CHAPTER 3: Reaction Mechanism: Structure and Reactivity 203

❖ The Hammett Equation and Linear Free Energy Relationship

In this section, we will discuss the quantitative treatments of the effect of structure on reactivity i.e.
how the resonance effect, field-effect, and steric effect impact the reaction rate in measurable numbers.
➢ The Hammett Equation
Consider an organic reaction is carried out on a substrate which can be denoted as XRY, X a variable
substituent and Y is the reaction spot, and R represents the basic substrate structure. In this type of case,
replacing X = H with X = CH3 results in an increment in the rate of reaction up ten times. However, it is still
a mystery what part of the rate enhancement comes from resonance effect, field-effect, or steric effect. To do
so, it is reasonable to use compounds where one or two effects are so small that they simply can be neglected.
Although it is the oversimplification of the problem, quantitative results can still be obtained. The Hammett
equation is the first attempt to give numerical values for the quantitative treatment of structure on reactivity.
Hammett proposed the equation for the cases of m- and p-XC6H4Y as given below.

𝑘 (23)
log = 𝜎𝜌
𝑘0

where k and k0 are the constant for the group X ≠ H and X = H; ρ and σ are the constants for reaction conditions
and substituent X, respectively.
➢ Derivation of Hammett Equation
To derive the Hammett equation, we need to recall the quantitative relationship between the structure
and reactivity first. To do so, we need to find some mathematical parameter that can be used to represent the
combined magnitude of inductive and resonance effects of different substituents. This can be achieved by
considering the hydrolysis of a series of different benzoic acids as given below.

𝐾𝑎 (24)
XC6 H4 COOH + H2 O ⇌ XC6 H4 COO− + H3 O+

Where X is a substituent at the m- or p-position and Ka is the dissociation constant. As expected, the
dissociation constant was found to be different for differently substituted substrates.
Since an electron-withdrawing group will better stabilize the conjugate base (i.e., XC 6H4COO−),
resulting in a larger magnitude of Ka (lower pKa). On the other hand, an electron-donating group will
destabilize the conjugate base (i.e., XC6H4COO−), resulting in a smaller magnitude of Ka (higher pKa).
Therefore, we can say that the electronic effect (inductive plus mesomeric effect) of a substituent can be
represented as the difference between the pKa value of its benzoic acid derivative and the pKa value of benzoic
acid itself; mathematically, we can say

𝜎𝑋 = log(𝐾𝑎 ) − log(𝐾𝑎 )0 = − 𝑝(𝐾𝑎 ) + 𝑝(𝐾𝑎 )0 (25)

Where the parameter σX (or simply σ) is called as substituent constant; and was found for several different
groups just subtracting its benzoic acid derivative’s pKa value from pKa value of benzoic acid.

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 204 A Textbook of Organic Chemistry – Volume I

Table 1. pKa values and substituent constants for XC6H6COOH using benzoic acids p(Ka)0 = 4.21.

Substituent 𝑝𝑚 (𝐾𝑎 ) 𝑝𝑝 (𝐾𝑎 ) 𝜎𝑚 = 𝑝(𝐾𝑎 )0 − 𝑝𝑚 (𝐾𝑎 ) 𝜎𝑝 = 𝑝(𝐾𝑎 )0 − 𝑝𝑝 (𝐾𝑎 )

NO2 3.50 3.43 0.71 0.78

CH3 4.28 4.38 −0.07 −0.17

OCH3 4.09 4.48 0.12 −0.27

CH(CH3)2 4.28 4.36 −0.07 −0.15

F 3.87 4.15 0.34 0.06

Br 3.82 3.98 0.39 0.23

Cl 3.84 3.98 0.37 0.23

I 3.86 3.93 0.35 0.28

COCH3 3.83 3.71 0.38 0.50

Using log 𝑚 − log 𝑛 = log 𝑚/𝑛, equation (36) can also be written as

(𝐾𝑎 ) (26)
log =𝜎
(𝐾𝑎 )0

Now if we plot a curve between log(𝐾𝑎 )/(𝐾𝑎 )0 vs σ, we will definitely get a straight line with a slope = 1.

Figure 17. Variation of log(𝐾𝑎 )/(𝐾𝑎 )0 vs σ for substituted benzoic acids.

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 CHAPTER 3: Reaction Mechanism: Structure and Reactivity 205

Now we need to check if these σ values (i.e., of substituted benzoic acids) can also be used for other
meta- or para-substituted benzene derivatives. To do so, consider two series of reactions; the first one is the
acid dissociation of phenyl phosphonic acid, and the second one is the base hydrolysis of substituted ethyl
benzoate. Here we will find if different substituents affect their dissociation constants or rates in the same
manner as affected in the case of substituted benzoic acid. Also, we did not use ortho-substituents or
substituents in the aliphatic system because they also contain steric factors and don’t not linear variation.

