysis, is the true formula of the sub-stance or whether the empirical formula must be multiplied by some integral factor to obtain themolecular formula In the example cited in Section 1.1, without knowledge of the molecularmass of the unknown, it is impossible to tell whether the molecular formula is C7H14O2 or

C14H28O4

In a modern laboratory, the molecular mass is determined using mass spectrometry The details ofthis method and the means of determining molecular mass can be found in Section 1.6 and Chapter 8,Section 8.6 This section reviews some classical methods of obtaining the same information

An old method that is used occasionally is the vapor density method In this method, a known

volume of gas is weighed at a known temperature After converting the volume of the gas to standardtemperature and pressure, we can determine what fraction of a mole that volume represents Fromthat fraction, we can easily calculate the molecular mass of the substance

Another method of determining the molecular mass of a substance is to measure the freezing-pointdepression of a solvent that is brought about when a known quantity of test substance is added This

is known as a cryoscopic method Another method, which is used occasionally, is vapor pressure osmometry, in which the molecular weight of a substance is determined through an examination of

the change in vapor pressure of a solvent when a test substance is dissolved in it

If the unknown substance is a carboxylic acid, it may be titrated with a standardized solution

of sodium hydroxide By use of this procedure, a neutralization equivalent can be determined.

The neutralization equivalent is identical to the equivalent weight of the acid If the acid has onlyone carboxyl group, the neutralization equivalent and the molecular mass are identical If the acidhas more than one carboxyl group, the neutralization equivalent is equal to the molecular mass

of the acid divided by the number of carboxyl groups Many phenols, especially those substituted

by electron-withdrawing groups, are sufficiently acidic to be titrated by this same method, as aresulfonic acids

1.4 INDEX OF HYDROGEN DEFICIENCY

Frequently, a great deal can be learned about an unknown substance simply from knowledge of itsmolecular formula This information is based on the following general molecular formulas:

Difference of 2 hydrogensDifference of 2 hydrogens

Notice that each time a ring or p bond is introduced into a molecule, the number of hydrogens in

the molecular formula is reduced by two For every triple bond (two p bonds), the molecular

for-mula is reduced by four This is illustrated in Figure 1.2

When the molecular formula for a compound contains noncarbon or nonhydrogen elements, theratio of carbon to hydrogen may change Following are three simple rules that may be used to predicthow this ratio will change:

1 To convert the formula of an open-chain, saturated hydrocarbon to a formula containing

Group V elements (N, P, As, Sb, Bi), one additional hydrogen atom must be added to the

molecular formula for each such Group V element present In the following examples, eachformula is correct for a two-carbon acyclic, saturated compound:

C2H6, C2H7N, C2H8N2, C2H9N3

2 To convert the formula of an open-chain, saturated hydrocarbon to a formula containing

Group VI elements (O, S, Se, Te), no change in the number of hydrogens is required In the

following examples, each formula is correct for a two-carbon, acyclic, saturated compound:

C CH

(also compare CHOH to C O)

F I G U R E 1 2 Formation of rings and double bonds Formation of each ring or double bond causes the

loss of 2H.

3 To convert the formula of an open-chain, saturated hydrocarbon to a formula containing

Group VII elements (F, Cl, Br, I), one hydrogen must be subtracted from the molecular

formula for each such Group VII element present In the following examples, each formula

is correct for a two-carbon, acyclic, saturated compound:

C2H6, C2H5F, C2H4F2, C2H3F3Table 1.3 presents some examples that should demonstrate how these correction numbers were de-termined for each of the heteroatom groups

The index of hydrogen deficiency (sometimes called the unsaturation index) is the number

of p bonds and/or rings a molecule contains It is determined from an examination of the lar formula of an unknown substance and from a comparison of that formula with a formula for acorresponding acyclic, saturated compound The difference in the number of hydrogens betweenthese formulas, when divided by 2, gives the index of hydrogen deficiency

molecu-The index of hydrogen deficiency can be very useful in structure determination problems Agreat deal of information can be obtained about a molecule before a single spectrum is examined

For example, a compound with an index of one must have one double bond or one ring, but it

can-not have both structural features A quick examination of the infrared spectrum could confirm thepresence of a double bond If there were no double bond, the substance would have to be cyclic

and saturated A compound with an index of two could have a triple bond, or it could have two

double bonds, two rings, or one of each Knowing the index of hydrogen deficiency of a substance,the chemist can proceed directly to the appropriate regions of the spectra to confirm the presence

or absence of p bonds or rings Benzene contains one ring and three “double bonds” and thus has

an index of hydrogen deficiency of four Any substance with an index of four or more may contain

a benzenoid ring; a substance with an index less than four cannot contain such a ring.

