Dependence of the frequency factor on temperature: The relationship between the reaction extent at the maximum reaction rate and the reaction mechanism

In the present paper, the correlation between the reaction extent at the maximum reaction rate (termed as αm) and the reaction mechanism has been mathematical derived from the fundamental kinetic equations for a solid-state reaction. In the derivation, the dependence of the frequency factor on temperature (A = A0Tn, where A is the frequency factor, A0 is a constant, T is the temperature, and n is the exponent) has been considered since the frequency factor is connected with temperature to some solid-state reactions. The results have shown that the values of αm are dependent on the reaction mechanism, the values of n and xm (= E/RTm, where E is the activation energy, R is the gas constant and Tm is the temperature at the maximum reaction rate). The αm values with different values of xm and n for each mechanism analyzed in this work have been calculated and the influences of some parameters on the αm values have also been discussed.

Graphical abstractThe relationship between the reaction extent at the maximum reaction rate and the reaction mechanism with the dependence of the frequency factor on temperature is given as follows:Figure optionsDownload full-size imageDownload as PowerPoint slide