The experimental log(𝐾𝑎 )/(𝐾𝑎 )0 for the reaction-I and experimental log 𝑘/𝑘0 for reaction-II are given below.

Table 2. Experimental values of log(𝐾𝑎 )/(𝐾𝑎 )0 and log 𝑘/𝑘0 for the acid dissociation of phenyl
phosphonic acid and base hydrolysis of substituted ethyl benzoates, respectively.

Substituent meta-log(𝐾𝑎 )/(𝐾𝑎 )0 para-log(𝐾𝑎 )/(𝐾𝑎 )0 meta-log 𝑘/𝑘0 para-log 𝑘/𝑘0

NO2 0.53 0.59 1.83935 2.06423

Br 0.29 0.23 − −

Cl 0.28 0.17 0.88536 0.63347

CH3 − −0.15 −0.16115 −0.34679

OCH3 − − − −0.67923

When plotted the experimental log(𝐾𝑎 )/(𝐾𝑎 )0 for the reaction-I and experimental log 𝑘/𝑘0 for reaction-II vs
the substituent constants obtained for the substituted benzoic acids, we get the following curves.

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 206 A Textbook of Organic Chemistry – Volume I

Figure 18. log(𝐾𝑎 )/(𝐾𝑎 )0 and log 𝑘/𝑘0 vs σ for reaction-I and reaction-II.

It is obvious that the plots are still linear like in Figure 3 but the slope has changed. This implies that the order
and relative effects for different substituents on both reactions remain the same though the magnitude has been
changed which can be attributed to the different nature reaction considers from ‘base reaction’.
Therefore, our aim, in this case, should be the determination of the slope (let us say ρ). Since on the
vertical side we have ‘[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑝𝑝𝑎 ’ for reaction-I (acid dissociation of phenyl phosphonic acid) and
on the horizontal side we have ‘𝜎 𝑜𝑟 [log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎 ’ for base reaction (hydrolysis of substituted benzoic
acid), the slope should be

[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑒𝑏 (27)

𝜌=
[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎

or

𝜌[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎 = [log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑒𝑏 (28)

But from equation (26), we know that [log(𝐾𝑎 )/log(𝐾𝑎 )0 ]𝑠𝑏𝑎 = 𝜎; and therefore, equation (40) takes the form

(𝐾𝑎 ) (29)
[log ] = 𝜌𝜎
(𝐾𝑎 )0 𝑠𝑒𝑏

For any reactions,

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 CHAPTER 3: Reaction Mechanism: Structure and Reactivity 207

log 𝐾𝑎 = 𝜌𝜎 − log (𝐾𝑎 )0 (30)

Similarly, on the vertical side we have ‘log 𝑘/𝑘0 ’ for reaction-II (base hydrolysis of substituted ethyl benzoate)
and on the horizontal side we have ‘𝜎 𝑜𝑟 [log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎 ’ for base reaction (hydrolysis of substituted
benzoic acid), the slope should be

[log 𝑘/𝑘0 ]𝑠𝑒𝑏 (31)

𝜌=
[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎

or

𝜌[log(𝐾𝑎 )/(𝐾𝑎 )0 ]𝑠𝑏𝑎 = [log 𝑘/𝑘0 ]𝑠𝑒𝑏 (32)

But from equation (26), we know that [log(𝐾𝑎 )/log(𝐾𝑎 )0 ]𝑠𝑏𝑎 = 𝜎; and therefore, equation (32) takes the form

𝑘 (33)
[log ] = 𝜌𝜎
𝑘0 𝑠𝑝𝑝𝑎

For any reactions,

log 𝑘 = 𝜌𝜎 − log 𝑘0 (34)

The results given by equation (29, 30, 33, 34) are called as Hammett’s equations; which shows that the rates
of ortho and para-substituted benzene derivatives can be obtained if the substituent contents for substituted
benzoic acid are known. Now we will discuss the substituent and reaction constants in more detail
➢ Linear Free Energy Relationship (LFER)
The Hammett equation is a linear free energy relationship that can be proved for any group X by
recalling the kinetics of organic reactions is in the framework of “Activated complex Theory”, which states
that the rate constant (k) for a typical reaction is

𝑅𝑇 −𝛥𝐺 ∗ (35)
𝑘= 𝑒 𝑅𝑇
𝑁ℎ
Where ΔG* is the free energy change of the activation step at temperature T. The symbols R, N, and h are the
gas constant, Avogadro number, and Planck’s constant, respectively. Similarly, for k0 we have

