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Química Orgânica Física · Mechanistic probes

Relações lineares de energia livre e efeitos isotópicos

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O que você vai aprender

  • Use the Hammett equation log(kX/kH) = ρσ to calculate σ and ρ and to read the sign, size and curvature of a Hammett plot as evidence about charge in the rate-determining transition state.
  • Decide when σ⁺ or σ⁻ must replace σ, and apply the Swain–Scott (nucleophilicity) and Grunwald–Winstein (solvent ionising power) equations.
  • Explain primary and secondary kinetic isotope effects from zero-point energies and use their size to locate C–H cleavage and rehybridisation in a mechanism.
  • Interpret solvent isotope effects and buffer-concentration tests for acid–base catalysis, and design and read crossover experiments that distinguish intramolecular from intermolecular pathways.

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The Hammett equation

Meta and para substituents change rates and equilibria of benzene derivatives in a regular way. The reference reaction is the ionisation of substituted benzoic acids in water at 25 °C: the substituent constant is σ = log(KX/KH) = pKa(H) − pKa(X). Benzoic acid has pKa 4.20 and 4-nitrobenzoic acid about 3.44, so the 4-nitro group has σp ≈ 4.20 − 3.44 = 0.76, close to the tabulated +0.78. Electron-withdrawing groups have σ > 0 (σp: Cl 0.23, CN 0.66, NO₂ 0.78); donors have σ < 0 (σp: CH₃ −0.17, OCH₃ −0.27). For any other reaction, log(kX/kH) = ρσ, and the reaction constant ρ measures how strongly that reaction responds to the same substituents. By definition ρ = 1.00 for benzoic acid ionisation. Ortho substituents are left out because their steric effects are not captured by σ.

Reading ρ

The sign of ρ says which way charge moves at the ring on going from reactant to the rate-determining transition state. ρ > 0: negative charge builds up (or positive charge is lost), so withdrawing groups accelerate; alkaline hydrolysis of ethyl benzoates has ρ ≈ +2.5 because hydroxide addition makes an anionic tetrahedral intermediate. ρ < 0: positive charge builds up, so donors accelerate. The size of |ρ| reflects how much charge develops and how close it is to the ring: ρ falls from 1.00 for ArCOOH to about 0.49 for ArCH₂COOH and 0.21 for ArCH₂CH₂COOH, because each CH₂ moves the carboxylate further away. A straight plot means one mechanism throughout. A break that is concave upward (a V shape) means a change of mechanism, because each substrate takes the faster of two paths; a break that is concave downward means a change in the rate-determining step within one mechanism, because the slower step always wins.

σ⁺ and σ⁻: through-conjugation

Ordinary σ values include only the resonance that occurs in benzoic acid ionisation, where the reacting carboxyl group is not directly conjugated with a para substituent. When a positive charge develops on a carbon attached to the ring, a para π donor can share that charge directly: the 4-methoxycumyl cation has a quinoid contributor with the charge on oxygen. Such reactions follow σ⁺, defined from solvolysis of cumyl chlorides (2-aryl-2-chloropropanes) in 90% aqueous acetone, ρ = −4.54. Para donors have much more negative σ⁺ than σ (OCH₃ −0.78 against −0.27; CH₃ −0.31 against −0.17). Electrophilic aromatic substitution also follows σ⁺; bromination by Br₂ in acetic acid has ρ ≈ −12. In the opposite case, a negative charge that a para π acceptor can take over, as in 4-nitrophenoxide, needs σ⁻ (NO₂ σ⁻ ≈ 1.27 against σp 0.78). Meta substituents cannot conjugate with the reacting centre, so σm⁺ ≈ σm.

Other free-energy scales: nucleophiles and solvents

The same idea works for other variables. The Swain–Scott equation, log(k/k₀) = s·n, compares nucleophiles in SN2 reactions in water, with k₀ the rate constant for water itself and s = 1.00 for methyl bromide. Standard n values: H₂O 0, CH₃COO⁻ 2.72, Cl⁻ 3.04, Br⁻ 3.89, OH⁻ 4.20, SCN⁻ 4.77, I⁻ 5.04. The Grunwald–Winstein equation, log(k/k₀) = mY, compares solvents: Y is the ionising power of a solvent relative to 80% aqueous ethanol (Y = 0), set by solvolysis of 2-chloro-2-methylpropane (m = 1); water has Y ≈ 3.49 and ethanol Y ≈ −2.03. A substrate with m near 1 ionises with a cation-like transition state; primary substrates that react by SN2 with the solvent have m around 0.3 and respond more to solvent nucleophilicity. Modern scales use 1-adamantyl derivatives as the reference, because the cage blocks backside attack by solvent and the bridgehead cannot form an alkene.

