Energy Diagrams and SN1/SN2 Mechanisms

Energy diagrams, transition states, and rate concepts

  • Energy diagrams visualize how a reaction proceeds along a reaction coordinate (x-axis) and its energy (y-axis).
  • The transition state (TS) is the highest-energy arrangement along the path between reactants and products or between intermediates and products.
    • The TS exists for a fleeting moment (about 10^{-15} s) and cannot be isolated in a bottle; it represents the bond-making and bond-breaking in progress.
    • In diagrams, curved arrows illustrate electron flow: electrons move from areas of high electron density toward atoms or bonds that are forming or breaking.
  • Activation energy (EA) is the energy difference between the transition state and the reactants: EA = E{ ext{TS}} - E{ ext{reactants}}
  • Overall energy change of the reaction is given by the enthalpy change: \Delta H = E{ ext{products}} - E{ ext{reactants}}
    • Downhill (exothermic) when \Delta H < 0; energy is released as heat.
    • Uphill (endothermic) when \Delta H > 0; energy must be put in.
  • Reaction coordinate diagrams can show either a direct, single-step path (no intermediate) or a path with one or more intermediates and multiple TSs.
  • For downhill reactions (overall exothermic), the diagram often shows the products at a lower energy than the reactants; the highest point along the path is still the TS.
  • Two key types of energy features appear in this lecture:
    • Transition State (one per single-step path; TS1 for the first step, etc.)
    • Intermediates (stable species that can be isolated on the diagram; e.g., carbocations)
  • The height of the TS relative to reactants determines the barrier the system must overcome; this height is the activation energy.
  • Hammond postulate (conceptual guide):
    • If a step is highly exothermic, its TS resembles the product more (lower barrier often associated with a later TS).
    • If a step is endothermic, its TS resembles the reactants more.
  • Temperature effects on rate:
    • Raising temperature increases the fraction of molecules with enough energy to cross the activation barrier, speeding up the reaction.
    • Activation energy itself does not change much with temperature, but the distribution of molecular energies does.
  • Two common notations for TS on diagrams:
    • TS or transition state (abbreviated)
    • The double dagger symbol (\ddag) as another designation for a transition state.
  • Relative energies and pathways depend on whether the reaction proceeds in one step or via intermediates:
    • A single-step substitution (no carbocation intermediate) has one TS and follows a simple rate law.
    • A two-step substitution via a carbocation intermediate has two TSs (TS1 and TS2) and an intermediate in between.
  • Practical insight: not every reaction goes to completion via a single path; competing pathways and intermediates can exist, especially when multiple reaction channels are possible.
  • Experimental logic behind kinetics: chemists determine how rate depends on reactant concentrations by varying concentrations and observing the effect on rate; this reveals whether the rate-determining step involves certain species.
  • The most important single factor governing rate is temperature; higher temperature generally increases rate via more molecules achieving the transition state energy, not by changing the activation energy itself.

SN2 reaction: cyanide with iodoethane (primary halide)

  • Reactants: iodoethane (EtI) + cyanide (CN^-)
  • Product: propionitrile (CH3CH2CN) + iodide (I^-)
  • Mechanism (concerted SN2):
    • Cyanide performs backside attack on the carbon attached to iodine; the C–I bond breaks as the C–CN bond forms at the same time in one step.
    • Curved arrows show electrons from cyanide attacking the carbon and the iodide leaving with its lone pair.
  • Energy diagram for SN2:
    • Path is a single-step, downhill process (goes from higher-energy reactants to lower-energy products).
    • The transition state is a point where a partial C–CN bond is forming and a partial C–I bond is breaking.
    • No discrete intermediate is formed.
  • Details of the transition state:
    • The TS features: a partial bond to cyanide, a partial bond to iodine, and partial charges developing (partially negative on CN^- and partial positive on carbon as the bond to I breaks).
    • The TS exists for a fleeting moment (~10^{-15} s).
  • Activation energy for SN2:
    • Represented as the energy difference between the reactants and the single TS: EA = E{ ext{TS}} - E_{ ext{reactants}}
  • Rate law for SN2 (rate-determining step involves both reactants):
    • ext{rate} = k [ ext{EtI}] [ ext{CN}^-]
    • Because the RDS (and TS) involves both reactants, the rate is first order in each.
  • Kinetic takeaway for SN2 (general rule mentioned): primary alkyl halides tend to undergo SN2 (one-step) because there is less steric hindrance to backside attack.
  • Additional context: increasing the concentration of either EtI or CN^- increases the rate; this is a direct consequence of the rate law.

SN1 reaction: bromotriphenylmethane with cyanide (tertiary halide)