To determine the index of hydrogen deficiency for a compound, apply the following steps:

1 Determine the formula for the saturated, acyclic hydrocarbon containing the same number

of carbon atoms as the unknown substance

2 Correct this formula for the nonhydrocarbon elements present in the unknown Add onehydrogen atom for each Group V element present and subtract one hydrogen atom for eachGroup VII element present

3 Compare this formula with the molecular formula of the unknown Determine the number ofhydrogens by which the two formulas differ

4 Divide the difference in the number of hydrogens by two to obtain the index of hydrogen

deficiency This equals the number of p bonds and/or rings in the structural formula of theunknown substance

1.4 Index of Hydrogen Deficiency 7

T A B L E 1 3

CORRECTIONS TO THE NUMBER OF HYDROGEN ATOMS WHEN GROUP V AND VII HETEROATOMS ARE INTRODUCED (GROUP VI HETEROATOMS DO NOT REQUIRE A CORRECTION)

S S

2 Correction for oxygens (no change in the number of hydrogens) gives the formula C7H16O2.

3 The latter formula differs from that of the unknown by two hydrogens

4 The index of hydrogen deficiency equals one There must be one ring or one double bond in

the unknown substance

Having this information, the chemist can proceed immediately to the double-bond regions of theinfrared spectrum There, she finds evidence for a carbon–oxygen double bond (carbonyl group)

At this point, the number of possible isomers that might include the unknown has been narrowedconsiderably Further analysis of the spectral evidence leads to an identification of the unknown

substance as isopentyl acetate.

O

CH3 C O CH2 CH2 CH CH3

CH3

� E X A M P L E 2

Nicotine has the molecular formula C10H14N2

1 The formula for a 10-carbon, saturated, acyclic hydrocarbon is C10H22

2 Correction for the two nitrogens (add two hydrogens) gives the formula C10H24N2

3 The latter formula differs from that of nicotine by 10 hydrogens

4 The index of hydrogen deficiency equals five There must be some combination of five p

bonds and/or rings in the molecule Since the index is greater than four, a benzenoid ring

could be included in the molecule

Analysis of the spectrum quickly shows that a benzenoid ring is indeed present in nicotine The tral results indicate no other double bonds, suggesting that another ring, this one saturated, must bepresent in the molecule More careful refinement of the spectral analysis leads to a structural formulafor nicotine:

spec-N

N

CH3The following examples illustrate how the index of hydrogen deficiency is determined and howthat information can be applied to the determination of a structure for an unknown substance

� E X A M P L E 3

Chloral hydrate (“knockout drops”) is found to have the molecular formula C2H3Cl3O2

1 The formula for a two-carbon, saturated, acyclic hydrocarbon is C2H6

2 Correction for oxygens (no additional hydrogens) gives the formula C2H6O2

3 Correction for chlorines (subtract three hydrogens) gives the formula C2H3Cl3O2

4 This formula and the formula of chloral hydrate correspond exactly

5 The index of hydrogen deficiency equals zero Chloral hydrate cannot contain rings or double

OH

1.5 THE RULE OF THIRTEEN

High-resolution mass spectrometry provides molecular mass information from which the user candetermine the exact molecular formula directly The discussion on exact mass determination inChapter 8 explains this process in detail When such molar mass information is not available, how-ever, it is often useful to be able to generate all the possible molecular formulas for a given mass Byapplying other types of spectroscopic information, it may then be possible to distinguish amongthese possible formulas A useful method for generating possible molecular formulas for a given

molecular mass is the Rule of Thirteen.1

As a first step in the Rule of Thirteen, we generate a base formula, which contains only carbon

and hydrogen The base formula is found by dividing the molecular mass M by 13 (the mass of one carbon plus one hydrogen) This calculation provides a numerator n and a remainder r.

which is a combination of carbons and hydrogens that has the desired molecular mass M.

