Collision theory unimolecular reactions

Theoretical chemistry is the discipline that uses quantum mechanics, classical mechanics, and statistical mechanics to explain the structures and dynamics of chemical systems and to correlate, understand, and predict their thermodynamic and kinetic properties. Modern theoretical chemistry may be roughly divided into the study of chemical structure and the study of chemical dynamics. The former includes studies of (1) electronic structure, potential energy surfaces, and force fields (2) vibrational-rotational motion and (3) equilibrium properties of condensed-phase systems and macromolecules. Chemical dynamics includes (1) bimolecular kinetics and the collision theory of reactions and energy transfer (2) unimolecular rate theory and metastable states and (3) condensed-phase and macromolecular aspects of dynamics. 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

Classical Trajectory Simulations Final Conditions Mixed Quantum-Classical Methods Rates of Chemical Reactions State to State Reactive Scattering Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Wave Packets. 

According to collision theory, chemical reactions occur through molecular collisions. A unimolecular elementary process in a reaction mechanism involves dissociation of a single molecule. How can these two ideas be compatible Explain. 

In the case of bunolecular gas-phase reactions, encounters are simply collisions between two molecules in the framework of the general collision theory of gas-phase reactions (section A3,4,5,2 ). For a random thennal distribution of positions and momenta in an ideal gas reaction, the probabilistic reasoning has an exact foundation. Flowever, as noted in the case of unimolecular reactions, in principle one must allow for deviations from this ideal behaviour and, thus, from the simple rate law, although in practice such deviations are rarely taken into account theoretically or established empirically. 

Gilbert R G, Luther K and Troe J 1983 Theory of thermal unimolecular reactions in the fall-off range. II. Weak collision rate constants Ber. Bunsenges. Phys. Chem. 87 169-77... 

Mies F H 1969 Resonant scattering theory of association reactions and unimolecular decomposition. Comparison of the collision theory and the absolute rate theory J. Cham. Phys. 51 798-807... 

Troe J 1977 Theory of thermal unimolecular reactions at low pressures. II. Strong collision rate constants. Applications J. Chem. Phys. 66 4758... 

As the system pressure is decreased at constant temperature, the time between collisions will increase, thereby providing greater opportunity for unimolecular decomposition to occur. Consequently, one expects the reaction rate expression to shift from first-order to second-order at low pressures. Experimental observations of this transition and other evidence support Linde-mann s theory. It provides a satisfactory qualitative interpretation of unimolecular reactions, but it is not completely satisfactory from a... 

The notion of a collision implies at least two collision partners, but collision-based theories are applicable for theories of unimolecular reactions as well. 

Letter from G. N. Lewis to Paul Ehrenfest, undated but probably 1925, G. N. Lewis Correspondence, BL.UCB. G. N. Lewis and D. F. Smith promised in their paper, "The Theory of Reaction Rate," JACS 47 (1925) 15081520, to publish a demonstration that a range of frequencies of radiation affecting degrees of freedom in a molecule is responsible for chemical reaction. This paper was the subject of the letter, with anonymous referee s report, from Arthur B. Lamb to G. N. Lewis, 28 February 1925, G. N. Lewis Papers, BL.UCB. The referee said "No real unimolecular reaction has actually been observed they have been shown to be merely catalytic the idea that a unimolecular reaction is due to collision between a quantum and a molecule is not original with Lewis."... 

Troe, J., Theory of Thermal Unimolecular Reactions in the Fall-Off Range. Strong Collision Rate Constants, Her. Bunsenges. Phys. Chem., 87, 161-169 (1983). 

Under ordinary mass spcctrometric conditions only unimolecular reactions of excited ions occur, but at higher ionization chamber pressures bimolecular ion molecule reactions are observed in which both the parent ions and their unimolecular dissociation product ions are reactants. Since it requires a time of 10 5 sec. to analyze and collect the ions after their formation all of the ions in the complete mass spectrum of the parent molecule are possible reactants. However, in radiation chemistry we are concerned with the ion distribution at the time between molecular collisions which is much shorter than 10 5 sec. For example, in the gas phase at 1 atm. the time between collisions is 10 10 sec. and in considering the ion molecule reactions that can occur one must know the amount of unimolecular decomposition within that time. By utilizing the quasi-equilibrium theory of mass spectra6 it is possible to calculate the ion distribution at any time. This has been done for propane at a time of 10 10 sec.,24 and although the parent ion is increased by a factor of 2 the relative ratios of the other ions are about the same as in the mass spectrum observed in 10 r> sec. Thus for gas phase radiolysis the observed mass spectrum is a fair first approximation to the ion distribution. In... 

Elementary reactions are initiated by molecular collisions in the gas phase. Many aspects of these collisions determine the magnitude of the rate constant, including the energy distributions of the collision partners, bond strengths, and internal barriers to reaction. Section 10.1 discusses the distribution of energies in collisions, and derives the molecular collision frequency. Both factors lead to a simple collision-theory expression for the reaction rate constant k, which is derived in Section 10.2. Transition-state theory is derived in Section 10.3. The Lindemann theory of the pressure-dependence observed in unimolecular reactions was introduced in Chapter 9. Section 10.4 extends the treatment of unimolecular reactions to more modem theories that accurately characterize their pressure and temperature dependencies. Analogous pressure effects are seen in a class of bimolecular reactions called chemical activation reactions, which are discussed in Section 10.5. 

J. Troe. Theory of Thermal Unimolecular Reactions at Low Pressures. II. Strong Collision Rate Constants. Applications. J. Chem. Phys., 66(11) 4758—4775,1977. 

Perrin s argument that the very nature of a unimolecular reaction demands independence of collisions, and therefore dependence on radiation, is adequately met both by the theory of Lindemann and by that of Christiansen and Kramers. Both these theories have the essential element in common that the distribution of energy among the molecules is not appreciably disturbed by the chemical transformation of the activated molecules thus the rate of reaction is proportional simply to the number of activated molecules and therefore to the total number of molecules, sinc in statistical equilibrium the activated molecules are a constant fraction of the whole. Thus the radiation theory is not necessary to explain the existence of reactions which are unimolecular over a wide range of pressures. 

Detailed reaction dynamics not only require that reagents be simple but also that these remain isolated from random external perturbations. Theory can accommodate that condition easily. Experiments have used one of three strategies. (/) Molecules in a gas at low pressure can be taken to be isolated for the short time between collisions. Unimolecular reactions such as photodissociation or isomerization induced by photon absorption can sometimes be studied between collisions. (2) Molecular beams can be produced so that motion is not random. Molecules have a nonzero velocity in one direction and almost zero velocity in perpendicular directions. Not only does this reduce collisions, it also allows bimolecular interactions to be studied in intersecting beams and increases the detail with which unimolecular processes that can be studied, because beams facilitate dozens of refined measurement techniques. 

It is the existence of this time lag between activation by collision and reaction which is basic and crucial to the theory of unimolecular reactions, and this assumption leads inevitably to first order kinetics at high pressures, and second order kinetics at low pressures. 

The crucial step in the development of unimolecular theory was the postulate of a time lag between the activation and reaction steps in the master mechanism for all elementary reactions given in Chapter 1. During this time an activated molecule can either be deactivated in a deactivating energy transfer collision, or it can alter configuration to reach the critical configuration and react. All elementary reactions involve three steps, two energy transfer steps and one reaction step, and for unimolecular reactions... 

Problem 14. Discuss the collision theory for unimolecular reactions. 

It seems to be difficult as to how the collision theory could possibly be used to explain the mechanism of unimolecular reactions. In unimolecular processes only one molecule takes part in the reaction, then a question arises ... 

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