ORGANIC MECHANISMS

ORGANIC MECHANISMS

Reactions, Methodology, andBiological Applications

XIAOPING SUNUniversity of CharlestonCharleston, West Virginia, USA

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Library of Congress Cataloging-in-Publication Data:

Sun, Xiaoping, 1960–Organic mechanisms : reactions, methodology, and biological applications / Xiaoping Sun,

University of Charleston, Charleston, West Virginia, USA.pages cm

Includes bibliographical references and index.ISBN 978-1-118-06564-8 (hardback)

1. Organic reaction mechanisms. I. Title.QD502.5.S86 2013547′.139–dc23

2013002855

Printed in the United States of America

ISBN: 9781118065648

10 9 8 7 6 5 4 3 2 1

CONTENTS

Preface xiii

1 Fundamental Principles 1

1.1 Reaction Mechanisms and their Importance 11.2 Elementary (Concerted) and Stepwise Reactions 21.3 Molecularity 4

1.3.1 Unimolecular Reactions 41.3.2 Bimolecular Reactions 4

1.4 Kinetics 51.4.1 Rate Laws for Elementary (Concerted) Reactions 51.4.2 Reactive Intermediates and the Steady-State Assumption 91.4.3 Rate Laws for Stepwise Reactions 12

1.5 Thermodynamics 131.5.1 Enthalpy, Entropy, and Free Energy 131.5.2 Reversible and Irreversible Reactions 141.5.3 Chemical Equilibrium 15

1.6 The Transition State 171.7 The Molecular Orbital Theory 19

1.7.1 Formation of Molecular Orbitals from Atomic Orbitals 191.7.2 Molecular Orbital Diagrams 251.7.3 Resonance Stabilization 251.7.4 Frontier Molecular Orbitals 28

1.8 Electrophiles/Nucleophiles versus Acids/Bases 291.8.1 Common Electrophiles 291.8.2 Common Nucleophiles 33

v

vi CONTENTS

1.9 Isotope Labeling 35Problems 38References 40

2 The Aliphatic C H Bond Functionalization 41

2.1 Alkyl Radicals: Bonding and their Relative Stability 422.2 Radical Halogenations of the C H Bonds on sp3-Hybridized

Carbons: Mechanism and Nature of the Transition States 472.3 Energetics of the Radical Halogenations of Alkanes and their

Regioselectivity 512.3.1 Energy Profiles for Radical Halogenation Reactions

of Alkanes 512.3.2 Regioselectivity for Radical Halogenation Reactions 52

2.4 Kinetics of Radical Halogenations of Alkanes 562.5 Radical Initiators 612.6 Transition-Metal-Compounds-Catalyzed Alkane C H Bond

Activation and Functionalization 642.6.1 The C H Bond Activation via Agostic Bond 642.6.2 Mechanisms for the C H Bond Oxidative

Functionalization 652.7 Superacids-Catalyzed Alkane C H Bond Activation and

Functionalization 682.8 Nitration of Aliphatic C H Bonds via the Nitronium NO2

+ Ion 692.9 Enzyme-Catalyzed Alkane C H Bond Activation and

Functionalization: Biochemical Methods 71Problems 75References 77

3 Functionalization of the Alkene C C Bond byElectrophilic Additions 78

3.1 Markovnikov Additions via Intermediate Carbocations 793.1.1 Additions of Alkenes to Hydrogen Halides

(HCl, HBr, and HI): Mechanism, Regiochemistry,and Stereochemistry 79

3.1.2 Acid- and Transition-Metal-Catalyzed Hydration ofAlkenes and Its Applications 84

3.1.3 Acid-Catalyzed Additions of Alcohols to Alkenes 893.1.4 Special Electrophilic Additions of the Alkene C C Bond:

Mechanistic and Synthetic Aspects 893.1.5 Electrophilic Addition to the C C Triple Bond via a

Vinyl Cation Intermediate 943.2 Electrophilic Addition of Hydrogen Halides to Conjugated Dienes 953.3 Non-Markovnikov Radical Addition 96

CONTENTS vii

3.4 Hydroboration: Concerted, Non-Markovnikov syn-Addition 973.4.1 Diborane (B2H6): Structure and Properties 973.4.2 Concerted, Non-Markovnikov syn-Addition of Borane

(BH3) to the Alkene C C Bond: Mechanism,Regiochemistry, and Stereochemistry 98

3.4.3 Synthesis of Special Hydroborating Reagents 1023.4.4 Reactions of Alkenes with Special Hydroborating

Reagents: Regiochemistry, Stereochemistry, and theirApplications in Chemical Synthesis 103

3.5 Transition-Metal-Catalyzed Hydrogenation of the Alkene C CBond (syn-Addition) 1073.5.1 Mechanism and Stereochemistry 1073.5.2 Synthetic Applications 1103.5.3 Biochemically-Related Applications: Hydrogenated

Fats (Oils) 1113.6 Halogenation of the Alkene C C Bond (Anti-Addition):

Mechanism and Its Stereochemistry 113Problems 117References 120

4 Functionalization of the Alkene C C Bond byCycloaddition Reactions 121

4.1 Cycloadditions of the Alkene C C Bond to FormThree-Membered Rings 1224.1.1 Epoxidation 1224.1.2 Cycloadditions via Carbenes and Related Species 124

