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 κk T + k = B e -ΔG /RT h + κk T + + = B e -ΔH /RT eΔS/R h + κk + + = B eΔS/R e -ΔH /RT Eyring equation h T + + κk + e -ΔH /RT C = B eΔS/R = C T h 7.2.2 Relationship to the Arrhenius rate law Arrhenius rate law A: frequency factor (pre-exponential factor) Ea: activation energy T: absolute temperature Eyring equation: analyzes a microscopic rate constant for a single-step conversion of a reactant to a product. In a multistep process involving reactive intermediates, there is an Eyring equation and thus a ΔG‡ for each and every step. Arrhenius rate law: arises from empirical observations of the macroscopic rate constants for a particular conversion, such as A going to B by various paths. It is ignorant of any mechanistic considerations, such as whether one or more reactive intermediates are involved in the overall conversion of A to B. Ea describes the overall transformation. 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.