The index of hydrogen deficiency (unsaturation index) U that corresponds to the preceding

for-mula is calculated easily by applying the relationship

Of course, you can also calculate the index of hydrogen deficiency using the method shown inSection 1.4.

If we wish to derive a molecular formula that includes other atoms besides carbon and hydrogen,then we must subtract the mass of a combination of carbons and hydrogens that equals the masses

of the other atoms being included in the formula For example, if we wish to convert the base mula to a new formula containing one oxygen atom, then we subtract one carbon and four hydro-gens at the same time that we add one oxygen atom Both changes involve a molecular massequivalent of 16 (O =CH4=16) Table 1.4 includes a number of C/H equivalents for replacement

for-of carbon and hydrogen in the base formula by the most common elements likely to occur in anorganic compound.2

To comprehend how the Rule of Thirteen might be applied, consider an unknown substance with

a molecular mass of 94 amu Application of the formula provides

ᎏ

91

43

ᎏ=7 +ᎏ

1

33

ᎏ

According to the formula, n=7 and r=3 The base formula must be

C7H10The index of hydrogen deficiency is

CARBON/HYDROGEN EQUIVALENTS FOR SOME COMMON ELEMENTS

respectively Always use this assumption when applying this method.

A substance that fits this formula must contain some combination of three rings or multiple bonds.

A possible structure might be

If we were interested in a substance that had the same molecular mass but that contained oneoxygen atom, the molecular formula would become C6H6O This formula is determined according

to the following scheme:

6 New index of hydrogen deficiency: U=4

A possible substance that fits these data is

There are additional possible molecular formulas that conform to a molecular mass of 94 amu:

C5H2O2 U=5 C5H2S U=5

C6H8N U=3⎯ 1

As the formula C6H8N shows, any formula that contains an even number of hydrogen atoms but an

odd number of nitrogen atoms leads to a fractional value of U, an unlikely choice.

Any compound with a value of U less than zero (i.e., negative) is an impossible combination Such

a value is often an indicator that an oxygen or nitrogen atom must be present in the molecular formula.When we calculate formulas using this method, if there are not enough hydrogens, we can

subtract 1 carbon and add 12 hydrogens (and make the appropriate correction in U) This procedure works only if we obtain a positive value of U Alternatively we can obtain another potential molecu- lar formula by adding 1 carbon and subtracting 12 hydrogens (and correcting U).

1.6 A QUICK LOOK AHEAD TO SIMPLE USES OF MASS SPECTRA

Chapter 8 contains a detailed discussion of the technique of mass spectrometry See Sections

8.1–8.7 for applications of mass spectrometry to the problems of molecular formula determination.Briefly, the mass spectrometer is an instrument that subjects molecules to a high-energy beam ofelectrons This beam of electrons converts molecules to positive ions by removing an electron Thestream of positively charged ions is accelerated along a curved path in a magnetic field The radius

of curvature of the path described by the ions depends on the ratio of the mass of the ion to its

charge (the m/z ratio) The ions strike a detector at positions that are determined by the radius of

curvature of their paths The number of ions with a particular mass-to-charge ratio is plotted as afunction of that ratio

The particle with the largest mass-to-charge ratio, assuming that the charge is 1, is the particle

that represents the intact molecule with only one electron removed This particle, called the molecular ion (see Chapter 8, Section 8.5), can be identified in the mass spectrum From its position in the

spectrum, its weight can be determined Since the mass of the dislodged electron is so small, themass of the molecular ion is essentially equal to the molecular mass of the original molecule Thus,the mass spectrometer is an instrument capable of providing molecular mass information

Virtually every element exists in nature in several isotopic forms The natural abundance of each ofthese isotopes is known Besides giving the mass of the molecular ion when each atom in the molecule

is the most common isotope, the mass spectrum also gives peaks that correspond to that same moleculewith heavier isotopes The ratio of the intensity of the molecular ion peak to the intensities of thepeaks corresponding to the heavier isotopes is determined by the natural abundance of each isotope.Because each type of molecule has a unique combination of atoms, and because each type of atomand its isotopes exist in a unique ratio in nature, the ratio of the intensity of the molecular ion peak tothe intensities of the isotopic peaks can provide information about the number of each type of atompresent in the molecule

For example, the presence of bromine can be determined easily because bromine causes a pattern

of molecular ion peaks and isotope peaks that is easily identified If we identify the mass of the

molecular ion peak as M and the mass of the isotope peak that is two mass units heavier than the molecular ion as M+2, then the ratio of the intensities of the M and M+2 peaks will be approxi-

mately one to one when bromine is present (see Chapter 8, Section 8.5, for more details) When chlorine is present, the ratio of the intensities of the M and M+ 2 peaks will be approximately

three to one These ratios reflect the natural abundances of the common isotopes of these elements.

