Prater relation

Equation (6.3.109) is called the Prater relation. From this relationship, the adiabatic temperature rise in a catalyst pellet can be calculated. The maximum... 

Prater (1958) has shown that without solving the complete equation the temperature increase can be related to the concentration drop inside the particle as ... 

There have been many attempts to relate bulk electronic properties of semiconductor oxides with their catalytic activity. The electronic theory of catalysis of metal oxides developed by Hauffe (1966), Wolkenstein (1960) and others (Krylov, 1970) is base d on the idea that chemisorption of gases like CO and N2O on semiconductor oxides is associated with electron-transfer, which results in a change in the electron transport properties of the solid oxide. For example, during CO oxidation on ZnO a correlation between change in charge-carrier concentration and reaction rate has been found (Cohn Prater, 1966). 

The Prater number (3 - in contrast to eq. (14.25) is related to Ts and not to TG - and the Arrhenius number have a major influence on the development of the T and c profiles. The pore utilization factor qp is therefore dependent upon Arr, (3 and Thiele modulus . The correlation between these four pi-numbers is represented in Fig. 83. For T]p and the following definitions apply ... 

J. Wei and C. D. Prater, The Structure and Analysis of Complex Reaction Systems. Advances in Catalysis and Related Subjects series, Vol. 13. New York Academic Press Inc., 1962. 

M. T. McClure, J. A. von Windheim, J. T. Glass, and J. T. Prater, Effect of native Si02 layer on the nucleation of diamond using a combustion flame. Diamond Relat. Mater., 3(3) 239-244 (1994)... 

In addition to illustrating many features of monomolecular reaction networks, Wei and Prater illustrated how these results, especially the straight line reaction paths, could be helpful in planning experiments for and the determination of rate constants, and this will be discussed later. Also, these same methods have been used in the stochastic theory of reaction rates, which consider the question of how simple macroscopic kinetic relations (e.g., the mass action law) can result from the millions of underlying molecular collisions—see Widom for comprehensive reviews [14]. 

Each of the values is experimentally accessible and the effectiveness factor can be computed such as shown in Figure 2.32. Hence, a set of graphs can be prepared relating fr to tj with the Arrhenius and Prater numbers as parameters and allowing estimation of the effectiveness factors directly from experimental results. An important number of criteria for estimating the influence of transport... 

Mainly with the idea of overcoming these objections to the peroxide value as a measure of rancidity, various tests have been developed for decomposition products of oxidized fats. The widely used Kreis test, which depends upon the development of a red color when rancid fats are treated with phloroglucinol, has recently been shown to be given by malonic dialdehyde and other closely related constituents of oxidizing fats (Patton et al., 1951). The test has been greatly improved in recent years by solution of all reactants in a single phase and colorimetric estimation of the color produced (Walters et al., 1938 Pool and Prater, 1945 Watts and Major, 1946). 

To calculate ripom, the mass and heat balances must be solved simultaneously. Analytical and numerical solutions are given by Petersen (1962), Tinkler and Pigford (1961), Carberry (1961), Tinkler and Metzner (1961), and Weisz and Hicks (1962). The behavior of a non-isothermal pellet in the regime of pore diffusion limitation is governed by the Thiele modulus (f> (related to Tsurface)> the Prater number and the Arrhenius number /int ... 

Table4.5.6 Values of Prater number Arrhenius number and Thiele modulus 4> [all related to Ts, data from Murzin and Salmi (2005) Baerns et al. (2006) and Hlavacek, Kubicek, and Marek (1969)].

The dimensionless quantities (sometimes called Prater number) and relate the concentration differences to the temperature differences within the pellet and external to the pellet, respectively, as will be seen later. 

Z Sitar, W Liu, PC Yang, CA Wolden, R Schlesser, JT Prater. Heteroepitaxial nucleation of diamond on nickel. Diamond and Related Materials 7 276, 1988. 

Thus, the temperature at any position within the solid is related to the concentration at the same position. Petersen [3] gives a more complete and rigorous derivation of Eq. (4.2.40) with the same result. This relationship was first derived by Damkohler [8] and shown by Prater [9] to be valid for all kinetics and geometries of the solid. 

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