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SN1 and SN2 substitution

T-059Home CU-206Threads kinetics · structure
Statement

Two contrasting routes for nucleophilic substitution.

Why it matters

Nucleophilic substitution at a saturated carbon is one of the most fundamental reaction classes in organic chemistry, and it does not proceed by a single, universal mechanism: depending on the substrate, nucleophile, leaving group and solvent, the same overall transformation (a nucleophile replacing a leaving group) can occur by two mechanistically distinct routes, \(\text{S}_\text{N}2\) and \(\text{S}_\text{N}1\), with different kinetics, different stereochemical outcomes, and different substrate preferences. reaction-energy-profiles supplies the energy-diagram vocabulary (transition states, intermediates, rate-determining steps) used to describe both mechanisms precisely, and e1-e2-elimination is the direct competing pathway available to exactly the same substrates under many of the same conditions.

Correctly diagnosing which mechanism a given substrate and nucleophile will follow is essential predictive chemistry: it determines not only the rate of reaction but which stereoisomer, or what mixture of stereoisomers, is obtained — a distinction of real consequence whenever the product's biological or chemical activity depends on its absolute configuration.

Hypotheses
\(\text{S}_\text{N}2\) proceeds in a single concerted step: nucleophilic attack and leaving-group departure happen simultaneously.There is no intermediate to isolate or trap; the mechanism instead has a single transition state in which the nucleophile is partially bonded on one side of the reacting carbon while the leaving group is partially detached on the other. This concertedness is what forces the reaction to proceed with a specific backside geometry (Proof, Step 2). \(\text{S}_\text{N}1\) proceeds in two distinct steps, via a discrete carbocation intermediate.The first step, ionisation of the substrate to form a planar, \(sp^2\)-hybridised carbocation and a departed leaving group, is rate-determining; the second step, nucleophilic capture of that carbocation, is fast and does not appear in the observed rate law at all. Real substitution reactions do not always sit cleanly at either extreme; ion-pair mechanisms, in which the leaving group has departed but remains loosely associated with the developing cation, can bias the stereochemical outcome of a nominally \(\text{S}_\text{N}1\) reaction away from complete racemisation, a genuine intermediate case between the two idealised limits described here.
Proof
1
\[ \text{rate} = k[\text{Nu}^-][\text{R-X}] \qquad (\text{S}_\text{N}2, \text{second order overall}) \]
Because the single \(\text{S}_\text{N}2\) transition state involves both the nucleophile and the substrate simultaneously (Hypotheses), the rate depends on the concentration of both reactants, giving a second-order rate law directly reflecting the concerted, bimolecular mechanism. A
2
\[ \text{Backside attack} \Rightarrow \text{complete inversion of configuration (Walden inversion) at the reacting carbon.} \]
The nucleophile must approach from directly opposite the leaving group (the only geometry that allows simultaneous bond formation and bond breaking without severe steric and electronic penalty), so the three remaining substituents flip through the reacting carbon exactly like an umbrella turning inside out, inverting configuration with total stereochemical fidelity in every single event. A
3
\[ \text{rate} = k[\text{R-X}] \qquad (\text{S}_\text{N}1, \text{first order overall, independent of }[\text{Nu}]) \]
Since ionisation of \(\text{R-X}\) to the carbocation is the slow, rate-determining step, and the fast nucleophilic capture that follows does not influence the overall rate, the observed rate law depends only on the substrate's concentration, not on the nucleophile's identity or concentration at all. A
4
\[ \text{Planar carbocation} \Rightarrow \text{attack from either face} \Rightarrow \text{racemisation (often partial).} \]
The \(sp^2\) carbocation intermediate is flat, presenting both faces to the nucleophile with comparable, though not always exactly equal, accessibility; capture from either face gives both possible configurations at the reacting carbon, so an optically pure \(\text{S}_\text{N}1\) substrate typically gives a largely, but not perfectly, racemic product (Hypotheses' ion-pair caveat). A
5
\[ \text{Steric bulk disfavours S}_\text{N}2\text{; cation stability favours S}_\text{N}1\text{: reactivity orders 1}^\circ{>}2^\circ{>}3^\circ \text{ vs } 3^\circ{>}2^\circ{>}1^\circ \text{ respectively.} \]
\(\text{S}_\text{N}2\)'s single transition state requires the nucleophile to approach closely from the backside, so increasing substitution at the reacting carbon crowds that approach and slows the reaction; \(\text{S}_\text{N}1\)'s rate-determining ionisation instead depends on how well the developing positive charge is stabilised, and more substituted carbocations (tertiary, or benzylic/allylic through resonance) are markedly more stable, giving the opposite substrate preference. B
Result
\[ \text{S}_\text{N}2:\ \text{rate}=k[\text{Nu}^-][\text{RX}],\ \text{inversion} \qquad\qquad \text{S}_\text{N}1:\ \text{rate}=k[\text{RX}],\ \text{racemisation} \]

