Organic Chemistry · Part 5 of 9 · Free
Elimination Reactions — formula sheet
Every key expression and definition from Reaction Mechanisms, Part 5, on one page. Free to read, no sign-in.
Key expressions
the E2 rate law
rate = k_2[substrate][base]
rate = k_2[substrate][base]
the electronic origin of Hofmann orientation
Hofmann orientation ↔ E1cb-like transition state ↔ poor or charged leaving group ↔ C–H breaking ahead of C–X breaking
Hofmann orientation ↔ E1cb-like transition state ↔ poor or charged leaving group ↔ C–H breaking ahead of C–X breaking
the zero-point-energy origin of the primary kinetic isotope effect
ΔE_a = ½hN_A(ν_C–H − ν_C–D) k_H/k_D = exp(ΔE_a/RT)
ΔE_a = ½hN_A(ν_C–H − ν_C–D) k_H/k_D = exp(ΔE_a/RT)
the E1 rate law
rate = k_1[substrate]
rate = k_1[substrate]
why heating favours elimination
ΔG‡ = ΔH‡ − TΔS‡ ⇒ the pathway with the more positive ΔS‡ (elimination) is favoured as T increases
ΔG‡ = ΔH‡ − TΔS‡ ⇒ the pathway with the more positive ΔS‡ (elimination) is favoured as T increases
Definitions worth memorising
β-Elimination (1,2-elimination): loss of two groups from adjacent carbons, generating a π bond between them. The carbon carrying the leaving group is Cα; the carbon losing the hydrogen is Cβ. Unless a question says otherwise, “elimination” in organic chemistry means β-elimination.
Periplanar: the dihedral angle H–Cβ–Cα–X is 0° or 180°, so all four atoms lie in a common plane.Anti-periplanar: dihedral 180° — H and X on opposite sides (a staggered arrangement).Syn-periplanar: dihedral 0° — H and X eclipsing each other.For an ordinary E2 with an external base, anti-periplanar is strongly preferred, and in rigid systems it is effectively compulsory.
Stereospecific reaction: one in which stereochemically different starting materials give stereochemically different products, by the same mechanism. Contrast stereoselective, where one starting material gives a mixture in which one stereoisomer predominates. E2 is stereospecific; E1 is at best stereoselective.
The cyclohexane E2 rule: an E2 elimination on a cyclohexane ring requires the leaving group and the β-hydrogen to be trans and both axial. If the leaving group cannot become axial, or if no β-hydrogen is axial when it is, E2 does not happen from that chair.
Zaitsev’s rule (Saytzeff): the major alkene is the more highly substituted one — that is, the more stable one.Hofmann’s rule: the major alkene is the less substituted one, usually the terminal alkene.Neither is a law. Each describes the outcome under a particular set of conditions, and the exam tests whether you know which conditions.
The variable transition-state theory of elimination: E1, E2 and E1cb are the corners of a continuum. A given reaction has a transition state at some point within it, determined by how well the substrate stabilises positive charge on Cα, how well it stabilises negative charge on Cβ, how good the leaving group is, and how strong the base is.
Kinetic isotope effect (KIE): the ratio k_H/k_D of the rate constants for the protium- and deuterium-labelled substrates.Primary KIE: the bond to the isotope is broken in the rate-determining step. Typically 2–8 at room temperature for C–H.Secondary KIE: the bond to the isotope is not broken, but its environment changes. Typically 0.7–1.4.
E_i (intramolecular / pyrolytic elimination): a concerted elimination in which the base is a heteroatom already bonded to the α carbon (or to its leaving group), so that proton removal and leaving-group departure occur through a cyclic transition state. The geometry of the ring forces syn stereochemistry. Kinetics are first order; no base is added; the reactions are usually run neat or in an inert solvent.
Bredt’s rule: a carbon–carbon double bond cannot be placed at the bridgehead of a bridged bicyclic ring system unless the rings are large enough. Alkenes that violate it are called anti-Bredt alkenes.
Wiseman’s reformulation: a bridgehead alkene is isolable if the largest ring containing the double bond is at least eight-membered — that is, if it corresponds to a trans-cyclooctene or larger. trans-Cyclooctene is the smallest isolable trans-cycloalkene, and the same limit transfers directly.
Where these come from
This sheet is distilled from Reaction Mechanisms, Part 5 — 10 sections that derive every one of these results and show you how to use them.
Read Part 5 All formula sheets