𝑅𝑇 −𝛥𝐺0∗ (36)
𝑘0 = 𝑒 𝑅𝑇
𝑁ℎ
After putting the value of equation (35) and equation (36) in Hammett equation (23), we get

𝑅𝑇 −𝛥𝐺
∗
(37)
𝑒 𝑅𝑇
log 𝑁ℎ 𝛥𝐺 ∗ = 𝜎𝜌
𝑅𝑇 − 𝑅𝑇0
𝑒
𝑁ℎ

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 208 A Textbook of Organic Chemistry – Volume I

𝛥𝐺 ∗ (38)
𝑒 − 𝑅𝑇
log 𝛥𝐺0∗
= 𝜎𝜌
𝑒 − 𝑅𝑇
Multiplying both sides by 2.303, we have
𝛥𝐺 ∗ (39)
𝑒 − 𝑅𝑇
2.303 log 𝛥𝐺0∗
= 2.303 𝜎𝜌
𝑒 − 𝑅𝑇
𝛥𝐺 ∗ (40)
𝑒 − 𝑅𝑇
ln 𝛥𝐺0∗
= 2.303 𝜎𝜌
𝑒 − 𝑅𝑇
𝛥𝐺 ∗ 𝛥𝐺 ∗
− 𝑅𝑇0 (41)
ln 𝑒 − 𝑅𝑇 − ln 𝑒 = 2.303 𝜎𝜌

or

𝛥𝐺 ∗ 𝛥𝐺0∗ (42)
(− ln 𝑒) − (− ln 𝑒) = 2.303 𝜎𝜌
𝑅𝑇 𝑅𝑇

or

𝛥𝐺 ∗ 𝛥𝐺0∗ (43)
− + = 2.303 𝜎𝜌
𝑅𝑇 𝑅𝑇
Which implies

𝛥𝐺0∗ 𝛥𝐺 ∗ (44)
− = 2.303 𝜎𝜌
𝑅𝑇 𝑅𝑇
or

𝛥𝐺0∗ − 𝛥𝐺 ∗ (45)
= 2.303 𝜎𝜌
𝑅𝑇
or

𝛥𝐺0∗ − 𝛥𝐺 ∗ = 2.303𝑅𝑇 𝜎𝜌 (46)

or

−𝛥𝐺 ∗ = 2.303𝑅𝑇 𝜌𝜎 − 𝛥𝐺0∗ (47)

Hence, the variation of negative of the free energy of activation varies linearly with slope 2.303RTρ and −𝛥𝐺0∗
as intercept.

