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Química Orgânica Física · Kinetics and energy surfaces

Acidez, solvatação e efeitos do solvente

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O que você vai aprender

  • Explain why pKa values change between water, DMSO and the gas phase, using hydrogen bonding, charge delocalisation and polarisability of the conjugate base.
  • Use the leveling effect and solvent windows to choose a solvent and base for a proton transfer, and calculate equilibrium constants and free energies from pKa differences.
  • Describe superacids and superbases: how their strength is measured (H₀, pKBH⁺) and what species they make observable or accessible.
  • Predict how solvent polarity and proticity change SN1 and SN2 rates and selectivity with the Hughes–Ingold charge rules and the behaviour of unsolvated (naked) anions.

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pKa belongs to an acid in a solvent

A pKa measures the free energy of HA → H⁺ + A⁻ in a particular solvent, so changing the solvent changes the number. Water is a hydrogen-bond donor and acceptor: it stabilises small, charge-localised anions such as hydroxide, alkoxides and carboxylates with several O–H···O⁻ hydrogen bonds. DMSO (drawn left, next to water) is polar and solvates cations and protons well through its oxygen, but it has no O–H or N–H to donate, so anions are much less stabilised. Neutral O–H acids therefore become much weaker in DMSO. Approximate Bordwell DMSO values, with water values in brackets: acetic acid ≈ 12.3 (4.8), phenol ≈ 18.0 (10.0), methanol ≈ 29.0 (15.5), water ≈ 31.4 (15.7). Acids whose anion spreads its charge over a large, polarisable or delocalised system shift far less: malononitrile is about 11 in both solvents, and thiophenol moves only from 6.6 to 10.3. Cationic acids such as triethylammonium (10.7 in water, 9.0 in DMSO) create no anion on ionising and barely move. Each pKa unit is 2.303RT ≈ 5.7 kJ/mol at 298 K.

Intrinsic acidity in the gas phase

Without a solvent, an anion is stabilised only by its own structure: electronegativity, resonance and polarisability. Alkyl groups are polarisable and spread a nearby negative charge, so in the gas phase tert-butanol is more acidic than ethanol, ethanol more than methanol and methanol more than water. In solution the alcohols fall in the reverse order (methanol > ethanol > tert-butanol), because the bulky tert-butoxide (drawn left, beside methoxide) is the hardest anion to surround with solvent. Amines show the same split: in the gas phase basicity rises steadily NH₃ < MeNH₂ < Me₂NH < Me₃N, but in water trimethylamine (pKaH 9.8) is weaker than dimethylamine (10.7), because Me₃NH⁺ has only one N–H to hydrogen-bond to water. The gas phase even makes toluene a stronger acid than water: the benzyl anion is delocalised, whereas hydroxide owes its stability in water almost entirely to hydration.

Leveling and the solvent window

No acid stronger than the solvent's conjugate acid, and no base stronger than its conjugate base, can survive in a solvent. In water, HCl, HBr and HClO₄ all ionise completely to H₃O⁺ and look equally strong; sodium amide reacts completely with water to give hydroxide. A less basic solvent such as glacial acetic acid differentiates the strong acids (HClO₄ is the strongest). The usable pKa range is therefore set by the solvent: roughly 0 to 14–16 in water, but up to about 35 in DMSO, whose conjugate base, the dimsyl anion (drawn), is made from DMSO and NaH. That is why carbon acids such as fluorene (≈ 22.6), acetone (≈ 26.5) and triphenylmethane (≈ 30.6) have measured DMSO pKa values, found by equilibrating them with indicator acids of known pKa. To compare two acids in one solvent, log K = pKa(acid formed) − pKa(acid consumed).

Superacids and superbases

In concentrated acids pH loses its meaning, so acidity is measured by the Hammett function H₀ = pKBH⁺ + log([B]/[BH⁺]), using weakly basic indicators such as nitroanilines. 100% sulfuric acid has H₀ ≈ −12; any medium more acidic is a superacid: triflic acid (≈ −14.1), fluorosulfuric acid HSO₃F (≈ −15.1), and magic acid (1:1 HSO₃F–SbF₅), about −23. SbF₅ binds the fluorosulfate or fluoride anion and leaves a very weakly basic, non-nucleophilic counterion, so carbocations (the tert-butyl cation), protonated arenes (arenium ions) and protonated alcohols persist at low temperature. At the other end, superbases combine high basicity with low nucleophilicity: 1,8-bis(dimethylamino)naphthalene, proton sponge (drawn, pKaH ≈ 12 in water against ≈ 5 for N,N-dimethylaniline), gains from relieving the clash of two nitrogen lone pairs and from a strong N–H···N hydrogen bond; phosphazene bases spread the positive charge of their conjugate acids over many nitrogens and reach pKBH⁺ above 40 in acetonitrile.