Reading. The two mechanisms are distinguished experimentally by kinetic order in the nucleophile and by the stereochemical fate of a single reacting stereocentre — clean, complementary diagnostic tests for which pathway is operating.

Scope. Applies to substitution at an \(sp^3\) carbon bearing a leaving group; both mechanisms directly compete with e1-e2-elimination under many of the same substrate/reagent conditions, particularly with strongly basic nucleophiles or at elevated temperature.

Corollaries & converses
  • reaction-energy-profiles' language makes the mechanistic contrast visual: \(\text{S}_\text{N}2\) has a single transition-state peak on its reaction coordinate diagram, while \(\text{S}_\text{N}1\) has two transition states flanking a genuine energy-well intermediate (the carbocation).
  • Tertiary substrates essentially never undergo \(\text{S}_\text{N}2\) (Step 5's steric argument), so a tertiary substrate under substitution conditions is forced toward \(\text{S}_\text{N}1\), or toward e1-e2-elimination if the nucleophile present is also a reasonably strong base.
  • Converse: observing net, complete inversion of configuration at a substitution's reacting stereocentre is strong evidence for an \(\text{S}_\text{N}2\) pathway, while observing substantial racemisation is strong evidence for \(\text{S}_\text{N}1\), letting stereochemical outcome alone diagnose the mechanism in many cases.
Fails without
  • Drop concertedness for \(\text{S}_\text{N}2\) (Hypotheses): without nucleophilic attack and leaving-group departure occurring simultaneously in a single transition state, there is no reason for the strict backside-attack geometry, and the observed complete inversion of configuration (Step 2) would not be forced to occur.
  • Drop the discrete carbocation intermediate for \(\text{S}_\text{N}1\): without a genuine planar intermediate open to attack from either face, there is no mechanistic explanation for the substantial racemisation typically observed when an \(\text{S}_\text{N}1\) reaction proceeds at a stereocentre.
Common errors
  • Assuming the \(\text{S}_\text{N}1\) rate law depends on nucleophile concentration, when in fact it is entirely independent of it (Step 3), since the nucleophile only enters after the rate-determining step.
  • Assuming \(\text{S}_\text{N}1\) always gives complete, exact racemisation, rather than the often only partial racemisation that results from ion pairing (Hypotheses' \(t3\) caveat).
  • Assuming a primary substrate can undergo \(\text{S}_\text{N}1\) under forcing conditions; primary carbocations are so unstable that this pathway is essentially never competitive, and primary substrates react by \(\text{S}_\text{N}2\) or not at all.
  • Treating nucleophilicity and basicity as interchangeable when predicting mechanism — the two properties correlate but are conceptually distinct, and the distinction matters specifically for predicting competition with e1-e2-elimination.
Discussion

The kinetic and stereochemical framework distinguishing \(\text{S}_\text{N}1\) from \(\text{S}_\text{N}2\) was established primarily by Edward D. Hughes and Sir Christopher Ingold at University College London through the 1930s, using precisely the two diagnostic handles emphasised here — reaction order and stereochemical outcome — to separate what had previously been treated as a single, undifferentiated substitution process into two mechanistically distinct extremes.