  • Reactants: bromotriphenylmethane (Ph_3CBr) + cyanide (CN^-)
  • Product: triphenylmethyl cyanide (Ph_3C-CN) + bromide (Br^-)
  • Mechanism (two-step SN1 via carbocation intermediate):
    • Step 1 (rate-determining): Ionization of bromide to form the triphenylmethyl carbocation:
    • Ph3CBr ⇌ Ph3C^+ + Br^-
    • This step is endergonic and forms a highly stabilized tertiary carbocation via resonance with three phenyl rings.
    • Step 2: Nucleophilic attack by CN^- on the carbocation to form the product: Ph3C^+ + CN^- → Ph3C-CN
  • Energetics and intermediates on the SN1 diagram:
    • The carbocation intermediate Ph_3C^+ is high in energy relative to reactants but stabilized by resonance with the three phenyl rings.
    • Transition state TS1 (for ionization) is high; the energy barrier for this step is typically the highest part of the pathway.
    • After TS1, the intermediate carbocation exists briefly before reacting with CN^- in Step 2.
    • TS2 (for carbocation + CN^- combination) is generally lower than TS1 because the recombination step is favorable (toward product formation).
  • Two transition states on the SN1 pathway:
    • TS1: associated with ionization to form the carbocation; often the rate-determining step because it has the highest barrier.
    • TS2: associated with attack of CN^- on the carbocation; typically a lower barrier than TS1.
  • Activation energies on this pathway:
    • EA for Step 1 = energy difference between reactants and TS1.
    • EA for Step 2 = energy difference between the carbocation intermediate and TS2.
  • Rate law for SN1:
    • Since the rate-determining step is the ionization to the carbocation, the rate is determined by the concentration of the substrate only: ext{rate} = k [ ext{Ph}_3 ext{CBr}]
    • The concentration of CN^- does not affect the rate in the RDS.
  • Thermodynamics and kinetics observations:
    • The overall process is downhill in energy (products lower than reactants) but involves an uphill first step to form the carbocation.
    • Carbocations are generally high-energy intermediates; tertiary carbocations are comparatively more stable than primary but still high-energy species.
    • The presence of resonance stabilization (three benzene rings) lowers the energy of the Ph_3C^+ relative to a non-resonance-stabilized tertiary cation.
  • Reversibility and energy landscape:
    • The reverse reaction (product back to starting materials) is possible and would proceed via the same two-step pathway in reverse, typically with different barrier heights (the reverse TSs).
  • Conceptual notes emphasized in the lecture:
    • The idea that secondary halides often require more nuanced analysis (can exhibit SN1 or SN2 depending on conditions), and that tertiary halides generally favor SN1 due to carbocation stability and steric hindrance against SN2.
    • The discussion that scientists learn these rules through experimentation (e.g., doubling concentrations and observing rate changes) rather than purely theoretical reasoning.

Kinetics, rate laws, and determining mechanism from rate data

  • For the SN2 reaction (EtI + CN^-):
    • Rate law: ext{rate} = k [ ext{EtI}] [ ext{CN}^-]
    • Both reactants appear in the rate law because both participate in the rate-determining, concerted transition state.
    • Doubling either reactant doubles the rate (first-order dependence in each).
  • For the SN1 reaction (Ph_3CBr + CN^-):
    • Rate law: ext{rate} = k [ ext{Ph}_3 ext{CBr}]
    • The nucleophile CN^- does not affect the rate since it does not participate in the rate-determining step.
    • Doubling the substrate doubles the rate; doubling the nucleophile has little to no effect on the rate.
  • How chemists learn these distinctions:
    • Through experiments that vary concentrations and observe how the overall rate changes.
    • For a primary halide (EtI), the rate-determining step involves the substrate and nucleophile, consistent with SN2.
    • For a tertiary halide (Ph_3CBr), the rate-determining step is the formation of the carbocation, independent of CN^- concentration.
  • Qualitative rule of thumb presented in the lecture:
    • Primary halide centers generally undergo SN2 (single-step).
    • Tertiary halide centers generally undergo SN1 (two-step via carbocation).
    • Secondary centers can be more complex and may exhibit either pathway depending on conditions; stereochemical outcomes (e.g., inversion vs racemization) are discussed in later chapters.
  • Connection to the broader theme of mechanism determination:
    • Mechanistic outcomes depend on carbocation stability (stabilized by resonance and substitution) and steric hindrance affecting backside attack.
    • The energy diagram shapes (one TS vs two TSs with an intermediate) reflect these mechanistic differences.

Temperature, pressure, and practical implications for rates

  • The most influential factor on reaction rate discussed is temperature:
    • Higher temperature increases the fraction of molecules with sufficient energy to reach the TS, thereby increasing the rate constant effectively via the population of energetic reactants.
    • Pressure effects are mentioned as generally less impactful for these types of solution-phase substitutions; the emphasis is on thermal energy distribution.
  • Practical takeaway:
    • By adjusting temperature, you can influence the rate by changing how many molecules can cross the activation barrier, not by changing the intrinsic barrier height itself.

Key concepts, clarifications, and follow-ups

  • The difference between transition states and intermediates:
    • Transition states are maxima along the reaction coordinate and cannot be isolated; intermediates are local minima (stable species) that can be drawn as separate species on the diagram.
  • The role of carbocation stability in SN1:
    • Tertiary carbocations are favored due to both hyperconjugation and resonance stabilization; this stability drives the SN1 pathway for tertiary halides.
  • The role of steric hindrance in SN2:
    • Less hindered (primary) centers are more accessible to nucleophiles, enabling a concerted backside attack in a single step.
  • Possible complications and real-world notes:
    • In real systems, multiple products and competing pathways can occur; sometimes secondary centers show mixed behavior.
    • The class foreshadows discussing secondary cases and the stereochemical outcomes of SN1/SN2 in future chapters.
  • Summary of the two archetypal reactions (for quick reference):
    • SN2 (EtI + CN^-): single-step, concerted displacement; rate law ext{rate} = k [ ext{EtI}] [ ext{CN}^-]; transition state with partial CN–C bond and partial C–I bond; downhill overall energy change (ΔH < 0).
    • SN1 (Ph3CBr + CN^-): two-step via carbocation; rate-determining step is ionization to Ph3C^+; rate law ext{rate} = k [ ext{Ph}_3 ext{CBr}]; two transition states TS1 and TS2 with an intermediate; carbocation stability is key; equilibrium often lies toward products (downhill overall).