Hughes–Ingold solvent rules

Compare the charges of the reactants with those of the transition state. If charge is created (neutral RX ionising in SN1, or a neutral amine attacking an alkyl halide in the Menshutkin reaction, which gives the ammonium salt drawn), a more polar solvent stabilises the transition state and speeds the reaction strongly. If charge is dispersed (an anion attacking a neutral alkyl halide, or a neutral nucleophile attacking a cationic substrate), a more polar solvent slows the reaction slightly. If charge is destroyed (hydroxide attacking trimethylsulfonium), a more polar solvent slows the reaction strongly. The Grunwald–Winstein Y scale puts numbers on ionising power: ethanol ≈ −2.0, methanol ≈ −1.1, 80% aqueous ethanol 0.0, water ≈ 3.5, and log k for tert-butyl chloride solvolysis rises one unit per unit of Y.

Protic versus polar aprotic: naked anions

Protic solvents (water, alcohols, carboxylic acids) hydrogen-bond most strongly to small, hard anions, so in methanol nucleophilicity runs I⁻ > Br⁻ > Cl⁻ > F⁻. Polar aprotic solvents (DMSO, DMF, acetonitrile, acetone) solvate the cation but leave the anion nearly bare, which can raise SN2 rates by around a million: chloride reacts with iodomethane roughly 10⁶ times faster in DMF than in methanol, and with tetrabutylammonium salts in acetone the halide order becomes Cl⁻ > Br⁻ > I⁻. Crown ethers (18-crown-6 drawn, which wraps K⁺) and strongly cation-binding cosolvents such as HMPA or DMPU free the anion further, so KF in acetonitrile with 18-crown-6 fluorinates benzyl bromide. Solvation also steers ambident anions: in DMF phenoxide reacts at its unsolvated oxygen, while water or trifluoroethanol hydrogen-bond to that oxygen and let ring-carbon alkylation compete.

What to carry forward

Before quoting or comparing a pKa or a rate, name the medium. Ask what the solvent does to the charged species: does it donate hydrogen bonds to the anion, solvate the cation, or leave a naked ion? Leveling sets which acids and bases can exist, ΔpKa × 5.7 kJ/mol converts acidity into energy, and the Hughes–Ingold charge rules predict whether a more polar solvent speeds or slows a substitution.

Problemas de prática (40)

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Desenhe o mecanismo 8

Acidity in water and DMSO

  • Dimsyl sodium deprotonates triphenylmethane in DMSODraw hydride removing a methyl proton of DMSO to give the dimsyl anion and H₂, then dimsyl deprotonating triphenylmethane, and use DMSO pKa values to judge where the second equilibrium lies.

Solvent effects on substitution

  • Hydroxide demethylates trimethylsulfoniumDraw the SN2 attack of hydroxide on trimethylsulfonium that gives methanol and dimethyl sulfide, and predict how solvent polarity changes its rate.
  • Menshutkin quaternisation of triethylamine with iodoethaneDraw the SN2 attack of triethylamine on iodoethane that gives tetraethylammonium iodide, and use the charge change on the way to the transition state to predict the solvent effect.
  • Crown-ether fluoride converts benzyl bromide into benzyl fluorideDraw the SN2 displacement of bromide from benzyl bromide by fluoride, and explain why the reaction needs a polar aprotic solvent and a crown ether.
  • O-Allylation of sodium phenoxide in DMFDraw the SN2 attack of phenoxide oxygen on allyl bromide in DMF, and explain why protic solvents shift this ambident anion toward ring-carbon alkylation.

Leveling, superacids and superbases

  • Mesitylene is protonated to a persistent arenium ion in superacidDraw ring-carbon protonation of mesitylene by a superacid and the resonance that spreads the positive charge over the methyl-bearing carbons, and explain why the arenium ion persists instead of losing the proton again.
  • Protonating proton spongeDraw the protonation of 1,8-bis(dimethylamino)naphthalene by hydronium and explain why this aromatic amine is about 10⁷ times more basic than N,N-dimethylaniline.
  • tert-Butanol gives the tert-butyl cation in magic acidDraw protonation of tert-butanol by fluorosulfuric acid, loss of water to give the tert-butyl cation, and protonation of the released water, and explain why the cation persists in this medium.

Preveja o produto 1

  • What can tert-butoxide fully deprotonate in DMSO?Predict whether a base deprotonates a carbon acid essentially completely in DMSO from the pKa difference.

