How the barrier is estimated
ΔG‡ is built additively from a reference reaction, CH₃–Br + H₂O in water at 25 °C (half-life about 20 days, ΔG‡ ≈ 28.6 kcal/mol). Each choice then shifts it. The nucleophile uses the Swain–Scott equation, log(k/k₀) = s·n with s = 1. The leaving group and the carbon use relative SN2 rates converted with ΔΔG‡ = −RT ln(krel). Rates come from the Eyring equation, k = (kBT/h)e−ΔG‡/RT, with the barrier held fixed as temperature changes. The half-life is for equal starting concentrations, t½ = 1/(k[A]₀). Treat the numbers as order-of-magnitude estimates for a polar protic solvent. In a polar aprotic solvent such as DMSO or acetone, anionic nucleophiles react far faster and their order can change.
SN1
The SN1 barrier is built the same way from a different reference: (CH₃)₃C–Cl ionizing in water at 25 °C (k ≈ 3 × 10⁻² s⁻¹, ΔG‡ ≈ 19.6 kcal/mol). The leaving group and the stability of the carbocation then shift it. The nucleophile is not in the rate law, so it only sets the small second barrier, from the carbocation to the products. The carbocation is drawn a few kcal/mol below the first transition state, which it closely resembles (Hammond postulate). The products, and so ΔG°, are the same as for SN2. Rates are first-order, k[R–X], with t½ = ln 2/k.
Solvent
Each solvent shifts the barrier by a factor relative to water. For SN1, the factors follow the Grunwald–Winstein ionizing power of the solvent (Y = 3.49 for water and −1.09 for methanol, with m = 1 for tert-butyl chloride). The aprotic values are rough estimates. For SN2 with anionic nucleophiles, protic solvents hydrogen-bond to the anion and slow it. Polar aprotic solvents speed it up by roughly 10³ for HS⁻ and 10⁵ for acetate, whose small, hard oxygens are the most strongly solvated in water. These are rounded from Parker's comparisons, which span 10¹–10⁶ depending on the anion. Neutral water as a nucleophile changes little. The solvent shell is drawn only for protic solvents, because they are the ones that hydrogen-bond to the anions.
E2 and E1
E2 is anchored to SN2: with methoxide at a 1° carbon, E2 is set to about 1% of SN2, as for ethyl bromide with ethoxide. It then scales with base strength (Brønsted β = 0.6 on the pKa of the conjugate acid), with the carbon (more β-H and a more substituted alkene: 1° : 2° : 3° ≈ 1 : 20 : 3000), and with the same leaving-group and solvent factors as SN2. Elimination is also given a small entropy advantage (6 cal mol⁻¹ K⁻¹), so heating favours it. These rounded values reproduce typical textbook outcomes: ethyl bromide + RO⁻ gives about 1% alkene, isopropyl bromide about 80%, tert-butyl bromide mostly alkene, and tert-butoxide eliminates even at 1° carbons. E1 shares the SN1 carbocation. The share that loses H⁺ is set to about 15% at 25 °C and rises with temperature (ΔH ≈ 4.5 kcal/mol, ΔS ≈ 11.5 cal mol⁻¹ K⁻¹ in favour of elimination). The Zaitsev/Hofmann panel uses typical textbook product ratios for 2-bromobutane and 2-bromo-2-methylbutane, not the model. Alkoxides in water would be leveled to HO⁻, so they are normally used in their own alcohol or in DMSO.
Comparing the pathways
The four pathways run side by side from the same reactants. SN2 and E2 rates are k[Nu or B] (with [H₂O] = 55 M when water is both reagent and solvent). SN1 and E1 share the ionization rate k₁, split by the E1 fraction. The share of each pathway is its rate divided by the total, and "mixed" means no pathway reaches 60%.
Energy diagram and geometry
The overall ΔG° is a rough guide from the basicity of the nucleophile and the leaving group (the weaker base is favored), and only sets where the products sit. The transition state shifts toward the side it resembles more (the Hammond postulate). In the model, partial bonds stretch about 0.5 Å at the transition state, the three groups on carbon pass through planar (90°), and the backside opening is the share of approach directions within 35° of the C–X axis where a probe 3 Å from the carbon does not overlap a substituent. Crowding counts the substituent atoms within 85% of their van der Waals contact distance from the nucleophile, and gives the closest distance.
| Nucleophile | Swain–Scott n | ΔΔG‡ vs H₂O |
|---|
| HS⁻ (strong) | 5.1 | −7.0 kcal/mol |
| CH₃COO⁻ (medium) | 2.7 | −3.7 kcal/mol |
| H₂O (weak) | 0.0 | 0 |
| Leaving group | Relative rate | ΔΔG‡ vs Br⁻ |
|---|
| I⁻ (good) | 30 000 | −0.7 kcal/mol |
| Cl⁻ (moderate) | 200 | +2.3 kcal/mol |
| F⁻ (bad) | 1 | +5.5 kcal/mol |
| Carbon | Relative SN2 rate | ΔΔG‡ vs CH₃ |
|---|
| Methyl (for reference) | 30 | 0 |
| 1° ethyl (unhindered) | 1 | +2.0 kcal/mol |
| 2° isopropyl (moderate) | 0.025 | +4.2 kcal/mol |
| 3° tert-butyl (hindered) | ≈ 0 (not observed) | +13.6 kcal/mol, set so SN2 is negligible in any solvent |
| SN1 ionization | Relative rate | ΔΔG‡ |
|---|
| I⁻ / Cl⁻ / F⁻ (leaving group) | 100 / 1 / 10⁻⁵ | −2.7 / 0 / +6.8 kcal/mol |
| 3° / 2° / 1° (carbocation) | 1 / 10⁻⁸ / ≈ 0 | 0 / +10.9 / +19.1 kcal/mol |
SN1 values are rough, rounded estimates in the spirit of the data. Measured 2° "SN1" rates in water include a lot of solvent-assisted SN2, and 1° carbocations do not form in solution at all.
Sources: R. A. Bartsch & J. Závada,
Chem. Rev. 1980, 80, 453 (base size and Hofmann/Zaitsev); W. H. Saunders & A. F. Cockerill,
Mechanisms of Elimination Reactions (Wiley, 1973); A. J. Parker,
Chem. Rev. 1969, 69, 1 (solvent effects on SN2); E. Grunwald & S. Winstein,
J. Am. Chem. Soc. 1948, 70, 846 (Y scale); S. Winstein & A. H. Fainberg,
J. Am. Chem. Soc. 1957, 79, 5937 (tert-butyl chloride solvolysis); C. G. Swain & C. B. Scott,
J. Am. Chem. Soc. 1953, 75, 141 (nucleophilicity n); A. Streitwieser,
Chem. Rev. 1956, 56, 571 (relative rates of alkyl groups); J. McMurry,
Organic Chemistry (Cengage), relative leaving-group reactivity; H. Eyring,
J. Chem. Phys. 1935, 3, 107.