Thus, isotope ratio studies in mass spectrometry can be used to determine the molecular formula

PRECISE MASSES FOR SUBSTANCES

OF MOLECULAR MASS EQUAL TO 44 amu

is even (or zero), the molecular mass will be an even number The Nitrogen Rule is explainedfurther in Chapter 8, Section 8.6.

Since the advent of high-resolution mass spectrometers, it is also possible to use very precisemass determinations of molecular ion peaks to determine molecular formulas When the atomicweights of the elements are determined very precisely, it is found that they do not have exactly inte-gral values Every isotopic mass is characterized by a small “mass defect,” which is the amount bywhich the mass of the isotope differs from a perfectly integral mass number The mass defect forevery isotope of every element is unique As a result, a precise mass determination can be used todetermine the molecular formula of the sample substance, since every combination of atomicweights at a given nominal mass value will be unique when mass defects are considered For exam-ple, each of the substances shown in Table 1.5 has a nominal mass of 44 amu As can be seen from

the table, their exact masses, obtained by adding exact atomic masses, are substantially different

when measured to four decimal places

*1 Researchers used a combustion method to analyze a compound used as an antiknock additive

in gasoline A 9.394-mg sample of the compound yielded 31.154 mg of carbon dioxide and7.977 mg of water in the combustion

(a) Calculate the percentage composition of the compound

(b) Determine its empirical formula

*2 The combustion of an 8.23-mg sample of unknown substance gave 9.62 mg CO2and 3.94 mg

H2O Another sample, weighing 5.32 mg, gave 13.49 mg AgCl in a halogen analysis Determinethe percentage composition and empirical formula for this organic compound

*3 An important amino acid has the percentage composition C 32.00%, H 6.71%, and N 18.66%.

Calculate the empirical formula of this substance

*4 A compound known to be a pain reliever had the empirical formula C9H8O4 When a mixture of5.02 mg of the unknown and 50.37 mg of camphor was prepared, the melting point of a portion

of this mixture was determined The observed melting point of the mixture was 156°C What isthe molecular mass of this substance?

*5 An unknown acid was titrated with 23.1 mL of 0.1 N sodium hydroxide The weight of the

acid was 120.8 mg What is the equivalent weight of the acid?

*6 Determine the index of hydrogen deficiency for each of the following compounds:

(a) C8H7NO (d) C5H3ClN4(b) C3H7NO3 (e) C21H22N2O2(c) C4H4BrNO2

*7 A substance has the molecular formula C4H9N Is there any likelihood that this materialcontains a triple bond? Explain your reasoning

*8 (a) A researcher analyzed an unknown solid, extracted from the bark of spruce trees, to

determine its percentage composition An 11.32-mg sample was burned in a combustionapparatus The carbon dioxide (24.87 mg) and water (5.82 mg) were collected andweighed From the results of this analysis, calculate the percentage composition of theunknown solid

(b) Determine the empirical formula of the unknown solid

P R O B L E M S

(c) Through mass spectrometry, the molecular mass was found to be 420 g/mole What is themolecular formula?

(d) How many aromatic rings could this compound contain?

*9 Calculate the molecular formulas for possible compounds with molecular masses of 136; use

the Rule of Thirteen You may assume that the only other atoms present in each molecule arecarbon and hydrogen

(a) A compound with two oxygen atoms(b) A compound with two nitrogen atoms(c) A compound with two nitrogen atoms and one oxygen atom(d) A compound with five carbon atoms and four oxygen atoms

*10 An alkaloid was isolated from a common household beverage The unknown alkaloid proved to

have a molecular mass of 194 Using the Rule of Thirteen, determine a molecular formula and

an index of hydrogen deficiency for the unknown Alkaloids are naturally occurring organic

substances that contain nitrogen (Hint: There are four nitrogen atoms and two oxygen atoms

in the molecular formula The unknown is caffeine Look up the structure of this substance in

The Merck Index and confirm its molecular formula.)