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Table of Contents
CHAPTER 1 ................................................................................................................................................. 11
Nature of Bonding in Organic Molecules ............................................................................................... 11
❖ Delocalized Chemical Bonding ...................................................................................................... 11
❖ Conjugation .................................................................................................................................... 14
❖ Cross Conjugation .......................................................................................................................... 16
❖ Resonance....................................................................................................................................... 18
❖ Hyperconjugation ........................................................................................................................... 27
❖ Tautomerism ................................................................................................................................... 31
❖ Aromaticity in Benzenoid and Nonbenzenoid Compounds ............................................................ 33
❖ Alternant and Non-Alternant Hydrocarbons ................................................................................... 35
❖ Huckel’s Rule: Energy Level of π-Molecular Orbitals ................................................................... 3 7
❖ Annulenes ....................................................................................................................................... 44
❖ Antiaromaticity ............................................................................................................................... 46
❖ Homoaromaticity ............................................................................................................................ 48
❖ PMO Approach ............................................................................................................................... 50
❖ Bonds Weaker Than Covalent ........................................................................................................ 58
❖ Addition Compounds: Crown Ether Complexes and Cryptands, Inclusion Compounds,
Cyclodextrins ................................................................................................................................. 65
❖ Catenanes and Rotaxanes ............................................................................................................... 75
❖ Problems ......................................................................................................................................... 79
❖ Bibliography ................................................................................................................................... 80
CHAPTER 2 ................................................................................................................................................. 81
Stereochemistry ........................................................................................................................................ 81
❖ Chirality .......................................................................................................................................... 81
❖ Elements of Symmetry ................................................................................................................... 86
❖ Molecules with More Than One Chiral Centre: Diastereomerism .................................................. 90
❖ Determination of Relative and Absolute Configuration (Octant Rule Excluded) with Special
Reference to Lactic Acid, Alanine & Mandelic Acid ..................................................................... 92
❖ Methods of Resolution.................................................................................................................. 102
❖ Optical Purity ............................................................................................................................... 104
❖ Prochirality ................................................................................................................................... 105
❖ Enantiotopic and Diastereotopic Atoms, Groups and Faces ......................................................... 107
❖ Asymmetric Synthesis: Cram’s Rule and Its Modifications, Prelog’s Rule .................................. 113
❖ Conformational Analysis of Cycloalkanes (Upto Six Membered Rings) ...................................... 116
❖ Decalins ........................................................................................................................................ 122
❖ Conformations of Sugars .............................................................................................................. 126
❖ Optical Activity in Absence of Chiral Carbon (Biphenyls, Allenes and Spiranes) ....................... 132
❖ Chirality Due to Helical Shape ..................................................................................................... 137
❖ Geometrical Isomerism in Alkenes and Oximes ........................................................................... 140
❖ Methods of Determining the Configuration .................................................................................. 146
 ❖ Problems ....................................................................................................................................... 151
❖ Bibliography ................................................................................................................................. 152
CHAPTER 3 ............................................................................................................................................... 153
Reaction Mechanism: Structure and Reactivity .................................................................................. 153
❖ Types of Mechanisms ................................................................................................................... 153
❖ Types of Reactions ....................................................................................................................... 156
❖ Thermodynamic and Kinetic Requirements .................................................................................. 159
❖ Kinetic and Thermodynamic Control ........................................................................................... 161
❖ Hammond’s Postulate ................................................................................................................... 163
❖ Curtin-Hammett Principle ............................................................................................................ 164
❖ Potential Energy Diagrams: Transition States and Intermediates ................................................. 166
❖ Methods of Determining Mechanisms .......................................................................................... 168
❖ Isotope Effects .............................................................................................................................. 172
❖ Hard and Soft Acids and Bases ..................................................................................................... 174
❖ Generation, Structure, Stability and Reactivity of Carbocations, Carbanions, Free Radicals, Carbenes
and Nitrenes................................................................................................................................. 176
❖ Effect of Structure on Reactivity .................................................................................................. 200
❖ The Hammett Equation and Linear Free Energy Relationship ...................................................... 203
❖ Substituent and Reaction Constants .............................................................................................. 209
❖ Taft Equation ................................................................................................................................ 215
❖ Problems ....................................................................................................................................... 219
❖ Bibliography ................................................................................................................................. 220
CHAPTER 4 ............................................................................................................................................... 221
Carbohydrates ........................................................................................................................................ 221
❖ Types of Naturally Occurring Sugars ........................................................................................... 221
❖ Deoxy Sugars ............................................................................................................................... 227
❖ Amino Sugars ............................................................................................................................... 229
❖ Branch Chain Sugars .................................................................................................................... 230
❖ General Methods of Determination of Structure and Ring Size of Sugars with Particular Reference
to Maltose, Lactose, Sucrose, Starch and Cellulose ...................................................................... 231
❖ Problems ....................................................................................................................................... 239
❖ Bibliography ................................................................................................................................. 240
CHAPTER 5 ............................................................................................................................................... 241
Natural and Synthetic Dyes ................................................................................................................... 241
❖ Various Classes of Synthetic Dyes Including Heterocyclic Dyes ................................................. 241
❖ Interaction Between Dyes and Fibers ........................................................................................... 245
❖ Structure Elucidation of Indigo and Alizarin ................................................................................ 247
❖ Problems ....................................................................................................................................... 252
❖ Bibliography ................................................................................................................................. 253