4.2 Cycloadditions to Form Four-Membered Rings 1284.3 Diels–Alder Cycloadditions of the Alkene C C Bond to Form

Six-Membered Rings 1314.3.1 Frontier Molecular Orbital Interactions 1324.3.2 Substituent Effects 1354.3.3 Other Diels–Alder Reactions 138

4.4 1,3-Dipolar Cycloadditions of the C C and other Multiple Bondsto Form Five-Membered Rings 1424.4.1 Oxidation of Alkenes by Ozone (O3) and Osmium

Tetraoxide (OsO4) via Cycloadditions 1424.4.2 Cycloadditions of Nitrogen-Containing 1,3-Dipoles

to Alkenes 1454.4.3 Cycloadditions of Alkenes, Alkynes, and Nitriles to the

Dithionitronium (NS2+) Ion: Making CNS-Containing

Aromatic Heterocycles 1474.5 Pericyclic Reactions 154

Problems 158References 161

viii CONTENTS

5 The Aromatic C H Bond Functionalization and Related Reactions 162

5.1 Aromatic Nitration: All Reaction Intermediates and FullMechanism for the Aromatic C H Bond Substitution byNitronium (NO2

+) and Related Electrophiles 1635.1.1 Charge-Transfer Complex [ArH, NO2

+] between Areneand Nitronium 164

5.1.2 Ion-Radical Pair [ArH+ �, NO2�] 164

5.1.3 Arenium [Ar(H)NO2]+ Ion 1655.1.4 Full Mechanism for Aromatic Nitration 166

5.2 Mechanisms and Synthetic Utility for Aromatic C H BondSubstitutions by Other Related Electrophiles 167

5.3 The Electrophilic Aromatic C H Bond Substitution Reactionsvia SN1 and SN2 Mechanisms 1745.3.1 Reactions Involving SN1 Steps 1755.3.2 Reactions Involving SN2 Steps 179

5.4 Substituent Effects on the Electrophilic AromaticSubstitution Reactions 1815.4.1 Ortho- and Para-Directors 1835.4.2 Meta-Directors 185

5.5 Isomerizations Effected by the Electrophilic AromaticSubstitution Reactions 187

5.6 Electrophilic Substitution Reactions on the AromaticCarbon–Metal Bonds: Mechanisms and Synthetic Applications 191

5.7 Nucleophilic Aromatic Substitution via a Benzyne (aryne)Intermediate: Functional Group Transformations onAromatic Rings 193

5.8 Nucleophilic Aromatic Substitution via an AnionicMeisenheimer Complex 197

5.9 Biological Applications of Functionalized Aromatic Compounds 200Problems 204References 207

6 Nucleophilic Substitutions on sp3-Hybridized Carbons: FunctionalGroup Transformations 209

6.1 Nucleophilic Substitution on Mono-Functionalizedsp3-Hybridized Carbon 209

6.2 Functional Groups which are Good and Poor Leaving Groups 2116.3 Good and Poor Nucleophiles 2136.4 SN2 Reactions: Kinetics, Mechanism, and Stereochemistry 215

6.4.1 Mechanism and Stereochemistry for SN2 Reactions 2156.4.2 Steric Effect on SN2 Reactions 2186.4.3 Effect of Nucleophiles 2206.4.4 Solvent Effect 222

CONTENTS ix

6.4.5 Effect of Unsaturated Groups Attached to theFunctionalized Electrophilic Carbon 224

6.5 Analysis of the SN2 Mechanism Using Symmetry Rules andMolecular Orbital Theory 2256.5.1 The SN2 Reactions of Methyl and Primary Haloalkanes

RCH2X (X = Cl, Br, or I; R = H or an Alkyl Group) 2256.5.2 Reactivity of Dichloromethane CH2Cl2 228

6.6 SN1 Reactions: Kinetics, Mechanism, and Product Development 2296.6.1 The SN1 Mechanism and Rate Law 2296.6.2 Solvent Effect 2316.6.3 Effects of Carbocation Stability and Quality of Leaving

Group on the SN1 Rates 2316.6.4 Product Development for SN1 Reactions 235

6.7 Competition between SN1 and SN2 Reactions 2376.8 Some Useful SN1 and SN2 Reactions: Mechanisms and

Synthetic Perspectives 2416.8.1 Nucleophilic Substitution Reactions Effected by

Carbon Nucleophiles 2416.8.2 Synthesis of Primary Amines 2466.8.3 Synthetic Utility of Triphenylphosphine: A Strong

Phosphorus Nucleophile 2476.8.4 Neighboring Group-Assisted SN1 Reactions 247

6.9 Biological Applications of Nucleophilic Substitution Reactions 2516.9.1 Biomedical Applications 2516.9.2 Biosynthesis Involving Nucleophilic Substitution

Reactions 2536.9.3 An Enzyme-Catalyzed Nucleophilic Substitution of

a Haloalkane 255Problems 256References 259

7 Eliminations 260

7.1 E2 Elimination: Bimolecular �-Elimination of H/LG and ItsRegiochemistry and Stereochemistry 2617.1.1 Mechanism and Regiochemistry 2617.1.2 E2 Eliminations of Functionalized Cycloalkanes 2647.1.3 Stereochemistry 267

7.2 Analysis of the E2 Mechanism Using Symmetry Rules andMolecular Orbital Theory 268

7.3 Basicity versus Nucleophilicity for Various Anions 2717.4 Competition of E2 and SN2 Reactions 2747.5 E1 Elimination: Stepwise �-Elimination of H/LG via an

