Nucleophilic Substitution Reactions Notes

Recommended Reading

• Reading Organic Chemistry (First Edition) Clayden, Greeves, Warren and Wothers Oxford University Press; Oxford, 2001 ISBN: 0-19-850346-6
• Organic Chemistry (Second Edition) Clayden, Greeves and Warren Oxford University Press; Oxford, 2012 ISBN: 978-0-19-927029-3
• Organic Chemistry (Second Edition) Klein John Wiley and Sons; 2014 ISBN: 978-1-118-45228-8
• Organic Chemistry (Fourth Edition as an E-Book) Klein John Wiley and Sons; 2020 ISBN: 978-1-119-74510-5
• Organic Chemistry (Third Edition) Karty W.W. Norton & Company; 2022 ISBN: 978-0-39-354401-5

Gibbs Free Energy, $\Delta G$ & Equilibrium Constant, K

• K is related to the free energy of the reaction ($\Delta G$).
• $R$ = gas constant $(8.314 \frac{J}{K \cdot mol})$
• $T$ = temperature (K)
• Small changes in $\Delta G$ can result in a large change in K.
• Equilibrium is determined by the concentration of reactants and products at equilibrium.
• $A + B \rightleftharpoons C + D$
  • reactants
  • products
• $K = \frac{[C][D]}{[A][B]}$
• $\Delta G = -RT \ln K$

Gibbs Free Energy, $\Delta G$

• $\Delta G = \Delta H - T \Delta S$
  • $\Delta G$: Gibbs Free Energy Function
  • $\Delta H$: enthalpy of reaction
  • $\Delta S$: entropy of reaction
• Ideal Reaction:
  • Exothermic reaction ($\Delta H$ is negative).
  • Reaction becomes more disordered ($\Delta S$ is positive).
• For spontaneous reactions, $\Delta G$ must be negative.
• Exergonic reactions have a negative $\Delta G$.
• Endergonic reactions have a positive $\Delta G$.
• Enthalpy:
  • Measure of changes of heat.
  • Exothermic reactions give out heat (e.g., bond formation).
  • Endothermic reactions take in heat (e.g., bond breaking).
• Entropy:
  • Measure of changes of order and disorder.
  • More disorder gives positive $\Delta S$.
  • Less disorder gives negative $\Delta S$.

Thermodynamics & Kinetics

• Reaction Kinetics
• Free Energy (G)
• Reaction Coordinate
• For a reaction to occur, the reactants must have enough energy to overcome an energy barrier. This barrier is the activation energy ($E_a$) also shown as $\Delta G^{\ddagger}$.
• Thermodynamics tells us how far the reaction will proceed, but gives no information about how fast the reaction goes.
• Thermodynamics: How far a reaction proceeds
• Kinetics: How fast a reaction proceeds
• Driving Force: Thermodynamics
• Rate of Reaction: Kinetics

The Bimolecular Nucleophilic Substitution ($S_N2$) Reaction

• Mechanism for the general $S_N2$ reaction
  • $Nu: + R-L \longrightarrow Nu-R + :L^-$
    • Nu: Nucleophile
    • R-L: Substrate

Bimolecular Nucleophilic Substitution ($S_N2$) Steps

• In a bimolecular nucleophilic substitution ($S_N2$) step, a molecular species (i.e., the substrate) undergoes substitution.

Characteristics of a Substrate

• In this case, the substrate is the molecule that contains a leaving group.
• Leaving groups are relatively stable with a negative charge.
• Leaving groups are typically conjugate bases of strong acids.
• A nucleophile tends to be attracted to an atom that bears a partial or full positive charge.

Characteristics of a Nucleophile

• Species that act as nucleophiles generally have an atom with:
  • A full negative charge or a partial negative charge
  • A lone pair of electrons

Free Energy Diagram of $S_N2$ Step

• $S_N2$ Reaction – Energy profile
• A concerted mechanism via a trigonal bipyramidal transition state

The Unimolecular Nucleophilic Substitution ($S_N1$) Reaction

• Mechanism for the general $S_N1$ reaction
  • Step 1: Leaving group leaves
  • Step 2: Nucleophile attacks
• A stepwise mechanism via a carbocation intermediate

The $S_N1$ Reaction

• Overall reaction: $Nu: + C-L \longrightarrow Nu-C + L^-$

Free Energy Diagram of an $S_N1$ Reaction

• This diagram has two humps connecting reactants to products because there are two separate elementary steps for the $S_N1$ mechanism.

Rate-Determining Steps

• The rate-determining step of a mechanism (also called the slow step) is the elementary step that dictates the rate of the overall reaction.
• If a species appears as a reactant in the rate-determining step of a mechanism, then the overall reaction rate will depend on the concentration of that species.

Rate-Determining Step of an $S_N2$ Reaction

• Because the mechanism of an $S<em>N2$ reaction consists of just a single step, the $S</em>N2$ step must be the rate-determining step of the reaction.

Rate-Determining Step of an $S_N1$ Reaction

• The first step of an $S_N1$ reaction is the slow step of the mechanism and is therefore the rate-determining step.

Free-Energy Diagram of an $S_N1$ Reaction

• $S_N1$ Reaction – Energy profile

Rate Laws for the $S<em>N2$ and $S</em>N1$

• The rates of $S<em>N1$ and $S</em>N2$ reactions differ in the way they depend on reactant concentrations.
• $S<em>N2$ Rate = $k</em>{S_N2} [Nu^-][R-L]$
• $S<em>N1$ Rate = $k</em>{S_N1} [R-L]$

Stereochemistry of an $S_N2$ Reaction

• An $S_N2$ reaction results in the inversion of the stereochemical configuration at the carbon initially attached to the leaving group.
• The $S_N2$ reaction is stereospecific.

Backside Attack

• In an $S_N2$ reaction, the nucleophile attacks the substrate exclusively from the side opposite the leaving group, in a backside attack.
• This is known as a Walden inversion.

Frontside Attack

• In a frontside attack, the three groups would remain on the same side in the products.
• Frontside attack does not occur in $S_N2$ reactions, in part due to steric hindrance of the leaving group and charge repulsion.

Frontside Attack and Charge Repulsion

• Charge repulsion

Stereochemistry of an $S_N1$ Reaction

• If an $S_N1$ reaction is carried out on a stereochemically pure substrate, then a mixture of both the R and S enantiomers is produced.

Loss of the Stereocentre

• Mechanism for $S_N1$ reaction

Both Configurations Produced

• Plane of symmetry

PROBLEM 1

• Draw the complete, detailed mechanism for the following reaction, assuming that it takes place by an $S_N2$ mechanism. Pay attention to stereochemistry.

PROBLEM 2

• Draw the complete, detailed mechanism for this reaction, assuming that it takes place by the $S_N1$ mechanism.
• Will the reaction produce a single stereoisomer, or will it produce a mixture of stereoisomers?
• If it produces a mixture, then will the isomers be produced in equal amounts?