Organic Chemistry · Part 4 of 9 · Free
Nucleophilic Substitution at Saturated Carbon — formula sheet
Every key expression and definition from Reaction Mechanisms, Part 4, on one page. Free to read, no sign-in.
Key expressions
the S_N2 rate law
rate = k_2[R–X][Nu−] (second order overall)
rate = k_2[R–X][Nu−] (second order overall)
the racemisation–exchange test for inversion
k_rac = 2 k_exch (complete inversion)k_rac = k_exch (complete retention or attack on a symmetric intermediate)
k_rac = 2 k_exch (complete inversion)k_rac = k_exch (complete retention or attack on a symmetric intermediate)
Taft steric correlation for a displacement series
log(k / k₀) = δ E_s
log(k / k₀) = δ E_s
the Swain–Scott equation
log(k / k₀) = s · n
log(k / k₀) = s · n
the S_N1 rate law
rate = k_1[R–X] (first order; the nucleophile does not appear)
rate = k_1[R–X] (first order; the nucleophile does not appear)
the polarimetric–titrimetric test for ion pairs
k_α > k_t ⇒ the substrate is racemising without reacting — internal return
k_α > k_t ⇒ the substrate is racemising without reacting — internal return
the mass-law expression for common-ion depression
rate = k_1[RX] ÷ (1 + α[X−])
rate = k_1[RX] ÷ (1 + α[X−])
the Grunwald–Winstein equation
log(k / k₀) = m Y
log(k / k₀) = m Y
the extended (two-parameter) Grunwald–Winstein equation
log(k / k₀) = m Y + l N
log(k / k₀) = m Y + l N
stereochemistry as a continuous read-out of mechanism
F_inv = fraction of product with inverted configuration; as k_s/k_c falls, F_inv → 0.5 (racemic)
F_inv = fraction of product with inverted configuration; as k_s/k_c falls, F_inv → 0.5 (racemic)
the Brønsted leaving-group correlation
log k = β_lg · pK_a(HX) + constant, with β_lg negative
log k = β_lg · pK_a(HX) + constant, with β_lg negative
Definitions worth memorising
Nucleophilic substitution at saturated carbon: a reaction in which a nucleophile Nu− (or Nu) replaces a leaving group X− at an sp³-hybridised carbon, with net retention of the carbon’s coordination number.General equation: Nu− + R–X → R–Nu + X−
Walden inversion: the inversion of spatial configuration at a stereogenic carbon that accompanies every S_N2 substitution. A clean S_N2 reaction on an enantiopure substrate gives an enantiopure product of inverted configuration — 100% inversion, 0% racemisation.
Basicity is a thermodynamic property: the position of the equilibrium B− + H–A ⇌ B–H + A−, reported as the pK_a of the conjugate acid. It refers to bonding at hydrogen.Nucleophilicity is a kinetic property: the rate constant for attack on a substrate, usually carbon. It refers to how fast a bond forms, not to how strong it is when formed.
The α effect: a nucleophile bearing a lone pair on the atom adjacent to the nucleophilic atom reacts faster than its basicity predicts — that is, it lies well above the Brønsted correlation line drawn through ordinary nucleophiles of the same type.
Intimate (contact, or tight) ion pair R⁺X−: cation and anion in direct contact, sharing a single solvent cage, with no solvent molecule between them. The anion still occupies the face it departed from.Solvent-separated ion pair R⁺∥X−: one or more solvent molecules have inserted between the ions, which remain associated as a unit.Dissociated ions R⁺ + X−: independent species, each with its own complete solvation shell.Internal return: recombination of an ion pair to regenerate covalent R–X, without any net reaction having occurred.
Solvolysis: a substitution in which the solvent is also the nucleophile. Because the solvent is present in vast excess its concentration does not change measurably during the reaction, so the kinetics are pseudo-first-order regardless of mechanism.
Leaving-group ability tracks the stability of the departing group as a free species. For anionic leaving groups that means the stability of X−, which is measured by the acidity of its conjugate acid HX. The weaker the base X− is, the better it leaves, so a lower pK_a of HX means a better leaving group.
Ambident nucleophile: an anion or neutral species whose negative charge is delocalised over two or more different atoms, either of which can attack. The two sites usually differ in hardness, so which one reacts is decided by the electrophile and the conditions.
S_N1′: ionisation to a delocalised allyl cation, followed by capture at either terminus. Since the cation is one species, S_N1 and S_N1′ products always appear together; their ratio reflects charge distribution, substitution pattern and sterics, and the two starting isomers converge on the same product mixture.S_N2′: a single concerted step in which the nucleophile attacks Cγ, the π bond shifts to Cα–Cβ, and the leaving group departs from Cα. No intermediate; the skeleton is rearranged.
Where these come from
This sheet is distilled from Reaction Mechanisms, Part 4 — 9 sections that derive every one of these results and show you how to use them.
Read Part 4 All formula sheets