Intermediate Carbocation and Its Rate Law 2767.5.1 Mechanism and Rate Law 276

x CONTENTS

7.5.2 E1 Dehydration of Alcohols 2787.5.3 E1 Elimination of Functionalized Alkanes 281

7.6 Special �-Elimination Reactions 2837.7 Elimination of LG1/LG2 in the Compounds that Contain Two

Functional Groups 2867.8 �-Elimination Giving a Carbene: A Mechanistic Analysis Using

Symmetry Rules and Molecular Orbital Theory 2887.9 E1cb Elimination and its Biological Applications 288

7.9.1 The E1cb Mechanism 2887.9.2 Biological Applications 291Problems 294References 297

8 Nucleophilic Additions and Substitutions on Carbonyl Groups 298

8.1 Nucleophilic Additions and Substitutions ofCarbonyl Compounds 298

8.2 Nucleophilic Additions of Aldehydes and Ketones and theirBiological Applications 3018.2.1 Acid- and Base-Catalyzed Hydration of Aldehydes

and Ketones 3018.2.2 Acid-Catalyzed Nucleophilic Additions of Aldehydes

and Ketones to Alcohols 3038.2.3 Biological Applications: Cyclic Structures

of Carbohydrates 3078.2.4 Addition of Sulfur Nucleophile to Aldehydes 3118.2.5 Nucleophilic Addition of Amines to Ketones

and Aldehydes 3118.2.6 Nucleophilic Additions of Aldehydes and Ketones to

Hydride Donors: Organic Reductions 3158.3 Biological Hydride Donors NAD(P)H and FADH2 3168.4 Activation of Carboxylic Acids via Nucleophilic Substitutions

on the Carbonyl Carbons 3208.4.1 Reactions of Carboxylic Acids with Thionyl Chloride 3208.4.2 Esterification Reactions and Synthetic Applications 3218.4.3 Formation of Anhydrides 3258.4.4 Nucleophilic Addition to Alkyllithium 326

8.5 Nucleophilic Substitutions of Acyl Derivatives and theirBiological Applications 3278.5.1 Nucleophilic Substitutions of Acyl Chlorides

and Anhydrides 3278.5.2 Hydrolysis and Other Nucleophilic Substitutions of Esters 3298.5.3 Biodiesel Synthesis and Reaction Mechanism 3318.5.4 Biological Applications 332

CONTENTS xi

8.6 Reduction of Acyl Derivatives by Hydride Donors 3358.7 Kinetics of the Nucleophilic Addition and Substitution

of Acyl Derivatives 337Problems 340References 342

9 Reactivity of the �-Hydrogen to Carbonyl Groups 344

9.1 Formation of Enolates and their Nucleophilicity 3449.1.1 Formation of Enolates 3449.1.2 Molecular Orbitals and Nucleophilicity of Enolates 348

9.2 Alkylation of Carbonyl Compounds (Aldehydes, Ketones, andEsters) via Enolates and Hydrazones 3499.2.1 Alkylation via Enolates 3499.2.2 Alkylation via Hydrazones and Enamines 351

9.3 Aldol Reactions 3549.3.1 Mechanism and Synthetic Utility 3549.3.2 Stereoselectivity 3619.3.3 Other Synthetic Applications 364

9.4 Acylation Reactions of Esters via Enolates: Mechanism andSynthetic Utility 367

9.5 Roles of Enolates in Metabolic Processes in Living Organisms 373Problems 376References 378

10 Rearrangements 380

10.1 Major Types of Rearrangements 38010.2 Rearrangement of Carbocations: 1,2-Shift 381

10.2.1 1,2-Shifts in Carbocations Produced fromAcyclic Molecules 382

10.2.2 1,2-Shifts in Carbocations Produced from CyclicMolecules—Ring Expansion 383

10.2.3 Resonance Stabilization of Carbocation—PinacolRearrangement 385

10.2.4 In vivo Cascade Carbocation Rearrangements:Biological Significance 387

10.2.5 Acid-Catalyzed 1,2-Shift in Epoxides 38810.2.6 Anion-Initiated 1,2-Shift 389

10.3 Neighboring Leaving Group-Facilitated 1,2-Rearrangement 39010.3.1 Beckmann Rearrangement 39110.3.2 Hofmann Rearrangement 39310.3.3 Baeyer–Villiger Oxidation (Rearrangement) 39410.3.4 Acid-Catalyzed Rearrangement of Organic Peroxides 396

10.4 Carbene Rearrangement: 1,2-Rearrangement of HydrogenFacilitated by a Lone Pair of Electrons 399

xii CONTENTS

10.5 Claisen Rearrangement 40110.6 Photochemical Isomerization of Alkenes and its

Biological Applications 40310.6.1 Photochemical Isomerization 40310.6.2 Biological Relevance 404

10.7 Rearrangement of Carbon–Nitrogen–Sulfur-ContainingHeterocycles 405Problems 409References 411

Index 413

PREFACE

In Summer 2010, I was contacted by Mr. Jonathan Rose, a senior editor of Wiley inHoboken, New Jersey, for book review and possibly writing an organic mechanisms-based textbook. We both agreed that a new book in this subject will meet the increasingneeds of various upper-level college students, instructors, and practicing chemists. Itook up the challenge and came up with a detailed proposal regarding the contents,style, and features of the book. The proposal received favorable peer reviews and wasapproved by Wiley in December 2010. Then I started the writing process. It took me18 months to finish writing the book. Meanwhile, I was teaching full-time as well.

