Reaction rate predictions

In setting up a reaction path, we find there is no entry in the thermo.dat database for Cr(OH)3(s). To write the kinetic reaction, we can use the mineral Cr203 as a proxy, since it is the dehydrated form of the hydroxide phase. This substitution alters the reaction s free energy yield, but forward progress is favored so strongly that the reaction rate predicted is not affected. If this were not the case, we would need to add to the database a mineral Cr(OH)3 (s) of appropriate stability. 

The kinetic factors Tb and Fa and thermodynamic potential factor Fj are largest where the electron donor and acceptor are abundant, and the reaction products are not. If under such conditions all three factors are equal to one, as is not uncommon, the reaction rate predicted by Equation 18.22 reaches its maximum value, rmax = nw k+ [X]. As the substrates are depleted with reaction progress, and reaction products accumulate, the factors eventually decrease toward zero, slowing the reaction to a near stop. 

It is interesting to consider the temperature dependence of the reaction rates predicted by these limiting expressions, which are contained in the effective rate coefficients. The true surface reaction rate coefficient has the temperature dependence... 

However, if it is known from kinetic or other evidence that a reaction M + N - Product is a simple elementary reaction, i.e., if it is known that its mechanism is simply the interaction between a molecule of M and a molecule of N, then the molecular theory of reaction rates predicts that the rate of this elementary step is proportional to the concentration of species M and the concentration of species N, i.e. it is second order overall. The reaction is also said to be bimolecular since two molecules are involved in the actual chemical transformation. 

The physical interpretation of this result is, relatively, simple. The reaction rate predicted by the model is equal to the collision frequency, Eq. (4.16), times the factor exp(—E /ksT). This factor is clearly related to the Boltzmann distribution.2 To that end, let us evaluate the probability of finding a relative velocity, irrespective of its direction, corresponding to a free translational energy EtI = (1 /2)/. v that exceeds i tr = E (see Problem 1.3) ... 

Because the energy of the transition state determines the energy of activation and therefore the reaction rate, predicting the relative energy of two transition states allows us to determine the relative rates of two reactions. 

The steady state reaction rates predicted by Reuter et al. at 600 K in terms of the turnover frequency (TOF) and a summary of the surface structures at this temperature are shown in Figure 1. For most combinations of the CO and 02 partial pressures, the surface is dominated by one adsorbed species and as a result the CO oxidation rate is low. However, if the partial pressures are chosen appropriately, a dynamic equilibrium between adsorbed O, CO, and empty sites exists and the oxidation rate can be large. These regions are shown in white... 

Reaction rates predicted by equation 12 were then compared to the rates given by the empirically determined equation ... 

Zhang, H Qu, X. and Ando, H. (2005) A simple method for reaction rate prediction of ester hydrolysis./. Mol. Struct. (Theochem), 725, 31-37. 

To predict catalyst performance, one needs to predict the rates of the elementary reaction steps at the catalyst surface. This must ultimately be integrated into a kinetic simulation which treats the interactions between the many different adsorbates present on the catalyst surface. In this chapter, we presented rate expressions derived from transition state reaction rate theory as a bridge to connect ab initio quantum mechanical information to reaction rate predictions. In Chapter 3, we present a more extensive treatment of kinetic simulations including many-body interactions and their influence on the catalytic performance. 

Expression (4.2) illustrates an important kinetic feature the order of a catalytic reaction depends strongly on the reaction concentration. At low pressure, the rate is first order in reactant and at high pressure the rate is zero order in reactant. Second, the overall rate depends on the intrinsic rate constant of an elementary reaction step, fcact, and also on the adsorption constants. Expression (4.2) is valid only under the ideal conditions that all catalytic centers are similar and there are no interactions between reactant and (or) product molecules. These conditions are rarely satisfied and, for this reason, practical rate-expressions are often more complicated than Elq. (4.2). Ekpression (4.2) illustrates, however, that the interplay between surface coverage and elementary rate constants is very important, so that for an overall prediction of the reaction rate one needs to integrate intrinsic reaction rate predictions with surface state predictions. As mentioned earlier, the equilibrium constants for adsorption can be calculated using either statistical or dynamical Monte Carlo methodsl 46]... 

MCBEND Calculations for Neutron Tlux and Reaction Rate Predictions... 

Kie reaction rates predicted from the kinetic model at lOJt conversion increments from 219 to 919 conversion of thiophene, have been used to construct Table II. At each conversion level the global reaction rate has been normalised to a fraction of the reaction rate for the unfouled catalyst. Only results falling within the experimental range have been included. The activity... 

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