Kinetics of Elementary Reactions

1. Kinetics of Elementary Reactions • A reaction is elementary if it takes place in a single irreducible act at the molecular level, just the way it is written in the stoichiometric equation. • No intermediate between reactants and products can be detected (or visualized). • The act of reaction is most often simple, where one bond is broken while another is formed. • Although catalytic reactions are not elementary, • they generally take place through a sequence of elementary steps • their rate can, in principle, be predicted from a knowledge of the rates of the constituent elementary reactions. • Therefore, before considering the overall kinetics of catalytic reactions, we must understand the dependence of elementary reactions on composition, temperature and pressure (volume).

2. Elementary Reactions • Since an elementary reaction represents a molecular event, its equation may not be written arbitrarily, but the way it takes place. • With this restriction, the molecularity of the reaction is identical to its stoichiometry.

3. Forward and Reverse Reactions • The principle of microscopic reversibility suggests that a reaction and its reverse proceed by the same mechanism. • Forward and reverse reactions must have the same intermediates and rate-determining transition states. • Example: Alcohol Dehydration

4. Theories of Elementary Reaction Kinetics • The rates of even the simplest reactions are very difficult to calculate from first principles. In engineering practice, you will rely on experimental data. • While the basic science of reaction kinetics is not sufficiently developed for design purposes, existing models of reaction dynamics provide a means of understanding reaction phenomena, analyzing experimental data, and extrapolating knowledge to other systems. • Atkins details three approaches to the calculation of rate constants: • Collision Theory • Transition State Theory • Molecular Reaction Dynamics • We will examine transition state theory.

5. Transition State Theory - Elementary Reactions • Transition state theory is founded on the expectation that during the transition from initial reagents to final products, an activated complex of higher “energy” is formed. • This transition state is not an intermediate, but a unique configuration of the system in transit from one state to another. • Although this activated complex is inherently unstable, we often assume that it possesses thermodynamic properties (albeit ill-defined), and propose molecular structures.

6. Transition State of an SN2 Reaction • You have seen the concept of a transition state in CHEM 245, where nucleophilic substitution reactions were introduced. • In the example below, the alkoxide ion is the nucleophile (Lewis base) displaces iodide, the weaker base. • The reaction is believed to be bimolecular, passing through a transition state as drawn below: • Clearly this transition state is not a stable compound, and therefore is not a reaction intermediate, but an activated complex.

7. Potential Energy Surface for Hydrogen Exchange • Owing to the complexity of potential energy calculations, one of the only systems to be analyzed is that of collinear hydrogen exchange.

8. Potential Energy of the Reaction Coordinate

9. Transition State Theory - Thermodynamic Formulation • The Rate of an Elementary Step • The number of elementary acts per unit time is determined the number of systems passing through the activated complex configuration. • We express the elementary reaction as: • At equilibrium, the activated complex Xy will be in equilibrium with the reactants and products, and the concentration can be calculated from thermodynamic principles. • Where q is the reference concentration, usually 1 mole/litre. • Transition state theory assumes that even when the system is not at equilibrium, activated complexes are at equilibrium with the reactants.

10. Transition State Theory - Thermodynamic Formulation • Based on this assumption, the concentration of the activated complex is derived from a thermodynamic treatment: • q = unit conc’n • which, can be expressed in terms of the relative Gibbs energy of the activated complex, • DGy represents the free energy of activation. • The difference between the Gibbs energy of the activated complex, and the Gibbs energies of the reactants at the reference state • This represents the free energy barrier to reaction that includes both potential energy (DH) and conformational restrictions (DS).

11. Transition State Theory - Thermodynamic Formulation • The rate of the forward elementary reaction • is expressed as: • q = unit conc’n • where n is the frequency of vibration of the activated complex in the mode that corresponds to decomposition into products. • This is the frequency of the molecular vibration which leads the complex to dissociate into products C and D. • For this diatomic reaction, statistical mechanics assigns • :sec-1 • where kb = Boltzmann’s constant = 1.38066*10-23 J/K • T = reaction temperature, K • h = Planck’s constant = 6.6262*10-34 J s

12. Transition State Theory - Thermodynamic Formulation • With a measure of the decomposition frequency, the rate of our elementary reaction takes the form: • Given our elementary rate expression for the reaction, • The rate constant, k, for the reaction is identifiable as: • q = unit conc’n • which ends our development of transition state theory. It correctly predicts the orders of the reaction, provides a means of interpreting the observed rate in terms of enthalpic and entropic contributions, and provides guidelines into the temperature dependence of k.

13. Temperature Dependence of Elementary Reactions • The variation of elementary reaction rate constants with temperature is almost always expressed as: • The term Ea is usually called the activation energy, although interpretations of this quantity differ between specific theories of reaction rate. The temperature exponent, m, does likewise. • m = 0 corresponds to classical Arrhenius theory • m = 1/2 is predicted by collision theory • m = 1 is generated by transition state theory • In practice, the dependence of the pre-exponential factor on temperature is usually much weaker than that of the activation energy. • If gathered under kinetic control, reaction rate data plotted as ln(k) versus 1/T or ln(k/T) versus 1/T is usually linear.

14. Temperature Dependence of Elementary Reactions

15. ‡ Product Reactant ‡ Reactant Product Early and Late Transition States • Endergonic reactions have transition states resembling the product in terms of energy and structure. • This is called a “late” transition state or product-like t.s. DG‡ DGo • Exergonic reactions have a transition state more closely resembling the reactants in terms of both energy and structure. • This is called an “early” transition state or reactant-like t.s. DGo DG‡

16. Hammond Postulate • The use of transition state theory to describe chemical kinetics requires us to consider the structure of the transition state. • By definition, the transition state cannot be isolated. How can we make meaningful inferences regarding its structure? • While there is no universal relationship between the stability of a reaction product and its rate of formation, many reactions can be characterized by the Hammond Postulate. • The position of the transition state along the reaction coordinate, its energy, and its geometry are related, and depend on the relative stabilities of the reactant and the product. • A simple statement: • The structure of a transition state resembles the structure of the nearest stable species.

17. Hammond Postulate: Examples • Classify these reaction • profiles in terms of: • A. Product stability • B. Transition State energy • C. Position of the transition • state (early/late) • What generalizations can be made regarding the position of the transition state and the rate of reaction?

18. Food for thought… • Consider the polymerization of methylmethacrylate to produce a transparent, glassy polymer (tradename plexiglass) • the reaction proceeds with “head-to-tail” regioselectivity to give linear polymer chains • as is the case for most polymerizations, it is strongly exothermic. • What would the reaction profile look like for these reactions? • Can product stability arguments (Hammond Postulate) be used to explain the head-to-tail preference?