Organic Chemistry · Part 2 of 9 · Free
Reactive Intermediates I — Carbocations & Carbanions — formula sheet
Every key expression and definition from Reaction Mechanisms, Part 2, on one page. Free to read, no sign-in.
Key expressions
the bridgehead-strain correlation
log(k_rel) ∝ −ΔΔE_strain(R–X → R^+) / 2.303RT
log(k_rel) ∝ −ΔΔE_strain(R–X → R^+) / 2.303RT
Grunwald–Winstein solvent equation
log(k / k_0) = m Y
log(k / k_0) = m Y
extended Grunwald–Winstein equation
log(k / k_0) = m Y + l N
log(k / k_0) = m Y + l N
the Brown–Okamoto relation
log(k / k_0) = ρ^+ σ^+ with ρ^+ = −4.54 for cumyl chloride solvolysis
log(k / k_0) = ρ^+ σ^+ with ρ^+ = −4.54 for cumyl chloride solvolysis
the Winstein ion-pair scheme
R–X ⇌ R^+X^− ⇌ R^+‖S‖X^− ⇌ R^+ + X^−
R–X ⇌ R^+X^− ⇌ R^+‖S‖X^− ⇌ R^+ + X^−
ionisation rate versus titrimetric rate
k_ion > k_t — the difference is internal return
k_ion > k_t — the difference is internal return
the three terms that decide a ring-size change
ΔGₓ(shift) ≈ ΔG(cation class) + ΔG(ring strain released) + geometric penalty
ΔGₓ(shift) ≈ ΔG(cation class) + ΔG(ring strain released) + geometric penalty
the two competing solvolysis channels
k_obs = k_Δ + k_s
k_obs = k_Δ + k_s
effective molarity
EM = k_intra (s^−1) / k_inter (M^−1 s^−1) — units of M
EM = k_intra (s^−1) / k_inter (M^−1 s^−1) — units of M
acidity and s character (aqueous scale)
pK_a (H–C sp³) ≈ 50 > pK_a (H–C sp²) ≈ 44 > pK_a (H–C sp) ≈ 25
pK_a (H–C sp³) ≈ 50 > pK_a (H–C sp²) ≈ 44 > pK_a (H–C sp) ≈ 25
Pauling estimate of ionic character
percent ionic character = 100 × [1 − exp(−0.25 (Δχ)²)]
percent ionic character = 100 × [1 − exp(−0.25 (Δχ)²)]
the Schlenk equilibrium
2 RMgX ⇌ R₂Mg + MgX₂
2 RMgX ⇌ R₂Mg + MgX₂
Definitions worth memorising
Carbocation: a species containing a carbon atom bearing a formal positive charge and only six valence electrons. Two structural families exist: carbenium ions, tricoordinate and electron-deficient (CH₃^+, (CH₃)₃C^+), and carbonium ions, penta- or hexacoordinate with a three-centre two-electron bond (CH₅^+, the bridged 2-norbornyl cation). Olah introduced this distinction; older texts use “carbonium ion” loosely for both, and exam questions still do.
1,2-shift (Wagner–Meerwein rearrangement): the migration of a group — hydrogen, alkyl or aryl — together with its bonding electron pair, from a carbon adjacent to a carbocation centre onto that centre. The migration origin becomes the new cationic carbon. Numbering is 1,2 because the group moves between adjacent atoms.
Ring expansion: a 1,2-alkyl shift in which the migration terminus is exocyclic and the migrating bond is endocyclic. A ring carbon migrates out to the exocyclic cation, and the exocyclic carbon is drawn into the ring. Ring contraction is the same event run the other way.
Non-classical (bridged) carbocation: a carbocation in which a σ bond, or a π bond, is delocalised over three centres, so that one electron pair binds three atoms. The positive charge is shared, and no single atom carries a conventional empty p orbital. Contrast a classical carbocation, in which the charge sits on one tricoordinate carbon and all bonds are ordinary two-centre two-electron bonds.
Neighbouring-group participation (NGP): the intramolecular displacement of a leaving group by a nucleophilic centre elsewhere in the same molecule, generating a cyclic intermediate which is then opened by the external nucleophile. Anchimeric assistance is the resulting rate acceleration — the “neighbouring help” the participating group provides in the rate-determining step.
Carbanion: a species containing a carbon atom bearing a formal negative charge and an unshared electron pair. It has a complete octet. Its conjugate acid is the corresponding C–H compound, so carbanion stability and carbon-acid pK_a are the same measurement, and pK_a is how the whole subject is quantified.
Ambident nucleophile: a nucleophile with two reactive sites bearing the shared charge. An enolate is ambident: the charge is mostly on oxygen, but the HOMO coefficient is largest on carbon. Hard electrophiles attack oxygen; soft electrophiles attack carbon.
Where these come from
This sheet is distilled from Reaction Mechanisms, Part 2 — 10 sections that derive every one of these results and show you how to use them.
Read Part 2 All formula sheets