Species Formation Rates

This chapter covers the second fundamental concept used in chemical reaction engineering—chemical kinetics. The kinetic relationships used in the analysis and design of chemical reactors are derived and discussed. In Section 3.1, we discuss the various definitions of the species formation rates. In Section 3.2, we define the rates of chemical reactions and discuss how they relate to the formation (or depletion) rates of individual species. In Section 3.3, we discuss the rate expression that provides the relationship between the reaction rate, the temperature, and species concentrations. Without going into the theory of chemical kinetics, we review the common forms of the rate expressions for homogeneous and heterogeneous reactions. In the last section, we introduce and define a measure of die reaction rate—the characteristic reaction time. In Chapter 4 we use the characteristic reaction time to reduce the reactor design equations to dimensionless forms. 

Definition of species formation rates on the basis of volume, mass, and surface and the relations among them... 

Definition of reaction rates and their relation to the species formation rates... 

Equation 4.2.2 is the integral form of the species-based design equation for an ideal batch reactor, written for species j. It provides a relation between the operating time, t, the amount of the species in the reactor, Nj(t) and Nj(0), the species formation rate, (rj), and the reactor volume, V. Note that when the reaetor volume does not change during the operation, Eq. 4.2.2 reduces to... 

Equation 4.2.11 provides a relation among the species flow rate at the inlet and outlet of the reactor, Fand Fthe species formation rate, (r ), and the volume of the reactor, Vr, for a plug-flow reactor. 

Relation between a species formation rate and rates of chemical reactions ... 

Consequently, the observed rate of polymerization, Vtot, is generally not identical to the propagation reaction rate, Vp. For example, the active species formation rate, which in turn depends on the initial initiator concentration, contributes to the directly observable rate of polymerization. In general, the following holds ... 

In the M. trichosporium OB3b system, a third intermediate, T, with kmax at 325 nm (e = 6000 M-1cm 1) was observed in the presence of the substrate nitrobenzene (70). This species was assigned as the product, 4-nitrophenol, bound to the dinuclear iron site, and its absorption was attributed primarily to the 4-nitrophenol moiety. No analogous intermediate was found with the M. capsulatus (Bath) system in the presence of nitrobenzene. For both systems, addition of methane accelerated the rate of disappearance of the optical spectrum of Q (k > 0.065 s-1) without appreciatively affecting its formation rate constant (51, 70). In the absence of substrate, Q decayed slowly (k 0.065 s-1). This decay may be accompanied by oxidation of a protein side chain. 

The photoreactivity of the involved catalyst depends on many experimental factors such as the intensity of the absorbed light, electron-hole pair formation and recombination rates, charge transfer rate to chemical species, diffusion rate, adsorption and desorption rates of reagents and products, pH of the solution, photocatalyst and reactant concentrations, and partial pressure of oxygen [19,302,307], Most of these factors are strongly affected by the nature and structure of the catalyst, which is dependent on the preparation method. The presence of the impurities may also affect the photoreactivity. The presence of chloride was found to reduce the rate of oxidation by scavenging of oxidizing radicals [151,308] ... 

Because of the lack of high-pressure experimental reaction rate data for HMX and other explosives with which to compare, we produce in Figure 15 a comparison of dominant species formation for decomposing HMX that have been obtained from entirely different theoretical approaches. The concentration of species at chemical equilibrium can be estimated through thermodynamic calculations with the Cheetah thermochemical code.32,109... 

Nitroarenes were formed under laboratory conditions when PAH reacted with gas-phase OH radical (in presence of NO ) and N2O540 45. The atmospheric nitroarene formation rate depends upon the concentration of the individual species N2O5-NO3-NO2 An analogous reaction sequence occurs when PAH reacts in N2O5-NO3-NO2 systems46. Naphthalene reacts with NO3 radical forms NO3-naphthalene adduct, which dissociates or reacts with NO2 to form nitronaphthalene and other products as shown in Figure 6. 

Rh s(CO)iis they revealed the presence of an unidentified complex which was suggested to be the previously unknown species Rh4(a-CO)i2-The BTEM protocol is an extremely powerful technique to recover pure component spectra of unknown species, even when present at very low concentrations. This was illustrated by a detailed mechanistic study of the promoting effect of HMn(CO)5 on the Rh4(CO)i2 catalyzed hydroformylation of 3,3-dimethylbut-l-ene [22], A dramatic increase in the hydroformylation rate was found when both metals were used simultaneously. Detailed in situ FTIR measurements using the BTEM protocol indicated the presence of homometallic complexes only during catalysis. The metal complexes that were identified under catalytic conditions were RC(0)Rh(C0)4, Rh4(CO)i2, Rh5(CO)i5, HMn(CO)s, and Mn2(CO)io (see Figure 6.6). The kinetics of product formation showed an overall product formation rate, Eq. (3) ... 

The Isometric ion plots of Figures A and 5 indicate that evolution of benzene from the silicone-epoxy samples occurs in two distinct stages, with the low temperature peak attributable to residual solvent species. Above 200°C, thermal degradation processes involving scission of the Si-phenyl bond occur and account for the increased formation rate of benzene. The other high temperature volatile products are similar to those observed for the novolac epoxy samples, and are attributed to decomposition of the epoxy fraction of samples D and E. 

Comparison of the silicone-epoxy ion profiles indicates that the presence of the flame retardant in sample E has little effect on the composition or formation rates of the major volatile species. The specific ion profiles characteristic of HBr and from the flame retardant in sample E... 

The above proposed pathway requires further verification of the reactivity of adsorbed intermediates by correlating their conversion rates with the product formation rates. Work is underway to study the adsorbed intermediates under transient condition to determine the reactivity of the IR-observable specie on the Au catalyst surface and to identify the nature of active sites (i.e., M", M °). 

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