A further complication, common in \(\text{S}_\text{N}1\) reactions specifically, is carbocation rearrangement: a hydride or alkyl shift from an adjacent carbon can convert a less stable carbocation into a more stable one before nucleophilic capture occurs, giving a substitution product with a different, sometimes unexpected, connectivity from what a naive analysis of the starting substrate alone would predict.

Common misconception: that \(\text{S}_\text{N}1\)'s multi-step character makes it somehow "less controlled" or unpredictable. It follows entirely well-defined steps — ionisation, then capture — each governed by ordinary kinetic and thermodynamic principles; its outcome is simply distributed between the two carbocation faces rather than being forced to one, as \(\text{S}_\text{N}2\)'s single transition-state geometry forces.

Worked examples
1
\[ (R)\text{-2-bromobutane} + \text{NaOH (strong Nu, polar aprotic solvent)} \to (S)\text{-butan-2-ol} \]
A secondary substrate with an unhindered backside approach reacting with a strong, small nucleophile favours \(\text{S}_\text{N}2\); a single, clean backside attack (Step 2) inverts the stereocentre completely, converting the \(R\) starting material entirely into the \(S\) product. A
2
\[ \text{tert-butyl bromide} + \text{H}_2\text{O (weak Nu, polar protic solvent)} \to \text{tert-butanol (largely racemic if chiral)} \]
A tertiary substrate cannot undergo \(\text{S}_\text{N}2\) at all (Step 5); ionisation to the stable tertiary carbocation is rate-determining, and water, a weak, poorly nucleophilic solvent, captures the planar cation from either face with little stereochemical bias. A
\[ \text{Substrate class + nucleophile/solvent strength} \Rightarrow \text{mechanism} \Rightarrow \text{predicted stereochemical outcome} \]

Reading. The same overall bond change (C–Br replaced by C–O) proceeds by opposite mechanisms and gives opposite stereochemical signatures purely as a function of substrate substitution pattern and nucleophile/solvent choice.

Scope. This substrate/nucleophile-driven mechanistic prediction is the standard, general basis for predicting the outcome of any nucleophilic substitution at a saturated carbon.

Further example. A kinetic study of the solvolysis of 2-bromo-2-methylpropane (tert-butyl bromide) in 80% aqueous ethanol at 25 °C yields a first-order rate constant of \(k = 1.2 \times 10^{-4} \, \text{s}^{-1}\). Calculate the half-life of the reaction and the percentage of substrate remaining after 1.0 hour.

1
\[ t_{1/2} = \frac{\ln(2)}{k} \]
The reaction is first-order (unimolecular ionisation is rate-determining in \(\text{S}_\text{N}1\)), so the half-life is independent of initial concentration and defined by the natural logarithm of 2 divided by the rate constant. A
2
\[ t_{1/2} = \frac{0.6931}{1.2 \times 10^{-4} \, \text{s}^{-1}} = 5776 \, \text{s} \]
Substituting the given rate constant yields the time required for the concentration to halve. A
3
\[ t = 1.0 \, \text{h} = 3600 \, \text{s} \]
Convert the elapsed time to seconds to match the units of the rate constant. A
4
\[ \frac{[\text{R}]}{[\text{R}]_0} = e^{-kt} = e^{-(1.2 \times 10^{-4})(3600)} \]
Apply the integrated first-order rate law to find the fraction of substrate remaining after time \(t\). A
5
\[ \frac{[\text{R}]}{[\text{R}]_0} = e^{-0.432} \approx 0.649 \]
Calculate the exponential term to determine the remaining fraction. A
6
\[ \% \text{ remaining} = 0.649 \times 100\% = 64.9\% \]
Convert the fraction to a percentage. A
\[ t_{1/2} = 5776 \, \text{s} \quad (\approx 1.6 \, \text{h}); \quad \% \text{ remaining} = 64.9\% \]

Reading. The reaction is relatively slow on a laboratory timescale, with about two-thirds of the starting material persisting after one hour. This is consistent with the high activation energy required to break the C–Br bond and form the carbocation intermediate.

