Reactant molecule

A bimoleciilar reaction can be regarded as a reactive collision with a reaction cross section a that depends on the relative translational energy of the reactant molecules A and B (masses and m ). The specific rate constant k(E ) can thus fonnally be written in tenns of an effective reaction cross section o, multiplied by the relative centre of mass velocity... 

As with the other surface reactions discussed above, the steps m a catalytic reaction (neglecting diffiision) are as follows the adsorption of reactant molecules or atoms to fomi bound surface species, the reaction of these surface species with gas phase species or other surface species and subsequent product desorption. The global reaction rate is governed by the slowest of these elementary steps, called the rate-detemiming or rate-limiting step. In many cases, it has been found that either the adsorption or desorption steps are rate detemiining. It is not surprising, then, that the surface stmcture of the catalyst, which is a variable that can influence adsorption and desorption rates, can sometimes affect the overall conversion and selectivity. 

In deriving the RRKM rate constant in section A3.12.3.1. it is assumed that the rate at which reactant molecules cross the transition state, in the direction of products, is the same rate at which the reactants fonn products. Thus, if any of the trajectories which cross the transition state in the product direction return to the reactant phase space, i.e. recross the transition state, the actual unimolecular rate constant will be smaller than that predicted by RRKM theory. This one-way crossing of the transition state, witii no recrossmg, is a fiindamental assumption of transition state theory [21]. Because it is incorporated in RRKM theory, this theory is also known as microcanonical transition state theory. 

Variational RRKM theory is particularly important for imimolecular dissociation reactions, in which vibrational modes of the reactant molecule become translations and rotations in the products [22]. For CH —> CHg+H dissociation there are tlnee vibrational modes of this type, i.e. the C—H stretch which is the reaction coordinate and the two degenerate H—CH bends, which first transfomi from high-frequency to low-frequency vibrations and then hindered rotors as the H—C bond ruptures. These latter two degrees of freedom are called transitional modes [24,25]. C2Hg 2CH3 dissociation has five transitional modes, i.e. two pairs of degenerate CH rocking/rotational motions and the CH torsion. 

The ability to assign a group of resonance states, as required for mode-specific decomposition, implies that the complete Hamiltonian for these states is well approxmiated by a zero-order Hamiltonian with eigenfunctions [M]. The ( ). are product fiinctions of a zero-order orthogonal basis for the reactant molecule and the quantity m. represents the quantum numbers defining ( ).. The wavefimctions / for the compound state resonances are given by... 

As discussed in section A3.12.2. intrinsic non-RRKM behaviour occurs when there is at least one bottleneck for transitions between the reactant molecule s vibrational states, so drat IVR is slow and a microcanonical ensemble over the reactant s phase space is not maintained during the unimolecular reaction. The above discussion of mode-specific decomposition illustrates that there are unimolecular reactions which are intrinsically non-RRKM. Many van der Waals molecules behave in this maimer [4,82]. For example, in an initial microcanonical ensemble for the ( 211 )2 van der Waals molecule both the C2H4—C2H4 intennolecular modes and C2H4 intramolecular modes are excited with equal probabilities. However, this microcanonical ensemble is not maintained as the dimer dissociates. States with energy in the intermolecular modes react more rapidly than do those with the C2H4 intramolecular modes excited [85]. 

Physical properties affecting catalyst perfoniiance include tlie surface area, pore volume and pore size distribution (section B1.26). These properties regulate tlie tradeoff between tlie rate of tlie catalytic reaction on tlie internal surface and tlie rate of transport (e.g., by diffusion) of tlie reactant molecules into tlie pores and tlie product molecules out of tlie pores tlie higher tlie internal area of tlie catalytic material per unit volume, tlie higher the rate of tlie reaction... 

Recall that the symmetry labels e and o refer to the symmetries of the orbitals under reflection through the one Cy plane that is preserved throughout the proposed disrotatory closing. Low-energy configurations (assuming one is interested in the thermal or low-lying photochemically excited-state reactivity of this system) for the reactant molecule and their overall space and spin symmetry are as follows ... 

Since the two reacting functional groups can be located in the same reactant molecule, we add the following ... 

The various expressions we have developed in this section relating p to the size of the polymer are all based on h. Accordingly, we note that the average reactant molecule in this mixture has a molecular weight of 100 as calculated above. Therefore the desired polymer has a value of = 50 based on this concept. 

