The Accuracy of Senum and Yang's Approximations to the Arrhenius Integral

The accuracy of the integral of the Arrhenius equation, as determined from the 1st to the 4th degree rational approximation proposed by Senum and Yang, has been calculated. The precision of the 5th to 8th rational approximations, here proposed for the first time, has also been analyzed. It has been concluded that the accuracy increases by increasing the order of the rational approximation. It has been shown that these approximations to the Arrhenius equation integral would allow an accuracy better than 10−8 % in the E/RT range generally observed for solid state reactions. Moreover, it has been demonstrated that errors closed to 10−2 % can be obtained even for E/RT=1, provided that high enough degrees of rational approximation have been used. Thus, it would be reasonable to assume that high degree rational approximations for the Arrhenius integral could be used for the kinetic analysis of processes, like adsorption or desorption of gases on solid surfaces, which can take place at low temperatures with very low values of E/RT.