Scope. This calculation holds for any first-order process, including \(\text{S}_\text{N}1\) solvolysis, provided the rate constant is measured under the same conditions and the reverse reaction is negligible.

Problems
  1. Predict the dominant mechanism for the reaction of 2-bromo-2-methylpropane with a weak nucleophile in a polar protic solvent, and state the expected stereochemical outcome if the carbon bearing the leaving group were a stereocentre.
    SolutionA tertiary substrate cannot undergo \(\text{S}_\text{N}2\) (steric hindrance) but readily forms a stable tertiary carbocation; combined with a weak nucleophile and a polar protic solvent (which stabilises the developing cation and departed leaving group by solvation), the reaction proceeds by \(\text{S}_\text{N}1\). If the reacting carbon were a stereocentre, the planar carbocation intermediate would give a largely racemic product (Step 4).
  2. An optically pure secondary alkyl halide reacts with a strong nucleophile in DMSO (a polar aprotic solvent) and gives a product with completely inverted, single-enantiomer configuration. Identify the mechanism and justify from the stereochemical result alone.
    SolutionComplete, single-event inversion of configuration is the diagnostic stereochemical signature of \(\text{S}_\text{N}2\) (Step 2); a planar carbocation intermediate (\(\text{S}_\text{N}1\)) would instead give substantial racemisation. The strong nucleophile and polar aprotic solvent (which does not hydrogen-bond to and deactivate the nucleophile) are independently consistent with, and favour, this same \(\text{S}_\text{N}2\) assignment.
  3. Explain why increasing solvent polarity (specifically, a polar protic solvent) generally accelerates an \(\text{S}_\text{N}1\) reaction but can actually slow an \(\text{S}_\text{N}2\) reaction run with a small, charged nucleophile.
    SolutionA polar protic solvent stabilises the charged carbocation and departed leaving group formed in \(\text{S}_\text{N}1\)'s rate-determining ionisation step (Step 3), lowering the activation energy and speeding the reaction. For \(\text{S}_\text{N}2\) with a small anionic nucleophile, the same protic solvent instead hydrogen-bonds to and stabilises the ground-state nucleophile itself, lowering its energy relative to the transition state and so raising the effective activation barrier, slowing the reaction — the reason polar aprotic solvents (which cannot hydrogen-bond to the nucleophile) are generally preferred to promote \(\text{S}_\text{N}2\).
  4. Optically pure (R)-2-bromooctane reacts with a nucleophile to give a substitution product that is 98% of the inverted configuration and 2% of the retained configuration. Assuming the S\(_\text{N}\)2 path gives only inversion and the S\(_\text{N}\)1 path gives a racemic product, what fraction of the reaction went by each path?
    SolutionLet \(f\) be the S\(_\text{N}\)1 fraction. Racemisation gives \(f/2\) retained and \(f/2\) inverted product, so retained \(= f/2 = 0.02\) and \(f = 0.04\). Hence 4% S\(_\text{N}\)1 and 96% S\(_\text{N}\)2 (check: inverted \(= 0.96 + 0.02 = 0.98\)). Retention never exceeds 50% from an S\(_\text{N}\)1 path, so small amounts of retention point to a small carbocation contribution.
  5. The initial rate of substitution of a secondary alkyl bromide doubles when the nucleophile concentration is doubled, while that of tert-butyl bromide in aqueous ethanol does not change. Write the rate law for each and explain the difference.
    SolutionSecondary substrate: rate \(= k[\text{RBr}][\text{Nu}^-]\), second order overall, as expected for S\(_\text{N}\)2, in which the nucleophile attacks in the rate-determining step. tert-Butyl bromide: rate \(= k[\text{RBr}]\), first order, as expected for S\(_\text{N}\)1: the slow step is ionisation to the tertiary carbocation, and the nucleophile only enters afterwards in a fast step. Back-side attack on the tertiary carbon is blocked sterically, while the tertiary cation is stabilised by hyperconjugation, which is why the mechanism switches.