Effect of Reaction Order on Gas-Solid Reactions

In the previous analyses of the combined effects of chemical reaction and diffusion, we have used first-order kinetics for the interfacial reaction. In this section we will examine the effect of reaction order with respect to the concentration of gaseous reactant ( , henceforth to be called simply, the reaction order ). We shall do this for the shrinking unreacted-core system without external-mass-transport resistance, and for irreversible reactions K oo). 

Equations (3.4.1) and (3.4.3) are solved simultaneously by eliminating xj/ to obtain the rate or the position of the reaction interface as a function of time [44]. 

The results are shown in Figs. 3.13-3.15 for infinite slabs and spheres, and for = 0, i, 1, and 2. Long cylinders are expected to exhibit behavior that is intermediate between those of infinite slabs and spheres. 

The results indicate that the use of Eq. (3.3.33), which is exact for first-order kinetics, for other reaction orders may introduce a serious error. This is in contrast to the result for the heterogeneous catalysis in a porous pellet or on a solid surface, in which the difference between the effectiveness factors for different reaction orders is much smaller, when plotted against the Thiele modulus generalized for different reaction order [25, 26]. 

The reason for the greater error in a noncatalytic system is that the gaseous reactant must first diffuse through the product layer to reach the reaction interface. The concentration at the interface is smaller than in the bulk, making the rate of chemical reaction more sensitive to the reaction order. (Generalization is made in terms of the bulk concentration.) 

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