§ C-38 Bimolecular Nucleophilic Substitution (S_N2) & Walden Inversion of Configuration (Grade 10–11 · Organic Reaction Mechanisms)
Chapter XXXVIII. Backside Attack HO⁻ + CH₃Br → [HO···CH₃···Br]‡ → CH₃OH + Br⁻ & Pentacoordinate Transition State. «The incoming group approaches the carbon atom on the side opposite to the replaced group, turning the tetrahedral configuration inside out.», Christopher K. Ingold & Edward D. Hughes, 1937
Theory Summary & Scientific Mechanism
Bimolecular nucleophilic substitution (S_N2) is a concerted, single-step reaction mechanism (HO⁻ + CH₃Br → CH₃OH + Br⁻) whose rate law is first-order in both substrate and nucleophile (v = k₂[R–X][Nu⁻], second-order overall).
The nucleophile attacks the electrophilic carbon from the backside (180^° opposite the leaving group) to overlap with the antibonding σ^*_C–X orbital. At the saddle point (ξ = 0.50), the system passes through a planar trigonal-bipyramidal pentacoordinate transition state [HO^δ-⋯CH₃⋯Br^δ-]^ddagger with no intermediate.
Departure of the leaving group flips the three substituents to the opposite side like an umbrella in a gale, resulting in 100% stereospecific Walden inversion of configuration ((R) → (S) at a chiral center).
Everyday Analogy
Picture an umbrella flipping inside-out in a strong gust of wind! In an S_N2 reaction, HO⁻ attacks carbon from the backside (180^°), kicking out Br⁻ and inverting the three C–H bonds through a planar transition state (Walden inversion)!
Interactive Question & Derivation
Why does the bimolecular nucleophilic substitution reaction HO⁻ + CH₃Br → CH₃OH + Br⁻ (S_N2) proceed in a single concerted step with 100% Walden inversion of stereochemical configuration?
- A: The nucleophile HO⁻ attacks the electrophilic carbon from the backside (180^° opposite the leaving group Br⁻) into the σ^*_C–Br antibonding orbital, passing through a planar trigonal-bipyramidal transition state [HO⋯CH₃⋯Br]^ddagger that flips the three C–H bonds like an umbrella in the wind
- B: The reaction first forms a stable carbocation intermediate CH₃⁺ that is attacked equally from both sides
- C: Reaction rate v = k[CH₃Br] is independent of nucleophile concentration [HO⁻]
Study Hint: Backside attack at 180^° proceeds through a planar pentacoordinate transition state [HO⋯CH₃⋯Br]^ddagger with 100% Walden inversion.
Proof & Explanation: In the concerted S_N2 mechanism (*Substitution Nucleophilic Bimolecular*), the rate law is second-order: v = k₂[R–X][Nu⁻]. The incoming nucleophile (HO⁻) approaches at 180^° to the C–Br bond (backside attack) to maximize overlap with the empty σ^*_C–Br orbital and minimize steric/electrostatic repulsion. At the energy maximum (ξ = 0.50), the carbon atom is sp²-hybridized in a planar pentacoordinate transition state [HO^δ-⋯CH₃⋯Br^δ-]^ddagger. As Br⁻ departs, the three substituents invert their tetrahedral umbrella (Walden inversion, (R) → (S)).
Key Equations & 3D Simulation Parameters
v = k₂[CH₃Br][OH⁻], HO⁻ + CH₃Br longrightarrow ≤ft[HO^δ- ⋯ CH₃⋯ Br^δ- ]^ddagger longrightarrow HOCH₃ + Br⁻
- Reaction coordinate ξ (0=Reactants, 0.5=TS‡, 1=Products): 0 … 1 (default: 0.5)
- Substrate concentration [CH₃Br]: 0.25 … 2.5 mol/L (default: 1 mol/L)
- Nucleophile concentration [OH⁻]: 0.25 … 2.5 mol/L (default: 1.5 mol/L)
- Activation energy barrier Eₐ‡: 45 … 110 kJ/mol (default: 75 kJ/mol)