Classificar 3

Acidity in water and DMSO

  • Spot the polar aprotic solventClassify common solvents as polar aprotic, protic or nonpolar from their structures.

Leveling, superacids and superbases

  • The strongest base water allowsIdentify the strongest base that can persist in water using the leveling effect.
  • Which is a superacid?Classify acids as superacids using the definition based on 100% sulfuric acid.

Comparar 6

Acidity in water and DMSO

  • Rank O–H acids in DMSORank alcohols, phenol and a carboxylic acid by acidity in DMSO from the stabilisation of their conjugate bases.
  • Which pKa barely changes in DMSO?Identify the acid whose pKa is least sensitive to replacing water with DMSO from the structure of its conjugate base.

Gas phase versus solution

  • Alcohol acidity without solventRank water and simple alcohols by intrinsic gas-phase acidity using the polarisability of alkyl groups.
  • Amine basicity without solventRank ammonia and methylamines by gas-phase basicity from the stabilisation of their conjugate acids.

Solvent effects on substitution

  • Halide nucleophilicity in acetoneRank halide nucleophilicity in a polar aprotic solvent where the anions are not hydrogen-bonded.
  • Which reaction does a polar solvent slow most?Apply the Hughes–Ingold charge rules to predict which substitution is most strongly slowed by increased solvent polarity.

Calcular 5

Acidity in water and DMSO

  • Equilibrium constant for a proton transfer in DMSOCalculate log K of a proton transfer in DMSO from Bordwell pKa values of the two acids.
  • Extra free energy of ionising acetic acid in DMSOConvert a solvent-induced pKa change into a difference in standard free energy of ionisation.

Leveling, superacids and superbases

  • Hammett acidity from an indicator ratioCalculate the Hammett acidity function of a strong acid medium from the protonation ratio of an indicator base.
  • pH after adding sodium amide to waterCalculate the pH produced when a base stronger than hydroxide is leveled by water.

Solvent effects on substitution

  • Barrier difference from a protic/aprotic rate ratioConvert a protic versus aprotic SN2 rate ratio into a difference in free energy of activation.

Encontre o erro 1

  • A sluggish nitrile synthesisDiagnose a slow SN2 reaction caused by a protic solvent and choose the solvent that fixes it.

Interprete as evidências 4

Gas phase versus solution

  • Why trimethylamine falls behind in waterInterpret the aqueous basicity order of methylamines by comparing it with the gas-phase order.
  • Where the 1500 kJ/mol goesUse a thermochemical cycle to identify which term converts a huge gas-phase deprotonation energy into a modest aqueous pKa.

Acidity in water and DMSO

  • Charge type and the solvent effect on pKaInterpret why cationic acids keep nearly the same pKa in DMSO while neutral O–H acids weaken.

Solvent effects on substitution

  • Rank solvents for tert-butyl chloride solvolysisUse Grunwald–Winstein Y values to rank solvents by the SN1 rate of tert-butyl chloride.

Planeje uma síntese 1

  • Choose a solvent that ranks strong acidsChoose a differentiating solvent that reveals the difference in strength between two acids leveled by water.

Explique por quê 11

Acidity in water and DMSO

  • Why acetic acid is weaker in DMSOExplain the rise in the pKa of a carboxylic acid on going from water to DMSO in terms of anion solvation.
  • Thiophenol shifts less than phenolExplain why a thiol's pKa is less sensitive to solvent than an alcohol's or phenol's.

Leveling, superacids and superbases

  • Why acetone's pKa is measured in DMSOExplain how a solvent's leveling limit decides which acids can be measured directly in it.
  • What SbF₅ adds to a superacidExplain how a Lewis acid increases the Brønsted acidity of HF or HSO₃F.
  • What makes a phosphazene a superbaseExplain the structural origin of the basicity and low nucleophilicity of phosphazene superbases.
  • Two strong acids, one pHExplain the leveling effect of water on acids stronger than hydronium.

Gas phase versus solution

  • Why SN2 slows down in waterExplain how solvation of the nucleophile raises SN2 barriers in solution relative to the gas phase.
  • Why the alcohol order flips in solutionExplain why tert-butanol is a stronger acid than methanol in the gas phase but a weaker one in solution.
  • Toluene out-acids water in the gas phaseExplain why a delocalised carbon acid can be intrinsically more acidic than water yet far less acidic in solution.

Solvent effects on substitution

  • Halide order in methanolExplain why hydrogen bonding reverses halide nucleophilicity in protic solvents.
  • Why HMPA speeds up enolate alkylationExplain how a strongly cation-solvating cosolvent accelerates the SN2 alkylation of a lithium enolate.

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