Chapter 7 Energy Surfaces and Kinetic Analyses

Chapters 7 and 8: learning tools to use deciphering reaction mechanisms -> a mechanism can never really be proven. 7.1 Energy surfaces and related concepts Kinetics of a reaction: determine how quickly product forms as a function of concentrations, temperature, and other variables. -> goal is to relate experimental observations to molecular scale concepts, such as molecular motions, molecular collisions, and molecular vibrations, as well as energy concepts such as free energy, enthalpy, and entropy. Reaction dynamics: the molecular scale analysis of reaction rates. When we are talking about individual (or small groups of) molecules traversing a well-defined surface, we will tend to call such analyses “dynamics studies”. Discussion of macroscopic measurements of real reacting systems will be termed “kinetics”. 7.1.1 Energy surface 7.1.2 Reaction coordinate diagrams

Reaction coordinate: the minimum energy pathways, or the pathway we depict as the weighted average of all the pathways

Reaction coordinate diagram Intermediates: any chemical structures that last longer than the time for a typical bond vibration (10-13 to 10-14 s) Rate-determining step: the step with the highest barrier.

Activation energy 7.1.4 Rates and rate constants

Rate constant (k): a proportionality constant between concentration of reactants and reaction rate 7.1.5 Reaction order and rate laws

Rate constant (k): a proportionality constant between concentration of reactants and reaction rate

a + b + c = reaction order Rate law -> determined by experimental measurements of the rates of reaction: does not give any information about mechanism

Molecularity: the number of molecules involved in the transition state of the reaction Elementary reaction: single-step reaction (단일반응) Unimolecular: only single molecule is involved in the transition state, eg) Cope rearrangement

Bimolecular: two molecules are involved in the transition state, eg) SN2 Termolecular: three molecules are involved in the transition state Molecularity applies only to elementary reactions and is basically a statement about the mechanism of the reaction. 7.2 Transition state theory and related topics 7.2.1 The mathematics of transition state theory: pre-equilibrium between the reactants and activated complex To understand the nature of the rate constant k -> analyze the energetic and entropic components of reaction process + k+ + A + B ←→ [AB ] → C + AB+ rate = + + [AB + ] Equilibrium constant of the K+ = [A][B] formation of activated complex A + B C + + = kK+ +[A][B]

+ + + + + + ΔG += ΔH + - TΔS + = -RTnK + K + = e -ΔG /RT

κk T + rate = B e -ΔG /RT [A][B] h κ: transmission coefficient ~ 1 = k [A][B] kB: Boltzmann constant h: Planck’s constant κk T + k = B e -ΔG /RT T: absolute temperature h for s are involved in the overall tes, there is an Eyring equation the macroscopic rate constants + + for a single-step conversion of a reactant conversion for a single-step S/R

Δ e B k h κ Eyring equation C = T A going to B by various paths. It is ignorant of any mechanistic mechanistic It is ignorant of any by various paths. A going to B one or more reactive intermediate + + ocess involving reactive intermedia ocess involving reactive + + H /RT S/R Δ Δ - e e a microscopic rate constant describes the overall transformation. T a + + + + + + S/R E G /RT H /RT Δ

Δ Δ + + - - e H /RT

e e Δ : arises from empirical observations of - T T B for each and every step. e : analyzes : analyzes B B k h ‡ h h k k

κ C κ κ G Δ = = = = k : activation energy : frequency factor (pre-exponential factor) factor (pre-exponential : frequency a : absolute temperature T A E Arrhenius rate law a particular conversion, such as a particular conversion, considerations, such as whether conversion of A to B. to a product. In multistep pr and thus a and Eyring equation Arrhenius rate law 7.2.2 Relationship to the Arrhenius7.2.2 Relationship rate law 7.2.3 Boltzmann distributions and temperature dependence

The higher temperature reaction proceeds faster due to the larger area under the curve past the activation energy

Boltzmann distribution 7.2.5 Experimental determinations of activation parameters and Arrhenius parameters

Eyring equation

Arrhenius equation

T -> k ---Æ ΔH‡, ΔS‡, ΔG‡

7.2.6 Examples of activation parameters and their interpretations

+ Diels-Alder reaction

Gas phase ΔH‡ = 15.5 kcal/mol ΔS‡ = -34 eu

Bu NNBu 2 Bu + N2

Gas phase ΔH‡ = 52 kcal/mol ΔS‡ = 19 eu ΔH‡ : the latter > the former why? the former; concerted reaction -> bond making accompanies bond breaking ΔS‡ : the latter > the former why? The former -> two molecules become one molecule -> the loss of translational and rotational degrees of freedom the latter -> one molecule becomes three molecules

Claisen rearrangement O O O

ΔS‡ = -8 eu 1, 2, 4, 6 -> molecules combine 3,5,7 -> bond breaking

1; -26 eu -> 26 cal/mol K x 298 K = 7.75 kcal/mol in ΔG‡ -> decrease in the rate constant by a factor of 500,000, relative to a reaction with a ΔS‡ = 0 7.3 Postulates and principles related to kinetic analysis

7.3.1 Hammond postulate Transition states are transient in nature and generally cannot be directly characterized by experimental means. This postulate is likely the most widely used principle for estimating the structures of activated complexes that give us insights into chemical reactivity. ; the activated complex most resembles the adjacent reactant, intermediate, or product that it is closest in energy to.

exothermic endothermic The Hammond postulate does not predict the height of the barrier compared to the reactant and product.

이런 경우도 있다. 그러나 대부분의 경우 To obey the Hammond postulate 7.9와같은reaction coordinates를 갖는다