Organic Chemistry · Part 8 of 9 · Free
Aromatic Substitution Mechanisms — formula sheet
Every key expression and definition from Reaction Mechanisms, Part 8, on one page. Free to read, no sign-in.
Key expressions
the maximum primary kinetic isotope effect for C–H cleavage
k_H/k_D ≈ exp[(ZPE_H − ZPE_D)/RT] with ZPE_H − ZPE_D = ½hc(ν̃_CH − ν̃_CD) ≈ 400 cm^−1 ≈ 4.8 kJ mol^−1 ⇒ k_H/k_D ≈ 7 at 25 °C
k_H/k_D ≈ exp[(ZPE_H − ZPE_D)/RT] with ZPE_H − ZPE_D = ½hc(ν̃_CH − ν̃_CD) ≈ 400 cm^−1 ≈ 4.8 kJ mol^−1 ⇒ k_H/k_D ≈ 7 at 25 °C
steady-state rate law for S_EAr
rate = k_1k_2[ArH][E^+][B] / (k_−1 + k_2[B])
rate = k_1k_2[ArH][E^+][B] / (k_−1 + k_2[B])
the reversibility of sulfonation
ArH + H_2SO_4 (conc.) ⇌ ArSO_3H + H_2O — concentrated acid drives it right; dilute acid and steam drive it left
ArH + H_2SO_4 (conc.) ⇌ ArSO_3H + H_2O — concentrated acid drives it right; dilute acid and steam drive it left
the additivity principle for partial rate factors
f_position(disubstituted) ≈ f_from X × f_from Y
f_position(disubstituted) ≈ f_from X × f_from Y
partial rate factors from a competition experiment
f_o = 3 × k_rel × (%o/100) f_m = 3 × k_rel × (%m/100) f_p = 6 × k_rel × (%p/100)
f_o = 3 × k_rel × (%o/100) f_m = 3 × k_rel × (%m/100) f_p = 6 × k_rel × (%p/100)
the Brown selectivity relationship
log f_p = c · S_f, with c ≈ 1.31 for toluene
log f_p = c · S_f, with c ≈ 1.31 for toluene
the Hammett equation
log(k/k_0) = ρσ or, for equilibria, log(K/K_0) = ρσ
log(k/k_0) = ρσ or, for equilibria, log(K/K_0) = ρσ
the Yukawa–Tsuno equation
log(k/k_0) = ρ[σ + r(σ^+ − σ)]
log(k/k_0) = ρ[σ + r(σ^+ − σ)]
Definitions worth memorising
Arenium ion (Wheland intermediate, σ complex, benzenonium ion): the cationic intermediate of electrophilic aromatic substitution. One ring carbon is sp^3 and bears two σ substituents (the electrophile and the hydrogen); the remaining five carbons carry four π electrons in a delocalised pentadienyl cation. It is a real intermediate sitting in a potential-energy well, not a transition state.
Primary kinetic isotope effect: the rate change seen when an atom whose bond is broken in the rate-determining step is replaced by a heavier isotope. For C–H/C–D the theoretical ceiling at room temperature is about 7; values of 2–7 are diagnostic of C–H cleavage in the slow step. A value of 1.0–1.2 says the C–H bond is not being broken there.
Activation / deactivation is about rate: is this ring attacked faster or slower than benzene itself?Orientation (directing effect) is about position: of the three kinds of site available, which does the electrophile prefer?A group can be strongly deactivating and still ortho/para-directing. The two questions are independent.
Statistical correction: before comparing an ortho yield with a para yield, divide the ortho yield by 2 (and the meta yield by 2). Only then are you comparing positions rather than groups of positions. The same correction, applied to rates rather than yields, is exactly what turns an isomer distribution into a partial rate factor in H.7.
Meisenheimer complex: the anionic intermediate of S_NAr. One ring carbon is sp^3 and bears both the nucleophile and the leaving group; the other five carry a delocalised cyclohexadienyl anion with negative charge at the two ortho and the para positions relative to that carbon. It is the exact electronic mirror image of the arenium ion.
Cine substitution: substitution in which the incoming group ends up on the carbon adjacent to the one vacated by the leaving group. It is the signature of an elimination–addition pathway. (Substitution at the original carbon is ipso; substitution further away still is tele.)
Partial rate factor, f: the rate of substitution at one specified position of a substituted benzene, divided by the rate at one position of benzene itself, under identical conditions. f > 1 means that position is activated; f < 1 means it is deactivated; f = 1 means it behaves exactly like a benzene carbon.
Where these come from
This sheet is distilled from Reaction Mechanisms, Part 8 — 9 sections that derive every one of these results and show you how to use them.
Read Part 8 All formula sheets