Reaction Mechanisms and Types of Reactions
1. Energy profiles, kinetic and thermodynamic control, Hammond and Curtin–Hammett; determining mechanisms
An energy-profile diagram plots free energy along the reaction coordinate: transition states are maxima (never isolable), intermediates are minima between them, and the highest transition state relative to the reactants sets the rate. When two products form by competing paths, the product formed faster dominates under kinetic control (low temperature, short times, irreversible conditions), and the more stable product dominates under thermodynamic control (higher temperature, reversible conditions, long times). HBr adds to 1,3-butadiene to give mainly the 1,2-adduct at −80 °C and the more substituted, more stable 1,4-adduct at 40 °C; naphthalene sulfonates at C1 at 80 °C and at C2 at 160 °C; LDA at −78 °C forms the less substituted (kinetic) enolate of 2-methylcyclohexanone, while an alkoxide at room temperature equilibrates to the more substituted (thermodynamic) one.
Hammond’s postulate: a transition state resembles the species (reactant, intermediate or product) nearest to it in energy. So an exothermic step has an early, reactant-like transition state and an endothermic step a late, product-like one — which is why the stability of a carbocation intermediate is a good guide to the rate of the endothermic step that forms it. The Curtin–Hammett principle: when two conformers interconvert much faster than either reacts, the product ratio depends only on the difference in free energy of the two transition states, not on the conformer populations. A ΔΔG‡ of 5.7 kJ/mol at 298 K gives a 10:1 ratio.
Determining mechanisms. The rate law shows which species are in or before the rate-determining step. Products and their stereochemistry discriminate (inversion for S_N2, racemisation for S_N1, rearranged skeletons for cations). Intermediates are detected spectroscopically, trapped (benzyne by furan, radicals by TEMPO), or revealed by crossover experiments (intramolecular reactions give no crossed products). Isotopic labelling follows atoms: base hydrolysis of an ester in H₂¹⁸O puts ¹⁸O in the acid, not the alcohol, proving acyl–oxygen cleavage; ¹⁴C in chlorobenzene reveals benzyne; and deuterium gives kinetic isotope effects (kH/kD ≈ 7 when C–H breaks in the rate-determining step, as in most E2 reactions; about 1 in electrophilic aromatic substitution, where the C–H is broken after the slow step).
2. Linear free-energy relationships and solvent effects
The Hammett equation log(k/k₀) = ρσ (or log(K/K₀) = ρσ for equilibria) separates the electronic effect of a meta or para substituent (σ, defined from benzoic acid ionisation, where ρ = 1) from the sensitivity of the reaction (ρ). Typical σ_p: NO₂ +0.78, CN +0.66, Cl +0.23, H 0, CH₃ −0.17, OCH₃ −0.27, NH₂ −0.66. A positive ρ means negative charge builds up (or positive charge is lost) at the reaction centre in the transition state — alkaline hydrolysis of ethyl benzoates, ρ ≈ +2.5; a negative ρ means positive charge builds up — S_N1 solvolysis of cumyl chlorides, ρ ≈ −4.5, where through-conjugating donors need the modified constants σ⁺. A break in a Hammett plot signals a change of mechanism or rate-determining step. The Taft equation log(k/k₀) = ρσ + δE_s extends the idea to aliphatic systems by separating a polar term σ* from a steric term E_s.
Solvent effects follow from how charge changes on reaching the transition state (the Hughes–Ingold rules). S_N1 and E1 create charge from a neutral substrate, so they are accelerated by polar protic solvents that solvate both the cation and the leaving anion (water, formic acid, alcohols). S_N2 between an anion and a neutral substrate disperses the charge, so it is slowed by protic solvents that hydrogen-bond the nucleophile and accelerated enormously by polar aprotic solvents (DMSO, DMF, acetone, HMPA), which leave anions "naked"; in them the halide nucleophilicity order becomes F⁻ > Cl⁻ > Br⁻ > I⁻, the reverse of that in water. Strongly basic, bulky nucleophiles and high temperature favour elimination over substitution.