*11 The Drug Enforcement Agency (DEA) confiscated a hallucinogenic substance during a drug

raid When the DEA chemists subjected the unknown hallucinogen to chemical analysis, theyfound that the substance had a molecular mass of 314 Elemental analysis revealed the presence

of carbon and hydrogen only Using the Rule of Thirteen, determine a molecular formula and an

index of hydrogen deficiency for this substance (Hint: The molecular formula of the unknown

also contains two oxygen atoms The unknown is tetrahydrocannabinol, the active constituent

of marijuana Look up the structure of tetrahydrocannabinol in The Merck Index and confirm its

molecular formula.)

12 A carbohydrate was isolated from a sample of cow’s milk The substance was found to have a

molecular mass of 342 The unknown carbohydrate can be hydrolyzed to form two isomericcompounds, each with a molecular mass of 180 Using the Rule of Thirteen, determine amolecular formula and an index of hydrogen deficiency for the unknown and for the hydrolysis

products (Hint: Begin by solving the molecular formula for the 180-amu hydrolysis products.

These products have one oxygen atom for every carbon atom in the molecular formula The

unknown is lactose Look up its structure in The Merck Index and confirm its molecular formula.)

O’Neil, M J., et al., eds The Merck Index, 14th ed.,

Whitehouse Station, NJ: Merck & Co., 2006.

Pavia, D L., G M Lampman, G S Kriz, and R G Engel,

Introduction to Organic Laboratory Techniques: A Small

Scale Approach, 2nd ed., Belmont, CA: Brooks-Cole

Thomson, 2005.

Pavia, D L., G M Lampman, G S Kriz, and R G Engel,

Introduction to Organic Laboratory Techniques: A

Micro-R E F E Micro-R E N C E S

scale Approach, 4th ed., Belmont, CA: Brooks-Cole

Thomson, 2007.

Shriner, R L., C K F Hermann, T C Morrill, D Y.

Curtin, and R C Fuson, The Systematic Identification

of Organic Compounds, 8th ed., New York, NY: John

Wiley, 2004.

*Answers are provided in the chapter, Answers to Selected Problems

INFRARED SPECTROSCOPY

Almost any compound having covalent bonds, whether organic or inorganic, absorbs various

frequencies of electromagnetic radiation in the infrared region of the electromagnetic spectrum.This region lies at wavelengths longer than those associated with visible light, which range fromapproximately 400 to 800 nm (1 nm =10−9m), but lies at wavelengths shorter than those associated with

microwaves, which are longer than 1 mm For chemical purposes, we are interested in the vibrational

portion of the infrared region It includes radiation with wavelengths (l) between 2.5 mm and 25 mm(1mm =10−6m) Although the more technically correct unit for wavelength in the infrared region of thespectrum is the micrometer (mm), you will often see the micron (m) used on infrared spectra Figure 2.1illustrates the relationship of the infrared region to others included in the electromagnetic spectrum.Figure 2.1 shows that the wavelength l is inversely proportional to the frequency n and is governed bythe relationship n=c/l, where c=speed of light Also observe that the energy is directly proportional to

the frequency: E=hn, where h=Planck’s constant From the latter equation, you can see qualitativelythat the highest energy radiation corresponds to the X-ray region of the spectrum, where the energy may

be great enough to break bonds in molecules At the other end of the electromagnetic spectrum, frequencies have very low energies, only enough to cause nuclear or electronic spin transitions withinmolecules—that is, nuclear magnetic resonance (NMR) or electron spin resonance (ESR), respectively.Table 2.1 summarizes the regions of the spectrum and the types of energy transitions observedthere Several of these regions, including the infrared, give vital information about the structures oforganic molecules Nuclear magnetic resonance, which occurs in the radiofrequency part of thespectrum, is discussed in Chapters 3, 4, 5, 6, and 10, whereas ultraviolet and visible spectroscopyare described in Chapter 7

radio-Most chemists refer to the radiation in the vibrational infrared region of the electromagnetic

spectrum in terms of a unit called a wavenumber (n苶), rather than wavelength (m or mm)

15

C H A P T E R 2

F I G U R E 2 1 A portion of the electromagnetic spectrum showing the relationship of the vibrational

infrared to other types of radiation.

