Rate constants of bimolecular reactions

The notion of the rate constant Ka (index v indicates that the collision velocity of particles v is unchanged), which is related to the notion of the cross section of the process is also used for the quantitative characterization of the rate of each of the processes considered. 

Let us discuss the most general case of collision 3 in which the internal energy changes and atoms are redistributed. The process rate W3 can be determined from the consumption of the reactant or from the accumulation of the reaction product. These determinations are not equivalent because when the rate is found from the reactant consumption, it includes other possible reaction 

With the introduction of the new laboratory reference system (where particles B are at rest), the rate W3 depends only on the relative velocity of particles V = a Vj. Therefore, for the W3 rate we can write 

Let the flux density --dl of particles A(i) decreases in collisions with particles B(j) only due to process 3. Since the I value is referred to unit surface and time, the decrease in the flux density during passing the dx distance is equal to the process rate W3 multiplied to the volume of a cylinder with the unit surflice area of the base and height dx, i.e.. 

For elementary processes in the bulk and in several cases, also for the real experiment in beams, the relative velocity of colliding particles is not the same for each collision act. To obtain the rate constant, in this case, we have to average k (i j — l,m) by the available set of relative velocities v. 

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The IPM as a semiempirical model of an elementary bimolecular reaction appeared to be very useful and efficient in the analysis and calculation of the activation energies for a wide variety of radical abstraction and addition reactions [108-113]. As a result, it became possible to classify diverse radical abstraction reactions and to differentiate in each class the groups of isotypical reactions. Later this conception was applied to the calculations of activation energies and rate constants of bimolecular reactions of chain generation [114]. In the IPM, the radical abstraction reaction, for example,... 

Enthalpies, Activation Energies, and Rate Constants of Bimolecular Reactions of Hydroperoxides 2ROOH —> R00 +H20 + RO Calculated by the IPM Method [122-124]... 

Influence of Plastification of Polymer on the Molecular Mobility and Rate Constant of Bimolecular Reaction [7,14,15,21]... 

Slow diffusion of molecules and radicals in polymer contracts the interval of the observed rate constants of bimolecular reactions. 

The basicity constants in water and micelles then have the same units (M 1), and values of K and Kb are not very different for arenimidazoles and nitroindoles under a variety of conditions (Table 10). The comparisons suggest that inherent basicities are not very different in water and cationic micelles, but, as with second-order rate constants of bimolecular reactions (Section 5), there is a limited degree of specificity because K /Kb is slightly larger for the nitroindoles than for the arenimidazoles, almost certainly because of interactions between the cationic micellar head groups and the indicator anions. 

Table 11 The rate constants of bimolecular reactions ( q, M s ) of singlet pura-substituted 2,3,5,6-tetrafluorophenylnitrenes with different organic compounds.

In order to derive an exact equation for the rate constant of bimolecular reactions on the basis of the collision theory expression (1.IV), we must calculate the partition function for motion along the reaction coordinate in the reactants region of configuration space. This, however, proves to be not a trivial problem. 

D24.3 The Eyring equation (eqn 24.53) results from activated complex theory, which is an attempt to account for the rate constants of bimolecular reactions of the form A + B iC -vPin terms of the formation of an activated complex. In the formulation of the theory, it is assumed that the activated complex and the reactants are in equilibrium, and the concentration of activated complex is calculated in terms of an equilibrium constant, which in turn is calculated from the partition functions of the reactants and a postulated form of the activated complex. It is further supposed that one normal mode of the activated complex, the one corresponding to displaconent along the reaction coordinate, has a very low force constant and displacement along this normal mode leads to products provided that the complex enters a certain configuration of its atoms, which is known as the transition stale. The derivation of the equilibrium constant from the partition functions leads to eqn 24.51 and in turn to eqn 24.53, the Eyring equation. See Section 24.4 for a more complete discussion of a complicated subject. 

Here kjj is the frequency of the interaction between particles having effective radii r and diffusion coefficients D Na is Avogadro s number which is introduced into equation (4.49) in order to obtain the general dimensionalities of the rate constants of bimolecular reactions. 

A plot of log k against 1/T should therefore be a straight line of slope — E/R. The measured rate constants of bimolecular reactions follow this relation closely. Equation (5.13) is called the Arrhenius equation, Arrhenius having been the first to establish it by experiment. The quantity E is called the activation energy of the reaction. 

Rates of chemical reactions vary within a wide region of magnitude. Due to diffusion limitations, the rate constant of bimolecular reaction cannot exceed 10 ° mol dm s [28] therefore, this value can be used as an upper limit of Reactions whose half-times are less than 10 s are considered fast [29] then, the rate constant for monomolecular reaction should exceed 0.1 s L In accordance with the reaction rate, metal complexes are classified as labile and inert, but it is not possible to draw a sharp boundary line between the two groups. 

The rate constant of bimolecular reactions represented by Reaction (2.26) is represented as... 

Kinetics of the reactions of singlet species 32b in solution at room temperature were studied using time-resolved IR spectroscopy (TRIR) " and nanosecond laser flash photolysis. The absolute rate constants of bimolecular reactions of 32b with... 

The temperature-independent A and E values are named the pre-exponential factor and Arrhenius activation energy, respectively. This is precisely the form which is appropriate for the majority of experimentally measured rate constants of bimolecular reactions. At the same time, as will be shown below, the theory predicts that... 

The statistical theory can be applied to the calculation of rate constants of bimolecular reactions that occur through a long-lived complex. Probable reaction profiles of such reactions are shown in Fig. 2.8. 

These energies can be estimated, first, by the partition coefficient of the substance between two liquid phases and, second, by the critical temperature of mutual dissolution of two phases. The ratio of the number of neighbors in the cage n to the number of moles of the solvent S (in mol/1) is usually close to unity. According to the encounter theory, the rate constant of bimolecular reaction k z, where z is the frequency factor of bimolecular collisions. In liquid a molecule is surrounded by n molecule-neighbors, vibrates in this cage with the frequency n, and collisions with each neighbor 6v times and with one molecule 6v/n times. The vibration of a particle sur-... 

In the framework of the encounter thetny in gas (see Chapter 2), the rate constant of bimolecular reaction... 

The formation of an activated complex from two particle-reactants is accompanied by a change in the volume. Therefore, the external pressure influences the rate constant of bimolecular reaction. Since the internal pressure about 10 -10 Pa exists in liquid due to the intermolecular interaction (in CCI4 at 293 K it is 3.48-10 Pa), the external pressure of an order of 10 -10 Pa should be created for a noticeable effect on the liquid. The study of the pressure effect on the reaction provides data on a change in the system volume during the formation of an activated complex. 

The compensation effect is absent from gas-phase reactions of atoms and radicals with molecules, it is not either observed for radical reactions in solutions when one of two reactants is a nonpolar particle. One of the sources of this effect is the influence of the medium on the elementary act of polar particles. The rate constant of bimolecular reaction in a solution depends on the association constant of particles Kj q, amplitude of vibrations of particles a and dielectric constant e. All these... 

Table 7.21. Rate constants of bimolecular reactions with translatory and rotational difiusion of reactants...

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