Since 1998, I have been on faculty at two higher educational institutions, WestVirginia University Institute of Technology (1998–2001) and University of Charleston(2001–present). My current and previous research interests have much emphasis onreaction mechanisms. When I teach upper-level organic chemistry and biochemistrycourses, the lectures are also strongly mechanisms based. In the past dozen years orso, my teaching and research have been reinforcing each other. Now I wish to sharemy experiences with other colleagues, students, and different scientific workers inthe chemical community by publishing this book.

The book consists of 10 chapters. It starts with reviews of various fundamen-tal physicochemical principles (Chapter 1) which are essential for studying organicmechanisms. Then each of the following chapters is devoted to one major class oforganic reactions. Thorough discussions on various reaction mechanisms are pre-sented in the book in a very good detail, and a sophisticated and readily understand-able manner. Special attention has been paid to mechanisms of different organicfunctionalization processes, such as methodology of aliphatic C H bond activa-tion and functionalization, charge-transfer aromatic nitration and recently developedchemistry of aromatic compounds, and cycloaddition of alkenes to 1,3-dipolar-like

xiii

xiv PREFACE

molecules. Substantial efforts have been made in demonstrating direct applicationsof organic mechanisms in elucidating sophisticated biological and biochemical pro-cesses and designing organic synthesis. This can be seen throughout all the chaptersand reflects a remarkable feature of the book. To facilitate teaching and learning, aSolutions Manual and PowerPoint slides of all the figures will be provided by theauthor and will be available for professors on the book’s page on www.wiley.com. Igreatly appreciate all the constructive comments given by seven peer-reviewers on theinitial manuscript. The reviewers’ comments have helped the author tremendously inimproving the book.

I would like to take this opportunity to dedicate my book to Dr. Jack Passmore,my former PhD supervisor, and to my organic chemistry and biochemistry studentsat University of Charleston. The book is also dedicated to my wife Cindy and myson Oliver.

Xiaoping Sun, PhD

Professor of ChemistryCharleston, West Virginia

1FUNDAMENTAL PRINCIPLES

1.1 REACTION MECHANISMS AND THEIR IMPORTANCE

The microscopic steps in a chemical reaction which reflect how the reactant moleculesinteract (collide) with each other to lead to the formation of the product moleculesare defined as the mechanism of the reaction. The mechanism of a reaction revealsdetailed process of bond breaking in reactants and bond formation in products. Itis a microscopic view of a chemical reaction at molecular, atomic, and/or evenelectronic level.

The structure of most organic compounds is well established by X-ray crystallog-raphy and various spectroscopic methods with the accuracy of measurement in bonddistances and angles being the nearest to 0.01 A and 1o, respectively. Only effectivemolecular collisions, the collisions of the molecules with sufficient energy that takeplace in appropriate orientations, lead to chemical reactions. The extent of a chemicalreaction (chemical equilibrium) is determined by the changes in thermodynamic statefunctions including enthalpy (�H), entropy (�S), and free energy (�G). The combi-nation of kinetic and thermodynamic studies, quantum mechanical calculations, andgeometry and electronic structure-based molecular modeling has been employed toreveal mechanisms of various organic chemical reactions.

Reaction mechanisms play very important roles in the study of organic chemistry.The importance of mechanisms lies in that they not only facilitate understandingof various chemical phenomena, but also can provide guideline for exploring newchemistry and developing new synthetic methods for various useful substances, drugs,and materials. On this regard, mechanistic studies will allow synthetic chemists to vary

Organic Mechanisms: Reactions, Methodology, and Biological Applications, First Edition. Xiaoping Sun.© 2013 John Wiley & Sons, Inc. Published 2013 by John Wiley & Sons, Inc.

1

2 FUNDAMENTAL PRINCIPLES

reaction conditions, temperatures, and proportions of chemical reagents to maximizeyields of targeted pure products. For industrial chemists, mechanistic knowledgeallows the prediction of new reagents and reaction conditions which may affectdesired transformations. It also allows the optimization of yields, reducing the costson raw materials and waste disposals. For biochemists and medicinal chemists, themicroscopic view of organic reactions can help them better understand how themetabolic processes in living organisms work at molecular level, how diseases affectmetabolism, and how to develop appropriate drug molecules to assist or preventparticular biochemical reactions [1].

Overall, the goal of this book is to tie reaction mechanisms, synthetic methodol-ogy, and biochemical applications together to form an integrated picture of organicchemistry. While the book emphasizes mechanistic aspects of organic reactions, it is apractical textbook presenting the synthetic perspective about organic reaction mecha-nisms appealing to senior undergraduate-level and graduate-level students. The bookprovides a useful guide for how to analyze, understand, approach, and solve theproblems of organic reactions with the help of mechanistic studies.

In this chapter, fundamental principles which are required for studies and under-standing of organic reaction mechanisms are briefly reviewed. These principlesinclude basic theories on chemical kinetics, transition states, thermodynamics, atomicorbitals (AOs), and molecular orbitals (MOs).

