First-order reactions surface reaction

For comparison reasons, the results derived from the simulation were additionally calculated by means of the Thiele modulus (Equation 12.12), i.e., for a simple first-order reaction. The reaction rate used in the model is more complex (see Equation 12.14) thus, the surface-related rate constant kA in Equation 12.12 is replaced by... 

For a first-order reaction, the reaction rate, M = kCsr] where Cs is the concentration at the particle surface. On the basis of unit volume of the three-phase dispersion, the reaction rate becomes kmol/m3s. 

First-Order Unimolecular Surface Reaction For the reaction... 

An example with the first order irreversible surface reaction 32... 

Table 10 Case of the first order irreversible surface reaction [K = +oo) comparison between the volume concentrations c" ° and (1/H) c dz at the time t = 50 s...

Figure 8 Case of the first order irreversible surface reaction K — +oo) Comparison between concentration obtained using our effective problem (eff), average of the section of the concentration from the original problem (pbreel) and the concentration coming from the simple average (moy) at t = 70s.

A different model [11] that can be used to obtain the kinetics equation for a pyrolytic reaction is adapted from the theory developed for the kinetics of heterogeneous catalytic reactions. This theory is described in literature for various cases regarding the determining step of the reaction rate. The case that can be adapted for a pyrolytic process in solid state is that of a heterogeneous catalytic reaction with the ratedetermining step consisting of a first-order unimolecular surface reaction. For the catalytic reaction of a gas, this case can be written as follows ... 

The case of charge transfer process preceded by a first-order bulk-surface reaction has been described by Guidelli (1971). Here, the parent electroinactive species is transformed into an electroactive species both through a homogeneous chemical reaction taking place within a thin solution layer adjacent to the electrode (with rate constant, Ay) and through a heterogeneous chemical reaction catalyzed by the electrode surface (with rate constant The chronoamperometric current becomes ... 

For a simple first-order, irreversible surface reaction ... 

The isothermal internal effectiveness factor, r/, for the single cylindrical pore and first-order irreversible surface reaction is obtained from the aforementioned expressions for -Ra)p and -Ra)s using Equation 2.60 ... 

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 first-order reaction of hydrogen with Ni3C at 443 K is relatively more rapid than the decomposition [669], indicating facile hydrogenation of the residual carbon at the reactant surface and the possibility of diffusion control is mentioned. 

Solve the above equation for a first-order reaction under steady-state conditions, and obtain an expression for the mass transfer rate per unit area at the surface of a catalyst particle which is in the form of a thin platelet of thickness 2L. 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

Concentration of ethanol in the compound surface layer in equilibrium with the gas phase First-order reaction constant for the silanization reaction Volumetric flow rate of ethanol from the compound to the gas phase Time... 

Only 6% of the iifitial total lycopene prepared as a thin film on the surface of each vial remained after 144 hr under fluorescent light (2000 to 3000 lux) at 25°C under N2. Lycopene degradation occurred as a first-order reaction at 2.93 x 10" /min, and the concentration of aU lycopene mono-c isomers already present in the sample, 5-cis-, 9-cis-, l3-cis- and 15-d5 -, showed an inconsistent change in this period. Nevertheless, formation of lycopene di-c isomers was observed after 32 hr of light exposure and when considering relative percentage, loss of 13% of all-trani-lycopene occurred while an increase of 11% for total cis isomers was found after 144 hr. ... 

In order to verify that the fixed bed and the micro-channel reactor are equivalent concerning chemical conversion, an irreversible first-order reaction A —) B with kinetic constant was considered. For simplicity, the reaction was assumed to occur at the channel surface or at the surface of the catalyst pellets, respectively. Diffusive mass transfer to the surface of the catalyst pellets was described by a correlation given by Villermaux [115]. 

For catalytic reactions carried out in the presence of a heterogeneous catalyst, the observed reaction rate could be determined by the rate of mass transfer from the bulk of the reaction mixture and the outer surface of the catalyst particles or the rate of diffusion of reactants within the catalyst pores. Consider a simple first order reaction its rate must be related to the concentration of species S at the outer surface of the catalyst as follows ... 

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