Application of a nonisothermal thermogravimetric method to the kinetic study of the reduction of metallic oxides: Part I
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INTRODUCTION
AN understanding
of the mechanism of a reaction requires a knowledge of the kinetics of the reactions. For example, in the case of gas-solid reactions, high activation energy values are often associated with the chemical reaction at the interface as rate-controlling, whereas lower values could indicate a diffusion-controlled mechanism. Among the various experimental techniques that are used for kinetic studies of gas-solid reactions, thermogravimetry is the most widely used method. During kinetic studies, the reaction is normally conducted at various temperatures and the activation energy is evaluated by an Arrhenius plot. The amount of experimental work can be significantly reduced if the activation energy of a reaction could be reasonably estimated from a single non-isothermal experiment. In the present work, a method for such an estimation is developed and its reliability is examined by applying the same to the reduction of oxides of molybdenum. While theoretical analyses of isothermal kinetic studies are well developed today, to the present knowledge of the authors, very few attempts have been made to describe nonisothermal experiments in a systematic way. Gentry et al. tq have derived an expression for the activation energy in the case of temperature-programmed reduction of copper ions in zeolites carried out in a tubular reactor. These authors obtained a relationship between the activation energy of the reaction and the temperature of maximum reaction rate observed experimentally, which had been used in later studies. ~z,31 Arnoldy et a l . [41 applied this theory to the temperature-programmed reduction of MoO3 and MOO2. In the present work, the theoretical approach is somewhat different in the sense that it deals with the reaction at a microscopic level between the reactant gas and single particles of the solid reactant. DU SICHEN, Research Associate, and S. SEETHARAMAN, Professor, are with the Department of Theoretical Metallurgy, Royal Institute of Technology, S-100 44 Stockholm, Sweden. Manuscript submitted September 16, 1991. METALLURGICAL TRANSACTIONS B
II.
THEORETICAL CONSIDERATIONS
OF NONISOTHERMAL
REDUCTION
Let us consider the reaction aA (g) + B (s) = eE (g) + f F (s)
[ll
The reactant solid B can be considered to be made up of a loose compact of small particles and considerably porous. Let us assume that in view of the openness and the "large" diameter of the pores, the resistance to both molecular as well as Knudsen diffusion of the gas is negligible so that the reactant gas A has access to all the small particles and the product gas E can leave the site without any hindrance. In such a case, the "shrinkingcore model "151 can be applied to the individual particle. The possible rate-controlling step can be the chemical reaction at the interface or the intraparticle diffusion. The latter stands for the inward diffusion of A through the product layer of each particle and outward diffusion of E. In order to simplify the present treatment, it may be assumed that all the particles a
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