1.2 ELEMENTARY (CONCERTED) AND STEPWISE REACTIONS

Some chemical reactions only involve one microscopic step. In these reactions,the effective molecular collision, the collision of reactant molecules with sufficientenergy in appropriate orientation, leads to simultaneous breaking of old bonds inreactants and formation of new bonds in products. This type of reactions is defined aselementary (or concerted) reactions. An elementary (concerted) reaction proceedsvia a single transition state. The transition state is a short-lived (transient) activatedcomplex in which the old bonds are being partially broken and new bonds are beingpartially formed concurrently. It possesses the maximum energy level in the reactionprofile (energy profile).

Many other chemical reactions involve many microscopic elementary (concerted)steps in the course of the overall reactions. These reactions are defined as stepwise (ormultistep) reactions. A stepwise reaction proceeds via more than one transitionstate. Each microscopic concerted step proceeds through one transition state, givinga distinct product which is referred to as an intermediate. Each intermediate formedin the course of a reaction is metastable and usually highly reactive, possessing arelatively high energy level. Once formed, the intermediate undergoes a subsequentreaction eventually leading to the formation of the final product.

Figure 1.1 shows the reaction profiles for concerted and stepwise reactions usingexamples of SN2 and SN1 reactions, respectively [1]. In a concerted reaction such asthe SN2 reaction of bromomethane (CH3Br) with hydroxide (OH−) (Fig. 1.1a), as thereactant molecules start colliding effectively, namely that OH− approaches (attacks)

ELEMENTARY (CONCERTED) AND STEPWISE REACTIONS 3

C BrH

H

H

HO:-....

C

H H

H

HO Br

Transition state

CHO Br-

H

HH

SN2C BrMe

Me

Me

C

Me Me

Me

+

Transition states

C OHMeMe

Me

H2OSN1

:OH2

..

Br-

ReactantsReactants

ProductsProducts

E

(a) (b)

+

-

Intermediate

+ HBr

FIGURE 1.1 Reaction profiles for a concerted SN2 reaction and a stepwise SN1 reaction.

the carbon atom in CH3Br from the opposite side of the Br group, formationof a new bond (the O C bond) and breaking of an old bond (the C Br) occursimultaneously. At the same time, the hydrogen atoms in CH3Br move graduallyfrom the left side toward the right side. The reaction proceeds via a single transitionstate (activated complex) in which the old C Br bond is being partially broken,coincident with the partial formation of a new O C bond. The hydrogen atomshave moved to the “middle,” forming a roughly trigonal-planar configuration. Thetransition state possesses the maximum energy level in the reaction profile. It isshort lived and highly reactive. As the reaction progresses further, the transition statecollapses (dissociates) spontaneously to lead to full breaking of the old C Br bond inthe reactant and concurrent complete formation of the new O C bond in the product.Simultaneously, the hydrogen atoms move to the right side. The overall process is aone-step transformation. The extent of the reaction is determined by the difference infree energy (�G) between reactants and products.

In contrast to a concerted reaction, a stepwise reaction proceeds via more than onetransition state. It consists of two or more elementary (concerted) steps (Fig. 1.1b),and distinct reactive intermediate(s) is formed in the course of the reaction [1]. TheSN1 reaction of 2-bromo-2-methylpropane (Me3CBr) in Figure 1.1b demonstratesthe general feature of a stepwise reaction. The first step is the dissociation of Me3CBrto a reactive carbocation Me3C+ intermediate. In the second step, Me3C+ reactswith water to give a tertiary alcohol product. Each concerted step proceeds via atransition state. The extent of a stepwise reaction is also determined by the differencein free energy (�G) between reactants and products, while the overall reaction rateis dictated by the relative stability of the reactive intermediate(s).

Whether a chemical reaction is concerted or stepwise is determined by the geome-try and electronic structure of reactant and product molecules and reaction conditions.In many cases, the mechanism is predictable. In the individual chapters of the book,

4 FUNDAMENTAL PRINCIPLES

we will study various types of concerted and stepwise reactions and the specificconditions which make them happen.

1.3 MOLECULARITY

The number of molecules contained in the transition state of a concerted reaction iscalled the molecularity of the reaction. Clearly, the molecularity is determined bythe number of reactant molecules that are involved in the mechanism (microscopicstep) of a concerted reaction.

1.3.1 Unimolecular Reactions

The microscopic steps of many concerted chemical reactions only involve a sin-gle reactant molecule. Such a concerted reaction whose mechanism involves onlyone reactant molecule is defined as a unimolecular reaction. It is generalized asfollows (Eq. 1.1):

A A*Activated

P(1.1)

A, A∗, and P represent a reactant molecule, an activated reactant molecule (tran-sition state), and a product molecule, respectively. In a unimolecular reaction, areactant molecule can possibly gain energy and then is activated by several means,including collision of the reactant molecule with a solvent molecule or with thewall of the reactor, thermally induced vibration of the reactant molecule, and photo-chemical excitation of the reactant molecule. After the molecule is activated, somesimultaneous bond-breaking and bond-formation processes will take place in A∗

intramolecularly. As a result, the reactant molecule A will be transformed into one ormore product molecules. Common examples of unimolecular reactions are thermal orphotochemical dissociation of a halogen molecule (Reaction 1.2) and intramolecularring-opening and ring-closure reactions (Reaction 1.3):

X Xh

2 X. (X = Cl, Br, or I)or Δ

ν(1.2)

hν

Δ(1.3)