3. Nucleophilic and electrophilic substitution, aliphatic and aromatic
| Feature | S_N2 | S_N1 |
|---|---|---|
| Rate law | k[RX][Nu] | k[RX] |
| Substrate order | CH₃ > 1° > 2° ≫ 3° (neopentyl very slow) | 3° > 2°, benzylic, allylic ≫ 1° |
| Stereochemistry | inversion (Walden) | racemisation, often with some inversion (ion pairs) |
| Rearrangement | none | possible (hydride and alkyl shifts) |
| Best solvent | polar aprotic | polar protic |
The S_Ni reaction of alcohols with SOCl₂ gives retention through a chlorosulfite ion pair, but inversion when pyridine is added. Electrophilic aromatic substitution proceeds through a σ-complex (arenium or Wheland ion) whose formation is rate-determining; loss of H⁺ then restores aromaticity, which is why kH/kD ≈ 1. Substituents that donate electrons (OH, NH₂, OR, alkyl) activate and direct ortho/para by stabilising the cation at those positions; withdrawing groups (NO₂, CN, COR, SO₃H, CF₃) deactivate and direct meta; halogens deactivate by induction but direct ortho/para by resonance. The electrophiles are generated in situ: NO₂⁺ from HNO₃/H₂SO₄, R⁺ or RCO⁺ from halides with AlCl₃ (Friedel–Crafts alkylation, prone to rearrangement and polyalkylation; acylation, which stops at one because the product is deactivated).
Nucleophilic aromatic substitution needs help. In the S_NAr (addition–elimination) path, a nucleophile adds to a ring carrying strong electron-withdrawing groups ortho or para to the leaving group, forming a resonance-stabilised anionic Meisenheimer complex; because addition is rate-determining, the leaving-group order is F > Cl ≈ Br > I (fluorine best activates the carbon), the reverse of S_N2. Without activation, very strong bases such as NaNH₂ in liquid NH₃ act by elimination–addition through benzyne: chlorobenzene labelled with ¹⁴C at C1 gives aniline with NH₂ at the labelled carbon and at the adjacent carbon in equal amounts.
4. Addition to C=C, C=O and C=N bonds; elimination
Electrophilic addition to alkenes: HX adds through the more stable carbocation, putting H on the carbon with more hydrogens (Markovnikov), with possible rearrangement; HBr with peroxides adds by a radical chain in the anti-Markovnikov sense, because Br• adds to give the more stable radical. Br₂ adds anti through a bridged bromonium ion (and in water gives the halohydrin, OH on the more substituted carbon); hydroboration adds syn and anti-Markovnikov (see the oxidation chapter). Nucleophilic addition to C=O: hydration, cyanohydrins, organometallic additions and hydride reduction; with alcohols under acid, hemiacetals then acetals; with primary amines, imines (fastest near pH 4–5, where there is enough acid to activate the carbonyl and remove water but the amine is not all protonated), with secondary amines enamines. α,β-Unsaturated carbonyls take hard, reactive nucleophiles (RLi, RMgX) at C=O (1,2-addition) and soft ones (cuprates, enolates, thiols, amines) at the β-carbon (1,4-, conjugate or Michael addition).
Elimination. E2 is concerted, second order, needs an anti-periplanar H, and with small bases gives the more substituted (Zaitsev) alkene; bulky bases (t-BuOK) and poor, charged leaving groups (NMe₃⁺ in the Hofmann elimination) give the less substituted (Hofmann) alkene. E1 goes through the carbocation, competes with S_N1, and gives Zaitsev products with possible rearrangement. E1cB (via the conjugate base) operates when the β-hydrogen is acidic and the leaving group poor, as in the dehydration of β-hydroxy carbonyl compounds after an aldol reaction. Syn eliminations occur thermally through cyclic transition states: the Cope elimination of amine oxides, ester pyrolysis and the Chugaev xanthate elimination.
