Reaction collisions

Figure C3.3.10. A schematic energy-level diagram for a molecule capable of undergoing unimolecular reaction above tlie energy depicted as tlie reaction barrier. Arrows to tlie right indicate reaction (collision-free) at a rate kg tliat depends on tlie energy E. Down arrows represent collisional redistribution of tlie hot molecules botli above and below tlie reaction barrier.

Rate of reaction = collision frequency X fraction with sufficient energy... 

The shape of a reactant can affect the rate of a reaction. Collision theory tells us that in order for a reaction to occur there must be an effective collision. For a collision to be effective, the reacting species must... 

By increasing the temperature T, we have not changed the magnitude of the activation energy, nor have we changed the value of AH of reaction. The increased rate is a kinetic result we have enhanced the number of successful reaction collisions per unit time. 

Another term used to describe rate processes is molecu-larity, which can be defined as an integer indicating the molecular stoichiometry of an elementary reaction, which is a one-step reaction. Collision theory treats mo-lecularity in terms of the number of molecules (or atoms, if one or more of the reacting entities are single atoms) involved in a simple collisional process that ultimately leads to product formation. Transition-state theory considers molecularity as the number of molecules (or entities) that are used to form the activated complex. For reactions in solution, solvent molecules are counted in the molecularity, only if they enter into the overall process and not when they merely exert an environmental or solvent effect. 

The atomic processes that are occurring (under conditions of equilibrium or non equilibrium) may be described by statistical mechanics. Since we are assuming gaseous- or liquid-phase reactions, collision theory applies. In other words, the molecules must collide for a reaction to occur. Hence, the rate of a reaction is proportional to the number of collisions per second. This number, in turn, is proportional to the concentrations of the species combining. Normally, chemical equations, like the one given above, are stoichiometric statements. The coefficients in the equation give the number of moles of reactants and products. However, if (and only if) the chemical equation is also valid in terms of what the molecules are doing, the reaction is said to be an elementary reaction. In this case we can write the rate laws for the forward and reverse reactions as Vf = kf[A]"[B]6 and vr = kr[C]c, respectively, where kj and kr are rate constants and the exponents are equal to the coefficients in the balanced chemical equation. The net reaction rate, r, for an elementary reaction represented by Eq. 2.32 is thus... 

As for bimolecular reactions, collision theory can also be used to describe the kinetics of interfacial reactions between a solid surface and solutes in the liquid phase. Astumian and Schelly have described the theory for the kinetics of interfacial reactions in detaiL The complete rate expression, derived by Astumian and Schelly, for solutes reacting with suspended solid spherical particles is given by Eq. (1)... 

As in all mathematical descriptions of transport phenomena, the theory of polydisperse multiphase flows introduces a set of dimensionless numbers that are pertinent in describing the behavior of the flow. Depending on the complexity of the flow (e.g. variations in physical properties due to chemical reactions, collisions, etc.), the set of dimensionless numbers can be quite large. (Details on the physical models for momentum exchange are given in Chapter 5.) As will be described in detail in Chapter 4, a kinetic equation can be derived for the number-density function (NDF) of the velocity of the disperse phase n t, X, v). Also in this example, for clarity, we will assume that the problem has only one particle velocity component v and is one-dimensional in physical space with coordinate x at time t. Furthermore, we will assume that the NDF has been normalized (by multiplying it by the volume of a particle) such that the first three velocity moments are... 

A similar mechanism has been postulated for the reaction when conducted in the presence of silica gel metallized with silver, gold, platinum, and palladium.10 Collisions of ethylene molecules with oxygen molecules adsorbed and activated by the effective catalyst centers result in reaction. Collisions of oxygen molecules with adsorbed ethylene molecules, however, are ineffective. 

Reaction collision Elastic collision Atomic isotope shift... 

There is another aspect of collisions in liquid solution that is of particular interest with regard to chemical reactions. Collisions in solution are often repeated, so that multiple collisions of the same two molecules occur. Consider the molecules labeled A and B in Figure 7.1. Each molecule is surrounded by several neighboring molecules. In view of the short-range order typical of liquids, the neighboring molecules will all be located at... 

Chapter VII discusses the three main methods for estimating the kinetic parameters of elementary reactions collision theory, thermochemical kinetics, structure-reactivity correlations. 

In some reactions, collisions are productive only if the reactants are properly oriented relative to each other upon collision. 

The exponent, m, in (1) is generally set equal to zero, i.e. the Arrhenius assumption is followed. Transition State theory predicts m = 1, and in homogeneous gas phase reactions, collision theory predicts m = In what follows, it is assumed that... 

The second step, the fragmentation, is of completely different nature. It is motion of heavy nuclei against each other on an excited state potential surface. Because the break up of the excited molecule to products resembles the second half of a reaction collision, photodissociation processes are sometimes called half collisions . 

In most reactions, collisions between molecules result in a chemical reaction only if the molecules are oriented in a certain way when they collide. The relative orientations of the molecules during collision determine whether the atoms are suitably positioned to form new bonds. For example, consider the reaction... 

Reaction Collision probability that colliding molecules rate frequency possess necessary energy to react... 

---