1.3.2 Bimolecular Reactions

For most of the concerted chemical reactions, their microscopic steps (mechanisms)involve effective collisions between two reactant molecules. Such a concerted reaction

KINETICS 5

that is effected by collision of two reactant molecules to directly lead to the formationof products is defined as a bimolecular reaction. A bimolecular reaction can beeffected by collision of two molecules of a same compound (Eq. 1.4) or two moleculesof different compounds (Eq. 1.5):

Activated

A + A A2* P(1.4)

Activated+A B [AB]* P (1.5)

As a result, simultaneous bond breaking and bond formation take place within theactivated complex (transition state) A2

∗ or [AB]∗. This leads to spontaneous collapseof the activated complex (transition state) giving product molecules. Common exam-ples of bimolecular reactions are thermal decomposition of hydrogen iodide (HI) toelemental iodine (I2) and hydrogen (H2) (Reaction 1.6), the SN2 reaction of hydroxidewith bromomethane (Reaction 1.7), and Diels–Alder reaction of 1,3-butadiene andethylene (Reaction 1.8):

H I

H I

+H I

H I

(HI)2*

H I

H I+

=

Δ(1.6)

HO– + CH3 Br Br CH3HO–

Br– CH3HO + (1.7)

+=

Δ (1.8)

Almost all the concerted processes in organic reactions are either unimolecular orbimolecular steps.

1.4 KINETICS

1.4.1 Rate Laws for Elementary (Concerted) Reactions

For elementary reactions, the reaction orders are consistent with the molecularity. Aunimolecular reaction is first order in the reactant and a bimolecular reaction has asecond- order rate law.

6 FUNDAMENTAL PRINCIPLES

Unimolecular reactions: A unimolecular reaction (Eq. 1.1: A → P) follows thefirst-order rate law as shown in Equation 1.9:

− d[A]

dt= k[A] (1.9)

where k is the rate constant (with the typical unit of s−1) for the reaction and it isindependent of the concentration of the reactant. The rate constant is the quantitativemeasure of how fast the reaction proceeds at a certain temperature.

Rearranging Equation 1.9 leads to

d[A]

[A]= −k dt (1.10)

Integrating Equation 1.10 on both sides and applying the boundary conditiont = 0, [A] = [A]0 (initial concentration), we have

[A]∫

[A]0

d[A]

[A]= −

t∫

0

k dt (1.11)

From Equation 1.11, we have ln[A] – ln[A]0 = –kt.Therefore,

ln[A] = −kt + ln[A]0 or [A] = [A]0e−kt (1.12)

Equation 1.12 is the integrated rate law for a unimolecular reaction.The half-life (t1/2) of reactant A (the time required for conversion of one-half of

the reactant to the product, i.e., when t = t1/2, [A] = 1/2 [A]0) can be solved fromEquation 1.12 as follows:

ln(1/2[A]0) = −kt1/2 + ln[A]0

Therefore,

t1/2 = ln 2

k(1.13)

Equation 1.13 shows that the half-life of a substance that undergoes first-orderdecay is inversely proportional to the rate constant and independent of the initialconcentration.

KINETICS 7

Bimolecular reactions: A bimolecular reaction that involves two reactantmolecules of the same compound (Eq. 1.4: 2A → P) follows the second-order ratelaw as shown below:

− d[A]

dt= k[A]2 (1.14)

where k is the rate constant (with the typical unit of M−1s−1) for the reaction.Rearranging Equation 1.14 leads to

d[A]

[A]2 = −k dt (1.15)

Integrating Equation 1.15 on both sides and applying the boundary condition t =0, [A] = [A]0 (initial concentration), we have

[A]∫

[A]0

d[A]

[A]2 = −t∫

0

k dt (1.16)

From Equation 1.16, we have

1

[A]= kt + 1

[A]0(1.17)

Equation 1.17 is the integrated rate law for a bimolecular reaction involving twomolecules from the same compound.

A bimolecular reaction that involves two reactant molecules of different com-pounds (Eq. 1.5: A + B → P) also follows the second-order rate law (first order ineach of the reactants) as shown in Equation 1.18:

− d[A]

dt= −d[B]

dt= d[P]

dt= k[A][B] (1.18)

Assume that at a given time t, the molar concentration of the product P is x.Therefore, the molar concentrations of reactants A and B are [A] = [A]0 – x and[B] = [B]0 – x, respectively. [A]0 and [B]0 are initial concentrations of reactants Aand B, respectively.

From Equation 1.18, we have

dx

dt= k([A]0 − x)([B]0 − x) (1.19)

8 FUNDAMENTAL PRINCIPLES

If the quantities of the two reactants A and B are in stoichiometric ratio ([A]0 =[B]0), Equation 1.19 becomes

dx

dt= k([A]0 − x)2 (1.20)

Rearranging Equation 1.20 leads to Equation 1.21:

dx

([A]0 − x)2 = k dt (1.21)

Integrating Equation 1.21 on both sides and applying the boundary condition t =0, x = 0, we have

x∫

0

dx

([A]0 − x)2=

t∫

0

k dt (1.22)

From Equation 1.22, we have

1

[A]0 − x= kt + 1

[A]0(1.23)

Since [A] = [A]0 – x, Equation 1.23 becomes

1

[A]= kt + 1

[A]0(the same as Eq. 1.17)

If the reactants A and B have different initial concentrations, Equation 1.19becomes

dx

([A]0 − x)([B]0 − x)= k dt (1.24)

Integrating Equation 1.24 on both sides and applying the boundary condition t =0, x = 0, we have

x∫

0

dx

([A]0 − x)([B]0 − x)=

t∫

0

k dt (1.25)

From Equation 1.25, we have

ln[A]0 − x

[B]0 − x= k([A]0 − [B]0)t + ln

[A]0

[B]0(1.26)

KINETICS 9

Since [A] = [A]0 – x and [B] = [B]0 – x, Equation 1.26 becomes

ln[A]

[B]= k([A]0 − [B]0)t + ln

[A]0

[B]0(1.27)

Equation 1.27 represents the integrated rate law for a bimolecular reaction involv-ing two different reactant molecules with different initial concentrations.