5. Reactive intermediates: carbocations, carbanions, radicals, carbenes, nitrenes and arynes
| Intermediate | Structure | Stabilised by | Typical reactions |
|---|---|---|---|
| Carbocation R₃C⁺ | planar, sp², empty p | alkyl hyperconjugation (3° > 2° > 1°), allyl, benzyl, adjacent O or N lone pairs | S_N1, E1, 1,2-shifts, capture by nucleophiles |
| Carbanion R₃C⁻ | pyramidal, sp³ (planar if conjugated) | s-character, C=O, NO₂, CN, aromaticity; 1° > 2° > 3° | alkylation, aldol, E1cB |
| Radical R₃C• | nearly planar | 3° > 2° > 1°, allyl, benzyl | halogenation, addition, chain reactions, coupling |
| Singlet carbene | bent, paired electrons in sp², empty p | π-donor substituents (Cl, OMe, NR₂) | stereospecific cyclopropanation, C–H insertion |
| Triplet carbene | two unpaired electrons (diradical) | ground state of CH₂ and diarylcarbenes | stepwise, non-stereospecific cyclopropanation |
| Nitrene R–N | N analogue of a carbene | acyl and aryl groups | aziridination, C–H insertion, Curtius-type rearrangement |
| Aryne (benzyne) | strained "triple bond" in the ring, low-lying LUMO | — | nucleophilic addition, Diels–Alder with furan or anthracene |
Dichlorocarbene, generated from CHCl₃ and base by α-elimination, is a singlet (stabilised by the chlorine lone pairs) and adds to cis-2-butene to give only cis-1,1-dichloro-2,3-dimethylcyclopropane; a triplet carbene adds in two steps through a diradical that can rotate, scrambling the stereochemistry. Carbocations rearrange to more stable ions by 1,2-shifts of H, alkyl or aryl — the basis of the Wagner–Meerwein and pinacol rearrangements — and the 2-norbornyl cation is the classic non-classical, σ-bridged ion.
6. Molecular rearrangements; Barton, Barton–McCombie and Hunsdiecker reactions
| Rearrangement | Substrate → product | Key feature |
|---|---|---|
| Wagner–Meerwein | carbocation → more stable carbocation | 1,2-alkyl or hydride shift |
| Pinacol | 1,2-diol + acid → ketone (pinacolone) | the more stable cation forms; the group best able to stabilise positive charge migrates |
| Beckmann | ketoxime + acid → amide | the group anti to OH migrates to N |
| Hofmann | RCONH₂ + Br₂/NaOH → RNH₂ | via isocyanate; one carbon lost |
| Curtius, Lossen, Schmidt | acyl azide, hydroxamate ester, acid + HN₃ → isocyanate → amine | migration to N with loss of N₂ or carboxylate |
| Favorskii | α-haloketone + alkoxide → ester | cyclopropanone intermediate; cyclic ketones ring-contract |
| Benzilic acid | 1,2-diketone + OH⁻ → α-hydroxy acid | aryl migration in the tetrahedral adduct |
In every 1,2-shift the migrating group keeps its configuration, because it never leaves the molecule. The Hofmann and Curtius rearrangements therefore convert an optically active acid derivative into an amine of the same configuration with one carbon fewer. The syllabus also names three radical chain reactions. Barton decarboxylation: the carboxylic acid is converted to a thiohydroxamate (Barton) ester, whose weak N–O bond breaks on heating or irradiation; the carboxyl radical loses CO₂, and the alkyl radical abstracts H from a donor (Bu₃SnH or a thiol) or is trapped by another group, so RCOOH → R–H or R–X. Barton–McCombie deoxygenation replaces an alcohol OH by H: the alcohol is made into a xanthate or thiocarbonyl ester, a tin radical (Bu₃SnH, initiated by AIBN) adds to sulfur, and fragmentation releases the alkyl radical, which takes H from Bu₃SnH. Hunsdiecker reaction: the silver salt of a carboxylic acid with Br₂ gives the alkyl bromide with one fewer carbon, RCOOAg + Br₂ → RBr + CO₂ + AgBr, through an acyl hypobromite and a radical chain; stereochemistry at the carbon is lost.
Key takeaways
- Kinetic control gives the faster-formed product (low T, irreversible), thermodynamic control the more stable one; Hammond: the TS resembles the nearer species; Curtin–Hammett: the product ratio depends on ΔΔG‡ of the transition states.
- Hammett log(k/k₀) = ρσ: positive ρ means negative charge builds in the TS; Taft adds a steric term. Polar aprotic solvents speed S_N2, polar protic S_N1.
- S_N2 inverts, S_N1 racemises and rearranges; EAS via the arenium ion (kH/kD ≈ 1); S_NAr via the Meisenheimer complex with F the best leaving group; benzyne from unactivated aryl halides and NaNH₂.
- Markovnikov via the more stable cation, anti-Markovnikov HBr by radicals, Br₂ anti; hard nucleophiles 1,2, soft 1,4 on enones; E2 anti-periplanar, Zaitsev with small bases, Hofmann with bulky ones; E1cB for poor leaving groups.