Primary kinetic isotope effects

Replacing H by D leaves the potential-energy surface unchanged but lowers the zero-point energy (ZPE = ½hcν̃) of the bond, because the heavier atom vibrates more slowly: a C–H stretch near 2900 cm⁻¹ becomes a C–D stretch near 2100 cm⁻¹. If that stretch is lost in the transition state, the C–D compound has the higher barrier, giving kH/kD up to about 7 at 25 °C. A primary isotope effect (typically 2–7) therefore shows that the bond to the labelled hydrogen breaks in or before the rate-determining step; kH/kD ≈ 1 shows that it breaks after it, as in nitration of benzene, where attack on NO₂⁺ is slow and loss of the proton is fast. The effect is largest when the proton is transferred in a symmetric transition state, half-bonded to donor and acceptor, and smaller for early or late transition states. Values well above about 10 at room temperature indicate tunnelling.

Secondary and solvent isotope effects

Secondary isotope effects arise when the labelled bond is not broken. α-Effects report rehybridisation of the carbon that carries the label: sp³ → sp² (SN1 ionisation) loosens the C–H bending vibrations and gives kH/kD ≈ 1.1–1.25 per deuterium, SN2 gives values near 1, and sp² → sp³ (addition to a carbonyl) gives inverse values below 1. β-Effects report hyperconjugation: in the ionisation of (CD₃)₃CCl the β C–H bonds donate into the developing empty p orbital, and the fully deuterated compound reacts about 2.4 times more slowly. Solvent isotope effects compare H₂O with D₂O. A reaction with a proton in flight in its rate-determining step (general acid or general base catalysis) is typically 2–3 times slower in D₂O. Specific acid catalysis, with fast pre-equilibrium protonation before a slow step, is usually faster in D₂O (kH₂O/kD₂O ≈ 0.3–0.5), because more of the substrate is protonated by D₃O⁺ than by H₃O⁺. A rate that depends on buffer concentration at constant pH also signals general catalysis.

Crossover experiments

To find out whether a group that migrates ever leaves its molecule, heat a mixture of two substrates that are labelled differently in both the migrating group and the remaining fragment, then look for crossed products that combine the group from one with the fragment of the other. Allyl 4-methylphenyl ether and 2-methylallyl phenyl ether, heated together, give only 2-allyl-4-methylphenol and 2-(2-methylallyl)phenol in the aromatic Claisen rearrangement: no crossover, so the allyl group never becomes free. If both substrates carry the same fragment, crossed and uncrossed products are identical and the experiment tells you nothing. Crossover products must also be checked against scrambling of the products after they form, by subjecting the products themselves to the reaction conditions. Absence of crossover rules out free fragments that escape into solution; it does not by itself prove a concerted mechanism.

What to carry forward

Linear free-energy relationships and isotope effects are the two main experimental probes of transition states. ρ tells you the sign and amount of charge that develops near a ring; σ⁺ or σ⁻ tells you whether that charge is in direct conjugation; m and s tell you how strongly a reaction responds to solvent ionising power and to nucleophiles. A primary kinetic isotope effect locates C–H cleavage at or before the rate-determining step, secondary effects report rehybridisation and hyperconjugation, solvent isotope effects separate pre-equilibrium protonation from proton transfer in the slow step, and crossover experiments test whether fragments ever separate.

Problemas de prática (40)

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Desenhe o mecanismo 8

σ⁺, σ⁻ and other free-energy scales

  • Solvolysis of 1-chloroadamantane: a limiting SN1 referenceDraw the SN1 solvolysis of 1-chloroadamantane and explain why its rigid cage makes it a reference substrate for measuring solvent ionising power.
  • SN1 hydrolysis of 4-methoxycumyl chloride: why σ⁺ is neededDraw the SN1 hydrolysis of 4-methoxycumyl chloride and explain why its rate follows σ⁺ rather than σ.
  • SN2 of thiocyanate with methyl bromide (Swain–Scott n = 4.77)Draw the one-step SN2 attack of thiocyanate sulfur on methyl bromide and use the Swain–Scott equation to compare thiocyanate with water as a nucleophile.

Kinetic isotope effects

  • Acid-catalysed bromination of cyclohexanone: enolisation is rate-determiningDraw the acid-catalysed α-bromination of cyclohexanone and use the rate law and the primary isotope effect to show that enol formation, not reaction with bromine, is rate-determining.
  • E2 of (2-bromoethyl)benzene: isotope effect and ρDraw the concerted E2 of (2-bromoethyl)benzene with ethoxide and interpret its primary isotope effect and positive ρ as evidence about C–H cleavage and charge in the transition state.

Solvent isotope effects and crossover

  • Acid hydrolysis of 2-methoxyoxane: an inverse solvent isotope effectDraw the specific-acid-catalysed hydrolysis of 2-methoxyoxane through its cyclic oxocarbenium ion and explain why such reactions run faster in D₂O than in H₂O.

Hammett σ and ρ

  • Saponification of ethyl 4-nitrobenzoate (ρ ≈ +2.5)Draw the addition–elimination hydrolysis of ethyl 4-nitrobenzoate by hydroxide and connect the positive ρ of ester saponification to the anionic tetrahedral intermediate formed in the rate-determining step.
  • Ionisation of 4-nitrobenzoic acid: the Hammett reference reactionDraw the proton transfer from 4-nitrobenzoic acid to water and relate the substituent constant σp of the nitro group to the acidity it produces.