If one of the reactants (such as B) in Equation 1.5 (the bimolecular reaction:A + B → P) is in large excess (typically 10–20 folds, i.e., [B]0/[A]0 = 10−20),the change in molar concentration of reactant B in the course of the reaction can beneglected ([B] ∼ [B]0) [2]. The rate law (Eq. 1.18) becomes

−d[A]/dt = k[A][B] = k[B]0[A]

Let k′ = k[B]0 (the observed rate constant). We have

−d[A]/dt = k ′[A]

The reaction becomes pseudo first order. The integrated rate law is

ln[A] = −k ′t + ln[A]0

1.4.2 Reactive Intermediates and the Steady-State Assumption

First, let us consider a reaction that consists of two consecutive irreversible unimolec-ular processes as shown in Reaction 1.28:

X Yk1 k2 Z (1.28)

X is the reactant. Z is the product. Y is a reactive intermediate. k1 and k2 are rateconstants for the two unimolecular processes. In order to determine the way in whichthe concentrations of the substances change over time, the rate equation for each ofthe substances is written down as follows (Eqs. 1.29, 1.30, and 1.31) [2]:

− d[X]

dt= k1[X] (1.29)

d[Y]

dt= k1[X] − k2[Y] (1.30)

d[Z]

dt= k2[Y] (1.31)

Equation 1.30 shows the net rate of increase in the intermediate Y, which isequal to the rate of its formation (k1[X]) minus the rate of its disappearance (k2[Y]).Equation 1.31 shows the rate of formation of the product Z. Since Z is produced

10 FUNDAMENTAL PRINCIPLES

TimeC

once

ntra

tion

X

Y

Z

FIGURE 1.2 The changes in concentrations of the reactant (X), intermediate (Y), andproduct (Z) over time for Reaction 1.28. The intermediate Y is shown to remain in a steadystate (d[Y]/dt = 0) in the course of the overall reaction.

only from the k2 step which is a unimolecular process, the rate equation for Z is firstorder in Y.

It is tedious to obtain the accurate solutions of the above simultaneous differentialequations. Appropriate approximations may be employed to ease the situation [2].

In most of the stepwise organic reactions, the intermediates (such as radicals andcarbocations) possess high energies and are unstable and highly reactive. Therefore,formation of such an intermediate is usually relatively slow (with a high Ea), whilethe subsequent transformation the intermediate experiences is relatively fast (witha low Ea). Mathematically, k1 is much smaller than k2 (k1 � k2). As a result, theconcentration of the reactive intermediate (such as Y in Reaction 1.28) remains at alow level and it essentially does not change in the course of the overall reaction. Thisis referred to as the steady-state approximation. The changes in concentrations ofthe reactant, intermediate, and product over time for Reaction 1.28 are illustrated inFigure 1.2. It shows that the intermediate Y in Reaction 1.28 remains in a steadystate (an essentially constant low concentration) in the course of the overall reaction,formulated as

d[Y]

dt= 0 (1.32)

In general, the steady-state approximation is applicable to all types of reactionintermediates in organic chemistry. Equation 1.32 is the mathematical form of thesteady-state assumption.

With the help of the steady-state approximation, the dependence of concentrationsof all the substances in Reaction 1.28 on time can be obtained readily [2].

Integration of Equation 1.29 leads to Equation 1.33 (c.f. Eqs. 1.9, 1.10, 1.11,and 1.12):

[X] = [X]0e−k1t (1.33)

where [X]0 is the initial concentration of X.

KINETICS 11

From Equation 1.30 (rate equation for Y) and Equation 1.32 (steady-state assump-tion for Y), we have

[Y] = k1

k2[X] (1.34)

Substituting Equation 1.33 for Equation 1.34, we have

[Y] = k1

k2[X]0e−k1t (1.35)

On the basis of the stoichiometry for Reaction 1.28, the initial concentration ofthe reactant X can be formulated as

[X]0 = [X] + [Y] + [Z]

Therefore,

[Z] = [X]0 − [X] − [Y] (1.36)

Combination of Equations 1.33, 1.35, and 1.36 gives Equation 1.37:

[Z] = [X]0

{1 −

(1 + k1

k2

)e−k1t

}(1.37)

Equations 1.33, 1.35, and 1.37 show the dependence of concentrations of all thesubstances in Reaction 1.28 on time [2].