Wavenumbers are expressed as reciprocal centimeters (cm−1) and are easily computed by taking thereciprocal of the wavelength expressed in centimeters Convert a wavenumber 苶n to a frequency n by

multiplying it by the speed of light (expressed in centimeters per second)

苶n (cm−1) =ᎏ

l (

1cm)ᎏ n (Hz) =n苶c=ᎏc (

l

cm(c

/m

se)

c)

ᎏ

The main reason chemists prefer to use wavenumbers as units is that they are directly proportional

to energy (a higher wavenumber corresponds to a higher energy) Thus, in terms of wavenumbers,

the vibrational infrared extends from about 4000 to 400 cm−1 This range corresponds to lengths of 2.5 to 25 mm We will use wavenumber units exclusively in this textbook You may en-

wave-counter wavelength values in older literature Convert wavelengths (m or mm) to wavenumbers(cm−1) by using the following relationships:

INTRODUCTION TO INFRARED SPECTROSCOPY

2.1 THE INFRARED ABSORPTION PROCESS

As with other types of energy absorption, molecules are excited to a higher energy state when theyabsorb infrared radiation The absorption of infrared radiation is, like other absorption processes, aquantized process A molecule absorbs only selected frequencies (energies) of infrared radiation.The absorption of infrared radiation corresponds to energy changes on the order of 8 to 40 kJ/mole.Radiation in this energy range corresponds to the range encompassing the stretching and bendingvibrational frequencies of the bonds in most covalent molecules In the absorption process, thosefrequencies of infrared radiation that match the natural vibrational frequencies of the molecule in

question are absorbed, and the energy absorbed serves to increase the amplitude of the vibrational

motions of the bonds in the molecule Note, however, that not all bonds in a molecule are capable ofabsorbing infrared energy, even if the frequency of the radiation exactly matches that of the bond

motion Only those bonds that have a dipole moment that changes as a function of time are capable

T A B L E 2 1

TYPES OF ENERGY TRANSITIONS IN EACH REGION

OF THE ELECTROMAGNETIC SPECTRUM

Electronic spin (electron spin resonance)

2.2 Uses of the Infrared Spectrum 17

2.2 USES OF THE INFRARED SPECTRUM

Since every type of bond has a different natural frequency of vibration, and since two of the sametype of bond in two different compounds are in two slightly different environments, no two mole-

cules of different structure have exactly the same infrared absorption pattern, or infrared trum Although some of the frequencies absorbed in the two cases might be the same, in no case of

spec-two different molecules will their infrared spectra (the patterns of absorption) be identical Thus, theinfrared spectrum can be used for molecules much as a fingerprint can be used for humans By com-paring the infrared spectra of two substances thought to be identical, you can establish whether theyare, in fact, identical If their infrared spectra coincide peak for peak (absorption for absorption), inmost cases the two substances will be identical

A second and more important use of the infrared spectrum is to determine structural informationabout a molecule The absorptions of each type of bond (NIH, CIH, OIH, CIX, CJO, CIO, CIC,

CJ C, CKC, CKN, and so on) are regularly found only in certain small portions of the vibrational red region A small range of absorption can be defined for each type of bond Outside this range, absorp-tions are normally due to some other type of bond For instance, any absorption in the range 3000 ±

infra-150 cm−1is almost always due to the presence of a CIH bond in the molecule; an absorption in the range

1715 ±100 cm−1is normally due to the presence of a CJO bond (carbonyl group) in the molecule Thesame type of range applies to each type of bond Figure 2.2 illustrates schematically how these are spreadout over the vibrational infrared Try to fix this general scheme in your mind for future convenience

of absorbing infrared radiation Symmetric bonds, such as those of H2or Cl2, do not absorb infraredradiation A bond must present an electrical dipole that is changing at the same frequency as the in-coming radiation for energy to be transferred The changing electrical dipole of the bond can thencouple with the sinusoidally changing electromagnetic field of the incoming radiation Thus, a sym-metric bond that has identical or nearly identical groups on each end will not absorb in the infrared.For the purposes of an organic chemist, the bonds most likely to be affected by this restraint arethose of symmetric or pseudosymmetric alkenes (CJ C) and alkynes (CK C)

F I G U R E 2 2 The approximate regions where various common types of bonds absorb (stretching

vibrations only; bending, twisting, and other types of bond vibrations have been omitted for clarity).