- Singlet carbenes cyclopropanate stereospecifically, triplets do not; migrating groups keep their configuration (Beckmann: anti group; Hofmann/Curtius lose one carbon); Barton, Barton–McCombie and Hunsdiecker are radical chains.
Practice questions (17)
Attempt each one before opening the answer. Every explanation names the tempting wrong option as well as the right one, because that is where marks are lost.
The alkaline hydrolysis of ethyl benzoates has ρ = +2.5. Using σ_p(NO₂) = +0.78, by what factor is ethyl p-nitrobenzoate hydrolysed faster than ethyl benzoate, to the nearest whole number?
Numerical answer — type the value.
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Answer: 89
log(k/k₀) = ρσ = 2.5 × 0.78 = 1.95, so k/k₀ = 10^1.95 = 89. The positive ρ means negative charge builds up in the transition state for hydroxide attack, which the nitro group stabilises. Using e^1.95 = 7.0 confuses log₁₀ with ln.For a reaction with ρ = +2.0, a para substituent halves the rate relative to hydrogen. What is its σ value, to two decimal places?
Numerical answer — type the value.
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Answer: -0.15
σ = log(k/k₀)/ρ = log(0.5)/2.0 = −0.301/2.0 = -0.15, an electron donor about as strong as methyl (−0.17). A positive answer would mean the substituent accelerates a reaction with positive ρ, which contradicts the halved rate.The S_N1 solvolysis of substituted cumyl chlorides, ArC(CH₃)₂Cl, has ρ⁺ ≈ −4.5. What does the large negative value show?
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Answer: A — A large positive charge develops at the benzylic carbon in the transition state and is delocalised into the ring
A negative ρ means electron donors accelerate, so positive charge builds up; its large size, and the need for σ⁺ constants, show the charge is conjugated directly with para donors, as in a benzylic carbocation. An S_N2 transition state would show a small ρ.Two rapidly interconverting conformers each react irreversibly to a different product. The transition state leading to product A is 5.7 kJ/mol lower in free energy than that leading to B. By the Curtin–Hammett principle, what percentage of the product is A at 298 K, to the nearest whole number? (R = 8.314 J mol⁻¹ K⁻¹)
Numerical answer — type the value.
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Answer: 91
[A]/[B] = exp(ΔΔG‡/RT) = exp(5700/(8.314 × 298)) = exp(2.30) = 10.0, so A is 10/11 = 0.909, i.e. 91%. The conformer populations do not enter, because interconversion is faster than reaction; that is the whole point of the principle.HBr adds to 1,3-butadiene to give mainly 3-bromo-1-butene at −80 °C but mainly 1-bromo-2-butene at 40 °C. This is an example of
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Answer: A — kinetic versus thermodynamic control
Both products come from the same allylic cation. At low temperature the 1,2-adduct, formed faster because Br⁻ is nearest C2, is trapped irreversibly; at 40 °C the adducts equilibrate and the more substituted internal alkene, the 1,4-adduct, dominates. Both are Markovnikov products.According to Hammond’s postulate, the transition state of a strongly endothermic step
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Answer: A — resembles the product of that step
An endothermic step has its transition state close in energy, and so in structure, to the higher-energy product; this is why factors that stabilise a carbocation also lower the barrier to forming it. Exothermic steps have early, reactant-like transition states.An ester RCOOR′ is hydrolysed by NaOH in H₂¹⁸O. Where is the ¹⁸O found, and what does it show?
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Answer: A — In the carboxylate, showing acyl–oxygen cleavage by addition to C=O
Hydroxide adds to the carbonyl carbon (the B_AC2 mechanism) and the alkoxide leaves, so the labelled oxygen ends up in the acid and R′OH keeps its original oxygen — and an optically active R′ keeps its configuration. Alkyl–oxygen cleavage is found only for special esters such as tert-butyl in acid.Which statements about S_N1 and S_N2 reactions are correct?
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Answer: A — S_N2 reactions of anionic nucleophiles are accelerated in DMSO relative to methanol; B — S_N1 reactions can be accompanied by carbocation rearrangement
Aprotic DMSO does not hydrogen-bond the anion, leaving it far more reactive; carbocations shift H or alkyl to more stable ions. Neopentyl is primary but its β-tert-butyl blocks the backside, making S_N2 extremely slow, and S_N2 gives inversion, not retention.In nucleophilic aromatic substitution of 1-X-2,4-dinitrobenzenes by methoxide, which halogen X reacts fastest?