Substituting Equation 1.34 (derived from the steady-state approximation for Y)for Equation 1.31 gives Equation 1.38:

d[Z]

dt= k1[X] (1.38)

Comparing Equations 1.29 and 1.38 indicates that the rate for consumption of thereactant X is approximately equal to the rate for formation of the product Z (Eq. 1.39):

− d[X]

dt= d[Z]

dt(1.39)

12 FUNDAMENTAL PRINCIPLES

1.4.3 Rate Laws for Stepwise Reactions

Let us use the following consecutive reaction (Reaction 1.40) which involves bothreversible and irreversible elementary processes to demonstrate the general procedurefor obtaining rate laws for stepwise reactions [3]:

X Yk1 k2 Zk–1

(1.40)

The rate (r) for the overall reaction can be expressed as increase in concentrationof the product (Z) per unit time (Eq. 1.41):

r = d[Z]

dt= k2[Y] (1.41)

Since Z is produced only from the k2 step which is a unimolecular process, therate equation for Z is first order in Y.

The steady-state assumption is applied to the intermediate Y, and its rate equationis written as follows:

d[Y]

dt= 0 = k1[X] − k−1[Y] − k2[Y] (1.42)

From Equation 1.42, we have

[Y] = k1

k−1 + k2[X] (1.43)

Substituting Equation 1.43 for Equation 1.41 leads to Equation 1.44, the rate law forReaction 1.40:

r = k1k2

k−1 + k2[X] = kobs[X] (1.44)

where kobs = k1k2/(k−1 + k2) is the observed rate constant.There are several limiting situations for such a stepwise process [3]. If k2 � k−1

(the intermediate Y is converted to the product Z much faster than going back to thereactant X), Equation 1.44 can be simplified to

r = k1[X] (for k2 � k−1)

In this case, the first step of Reaction 1.40 is the rate-determining step and actuallyirreversible.

If k2 � k−1 (the intermediate Y is converted to the product Z much more slowlythan going back to the reactant X), there is a fast preequilibrium between the reactant

THERMODYNAMICS 13

X and the intermediate Y before the product Z is formed. In this case, Equation 1.44can be simplified to

r = (k1/k−1)k2[X] = Keqk2[X] (for k2 � k−1)

where Keq = (k1/k−1) is the equilibrium constant for the fast preequilibrium betweenX and Y (Keq = [Y]/[X]). Therefore, r = k2[Y], and the second k2 step is therate-determining step. Since the fast preequilibrium between X and Y is establishedprior to the formation of the product, the steady-state assumption is not necessary ifk2 � k−1.

If the values of k2 and k−1 are comparable, the full steady-state assumption isneeded to establish the rate equation as shown in Equation 1.44.

1.5 THERMODYNAMICS

1.5.1 Enthalpy, Entropy, and Free Energy

Enthalpy (H), entropy (S), and free energy (G) are all thermodynamic state functions.Enthalpy (H) is defined as the sum of internal energy (U) and the product of pressure(P) and volume (V), formulated as

H = U + PV (1.45)

From Equation 1.45, the change in enthalpy (�H) can be calculated as

�H = �U + �(PV ) (1.46)

At constant pressure (P), Equation 1.46 becomes

�H = �U + P�V = �U − w

According to the first law of thermodynamics, qP = �U – w (heat).Therefore,

�H = qP (1.47)

The physical meaning of Equation 1.47 is that the enthalpy change in a process(including a chemical reaction) at constant pressure is equal to the heat evolved.Since most of the organic reactions are conducted at constant pressure, the reactionheat can be calculated on the basis of the enthalpy change for the reaction.

14 FUNDAMENTAL PRINCIPLES

Entropy (S) is considered as the degree of disorder. In thermodynamics, theinfinitesimal change in entropy (dS) is defined as the reversible heat (dqrev) dividedby the absolute temperature (T), formulated as

dS = dqrev/T

For a finite change in state,

�S =∫

dqrev

T(1.48)

Free energy (G) is defined as

G = H − TS

At constant temperature and pressure, the change in free energy (�G) can becalculated as

�G = �H − T �S (1.49)

1.5.2 Reversible and Irreversible Reactions

In general, chemical reactions in thermodynamics can be classified as two types,reversible and irreversible reactions. An irreversible reaction is such a reaction thatproceeds only in one direction. As a result, the reactant is converted to the productcompletely (100%) at the end of the reaction. In contrast, a reversible reactionis such a reaction that can proceed to both forward and backward directions. Inother words, there is an interconversion between the reactants and the products in areversible reaction. As a result, all the reactants and the products coexist at theend of the reaction, and the conversion is incomplete.

The reversibility of a chemical reaction can be judged by the second law of ther-modynamics. Originally, the second law is stated based on the entropy criterionas follows: A process (including a chemical reaction) is reversible if the universalentropy change (�SUNIV) associated to the process is zero; and a process is irre-versible if the universal entropy change (�SUNIV) associated to the process is positive(greater than zero). �SUNIV = �S + �SSURR, the sum of the entropy change in thesystem (�S) and the entropy change in surroundings (�SSURR).

Since it is difficult to calculate the entropy change in surroundings (�SSURR),very often the free energy criterion is used to judge reversibility for any processesthat take place at constant temperature and pressure. By employing the free energychange (�G) in a system, the second law can be modified as follows: At constanttemperature and pressure, a process (including a chemical reaction) is irreversible(spontaneous) if the free energy change (�G) of the process is negative (�G < 0), aprocess is reversible (at equilibrium) if the free energy change (�G) of the process iszero (�G = 0), and a process is nonspontaneous if the free energy change (�G) of