Preveja o produto 2

σ⁺, σ⁻ and other free-energy scales

  • Fastest arene in brominationPredict the most reactive arene in electrophilic bromination from σ⁺ values and a large negative ρ.

Solvent isotope effects and crossover

  • Spot the crossover productPredict which product of a double-label crossover experiment would reveal an intermolecular Claisen rearrangement.

Classificar 4

Kinetic isotope effects

  • An α-deuterium isotope effectClassify substitution reactions as SN1 or SN2 from their α-secondary deuterium isotope effects.

Solvent isotope effects and crossover

  • A proton in flightClassify a buffer-catalysed hydrolysis as general base catalysis from its rate law and normal solvent isotope effect.

σ⁺, σ⁻ and other free-energy scales

  • Which phenol needs σ⁻?Identify the substituent whose effect on phenol acidity requires σ⁻ because it conjugates directly with the phenoxide oxygen.
  • Which point falls off the σ line?Identify which substituent needs σ⁺ in a reaction that develops positive charge in conjugation with the ring.

Comparar 3

Hammett σ and ρ

  • Rank benzoic acids by acidityOrder substituted benzoic acids by acidity using their Hammett σ values.
  • Which methoxy acid is stronger?Use σm and σp to show that a methoxy group withdraws electrons from the meta position but donates from the para position.

σ⁺, σ⁻ and other free-energy scales

  • Rank cumyl chlorides by solvolysis rateOrder para-substituted cumyl chlorides by SN1 solvolysis rate from σ⁺ values and a negative ρ.

Calcular 7

σ⁺, σ⁻ and other free-energy scales

  • σ⁺ for a para-methoxy cumyl chlorideCalculate the rate enhancement for solvolysis of a para-donor-substituted cumyl chloride using σ⁺ rather than σ.
  • Iodide versus chloride toward methyl bromideUse the Swain–Scott equation to compare two nucleophiles in an SN2 reaction.

Kinetic isotope effects

  • Calculate a primary isotope effectCalculate kH/kD from the rate constants of a compound and its deuterated analogue and judge whether it is a primary effect.
  • The largest C–H/C–D isotope effectEstimate the maximum primary kinetic isotope effect from the zero-point energies of C–H and C–D stretches.

Hammett σ and ρ

  • Find ρ from one rate ratioCalculate a reaction constant ρ from the rate ratio of a meta-substituted substrate and the parent compound.
  • How much faster does the nitro ester hydrolyse?Use ρ and σ to estimate the rate ratio for saponification of a para-substituted ethyl benzoate.
  • Calculate σp for chlorineCalculate a Hammett substituent constant from the pKa values of a substituted and unsubstituted benzoic acid.

Encontre o erro 2

Solvent isotope effects and crossover

  • Crossover found: what must you check?Identify the control experiment that rules out product scrambling before a crossover result is taken as evidence of an intermolecular mechanism.

Kinetic isotope effects

  • Does a big isotope effect prove E1cB?Diagnose an over-interpretation of a primary isotope effect in an elimination reaction.

Interprete as evidências 6

σ⁺, σ⁻ and other free-energy scales

  • Reading Grunwald–Winstein m valuesInterpret Grunwald–Winstein m values as a measure of how much ionic character develops in a solvolysis transition state.

Hammett σ and ρ

  • A V-shaped Hammett plotInterpret a concave-upward Hammett plot as a change of mechanism rather than a change of rate-determining step.

Solvent isotope effects and crossover

  • What no crossover tells youInterpret the absence of crossover products correctly, without over-claiming a concerted mechanism.
  • Specific or general acid catalysis?Use buffer-concentration dependence and the solvent isotope effect to classify acid catalysis as specific or general.

Kinetic isotope effects

  • Three reactions, one rateInterpret equal rates of racemisation and halogenation of a ketone as evidence for a shared rate-determining enolisation.
  • When is kH/kD largest?Explain why primary isotope effects for proton transfer are largest for a symmetric transition state.

Planeje uma síntese 2

Solvent isotope effects and crossover

  • Design a crossover pairPlan a crossover experiment in which both the migrating group and the remaining fragment are labelled, so that crossed products are distinguishable.

Kinetic isotope effects

  • Design a test for the slow stepChoose the isotopic labelling experiment that tests whether C–H bond cleavage is rate-determining.

Explique por quê 6

Kinetic isotope effects

  • An isotope effect without bond breakingExplain a β-secondary deuterium isotope effect in SN1 ionisation by hyperconjugation.
  • Why a C–D bond breaks more slowlyExplain the origin of the primary kinetic isotope effect in terms of zero-point energy.

Hammett σ and ρ

  • Fluorine: meta versus paraExplain the difference between σm and σp of fluorine in terms of inductive withdrawal and π donation.
  • Why ρ falls with each CH₂Explain how inserting CH₂ groups between the ring and the reacting centre reduces the magnitude of ρ.
  • What a positive ρ meansExplain what the sign of a reaction constant ρ says about charge development in the rate-determining transition state.

σ⁺, σ⁻ and other free-energy scales

  • Choosing a solvent-scale referenceExplain why a 1-adamantyl substrate is the best reference for a scale of solvent ionising power.

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