2.3 THE MODES OF STRETCHING AND BENDING

The simplest types, or modes, of vibrational motion in a molecule that are infrared active—those,

that give rise to absorptions—are the stretching and bending modes

However, other, more complex types of stretching and bending are also active The following tions of the normal modes of vibration for a methylene group introduce several terms In general,asymmetric stretching vibrations occur at higher frequencies than symmetric stretching vibrations;

illustra-also, stretching vibrations occur at higher frequencies than bending vibrations The terms scissoring, rocking, wagging, and twisting are commonly used in the literature to describe the origins of

infrared bands

In any group of three or more atoms, at least two of which are identical, there are two modes of

stretching: symmetric and asymmetric Examples of such groupings are ICH3, ICH2I(see p 19),

INO2, INH2, and anhydrides The methyl group gives rise to a symmetric stretching vibration atabout 2872 cm−1and an asymmetric stretch at about 2962 cm−1 The anhydride functional groupgives two absorptions in the CJ O region because of the asymmetric and symmetric stretchingmodes A similar phenomenon occurs in the amino group, where a primary amine (NH2) usually hastwo absorptions in the NIH stretch region, while a secondary amine (R2NH) has only one absorp-tion peak Amides exhibit similar bands There are two strong NJ O stretch peaks for a nitro group,with the symmetric stretch appearing at about 1350 cm−1and the asymmetric stretch appearing atabout 1550 cm−1

C H

Stretching

H

OCBending

2.3 The Modes of Stretching and Bending 19

The vibrations we have been discussing are called fundamental absorptions They arise from

excitation from the ground state to the lowest-energy excited state Usually, the spectrum is

compli-cated because of the presence of weak overtone, combination, and difference bands Overtones

re-sult from excitation from the ground state to higher energy states, which correspond to integralmultiples of the frequency of the fundamental (n) For example, you might observe weak overtonebands at 2n苶, 3n苶, Any kind of physical vibration generates overtones If you pluck a string on a

cello, the string vibrates with a fundamental frequency However, less-intense vibrations are also set

up at several overtone frequencies An absorption in the infrared at 500 cm−1may well have an companying peak of lower intensity at 1000 cm−1—an overtone

ac-When two vibrational frequencies (n苶1and n苶2) in a molecule couple to give rise to a vibration of

a new frequency within the molecule, and when such a vibration is infrared active, it is called a

combination band This band is the sum of the two interacting bands (n苶comb=n苶1+n苶2) Not allpossible combinations occur The rules that govern which combinations are allowed are beyond thescope of our discussion here

Difference bands are similar to combination bands The observed frequency in this case results

from the difference between the two interacting bands (ndiff=n苶1−n苶2)

One can calculate overtone, combination, and difference bands by directly manipulating quencies in wavenumbers via multiplication, addition, and subtraction, respectively When a funda-mental vibration couples with an overtone or combination band, the coupled vibration is called

fre-Fermi resonance Again, only certain combinations are allowed fre-Fermi resonance is often observed

in carbonyl compounds

Although rotational frequencies of the whole molecule are not infrared active, they often couplewith the stretching and bending vibrations in the molecule to give additional fine structure to theseabsorptions, thus further complicating the spectrum One of the reasons a band is broad rather thansharp in the infrared spectrum is rotational coupling, which may lead to a considerable amount ofunresolved fine structure

N H

H

N O

N H

H

N O

2.4 BOND PROPERTIES AND ABSORPTION TRENDS

Let us now consider how bond strength and the masses of the bonded atoms affect the infraredabsorption frequency For the sake of simplicity, we will restrict the discussion to a simple hetero-

nuclear diatomic molecule (two different atoms) and its stretching vibration.