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Answer: A — F
The rate-determining step is addition to form the Meisenheimer complex, not loss of X⁻; fluorine’s strong induction makes the ipso carbon most electrophilic and stabilises the anionic intermediate, so F reacts fastest. The S_N2 order I > Br > Cl > F applies only when C–X breaks in the slow step.Chlorobenzene labelled with ¹⁴C at C1 is treated with NaNH₂ in liquid NH₃. What percentage of the aniline formed carries the NH₂ group on the labelled carbon?
Numerical answer — type the value.
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Answer: 50
Elimination of HCl gives benzyne with the label on one of the two triple-bond carbons; NH₂⁻ adds to either end with equal probability, so half the aniline (50%) has NH₂ at C1 and half at C2. Direct substitution would put all of it (100%) on C1.Lithium dimethylcuprate and methyllithium are each added to cyclohex-2-en-1-one. Which statement is correct?
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Answer: A — The cuprate gives 3-methylcyclohexanone (1,4-addition); MeLi gives the tertiary allylic alcohol (1,2-addition)
Organocuprates are soft nucleophiles and add to the soft β-carbon (conjugate addition), giving the enolate and then the 3-substituted ketone. Hard, highly reactive MeLi attacks the carbonyl carbon directly, under kinetic control, giving 1-methylcyclohex-2-en-1-ol.2-Bromo-2-methylbutane is heated with potassium tert-butoxide in tert-butanol. The major alkene is
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Answer: A — 2-methyl-1-butene (Hofmann product)
The bulky base removes the more accessible primary CH₃ hydrogen rather than the hindered secondary CH₂ hydrogen, so the less substituted 2-methyl-1-butene dominates. With ethoxide the more stable trisubstituted 2-methyl-2-butene would be the major product.Dichlorocarbene, from CHCl₃ and KOt-Bu, adds to cis-2-butene to give only the cis-dimethylcyclopropane. This shows that the carbene
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Answer: A — is a singlet and adds in one concerted step
A singlet carbene forms both new bonds at once, so the alkene geometry is preserved (stereospecific syn addition). A triplet would add one bond first to give a diradical that rotates before closing, giving both cis and trans cyclopropanes. The chlorine lone pairs stabilise the singlet.Hexanamide, CH₃(CH₂)₄CONH₂, undergoes the Hofmann rearrangement with Br₂ and NaOH. How many carbon atoms does the amine product contain?
Numerical answer — type the value.
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Answer: 5
The alkyl group migrates from the carbonyl carbon to nitrogen, giving the isocyanate C₅H₁₁N=C=O, whose carbonyl carbon is lost as CO₂ (carbonate) on hydrolysis: pentylamine, C₅H₁₁NH₂, with five carbons. Keeping all six carbons would describe an amide reduction, not the Hofmann reaction.In the Beckmann rearrangement of a ketoxime in acid, which group migrates to nitrogen?
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Answer: A — The group anti to the oxime OH
Protonated OH leaves as water while the group anti-periplanar to it migrates from carbon to nitrogen in a concerted step, with retention of its configuration; water then adds to the nitrilium ion and tautomerisation gives the amide. Which group is anti depends on the oxime geometry, not on size.What is the overall result of the Barton–McCombie reaction?
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Answer: A — Replacement of an alcohol OH by H through a thiocarbonyl derivative and a tin radical
The alcohol is made into a xanthate or thionocarbonate; Bu₃Sn• adds to sulfur, the C–O bond fragments to an alkyl radical, and Bu₃SnH delivers H: R–OH → R–H, a deoxygenation. The Ag salt/Br₂ route is the Hunsdiecker reaction and the amide route the Hofmann rearrangement.The silver salt of butanoic acid is heated with Br₂ in CCl₄ (the Hunsdiecker reaction). The organic product is
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Answer: A — 1-bromopropane
CH₃CH₂CH₂COOAg + Br₂ gives the acyl hypobromite, whose O–Br bond homolyses; the carboxyl radical loses CO₂ to give the propyl radical, which takes Br: CH₃CH₂CH₂Br, one carbon fewer. α-Bromination of the acid is the Hell–Volhard–Zelinsky reaction, a different process.