Reactant molecules are able to withstand more fluorine coUisions, as they become more highly fluorinated, without decomposition because some sites are stericaUy protected, ie, coUisions at carbon—fluorine sites are obviously nonreactive. The fluorine concentration may therefore be increased as the... 

As a reactant molecule from the fluid phase surrounding the particle enters the pore stmcture, it can either react on the surface or continue diffusing toward the center of the particle. A quantitative model of the process is developed by writing a differential equation for the conservation of mass of the reactant diffusing into the particle. At steady state, the rate of diffusion of the reactant into a shell of infinitesimal thickness minus the rate of diffusion out of the shell is equal to the rate of consumption of the reactant in the shell by chemical reaction. Solving the equation leads to a result that shows how the rate of the catalytic reaction is influenced by the interplay of the transport, which is characterized by the effective diffusion coefficient of the reactant in the pores, and the reaction, which is characterized by the first-order reaction rate constant. 

The reaction constant k was related to a collision number Z, the number of reactant molecules colliding/unit time, and an activation energy E by the Anhenius equation... 

In all of these expressions the order appears to be related to the number of molecules involved in tire original collision which brings about the chemical chatrge. For instance, it is clear that the bitrrolecular reaction involves the collision between two reactant molecules, which leads to the formation of product species, but the interpretation of tire first and third-order reactions cannot be so simple, since the absence of the role of collisions in the first order, and the rare occunence of tlrree-body collisions are implied. 

An explanation which is advanced for these reactions is that some molecules collide, but do trot immediately separate, and form dimers of dre reactant species which have a long lifetime when compared with the period of vibration of molecules, which is about 10 seconds. In the first-order reaction, the rate of tire reaction is therefore determined by the rate of break-up of tirese dimers. In the thud-order reaction, the highly improbable event of a tluee-body collision which leads to the formation of tire products, is replaced by collisions between dimers of relatively long lifetime widr single reactant molecules which lead to tire formation of product molecules. 

Botli reactions involve the formation of a vapour-uatisporting species from four gaseous reactant molecules, but whereas the tetra-iodide of zirconium is a stable molecule, the nickel teU acarbonyl has a relatively small stability. The equilibrium constatits for these reactions are derived from the following considerations ... 

Preparation of enantiomerically enriched materials by use of chiral catalysts is also based on differences in transition-state energies. While the reactant is part of a complex or intermediate containing a chiral catalyst, it is in a chiral environment. The intermediates and complexes containing each enantiomeric reactant and a homochiral catalyst are diastereomeric and differ in energy. This energy difference can then control selection between the stereoisomeric products of the reaction. If the reaction creates a new stereogenic center in the reactant molecule, there can be a preference for formation of one enantiomer over the other. 

We will discuss shortly the most important structure-reactivity features of the E2, El, and Elcb mechanisms. The variable transition state theoiy allows discussion of reactions proceeding through transition states of intermediate character in terms of the limiting mechanistic types. The most important structural features to be considered in such a discussion are (1) the nature of the leaving group, (2) the nature of the base, (3) electronic and steric effects of substituents in the reactant molecule, and (4) solvent effects. 

Sensitizer singlet formed Intersystem crossing of sensitizer Energy transfer to reactant molecule... 

In this reaction I" is the nucleophile, and Br" is called the leaving group (or nucleofuge). Beyond this, the classification symbolism may include a designation of the molecularity of the reaction. Molecularity is the number of reactant molecules included in the transition state. The above reaction is an 8 2 reaction, because both reactants are present in the transition state. On the other hand, this substitution... 

Consider a dilute solution of two reactant molecules, A and B. Inevitably an A molecule and a B molecule will undergo an encounter, the frequency of such encounters depending upon the concentrations of A and B. If, upon each encounter of A and B, they undergo bimolecular reaction, then the rate of this reaction is determined solely by the rate of encounter of A and B that is, the rate is not controlled by the chemical requirement that an energy barrier be overcome. One way to find this rate is to treat the problem as one of classical diffusion, and so this maximum possible rate of reaction is often called the diffusion-controlled rate. This problem was solved by Smoluchowski. In the following development no provision is made for attractive forces between the molecules. ... 

Chemical reaction rates increase with an increase in temperature because at a higher temperature, a larger fraction of reactant molecules possesses energy in excess of the reaction energy barrier. Chapter 5 describes the theoretical development of this idea. As noted in Section 5.1, the relationship between the rate constant k of an elementary reaction and the absolute temperature T is the Arrhenius equation ... 

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