A diatomic molecule can be considered as two vibrating masses connected by a spring The bonddistance continually changes, but an equilibrium or average bond distance can be defined.Whenever the spring is stretched or compressed beyond this equilibrium distance, the potential en-ergy of the system increases

As for any harmonic oscillator, when a bond vibrates, its energy of vibration is continually andperiodically changing from kinetic to potential energy and back again The total amount of energy

is proportional to the frequency of the vibration,

2 2

ᎏ

K is a constant that varies from one bond to another As a first approximation, the force constants for

triple bonds are three times those of single bonds, whereas the force constants for double bonds aretwice those of single bonds

Two things should be noticeable immediately One is that stronger bonds have a larger force

con-stant K and vibrate at higher frequencies than weaker bonds The second is that bonds between

atoms of higher masses (larger reduced mass,m) vibrate at lower frequencies than bonds betweenlighter atoms

In general, triple bonds are stronger than double or single bonds between the same two atomsand have higher frequencies of vibration (higher wavenumbers):

2.4 Bond Properties and Absorption Trends 21

Bending motions occur at lower energy (lower frequency) than the typical stretching motions

be-cause of the lower value for the bending force constant K.

Hybridization affects the force constant K, also Bonds are stronger in the order sp>sp2>sp3, andthe observed frequencies of CIH vibration illustrate this nicely

Resonance also affects the strength and length of a bond and hence its force constant K Thus,

whereas a normal ketone has its CJ O stretching vibration at 1715 cm−1, a ketone that is conjugatedwith a CJ C double bond absorbs at a lower frequency, near 1675 to 1680 cm−1 That is because res-onance lengthens the CJ O bond distance and gives it more single-bond character:

Resonance has the effect of reducing the force constant K, and the absorption moves to a lower

c =velocity of light =3 ×1010cm/sec

K =force constant in dynes/cm

2 2

ᎏ, masses of atoms in grams,

Removing Avogadro’s number (6.02 ×1023) from the denominator of the reduced mass expression(m) by taking its square root, we obtain the expression

∼3000 cm−1

T A B L E 2 2

CALCULATION OF STRETCHING FREQUENCIES FOR DIFFERENT TYPES

C

C

+

M M

C C

1

1 2

2)

+

(1 1

2 2

)

ᎏ = 6

n 苶=1650 cm−1 (experimental) CIH bond:

n 苶=4.12冪莦

K= 5 × 10 5 dynes/cm

M M

C

C

+

M M

H H

ᎏ =ᎏ(

1

1 2

2)

+

(1 1

)

n 苶=4.12冪莦= 3032 cm−1 (calculated)

n 苶=3000 cm−1 (experimental) CID bond:

n 苶=4.12冪莦

K= 5 × 10 5 dynes/cm

M M

C

C

+

M M

D D

ᎏ = ᎏ(

1

1 2

2)

+

(2 2

2.5 The Infrared Spectrometer 23

A Dispersive Infrared Spectrometers

Figure 2.3a schematically illustrates the components of a simple dispersive infrared ter The instrument produces a beam of infrared radiation from a hot wire and, by means of mir-rors, divides it into two parallel beams of equal-intensity radiation The sample is placed in one

spectrome-beam, and the other beam is used as a reference The beams then pass into the monochromator,

which disperses each into a continuous spectrum of frequencies of infrared light The chromator consists of a rapidly rotating sector (beam chopper) that passes the two beams alter-nately to a diffraction grating (a prism in older instruments) The slowly rotating diffractiongrating varies the frequency or wavelength of radiation reaching the thermocouple detector.The detector senses the ratio between the intensities of the reference and sample beams In thisway, the detector determines which frequencies have been absorbed by the sample and whichfrequencies are unaffected by the light passing through the sample After the signal from thedetector is amplified, the recorder draws the resulting spectrum of the sample on a chart It isimportant to realize that the spectrum is recorded as the frequency of infrared radiation changes

mono-by rotation of the diffraction grating Dispersive instruments are said to record a spectrum in the

A new expression is obtained by inserting the actual values of p and c:

This equation may be used to calculate the approximate position of a band in the infrared spectrum

by assuming that K for single, double, and triple bonds is 5, 10, and 15 × 105dynes/cm, tively Table 2.2 gives a few examples Notice that excellent agreement is obtained with the experi-mental values given in the table However, experimental and calculated values may varyconsiderably owing to resonance, hybridization, and other effects that operate in organic molecules

respec-Nevertheless, good qualitative values are obtained by such calculations.

2 2

ᎏ, where M1and M2are atomic weights

K=force constant in dynes/cm (1 dyne =1.020 ×10−3g)

2.5 THE INFRARED SPECTROMETER