Graph Theory in Chemical Kinetics Practice Problems

Abstract

In this work, a novel idea for obtaining in processes performed in real-world processes (here, the illustrative example is the gas phase hydrogenation of propene) a precise kinetic equation that corresponds to the experimental results was examined. The considerations are based on quasi-steady-state hypothesis and using elements of graph theory. The mathematical basis of the method used was developed by Lazman and Yablonsky [1], further considerations are presented in Yablonski et al. [2], Marin et al. [3]. The exemplary derivations of kinetic equations without simplifications are presented in the aforementioned works. The lack of assumptions allows consideration of all possible interactions between the reagents and the surface species, which is a pro of the method. However, the equation obtained usually has a complex form. Some of the parameters that result from theoretical considerations are simply insignificant for the real-world process. To eliminate this problem, the original procedure, based on statistical and process analysis, was employed. The previously determined kinetic equation, which does not have additional assumptions, was simplified. Statistical analysis helps to find and justify possible simplifications of the kinetic equation by eliminating insignificant parameters present in the kinetic equation and provides strong evidence for the correctness of the approach. The resulting kinetic equation indicates that the new proposed mechanism for the propene hydrogenation process that accepts reactions between adsorbed propene and gaseous hydrogen corresponds to the experiment. The residual sum of squares is significantly lower than those for the equations presented in the literature. The statistical test (the Akaike criterion) also indicates that the new model is better than the others. The results obtained indicate that the commonly applied approach based on the rate-determining step concept has become obsolete, apart from obvious cases. The application of the more advanced mathematical approach gives better results, as was presented.