CHAPTER 6 ............................................................................................................................................... 254
Aliphatic Nucleophilic Substitution ...................................................................................................... 254
❖ The SN2, SN1, Mixed SN1 and SN2, SNi, SN1′, SN2′, SNi′ and SET Mechanisms ......................... 254
 The Neighbouring Group Mechanisms ......................................................................................... 263
❖
Neighbouring Group Participation by π and σ Bonds . .................................................................. 2 65
❖
Anchimeric Assistance ................................................................................................................. 269
❖
Classical and Nonclassical Carbocations ...................................................................................... 272
❖
Phenonium Ions ............................................................................................................................ 283
❖
Common Carbocation Rearrangements ........................................................................................ 284
❖
Applications of NMR Spectroscopy in the Detection of Carbocations ......................................... 286
❖
Reactivity – Effects of Substrate Structure, Attacking Nucleophile, Leaving Group and Reaction
❖
Medium ........................................................................................................................................ 288
❖ Ambident Nucleophiles and Regioselectivity ............................................................................... 294
❖ Phase Transfer Catalysis ............................................................................................................... 297
❖ Problems ....................................................................................................................................... 300
❖ Bibliography ................................................................................................................................. 301
CHAPTER 7 ............................................................................................................................................... 302
Aliphatic Electrophilic Substitution ...................................................................................................... 302
❖ Bimolecular Mechanisms − SE2 and SEi ...................................................................................... 3 02
❖ The SE1 Mechanism ..................................................................................................................... 305
❖ Electrophilic Substitution Accompanied by Double Bond Shifts ................................................. 307
❖ Effect of Substrates, Leaving Group and the Solvent Polarity on the Reactivity .......................... 308
❖ Problems ....................................................................................................................................... 310
❖ Bibliography ................................................................................................................................. 311
CHAPTER 8 ............................................................................................................................................... 312
Aromatic Electrophilic Substitution ..................................................................................................... 312
❖ The Arenium Ion Mechanism ....................................................................................................... 312
❖ Orientation and Reactivity ............................................................................................................ 314
❖ Energy Profile Diagrams .............................................................................................................. 316
❖ The Ortho/Para Ratio .................................................................................................................... 317
❖ ipso-Attack ................................................................................................................................... 319
❖ Orientation in Other Ring Systems ............................................................................................... 320
❖ Quantitative Treatment of Reactivity in Substrates and Electrophiles .......................................... 321
❖ Diazonium Coupling..................................................................................................................... 325
❖ Vilsmeier Reaction ....................................................................................................................... 326
❖ Gattermann-Koch Reaction .......................................................................................................... 327
❖ Problems ....................................................................................................................................... 329
❖ Bibliography ................................................................................................................................. 330
CHAPTER 9 ............................................................................................................................................... 331
Aromatic Nucleophilic Substitution ...................................................................................................... 331
❖ The ArSN1, ArSN2, Benzyne and SRN1 Mechanisms.................................................................... 331
❖ Reactivity – Effect of Substrate Structure, Leaving Group and Attacking Nucleophile................ 336
❖ The von Richter, Sommelet-Hauser, and Smiles Rearrangements ................................................ 339
❖ Problems ....................................................................................................................................... 343
❖ Bibliography ................................................................................................................................. 344
CHAPTER 10 ............................................................................................................................................. 345
Elimination Reactions ............................................................................................................................ 345
❖ The E2, E1 and E1CB Mechanisms ................................................................................................ 345
❖ Orientation of the Double Bond.................................................................................................... 348
❖ Reactivity – Effects of Substrate Structures, Attacking Base, the Leaving Group and The Medium
....................................................................................................................................................352
❖ Mechanism and Orientation in Pyrolytic Elimination ................................................................... 355
❖ Problems ....................................................................................................................................... 358
❖ Bibliography ................................................................................................................................. 359
CHAPTER 11 ............................................................................................................................................. 360
Addition to Carbon-Carbon Multiple Bonds ....................................................................................... 360
❖ Mechanistic and Stereochemical Aspects of Addition Reactions Involving Electrophiles,
Nucleophiles and Free Radicals .................................................................................................... 360
❖ Regio- and Chemoselectivity: Orientation and Reactivity ............................................................ 370
❖ Addition to Cyclopropane Ring .................................................................................................... 374
❖ Hydrogenation of Double and Triple Bonds ................................................................................. 375
❖ Hydrogenation of Aromatic Rings ................................................................................................ 377
❖ Hydroboration .............................................................................................................................. 378
❖ Michael Reaction .......................................................................................................................... 379
❖ Sharpless Asymmetric Epoxidation .............................................................................................. 380
❖ Problems ....................................................................................................................................... 382
❖ Bibliography ................................................................................................................................. 383
CHAPTER 12 ............................................................................................................................................. 384
Addition to Carbon-Hetero Multiple Bonds ......................................................................................... 384
❖ Mechanism of Metal Hydride Reduction of Saturated and Unsaturated Carbonyl Compounds, Acids,
Esters and Nitriles ......................................................................................................................... 384
❖ Addition of Grignard Reagents, Organozinc and Organolithium Reagents to Carbonyl and
Unsaturated Carbonyl Compounds ............................................................................................... 400
❖ Wittig Reaction ............................................................................................................................. 406
❖ Mechanism of Condensation Reactions Involving Enolates: Aldol, Knoevenagel, Claisen, Mannich,
Benzoin, Perkin and Stobbe Reactions .......................................................................................... 411
❖ Hydrolysis of Esters and Amides .................................................................................................. 433
❖ Ammonolysis of Esters ................................................................................................................. 437
❖ Problems ....................................................................................................................................... 439
❖ Bibliography ................................................................................................................................. 440
INDEX......................................................................................................................................................... 441